econ- ct7

ORIGINAL PAPER

Hospital heterogeneity: what drives the quality of health care

Manhal Ali1 • Reza Salehnejad1 • Mohaimen Mansur1

Received: 8 July 2016 / Accepted: 28 March 2017 / Published online: 24 April 2017

� The Author(s) 2017. This article is an open access publication

Abstract A major feature of health care systems is sub-

stantial variation in health care quality across hospitals.

The quality of stroke care widely varies across NHS hos-

pitals. We investigate factors that may explain variations in

health care quality using measures of quality of stroke care.

We combine NHS trust data from the National Sentinel

Stroke Audit with other data sets from the Office for

National Statistics, NHS and census data to capture hos-

pitals’ human and physical assets and organisational

characteristics. We employ a class of non-parametric

methods to explore the complex structure of the data and a

set of correlated random effects models to identify key

determinants of the quality of stroke care. The organisa-

tional quality of the process of stroke care appears as a

fundamental driver of clinical quality of stroke care. There

are rich complementarities amongst drivers of quality of

stroke care. The findings strengthen previous research on

managerial and organisational determinants of health care

quality.

Keywords Health care quality � Stroke � NHS � Machine learning � Regression trees � Panel data � Prediction � Mixed effects model

JEL Classification C23 � C40 � C52 � C53 � D23 � I10 � ILL � L22

Introduction

A central observation of the health care systems is the

existence of substantial heterogeneity in the quality of

health care services across hospitals. The quality of health

care measured along dimensions such as mortality or the

process of care for medical conditions such as cancer,

stroke and pneumonia varies widely across hospitals

[3, 42]. Figure 1 captures the distribution of the quality of

the process of care for stroke across NHS hospitals or trusts

using the data from the Royal College of Physicians for the

years 2004–2010.

It is evident that the quality of the process of stroke care

varies across hospitals. The figure also reveals a

notable positive shift in the distribution of the quality of

stroke care over the years. Notwithstanding this, variations

remain, with some hospitals still performing above the

median quality whereas others are performing below the

median quality. Mooney [55] and Rudd et al. [69] reveal

wide variations in the quality of stroke care across the

regions in the UK and England. Mohammed et al. [54] also

document similar variations in the case of NHS hospitals.

And Ayanian and Weissman [3] and Kupersmith [42]

provide a systematic review on the differences in health

care quality across teaching and non-teaching hospitals.

Hospitals are major providers of health care services and

account for a major expenditure of the overall health care

budget. Any effort at reducing the heterogeneity and

enhancing the quality of care across hospitals can bring

substantial benefits to society. Such efforts demand

understanding why some hospitals perform better than

other hospitals, providing a higher quality of care.

The literature on the drivers of hospital quality is vast,

offering a rich list of explanations for the observed

heterogeneity in the quality of care. We borrow a

& Reza Salehnejad [email protected]

Manhal Ali

[email protected]

Mohaimen Mansur

[email protected]

1 University of Manchester, Manchester, UK

123

Eur J Health Econ (2018) 19:385–408

https://doi.org/10.1007/s10198-017-0891-9

theoretical framework from the economic literature on

productivity [75] to shape our analysis. Using the frame-

work, we distinguish between internal and environmental

drivers of the quality of health care. Internal drivers refer to

factors that are under the control of the hospital’s man-

agement team. The literature studying internal drivers has

paid most attention to hospital size, physical assets, human

capital, financial constraints, IT investment, R&D and

organisation of decisions. External drivers refer to com-

petition in the output market, regulatory environment and

general socio-economic conditions.

Starting with the empirical literature on the internal

drivers of hospital performance, a series of papers studies

impacts of hospital size, physical assets, human capital and

information technology on the quality of health care.

Raerty et al. [64] and Needleman et al. [57] study the role

of human capital and find a positive relationship between

nurse staffing and health care quality in NHS and US

hospitals. Athey and Stern [2] and Menachemi et al. [51]

provide evidence on a positive relationship between health

information technology and outcomes. Information tech-

nology reduces communication costs, facilitates coordina-

tion across diverse and complex activities and assists

information processing and decision making. All these can

reduce errors and enhance quality. Gaynor et al. [30],

O’Brien et al. [58] and Hentschker and Mennicken [34]

document a positive relationship between volume and

outcome and process measures of quality of care. The

association is likely due to the ability of larger hospitals to

capitalise on the economies of scale and benefit from

specialisation that can enhance the quality of care.

An emerging finding in the literature is that the above

factors do not fully account for the observed heterogeneity.

Variations in care measured in mortality for disease con-

ditions or the process of care measures persist even after

controlling for case mix, human capital (medical and non-

medical staff), information technology, hospital

characteristics such as bed size, teaching status or foun-

dational trust status, cost–contributing factors, post-opera-

tive complications and statistical noise

[5, 10, 11, 31, 35, 47, 68].

The finding has led researchers to turn attention towards

management practices and organisational factors. Bloom

et al. [8] collect survey data on management styles and

practices from 2000 hospitals across the UK, USA,

Canada, France, Germany, Sweden, Italy, Brazil and India

and join the survey data with hospital performance data.

The researchers find that the quality of management prac-

tices and hospital performance are highly correlated, sug-

gesting a possible role of management practices in driving

hospital outcomes. Bray et al. [12] study the possible

impact of the organisation of the provision of care on the

quality of stroke care, using the data on English NHS trusts

for the year 2010. The authors employ a composite mea-

sure of the quality of the organisation of stroke services by

taking into account staffing (e.g., training level), facilities

(e.g., provision of continuous physiological monitoring)

and service level (e.g., access to round-the-clock emer-

gency imaging and thrombolysis). Adjusting for patient

characteristics, the researchers find that hospitals with

higher organisational scores are more likely to achieve

higher clinical quality measured by stroke process of care

measures. Flood [25], West [77], McConnell et al. [48, 49]

and Ghaferi et al. [31] also highlight the importance of

managerial and organisational practices as an underlying

cause of the variations in the quality of care across hos-

pitals. The increasing evidence on the critical role of

managerial and organisational factors points to the view

that it is the organisation of resources and management

routines that eventually link hospital inputs to outputs.

There is no production function independent of the

organisation of the firm or, in our case, hospital [46]. As the

organisational characteristics of a hospital change, so does

the hospital’s production function.

0

5

10

20 40 60 80 score

co un

t

2004

0

5

10

40 60 80 score

co un

t

2006

0 5

10 15

40 60 80 100 score

co un

t

2008

0 5

10 15

50 60 70 80 90 100 score

co un

t

2010

Fig. 1 Histogram of the total process score

386 M. Ali et al.

123

Another substantial body of literature examines the role

of external factors in shaping hospital performance. A key

result in this literature is that competition, provided prices

are regulated, has a positive impact on health care quality.

NHS hospitals in more competitive regions provide higher

health care quality compared to hospitals located in regions

where there is less competition [61]. In the same line,

Bijlsma et al. [4] study the impact of competition intro-

duced in The Netherlands from 2004 to 2008 on a wide

range of quality measures. The results indicate that hos-

pitals in areas with stronger competition show higher

improvement in several process measures of quality but the

impact of competition on outcome measures appears neg-

ligible. Other researchers have looked, among other fac-

tors, at the impact of government policies on mergers [29],

public reporting of performance [44] and provision of

information [38].

This study seeks to contribute to the literature in health

economics that argues for the impact of management

practices and organisational factors in driving hospital

performance and the quality of clinical care, where by

organisational factors we also mean organisation of

resources [18, 75]. Building on the literature, our general

hypothesis is that hospital performance is not only

dependent on the overall availability of resources but,

more critically, depends also on the organisation and

management of the resources and the fit between the

resources and management practices [18, 28]. Variations

in the organisation and management of resources partly

account for the observed heterogeneity in the quality of

care across hospitals [19]. The significance of such factors

is likely to be higher for some of the services a hospital

provides, such as provision of care for stroke patients

[12]. Stroke is a medical emergency that requires imme-

diate medical intervention as the benefit to the patient is

time dependent. To achieve this, a high level of coordi-

nation is required between various steps of care from the

onset of stroke to rehabilitation. And this is only feasible

if relevant complementary resources are in place and well

organised and stroke specialists and trained staff collab-

orate in a multidisciplinary and timely manner. As an

attempt to further investigate the general hypothesis, we

focus on the provision of stroke care. Our specific

hypothesis, thus, is that variations in the management and

organisational quality of the process of hospital services

such as stroke care partly drive variations in the clinical

quality of stroke care.

Our emphasis on the organisation of resources and

management practices is by no means new. A substantial

body of literature, as mentioned above, has already docu-

mented evidence on the possible impact of organisational

and management factors in driving hospital performance.

The literature, however, has so far mainly sought to

identify factors that drive the quality of care and has paid

little systematic attention to possible interactions among

the factors driving hospital performance. This is partly

because the theory is silent on complex interactions that

may exist among key variables driving performance and

partly because common econometric techniques are not

equipped to reveal interactive structures based on the data

alone. The theory, though, emphasises the importance of

complementarity among assets and skills that drive pro-

ductivity and, in our case, health care quality. In other

words, it points to the importance of critical interactions

among factors driving quality, not simply the mere pres-

ence or absence of the factors or the level of the factors

[14]. We aim to take a first step towards systematically

exploring interactive structures (complementarities) among

the variables that drive hospital quality in a data-driven

manner. With this in mind, our research hypothesis runs as:

Research hypothesis: Variations in the organisation and

management of resources involved in the process of hos-

pital services such as stroke care partly drive variations in

the clinical quality of the services (stroke care). Moreover,

it is the joint presence of complementary resources and

management practices that critically affects the quality of

the clinical process of the services (stroke care).

To assess this hypothesis, we put together a wide panel

data set on a rich list of candidate variables that could

possibly drive hospital quality in stroke care for which the

organisation of resources and management of the process

of care matter critically. The panel spans from year

2004–2010. To our knowledge the only significant policy

change that took place during this period is the introduction

of Department of Health’s National Stroke Strategy

implemented in England in December 2007. We appro-

priately account for this change in our analysis in order to

capture the potential impact this policy may have on the

quality of stroke care in English hospitals. As our measure

of quality, we employ an index that captures the quality of

the process of stroke care as opposed to an outcome

measure. Process of care measures illuminate the compli-

cated process of delivering health care and describe the

specific actions associated with health care delivery. It

describes the care that patients actually receive and

assesses the extent to which hospitals perform health care

processes to achieve the desired aims. An important

advantage of process measures over outcomes is that it

does not suffer from the case-mix adjustment bias [12, 22].

Outcome measures such as mortality, in contrast, may be

confounded by variations in demographics or case mix and

may be susceptible to coding or measurement errors.

However, the validity of process measures depends on

whether they are a useful proxy of subsequent outcomes

and that the interventions being measured are related to the

expected effects [76].

Hospital heterogeneity: what drives the quality of health care 387

123

We combine our measure of the clinical quality of

stroke care with a measure of the organisational quality of

the process of care and other data drawn from several

sources. We will employ a new class of unbiased panel

regression tree estimator from the machine learning liter-

ature to study the data. A reason behind the choice of the

method is the intuitive interpretability of the results. The

non-parametric method can reveal potential interactions

among the variables, which could offer valuable informa-

tion about the processes that drive variations in quality of

stroke care across NHS hospitals. We use an out of sample

prediction error estimator to calculate the predictive

accuracy of the models.

Our results point to the significant role of organisational

features of the process of stroke care in driving the clinical

quality of the process of stroke care. Including a composite

measure of organisational design for the provision of stroke

care improves the predictive accuracy of the models. The

predictive results are robust to the inclusion of year as an

additional variable to capture trends in the data. Using year

as an additional predictor, our measure of organisational

design for the provision of stroke care still has a significant

predictive role in that it reduces both the in-sample and

out-of-sample prediction error rate. Furthermore, the

results of the unbiased panel regression tree estimator are

consistent with our benchmark linear mixed effects model.

The coefficients in the linear mixed effects model are

consistent with the variables entering in the tree models.

Specifically, the coefficient of the organisation score is

substantial and statistically significant. The results are

robust to the inclusion of fixed hospital and year effects.

The key result also remains unchanged when we rescale the

clinical and organisational measures of quality by taking

out the within-hospital means of the variables to eliminate

potential hospital-specific unobserved time-invariant

factors.

Our findings are consistent with the theories from the

organisational economics and productivity literature when

extended to the health care setting. The results are partic-

ularly in line with the findings of Bloom and Van Reenen

[9], Bloom et al. [6] and Bloom et al. [7] who find that

capital intensity or technology cannot alone fully account

for large differences in total factor productivity (TFP)

across firms. Management practices and organisational

design are most fundamental in driving hospital perfor-

mance and quality. High organisational quality enhances

performance, productivity and quality. At the heart of any

policy effort to eliminate the observed heterogeneity in the

quality of care across hospital there should be a well-

founded effort to reduce heterogeneity in organisational

quality and management practices.

The rest of the article is organised as follows. ‘‘Data and

descriptive statistics’’ introduces the data. ‘‘Panel

regression trees’’ outlines the predictive approach and

describes a class of non-parametric regression methods for

the study of panel data. ‘‘Empirical analysis’’ presents our

basic empirical results by assessing the predictive accuracy

of the hypotheses. ‘‘Robustness analysis’’ carries out

robustness checks. ‘‘Conclusion’’ concludes the analysis.

Data and descriptive statistics

The study has gathered hospital and regional level panel

data from several administrative sources. Our two key

variables include composite measures of the clinical and

organisational quality of the process of stroke care. We

obtain the data on these measures from the Royal College

of Physician’s National Sentinel Stroke Audit from 2004 to

2010 where the data have been collected at the hospital

level. The Royal College of Physicians carried out rounds

of the National Sentinel Stroke Audit (NSSA) in every

2-year cycle from 1998 to 2010. The NSSA monitored the

progress of stroke care in England, Wales and Northern

Ireland. Between 1998 and 2010, the NSSA achieved 100%

voluntary participation of hospitals, collecting data on

more than 60,000 patients from England, Wales and

Northern Ireland. The focus of the audit was centred on two

components: clinical and organisational. The former mea-

sured the clinical quality of the process of stroke care

whereas the latter measured the organisational quality of

stroke care. NSSA was eventually replaced by Sentinel

Stroke National Audit Programme (SSNAP). As a result of

the replacement, some of the questions used to construct

the organisational and clinical components of the NSSA

data underwent changes, making it difficult to combine the

data from the two audits. For consistency, we have

restricted the sample to the NSSA data that are in public

domain and left the SSNAP data for a separate research.

The audit data have been used for research studies, for

instance, in Bray et al. [12] and McNaughton et al. [50].

Clinical process of care

In assessing the quality of the process of care for stroke, the

NSSA collected data on the practice of a set of clinical

standards relating to patients hospitalised with a primary

diagnosis of stroke with the ICD10 codes of I61 (intrac-

erebral haemorrhage), I63 (cerebral infarction) or I64

(stroke, not specified as haemorrhage or infarction). Data

were collected on 8697, 13,625, 11,369 and 11,353 patients

respectively for the years 2004, 2006, 2008 and 2010

across the NHS trusts or hospitals in England, Wales and

Northern Ireland. The clinical standards reflect scientifi-

cally based practices that are set by the National Institute

for Health and Clinical Excellence (NICE). The clinical

388 M. Ali et al.

123

standards are organised into six domains of the process of

stroke care, including initial patient assessment, multidis-

ciplinary assessment, screening and functional assessment,

care planning, communication with patients and carers, and

acute care. Table 4 lists these domains and their respective

clinical standards. A score of 0–100 is assigned to each

domain. An average of the scores of the six domains for

each NHS hospital is calculated to arrive at a composite

measure of the clinical quality of the process of care for the

hospital. We use the data for the 4-year period from the

year 2004 to 2010 for English NHS trusts. It is clear from

Fig. 1 that there is notable variation in the scores of hos-

pitals that also changed over time. We conducted an

analysis of variance, which shows that between-hospital

variance (70.06) and within-hospital variance (42.77)

account for 62 and 38% of the total variation in the data,

respectively. Further information about the data, organi-

sation, methods, proforma and questionnaire are available

on https://www.rcplondon.ac.uk/.

Organised stroke care

Stroke is a medical emergency that requires immediate

medical intervention as the benefits are critically time

dependent. To achieve this, a high level of coordination is

required between various steps of care from the onset of

stroke to rehabilitation. And this is only feasible if relevant

complementary resources are in place and stroke specialists

and trained staff collaborate with each other in a multi-

disciplinary and timely manner. To capture the organisa-

tional quality of the process of stroke care, the audit

included a set of questions on the availability of stroke

units, neurovascular facilities, TIA clinics and specialist

stroke teams and their features, on whether the hospital

provided education and engaged in clinical research, and

on whether the hospital sought patient’s views and had

produced reports within the last 12 months. The audit

further collected data on average waiting time for scanning.

Table 1 describes some of the hospital features about

which the audit collected data. The NSSA summarises

these features into eight organisational domains. They

consist of acute care organisation, organisation of care,

consultant sessions (overall service), interdisciplinary ser-

vices (stroke unit), TIA/neurovascular service, education

and research, team working and communication with

patient and carers. On this basis, a composite measure of

organisational quality is developed on a scale of 0 to 100 to

assess the organisational quality of the stroke care process.

The composite measure captures a mixture of organisa-

tional features and management practices critical for stroke

care. Audit queries regarding the presence of a specialist

stroke team or TIA clinic, for example, relate to the

availability of resources. In contrast, audit queries relating

to Stroke Unit Trialists’ Collaboration (STUC) character-

istics, e.g., multidisciplinary meetings at least weekly to

plan patient care, provision of information to patients about

stroke or continuing education programmes for staff, or

queries on whether patients’ views are sought refer to a

management practices.

Over the years 2006–2010, the NSSA organisational

audit went through changes in the form of inclusion of new

and exclusion of old questions to collect data on a hospi-

tal’s organisational quality for stroke care. Despite the

changes, a significant number of questions within the above

domains remained the same. Particularly, the question-

naires used to collect data between 2006 and 2008 organ-

isational audits were very similar or overlapping. We

expect any impact of the organisational component on

quality of stroke care to be slow. To capture these delayed

effects we use 1-year lagged values of predictors when

predicting the quality of stroke care instead of considering

contemporaneous information. This leaves us with 2006

and 2008 organisational scores. Given the strong resem-

blance between 2006 and 2008 audits, we do not expect

that the changes in the audits would distort our analysis.

Further information on the data, questionnaire proforma

Table 1 Disaggregated variables for organisational design of stroke care

Variables Description Measure

ASU Acute stroke unit 1 = yes; 0 otherwise

CSU Combined stroke unit 1 = yes; 0 otherwise

RSU Rehab stroke unit 1 = yes; 0 otherwise

Specialist Presence of specialist stroke team 1 = yes; 0 otherwise

Report Report produced with the last 12 months 1 = yes; 0 otherwise

PatientViews Whether patient views were sought 1 = yes; 0 otherwise

SUTC 5 key features of all stroke units by Stroke Unit

Trialists Collaboration

Integer scale from 1 to 5 where

5 if all features met

ESD Presence of early supported discharge team 1 = yes; 0 otherwise

NeuroClinic Presence of neurovascular/TIA clinic 1 = yes; 0 otherwsie

Hospital heterogeneity: what drives the quality of health care 389

123

and the method for constructing the composite organisa-

tional measure are available at https://www.rcplondon.ac.

uk/ and in https://www.rcplondon.ac.uk/projects/national-

sentinel-stroke-audit.

In addition to an aggregate measure, we supplement the

analysis using disaggregated measures or factors of stroke

organisation that are common across 2006 and 2008 and

are listed in Table 1 above. These factors included in the

audit are important markers for quality of care and capture

aspects of organisational design for stroke care for each

NHS hospital, i.e., their settings or configuration.

Table 2 below gives the descriptive statistics for the

clinical and organisational quality of the process of stroke

care for the NHS hospitals. Both the mean and median

scores for clinical and organisational measures of the

hospitals have been monotonically increasing over their

respective sample periods. Conversely, the measure of

variations captured by standard deviation for both the

clinical process score and organisational performance has

been decreasing except for an increase for process scores in

2006. Despite the gradual decline, variations in both clin-

ical quality and organisational performance across the

hospitals still persist. In other words, considerable hetero-

geneity exists with some hospitals providing better quality

services than others.

Hospital and regional characteristics

We add several explanatory variables to our data to control

for other factors that may affect health care quality. We add

Teaching and Foundation Trust (FT) status for each hos-

pital. Teaching hospitals tend to treat patients with the most

severe and complex illnesses and have a higher chance of

learning how to deal with complex cases. This may lead to

a higher quality of care. Conversely, teaching hospitals can

introduce a delay in the treatment process due to consul-

tants’ role in training medical students [1].

Foundation trust hospitals are non-profit public organ-

isations that enjoy greater managerial and financial

autonomy from the central government control. FT hos-

pitals are allowed to retain their surpluses, which they can

invest in staff salaries or capital equipment. They are also

allowed to borrow money to improve services. Hospitals

with FT status are likely to have higher quality of care for

stroke. Farrar et al. [23] find that FT hospitals provide a

better quality of care measured using lower in-hospital

mortality.

Larger NHS hospitals can lead to higher quality of care

because of economies of scale and the ‘‘volume-outcome’’

hypothesis. Or, they might lead to lower quality of care due

to diseconomies of scale from the greater complexity of

their organisational structure. A number of studies include

hospital size measured by the number of hospital beds

among factors affecting hospital quality [40, 49, 62, 65].

We control for hospital size and case-load capacity using

the number of hospital beds and the number of operating

day-case theatres.

A rich literature highlights the importance of adequate

specialists and neurologists in the prevention and man-

agement of stroke patients and improved stroke outcomes

of care [17, 20, 53, 59, 66, 70, 73, 74, 78]. Hospitals with

more skilled staff and specialists are likely to enjoy higher

medical knowledge and experience and be capable of

providing a relatively higher quality of stroke care. We

include the number of neurologists, neurosurgeons and

neurophysiology staff to control for the number of spe-

cialists. Park et al. [60] and Ketcham et al. [39] find that

larger size physician groups are likely to improve health

care quality. We add general measures of medical and non-

medical staffs including professionally qualified staff and

health care scientists.

A number of studies have found a positive relationship

between nurse staffing and health care quality. Fine et al.

[24] study the relationship between hospital characteristics

such as nurse staffing and organisation type and measures

of care for pneumonia. Raerty et al. [64] and Needleman

et al. [56, 57] find a positive relationship between nurse

staffing and health care quality in NHS and US hospitals.

Cho and Yun [20] find that adequate nurse staffing mea-

sured by the bed-to-nurse ratio is positively associated with

stroke care quality. We control for the number of nurses

and the nurse-to-bed ratio.

Table 2 Descriptive statistics for clinical process score and

organisational score

Clinical process score Organisational score

2004 2006 2008 2010 2006 2008 2010

Minimum 25.00 31.00 40.00 52.00 23.00 32.00 47.00

First quartile 51.75 58.25 63.00 73.00 57.25 63.75 62.00

Median 61.00 67.00 71.00 79.00 64.00 71.00 69.00

Mean 60.48 66.13 69.74 78.75 63.74 70.59 69.65

Third quartile 68.25 75.75 77.00 85.0 72.00 79.00 76.75

Maximum 93.00 93.00 96.00 97.00 89.00 95.00 96.00

Standard deviation 12.36 13.33 11.32 8.57 11.96 11.37 10.20

390 M. Ali et al.

123

Studies have also documented considerable regional

variations in health care quality [32, 37, 45, 71]. Mooney

[55] and Rudd et al. [69] find considerable variability in the

quality of care for stroke across England. We consider

median inflation-adjusted wage, inequality, the proportion

of regional population without any qualifications, the

number of stroke admissions, all-cause standardised mor-

tality rate and the stroke mortality rate to control for socio-

economic and regional-health factors. Gaynor et al. [29]

control for regional measures including the median wage to

proxy demand and need for care in a given area. Table 3 in

the ‘‘Appendix’’ provides the full list of the variables used

in the study, their definitions and sources.

Panel regression trees

While the main objective of this article is to determine

what predicts the quality of hospital care, our aim is to

portray any predictor-response relationship in a simple,

easy-to-understand and intuitive way. We are interested in

making meaningful sense of how several predictors may be

involved in complex interactions with one another when

helping to explain quality. For example, we would like to

understand whether the standard of care at hospitals that

are located in a wealthy area and have a low nurse-to-bed

ratio is different from the quality of care offered in hos-

pitals with a higher nurse-to-bed ratio situated in a rela-

tively lower income region. Traditional parametric

methods such as regression models do not always offer

straightforward interpretation of such intricate interplay of

variables. We, therefore, resort to a class of non-parametric

techniques, commonly known in machine learning litera-

ture as regression trees, that serve the purpose well. The

tree mechanism involves recursively partitioning the pre-

dictor space into a number of small regions based on

simple rules and then using the mean or median of the

realised values (e.g., quality of care) of observations (e.g.,

hospitals) belonging to a region as the predicted value for a

new observation that falls in that particular region. Most

importantly, the splitting decision rules, order of impor-

tance of selected predictors and their interactions are

summarised in a visually attractive and intuitive way. To

our knowledge, this is one of the very few studies in health

economics that exploit regression trees with an aim to find

drivers of quality of care.

Several tree growing algorithms are proposed in the

statistics and machine learning literature. The most widely

used are ‘CART’ [13] and ‘C4.5’ [63], which function by

maximising a statistical criterion over all possible predic-

tors and split points simultaneously. These methods are

often criticised for biased selection of variables, which

have many possible splits and missing values [36]. In this

article we opt to use a conditional inference framework

proposed in Hothorn et al. [36] that rectifies the problem of

selection bias by choosing predictors for splitting based on

a series of tests identifying statistically significant associ-

ation between the responses and predictors.

Since we observe a number of hospitals over several

years the data used in our study are longitudinal or panel.

Such a data structure requires careful accounting of pos-

sible variations across subjects that cannot be captured by

observed predictors and also autocorrelation across obser-

vations from the same subject. If we observe subjects (e.g.,

hospitals) i ¼ 1; 2; . . .; I at times t (years) ¼ 1; 2; . . .; T a general additive model can be defined as:

yit ¼ fðxitÞ þ ai þ uit ð1Þ

ui1

..

.

uiT

0 BB@

1 CCA � Nð0; RiÞ ð2Þ

ai � Nð0; DÞ ð3Þ

where for each subject i and time period t, yit denotes the

response of interest (e.g., quality of care),

xit ¼ ðxit1; . . .; xitKÞ 0 denotes a vector of K predictors (e.g.,

hospital characteristics, regional features, etc.) and uit denote the errors. The ai are the time-invariant, subject-

specific unobserved heterogeneity component. We allow

for serial correlation in errors uit from a particular subject

by defining their covariance matrix Ri to be non-diagonal.

The errors are, however, assumed to be independent across

subjects and uncorrelated with ai.

We seek to apply flexible tree-based methods for

approximating the unknown relationship f, which may well

be non-linear. It is only over the last decade that devel-

opments have been made in generalising trees for panel

data applications. This article uses a method called an

unbiased random effect expectation maximisation (RE-

EM) tree, only recently developed in Fu and Simono [27].

Unlike many existing methods including a standard RE-

EM tree of Sela and Simono [72], which rely on CART-

type tree building algorithms, the unbiased RE-EM tree

incorporates the conditional inference framework of

Hothorn et al. [36] and is, therefore, unbiased in nomi-

nating predictors for splitting. The unbiased RE-EM tree

operates by alternating between two principal steps: one

estimating f by using a tree method and the other esti-

mating unobserved heterogeneities ai by utilising a linear

panel regression model. The process is initialised by setting

the starting value of ai to zero.

As any non-parametric estimator, regression trees are

subject to over-fitting. To achieve an optimal trade-off

between the bias and variance (over-fitting), we rely on the

Hospital heterogeneity: what drives the quality of health care 391

123

out-of-sample predictive accuracy of the model, estimated

using cross validation. We select the regression tree model

with the lowest prediction error to identify variables that

potentially contribute to the quality of stroke care.

By adopting the regression tree method, we complement

the dominant tradition in econometrics, where the emphasis

is on parameter estimation and statistical significance

testing. There are no coefficients in regression trees.

Instead, the idea is whether the variable of interest or the

interactions implied by the background domain-specific

information or theory appear in the tree that best predicts

the outcome variable.

Our methodological stance comes close to the seminal

work of Milton Friedman [26] and the practice in science: a

minimum check for the empirical adequacy of a hypothesis

is whether the predictions of the hypothesis are consistent

with the empirical model that yields the best out-of-sample

predictions. Such an approach does not establish the

hypothesis. It can help narrow down the set of plausible

hypotheses that are consistent with our data. Predictive

consistency invites us to take a hypothesis seriously, assess

its compatibility with our background knowledge and

devise empirical studies that can support drawing causal

conclusions.

Empirical analysis

We employ an unbiased random regression tree estimator

for panel data to develop a series of predictive models to

identify key predictors of the quality of the process of

stroke care in NHS hospitals. In building the tree models,

we rely on the literature to decide on potential explanatory

variables that may drive the quality of the process of stroke

care across hospitals. Some of the potential control vari-

ables are highly correlated. The panel regression tree

estimator arbitrarily selects from among highly correlated

variables to build a model [41]. To gain insight into the

possible impact of each variable, we use a data-driven

method proposed in Kuhn and Johnson [41] to a priori

select from among the correlated variables to build a model

and further examine the effect of replacing the variables

with excluded variables to assess the robustness of the

results. (The supplementary results are available on

request.) Two variables are considered as highly correlated

when the correlation coefficient exceeds the threshold 0.75.

All unbiased REEM-Tree models are fitted using a random

intercept model to allow for variations in hospitals’ quality

due to unobserved attributes.

Among the variables measuring physical capital, the

variables operating theatres and day case theatres are

highly correlated (0.88). We a priori exclude the number of

operating theatres from the base model. The correlation

among nurses, general medicine group (gmg) staff, science

and allied professionals staff exceeds the threshold of 0.75.

We keep nurses in the base model, partly because this

choice will lead to models with overall lower out-of-sam-

ple prediction error. The number of nurses in a hospital is

highly correlated with the number of beds. We replace

nurses with the nurse-to-bed ratio in order to be able to

identify possible distinct effects of physical capital (or

hospital size) and non-specialist human capital. Among the

regional health and socio-economic variables, the weekly

median wage and inequality are highly correlated (0.845).

We exclude inequality from the base models. Also, stroke

mortality and the all-age standardised mortality ratio

(SMR) are highly correlated (0.87). We keep stroke

mortality.

We consider four unbiased regression tree models to

gain insights into the structure of the data. The first three

models regress the measure of the quality of the clinical

process of stroke care on the individual variables that

capture organisational features of the process of stroke

services and relevant control variables. The fourth regres-

sion tree model replaces the individual variables with the

composite measure of organisational quality of the process

of stroke care to better capture possible complementarity.

We next compare the results of the unbiased REEM-

Tree with linear mixed effects models (LME) to check the

robustness of the results. We rely on the in-sample and out-

of-sample predictive performance of the models to select a

model from among the trees that best fits the data.

Disaggregate models

Recall we categorised possible drivers of the quality of

stroke care into internal and external drivers of hospital

performance. Internal drivers refer to factors such as

physical assets, human capital, the structure of decisions

and the internal organisation of the hospital. External dri-

vers refer to regional health and socio-economic features.

We start with a model of internal drivers and next adds

variables capturing potential external drivers. Our under-

lying methodological principle is that if any of these factors

drive the quality of stroke care, variables measuring the

factors will appear in a model that best predicts the quality

of stroke care [26]. With these preliminaries, the first panel

regression tree model includes the primary organisational

variables and the variables measuring physical assets,

human capital and hospital characteristics. This means the

variables entering the formula underlying the model consist

of:

Model 1: Score � beds ? day case theatres ? nurses ? neurology ? neurophysiology ? neurosurgeons ?

teaching ? ft ? ASU ? RSU ? CSU ? SUTC ? Specialist

? ESD ? NeuroClinic ? PatientViews ? Report.

392 M. Ali et al.

123

The dependent variable score measures the quality of the

clinical process of stroke care. Table 3 defines the rest of the

variables. Applying the unbiased panel regression tree esti-

mator to the data yields the tree in Fig. 2. For the current

analysis, a significance threshold of 0.10 for unbiased

REEM-Trees has been set (i.e., a 10% false-positive rate for

statistical significance is set). The variable ‘specialist’

appears in the initial node of the tree, suggesting that the

presence of a specialist stroke team is the most important

predictor of the quality of stroke care. Hospitals with spe-

cialist stroke teams enjoy an overall higher quality score,

which is in line with the findings in Xian et al. [80]. Indeed,

the highest quality score belongs to hospitals with a specialist

stroke team and a higher nurse-to-bed ratio (with mean

quality score 84.94), confirming the findings in Cho and Yun

[20]. Also, as found in Farrar et al. [23], among hospitals with

a specialist stroke team, foundation trust hospitals yield a

higher quality score. The lowest quality score appears in

hospitals that lack a specialist stroke team, have a low nurse-

to-bed ratio and lack a combined stroke unit (CSU) (with the

mean quality being 65.61) [16]. Overall, the model points to

the significance of specialist human capital and organisa-

tional variables. The variables representing physical capital

do not appear in the unbiased panel tree. The model points to

critical complementarities between the presence of a spe-

cialist stroke team and a high nurse-to-bed ratio. It is the joint

presence of these features that predicts a higher quality.

Adding the variables representing potential external

drivers of quality will give rise to our second model:

Model 2: Score � beds ? day case theatres ? nurses ? neurology ? neurophysiology ? neurosurgeons ?

teaching hospital ? foundation trust ? ASU ? RSU ?

CSU ? SUTC ? Specialist ? ESD ? NeuroClinic ?

PatientViews ? Report ? stroke admissions ? stroke

mortality ? median wage ? no qualifications.

From the tree results in Fig. 3, median wage appears at

the initial node of the tree, suggesting that economic con-

ditions are among important predictors of the quality of

stroke care [37]. The mean quality of stroke care in areas

with a higher weekly median wage ([486.5) is on average

Model 1

Specialist p < 0.001

1

≤ 0 > 0

nursesBeds p < 0.001

2

≤ 1.899 > 1.899

CSU p = 0.013

3

≤ 0 > 0

n = 41 y = 65.61

4 n = 29

y = 71.196

5

RSU p = 0.012

6

≤ 0 > 0

n = 28 y = 71.18

7 n = 43

y = 76.472

8

nursesBeds p < 0.001

9

≤ 2.478 > 2.478

ft p = 0.022

10

≤ 0 > 0

nursesBeds p = 0.014

11

≤ 1.556 > 1.556

n = 11 y = 69.331

12 n = 68

y = 76.655

13

CSU p = 0.031

14

≤ 0 > 0

n = 35 y = 76.88

15 n = 28

y = 80.324

16

n = 20 y = 84.94

17

Fig. 2 The tree includes variables capturing hospital characteristics, human capital factors, teaching and foundation trust status, and

primary variables reflecting the quality of the organisation of the

process of stroke care. The higher a variable appears in the tree

structure, the more predictively significant the variable will be. The

organisational variable ‘Specialist’ appears at the initial node of the

tree as the predictively most important variable. Each box in the

terminal nodes show two figures, the first (n) stating the number of

observations falling in the branch and the second (y) giving the mean

value of the observations in the branch. Hospitals with the highest

quality score fall in the branch where the value of the dummy

‘‘specialist’’ equals one and the nurse-to-bed ratio exceeds 2.478

Hospital heterogeneity: what drives the quality of health care 393

123

higher. On the right-hand-side branch, the second predic-

tively most significant variable is the nurse-to-bed ratio.

The equality of the process of stroke care is the highest in

hospitals in affluent areas where the nurse-to-bed ratio

exceeds (2.512) [12]. On the left-hand side, specialist is the

second predictively most important variable. The quality of

the process of stroke care is overall higher in hospitals with

a specialist stroke team in place. The variables appearing in

the third layer of the tree include those that capture the

organisation of the process of stroke care. The presence of

a stroke specialist team, SUTC, and the presence of an

early support discharge team (ESD) occupy prominent

positions in the tree [43, 67]. The tree also reveals

important interactions (complementarities) among the

variables. The interaction between a comparatively lower

median wage (\486.5) and the absence of a stroke spe- cialist team where there is no early support discharge team

(ESD) yields the lowest mean average quality score.

Overall, the model points to several results. To begin

with, the model reveals variations in the quality of stroke

care across regions, consistent with the findings in Grimaud

et al. [33]. An explanation for the regional variation is that

wealthier regions have more access to higher quality

human capital resources, which is likely to enhance the

quality of care a hospital provides. Another explanation,

which receives support from our data, is that hospitals in

richer regions devote more resources to health care [21]. In

the sample, the median wage is reasonably highly corre-

lated with the nurse staff ratio (0.437), clinical staff ratio

(0.47) and gmg staff ratio (0.404). Median wage is also

negatively correlated with regional stroke mortality. A

third explanation is that a higher median wage is associated

with higher education [37]. Patients with higher levels of

education are likely to be aware of their rights and the

quality of services they receive. And this can translate into

pressures on hospitals to provide higher quality services.

Model 2

median_wage p < 0.001

1

≤ 486.5 > 486.5

Specialist p < 0.001

2

≤ 0 > 0

ESD p = 0.001

3

≤ 0 > 0

n = 85 y = 67.842

4 noqual

p = 0.005

5

≤ 14.3 > 14.3

n = 10 y = 68.59

6 n = 17

y = 76.698

7

neurosurRegion p = 0.002

8

≤ 17 > 17

n = 10 y = 68.177

9 median_wage

p = 0.006

10

≤ 420.5 > 420.5

n = 31 y = 73.081

11 n = 73

y = 78.552

12

nursesBeds p < 0.001

13

≤ 2.512 > 2.512

SUTC p = 0.003

14

≤ 4 > 4

n = 19 y = 74.325

15 nursesBeds p = 0.018

16

≤ 1.842 > 1.842

n = 11 y = 75.888

17 admissions p = 0.006

18

≤ 5176 > 5176

n = 13 y = 79.696

19 n = 12

y = 84.767

20

n = 22 y = 86.713

21

Fig. 3 The tree adds external variables such as weekly median wage to the variables underlying model 1. Weekly median wage appears at

the start of the tree as the predictively most significant variable,

followed by the nurse-to-bed ratio and specialist. Other variables

measuring the organisational feature of the process of stroke care

occupy important positions in the tree, supporting the idea that

organisational factors are among the most significant predictors of the

clinical quality of care

394 M. Ali et al.

123

The model also points to the pivotal role of the organisa-

tional features of the stroke care process in driving the

quality of stroke care. The organisational variables occupy

prominent positions in the regression tree. Finally, the

model casts doubt on whether hospital size affects the

quality of the process of stroke care. The number of beds,

which measures hospital size, does not appear in the tree.

Any claim for the causal validity of these results call for

further analysis.

Figure 1 previously revealed a shift in the distribution of

the stroke quality measure over the sample period. The

monotonic increase in the mean quality score could be due

to a change in the underlying joint probability distribution

of the variables driving the quality of stroke care. We next

include year dummies in the last model to capture the time

trend and examine whether the key patterns observed in the

trees remain unchanged. Our sample spans over four

periods from year 2004 to year 2010. However, the data on

the organisational variables are not available for year 2004.

Further, the predictor variables have been lagged to deal

with contemporaneous endogeneity. This means there are

effectively data for two periods in the unbiased tree esti-

mation. We take the year 2008 as the base year and

introduce a dummy variable ‘yr2010’ that takes value 1 if

an observation belongs to year 2010 and zero otherwise.

Adding the dummy variable to the list of variables will lead

to our third model:

Model 3: Score � beds ? day case theatres ? nurses ? neurology ? neurophysiology ? neurosurgeons ?

teaching hospital ? ft ? ASU ? RSU ? CSU ? SUTC ?

Specialist ? ESD ? NeuroClinic ? PatientViews ? Report

? stroke admissions ? stroke mortality ? median wage ?

no qualifications ? yr2010.

In Fig. 4 the year dummy appears in the initial node of

the tree, indicating a higher mean quality of stroke care in

year 2010. A reason for the split of the initial node at 2010

Model 3

yr2010 p < 0.001

1

≤ 0 > 0

neurosurRegion p < 0.001

2

≤ 71 > 71

SUTC p = 0.002

3

≤ 4 > 4

n = 38 y = 66.507

4 Report

p = 0.008

5

≤ 0 > 0

beds p = 0.004

6

≤ 631 > 631

n = 26 y = 64.129

7 n = 17

y = 73.663

8

n = 51 y = 71.764

9

n = 18 y = 79.587

10

median_wage p < 0.001

11

≤ 524.8 > 524.8

Specialist p = 0.002

12

≤ 0 > 0

teaching p = 0.007

13

≤ 0 > 0

neurology p = 0.003

14

≤ 1 > 1

n = 15 y = 76.639

15 n = 11

y = 70.261

16

n = 12 y = 79.676

17

n = 95 y = 78.928

18

n = 20 y = 86.1

19

Fig. 4 The tree adds a year dummy to the variables in tree model 2. The dummy variable for year 2010 appears at the initial node of the

tree as the most predictively significant factor, followed by median

weekly wage and neurosurgeon per region. The mean quality score is

higher in year 2010, consistent with the descriptive results in Fig. 1.

The variables reflecting the organisational quality of stroke care

occupy prominent positions. A number of variables including ‘day

case theatres’, ‘neurology’ and FT fails to appear in the tree

Hospital heterogeneity: what drives the quality of health care 395

123

can be the implementation of the National Stroke Strategy

Policy in NHS England, which was implemented in

December 2007. The policy measures included monitoring

and assessing the quality of stroke care across NHS hos-

pitals, which might have shifted the distribution of the

overall measure of the quality of stroke care. The second

set of most predictively significant variables are weekly

median wage and neurosurgeons per region. The average

clinical quality of stroke care is higher in wealthier regions

or regions with a higher number of neurosurgeons. Con-

sidering the fact that only a small proportion of stroke

patients requires surgery we take caution in interpreting the

relevance of the number of neurosurgeons by identifying it

as an indicator of broader specialist capacity rather than an

absolute/direct driver of quality of stroke care in hospitals.

Primary organisational variables occupy the next promi-

nent positions in the tree. Consistent with the previous

results, higher clinical quality of stroke care is correlated

with better organisation of stroke care. The presence of the

organisational score variable is robust to including year as

a predictor.

Composite measure

A fundamental insight of economic theory is the critical

complementarity among diverse elements that shape the

organisation of the firm and its performance [14]. In Fig. 2,

in the left-hand-side branch, the absence of a specialist

stroke team, a comparatively lower nurse-to-bed ratio and

the absence of a combined stroke unit jointly give rise to a

lower mean average quality of stroke care, or having a

stroke specialist team present in a foundation trust hospital

leads to higher mean stroke care quality. To capture

complementarities among organisational factors con-

tributing to the process of stroke care, we adopt a com-

posite measure of overall organisation of the process of

stroke care constructed in the National Sentinel Stroke

Audit (NSSA). Replacing the disaggregate indicators of

organisational quality with the composite measure, which

is derived from the primary indicators, while maintaining

other variables in the model, will yield the model:

Model 4: Score � beds ? day case theatres ? nurses ? neurology ? neurophysiology ? neurosurgery ?

teaching ? ft ? admissions ? stroke mortality ? median

wage ? no qualifications ? organisation score ? yr2010.

Figure 5 represents the unbiased panel regression tree

built from these variables. The composite measure of the

organisational quality appears at the initial node of the tree,

indicating the organisational quality of the process of

stroke care as the most prominent predictor of the clinical

quality of stroke care. Hospitals with high organisational

quality ([67) located in comparatively affluent areas enjoy

the highest quality of stroke care. The mean predicted

scores for year 2010 wherever the year dummy appears are

higher than the mean predicted scores for year 2008. Fur-

ther, but interestingly, hospitals with a low composite

organisation score (\67) but a larger number of beds ([591) reveal a relatively lower mean quality of stroke care. In the absence of proper organisation of resources,

larger hospitals might be at a disadvantage. Finally, the

lowest mean quality of stroke care belongs to hospitals in

regions with a comparatively lower number of neurosur-

geons (\61) and low composite organisation score (\64). The reason for the relative simplicity of the model is

manifold: Human capital variables strongly predict the

organisation score; weekly median wage is also highly

correlated with other variables capturing the health and

socio-economic regional characteristics; human capital

variables are highly correlated among themselves and with

variables such as (the number of) beds. Overall, once the

composite measure of organisation quality of the process of

care is included among the explanatory variables, it

appears as the predictively most significant variable, con-

sistent with the recent economic research on productivity

that identifies organisational features and management

practices and style as the deepest drivers of firm perfor-

mance. The figures highlight the importance of comple-

mentarity as in Milgrom and Roberts [52] and Brynjolfsson

and Milgrom [14]. The results of the tree models confirm

the insights of the wider economics productivity literature

on the importance of the organisation of resources,

organisational design and management practices.

Table 5 reports the in-sample goodness of fit measures

AIC and BIC for the four unbiased regression tree models.

The in-sample fit measure AIC and BIC scores monoton-

ically decrease from model 1 (2195.83) to model 4

(2096.64), suggesting that the unbiased regression tree

model 4, with the composite organisation measure, fits the

data best. According to Burnham and Anderson [15], dif-

ferences in the values of AIC of around 4–7 correspond to

roughly 95% significance. The table also reports the leave-

one-out and k-fold out-of-sample-predictive performance

measures for the unbiased tree models. Consistent with the

in-sample fit measures, the final model yields the lowest

out-of-sample prediction error among the models—(8.531)

and (8.268) respectively.

Figure 6 provides the diagnostic plots for unbiased

REEM-Tree model 4. The residuals from the model are

approximately normally distributed, as indicated from the

Normal Q–Q plot in the left panel of the figure. The right

panel of the figure gives the residuals versus fitted values

plot to check for constant variance or homoscedasticity

assumption of errors. The residuals are scattered around the

horizontal line and the width of the data points are equal

396 M. Ali et al.

123

throughout, confirming homoscedasticity. The model

enjoys a satisfactory in-sample goodness of fit.

Robustness analysis

The regression trees presented above do not take care of

hospital fixed effects features. In the absence of strong

theory, one requires alternative techniques to capture pos-

sible causal connections. We build a series of linear panel

data models to investigate whether the coefficients of the

variables appearing in the trees are statistically significant

and whether the coefficient estimates are robust to the

inclusion of hospital individual fixed effects. Further, we

report whether the results are robust to the choice of

alternative measures of physical capital, human capital and

regional factors. We also consider replacing our human

capital variables with relevant ratios.

Correlated random effects models

We first check the empirical validity of the patterns

observed in trees by comparing them to a class of linear

mixed effects models (LME). The LME results come quite

close to traditional random-effects results. Both assume

that ai in Eq. (1) uncorrelated with explanatory variables.

We have no theoretical ground to warrant such an

assumption. A prime reason for choosing LME as a

benchmark is its consistency with the REEMtree. The

unbiased panel tree estimator is built around LME. Further,

our interest is to estimate possible impacts of time invariant

variables such as the teaching or foundation trust status of

hospitals on quality of care, which makes a standard fixed

effect (FE) estimator unsuitable. Next we estimate a cor-

related random effects (CRE) model that is a flexible

extension to RE and is comparable to FE [79]. Consider the

simple case of the panel model in Eq. (1), with a single

Model 4

orgscore p < 0.001

1

≤ 67 > 67

yr2010 p < 0.001

2

≤ 0 > 0

orgscore p = 0.009

3

≤ 60 > 60

n = 47 y = 64.243

4 neurosurRegion

p = 0.011

5

≤ 61 > 61

orgscore p = 0.008

6

≤ 63 > 63

n = 14 y = 64.004

7 n = 13

y = 70.063

8

n = 12 y = 75.617

9

beds p < 0.001

10

≤ 591 > 591

n = 30 y = 78.9

11 n = 20

y = 71.924

12

median_wage p < 0.001

13

≤ 524.8 > 524.8

yr2010 p < 0.001

14

≤ 0 > 0

n = 55 y = 73.076

15 n = 89

y = 79.298

16

neurophysiology p = 0.004

17

≤ 0 > 0

n = 13 y = 85.649

18 n = 10

y = 90.902

19

Fig. 5 The unbiased tree replaces the composite organisational measure for the primary features of the organisation of the process of

stroke care. The variable appears as the most predictively significant

factor, followed by median weekly wage and the year dummy. The

highest quality score belongs to hospitals with a high organisational

score and with the neurophysiology variable taking a value located in

wealthier regions. Variables day case theatres, nurse-to-bed, neurol-

ogy, neurosurgery, teaching, FT, admissions, stork mortality and ‘no

qualifications’ fail to appear in the tree

Hospital heterogeneity: what drives the quality of health care 397

123

time-varying explanatory variable xit. ai may be correlated

with fxit : t ¼ 1; 2; . . .; Tg. yit ¼ bixit þ ai þ uit; t ¼ 1; 2; . . .; T: ð4Þ

In CRE, we model the correlation between ai and

fxit : t ¼ 1; 2; . . .; Tg. Since ai is, by definition, constant over time, it can be correlated with the average level of the

xit. More specifically, let �xi ¼ T�1Rti¼1xit be the time aver- age. It is plausible to assume the simple linear relationship

ai ¼ a þ k�xi þ ri ð5Þ

where ri, by assumption, is uncorrelated with each xit. The

correlated random effects approach uses (5) in conjunction

with (4). Substituting the former into the latter gives:

yit ¼ bixit þ a þ k�xi þ ri þ uit ¼ a þ bixit þ k�xi þ ri þ uit ð6Þ

The equation has a composite error term ri þ uit, consisting of a time-invariant unobservable ri and the idiosyncratic

shocks, uit. Further, because uit is assumed to be uncorre-

lated with xit, all s and t, uit is uncorrelated with �xi. With

these assumptions, the estimation problem becomes iden-

tical to the random effects estimation of

yit ¼ a þ bixit þ k�xi þ ri þ uit: ð7Þ

The addition of �xi controls for the correlation between ai and the sequence fxit : t ¼ 1; 2; . . .; Tg. Wooldridge (2010,

Chapter 10) shows that b̂CRE ¼ b̂FE, where b̂FE stands for the fixed effects estimator. The CRE approach, thus, pro-

vides a way to include time-invariant explanatory variables

in what is effectively a fixed effects analysis.

We assess the robustness of the four models introduced

earlier. In each case, we consider two LME models: (1) a

model with all the variables entering the corresponding tree

and (2) a model with the within-group means of the time-

varying variables to capture fixed effects.

Table 6 presents the first set of the LME results. Each

column belongs to the four models respectively. The first

column includes the internal drivers of quality of stroke

care entering unbiased regression tree model 1 along with

the dis-aggregate measures of organisational performance.

Consistent with the tree model 1, variables nurse-to-bed

ratio (5.490), specialist stroke team (5.172), foundation

trust (2.487) and CSU (3.795) all are statistically signifi-

cant at less than the 5% critical level. In addition, the

variable SUTC (2.461) is also statistically significant at less

than the 5% level. These predictors have material effects

on the quality of stroke care. For example, a unit change in

the nurse-to-bed ratio results in a 5.49-unit change in the

quality of care index, given other variables are held con-

stant. The quality of care in a hospital that has a Specialist

Stroke Team is 5.172 points higher than a hospital that

does not have such a specialist team. Presence of a Com-

bined Stroke Unit (CSU) is associated with a 3.795-point

Model (4): Residuals vs Fitted Values

60 70 80 90

−1 5

−1 0

−5 0

5 10

15

Fitted Score Values

R es

id ua

ls

−3 −2 −1 0 1 2 3 −1

5 −1

0 −5

0 5

10 15

Normal Q−Q Plot

Theoretical Quantiles

S am

pl e

Q ua

nt ile

s

Fig. 6 In-sample fit plot for the unbiased tree for model 5

398 M. Ali et al.

123

improvement in quality while a foundation trust status

accounts for an additional 2.461 points. Column 2 corre-

sponds to regression tree model 2, which adds potential

external drivers of the quality of stroke care to the variables

in the first model. Variables median wage (0.084), Neu-

roClinic (4.709), STUC (2.639), specialist (3.935) and

foundation trust (3.332) are statistically significant at less

than the 5% level. Presence of a Neuroclinic improves the

quality score by 4.709 units. Foundation trust status, pro-

vision for a specialist stroke team and availability of well-

equipped stroke units (SUTC) all maintain sizeable effects

on quality as before with coefficients of 3.332, 3.935 and

2.639, respectively, but the impact of median wage is small

(0.084). There are discrepancies between the regression

tree results and the LME results—notwithstanding, the

organisational variables appear prominent in both LME

models. Variables Specialist and SUTC, which are signif-

icant in both regression models, occupy prominent posi-

tions in the trees too. Column 3 adds the year dummy to the

list of the variables. With the inclusion of the year dummy,

median wage is no longer statistically significant. In

addition to the year dummy (6.574), SUTC (2.748), neu-

roclinc (3.437) and neurosurgeon per region (0.047) are all

statistically significant at less than the 5% level. The

quality score was on average 6.574 points higher in the

year 2010 compared to the year 2008. This implies that the

Department of Health’s National Stroke Strategy, which

was implemented across English NHS trusts in December

2007, resulted in profound and significant improvement in

hospital performance. Importantly, though, even after

controlling for the year effect, the effects of some stroke

care resources, such as SUTC and Neuroclinic, remain

considerably large (2.748 and 3.437, respectively). As for

regression tree results, we define neurosurgeons per region

as a wider measure of specialist input when interpreting its

importance in predicting quality of stroke care. Column 4

replaces the primary organisational features of the process

of stroke care with the composite measure of organisational

quality of the process of stroke care. With the composite

measure included, variables FT (foundation trust status)

(1.824), stroke mortality (0.230), median wage (0.057), the

year dummy (4.831) and organisation score (0.331) are all

statistically significant at less than the 5% level. The fact

that the composite organisational score has a small effect

(0.331) on stroke quality possibly suggests that individual

components have disproportionate, and in certain cases

opposite, effects on quality. Overall, if any lesson can be

drawn from these results, it is the conclusion that organi-

sation of the process of stroke care matters greatly. The

organisational variables in one form or another appear

prominent in both estimation approaches.

The Hausman test indicates the presence of fixed effects.

Table 7 represents the LME results when, in line with the

correlated random effects approach, we add the within-group

means of the time-varying variables to the list of the variables

to capture potential fixed effects. In column 1, we add the

within-group means of the time-varying variables to the list of

the variables in model 1 that only includes potential primary

internal drivers of the clinical quality of the process of stroke

care. The fixed effects coefficients of the key organisational

variables CSU (3.716), SUTC (2.389), specialist (5.394) and

foundationtrust (2.614) are all statistically significantat5%or

below. No other variables appear as statistically significant.

Column 2 adds the within-group means of the time-varying

external drivers of the quality score. The organisational vari-

ables SUTC (2.559), specialist (2.575) and NeuroClinic

(4.069) are statistically significant at the 5% level or below.

The variable stroke admissions is significant at below the 5%

level with fixed effect coefficient 0.030. Mean admissions

(�0:030) andstrokemortality(1.715) are significantatthe 5% level.Column 3addsthe yeardummy variable. Thevariableis

significant at the 5% level, with a high magnitude (11.414), emphasising again the important impact of the policy change

mentioned before. Importantly, the organisational variables

SUTC (2.58) and specialist (2.308) remain statistically sig-

nificant at the 5% level or below. Column 4 replaces the pri-

mary organisational variables in model 3 with the composite

organisationalmeasure.Besidestheyeardummy(10.570),the

mean of the composite measure appears statistically signifi-

cant (0.449) at below the 1% level. All in all, even when we

consider fixed effects coefficient estimates, the variables

capturing aspects of the organisational quality of the process

of stroke care such as SUTC remain significant. The fixed

effects coefficients of the rest of the variables are not statis-

tically significant.

In the above, we did not separate hospital fixed effects

from time fixed effects. Testing for hospital and time effects,

there is strong evidence for the presence of time effects,

which is consistent with the observed pattern in Fig. 1. We

turn to conventional panel regression to examine time fixed

effects separately. Table 8 shows three models with time

effects. Column 1 presents the results for the model with the

internal drivers of clinical quality of the process of stroke

care, using disaggregated organisational measures. Column

2 adds potential external drivers. Column 3 replaces the

disaggregate organisational indicators with the composite

measure of organisational quality of the process of stroke

care. The disaggregate organisational variables SUTC and

specialist are statistically significant in the first two columns.

The variable neurology in the first model and NeuroClinc

(the presence of a neuro clinic) in the second model are

statistically significant too. And the composite measure of

organisational quality of the process of stroke care appears

stronglystatistically significant in the third model too. All the

three models point to the statistical significance of organi-

sational features of the process of stroke care. [The presence

Hospital heterogeneity: what drives the quality of health care 399

123

of time effects points to the possibility that changes in the

environment (say policies) may have affected the quality of

stroke care, but in the same way for all the hospitals.]

Further, the nurse-to-bed ratio variable appears statisti-

cally significant in the first two models, with a positive sign

across all the models, suggesting complementarity between

the number of nurses and beds. The coefficient for beds, as a

measure of hospital size, has a negative sign across the

models and is significant only in the first model. The mea-

sures indicating external factors are statistically significant

in one form or another. The number of neurosurgeons per

region is statistically and positively significant in the second

model and weekly median wage in the third model. The

variable stroke mortality is statistically significant in both

models—suggesting that in areas where stroke mortality

increased over time the quality of the process of stroke care

has improved too. It is possible that extra resources are

devoted to the process of stroke care in areas with high stroke

mortality, leading to a higher correlation between stroke

mortality and the clinical quality of stroke care.

To further support the robustness of our key results, we

rescale the measures of the quality of the clinical and

organisation of the process of stroke care by taking out the

within-hospital means of the variables, while including the

control variables in their level form. Table 9 reports the

results with the transformed variables. Column 2 adds

median wage to the list of control variables in column 1,

column 3 excludes the data on London hospitals, and column

4 adds London to the list of control variables. In all the

columns, the coefficient estimate of the composite organi-

sational score, in its transformed form, is significant at 1%,

with the magnitude ranging from 0.297 to 0.326. Changes in

the quality of the clinical process of stroke care are strongly

positively associated with changes in the composite organ-

isational score. And the coefficient of the year dummy is no

longer statistically significant. The results are consistent with

the theoretically plausible conjecture that variations in the

quality of the organisation of the process of care drives

changes in the quality of the process of stroke care. While the

panel structure of the short sample supports our hypothesis,

there is no claim for causation. There could be unobserved

time-varying factors that drive changes in both clinical and

organisational measures of quality.

The fact that the organisational quality of the process of

stroke care appears among critical drivers of the clinical

quality of stroke care raises a deeper question as to what

factors drive organisational quality. Our sample is inade-

quate for fully shedding light on the subject. Nonetheless,

we have regressed the composite measure of organisational

quality on several theoretically plausible drivers of organ-

isational quality. Columns 1 and 2 in Table 10 include

several internal drivers. Column 1 controls for individual

fixed effects and column 2 controls for both individual and

time fixed effects. Columns 3 and 4 add weekly median

wage. The columns respectively control for individual

fixed effects and both individual and time fixed effects. In

all the columns, the nurse-to-bed ratio is statistically and

quantitatively significant at the (10%) level or below. The

median weekly wage appears as statistically significant in

the last column, suggesting that hospitals located in more

affluent areas have higher organisational quality.

The results from the traditional econometric approaches

corroborate the findings from the unbiased REEM-Trees.

All the analyses indicate the importance of the organisa-

tional quality of stroke care in determining the clinical

quality of stroke care. The tree models point to critical

interactions among various variables driving stroke care

quality. It is a complex interaction among hospital

resources that shapes quality. Our key results are robust to

the use of ratio variables or alternative measures of human

or physical capital left out in constructing the trees because

of the high correlation. Our results are not driven by hos-

pitals in London. Excluding data relating to London’s

hospitals will not change our results, as shown in Table 9.

Conclusion

A feature of the health care systems is substantial variation in

health care quality across hospitals. This study has focused on

the quality of the process of stroke care as an indicator of the

overallqualityofNHShospitals.Drawingonthe literature,we

conjectured several explanations for the observed cross-hos-

pital heterogeneity and tested their predictive implications

using a short panel spanning 2004 to 2010. Both the para-

metric and non-parametric methods identify several features

of the organisation of stroke care as key predictors of hospital

quality. Presences of specialist stroke teams, well-equipped

stroke units and neurovascular clinics have all been found to

improve thequalityofstrokecareandthe improvementsrange

between 2 to 5 points in a quality score measured on a 0–100

scale. When a composite score as a summary of such organ-

isation of care has been used separately it consistently

appeared to be a significantly important driver of quality. The

result persists when potential confounders/variables are con-

trolled for and is particularly robust to the inclusion of a time

trend, which accounted for a major policy change during the

study period. The non-parametric methods identify the mea-

sure of organisation score as the key predictor of hospital

quality. The result persists when potential confounders/vari-

ables are controlled for and is particularly robust to the

inclusion of a time trend. The result supports an emerging

literature that emphasises the critical role of organisation of

resources in productivity. The non-parametric methods also

reveal critical interactions among potential determinants of

the quality of the process of stroke care.

400 M. Ali et al.

123

Several limitations offer scope for further research. The

predictive results narrow down candidate hypotheses on the

sources of hospital heterogeneity but are only indicative of

the causal impact of organisational factors on the quality of

stroke care; they do not establish causation. A thorough

analysis will consider further control variables such as

stroke admissions, examine alternative measures of quality

and attempt to obtain a more comprehensive measure of

organisation quality. As another limitation, our study does

not control for clinical networks. Under these clinical net-

works, hospitals combine and integrate resources with other

hospitals in the networks to provide high quality of care to

the patients. As mentioned in [61], for example, cardiac

networks in the English NHS have led to an increase in the

rate of specialist interventions and faster access time. The

results trace differences in the quality of the process of care

to differences in the organisation of resources and man-

agement practices across NHS hospitals. Ultimately, it is

vital to explain organisational heterogeneity—why some

hospitals enjoy a higher level of organisational design than

others. Future research will benefit from using a longer

longitudinal framework to better identify trends in perfor-

mance. Equally, it will prove insightful to compare the

effects of the National Stroke Strategy that was imple-

mented in England and compare the quality for stroke care

with Wales and Northern Ireland. This allows one to draw

causal effects of such policy changes (using quasi-experi-

mental techniques such as difference in difference) since

health care systems across England and in Wales or

Northern Ireland are broadly comparable. Finally, future

research needs to take into account detailed staff data

related to stroke care including rehabilitation and geriatric

staff and control for cardiac networks.

Acknowledgements We would like to thank participants at the 18th International Conference on Econometrics, Operations Research and

Statistics, the Health e-Research Centre seminar at University of

Manchester and the BES seminar at the Alliance Manchester Business

School. We are grateful to Peter Kawalek, Nathan Proudlove and

Irene Roele for their very helpful comments.

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://crea

tivecommons.org/licenses/by/4.0/), which permits unrestricted use,

distribution, and reproduction in any medium, provided you give

appropriate credit to the original author(s) and the source, provide a

link to the Creative Commons license, and indicate if changes were

made.

Appendix

See Tables 3, 4, 5, 6, 7, 8, 9 and 10

Table 3 Definition and source of variables used in the analysis

Variable Definition Source

Clinical process of care

score Total clinical process score The National Sentinel

Stroke Audit; RCP

Organisational variables

Organisation score Total organisational score The National Sentinel

Stroke Audit; RCP

Hospital characteristics

Teaching hospital Whether the hospital is a teaching hospital Self-coded from hospital’s

website

Foundation trust Whether the hospital is a foundation trust Self-coded from Monitor

website

Human capital

Non-medical staff Headcount of non-medical staff as of 30 September NHS workforce; statistics,

(HCHS)

Scientific staff All qualified scientific, therapeutic and technical staff as of 30 September NHS workforce; statistics

(HCHS)

Allied professionals Qualified allied health professionals as of 30 September NHS workforce; statistics,

(HCHS)

Clinical staff Total number of medical and dental staff as of 30 September NHS workforce; statistics,

(HCHS)

Qualified clinical staff Headcount of professionally qualified clinical staff as of 30 September NHS workforce statistics

(HCHS)

Nurses Headcount of qualified nursing midwifery and health visiting staff as of 30

September

NHS workforce statistics

(HCHS)

Hospital heterogeneity: what drives the quality of health care 401

123

Table 4 Clinical process score domains

Clinical domains Clinical standards

Initial patient assessment Screening for swallowing 24 h

Visual fields

Sensory testing

Brain scan within 24 h of stroke

Multidisciplinary assessment Swallowing assessment speech and language therapist

Physiotherapy assessment within 72 h

Initial assessment of communication 7 days

Occupational therapy assessment within 4 working days

Social work assessment within 7 days of referral

Screening and functional assessment Patient weighed at least once during admission

Evidence mood assessed

Cognitive status assessed

Screening for malnutrition

Care planning Evidence of rehabilitation goals

Plan to promote urinary continence

Receiving nutrition within 72 h

Communication with patients and carers Discussion with patient about diagnosis

Carer needs for support assessed separately

Skills taught to care for patient at home

Follow-up appointment at 6 weeks

Driving advice

Acute care Aspirin within 48 h of stroke

90% of stay in a sroke unit

Admitted to an acute or combined Stroke Unit within 4 h

Receiving fluids within 24 h

Receiving thrombolysis

Table 3 continued

Variable Definition Source

General Medicine

Group

Total medical staff at General Medicine Group as of 30 September NHS workforce statistics

(HCHS)

Neurology Total medical staff at Neurology group as of 30 September NHS workforce; statistics,

(HCHS)

Neurophysiology Number of medical staff at clinical neurophysiology group as of 30 September NHS workforce statistics

(HCHS)

Neurosurgeons Number of neurosurgeons as of 30 September NHS workforce statistics

(HCHS)

Physical capital

Beds Total number of available beds Hospital Estate and facilities

data

Operating theatres Number of operating theatres, quarter ending September Dept. of Health QMCO

Day case theatres Number of dedicated day case theatres quarter ending September Dept. of Health QMCO

Regional characteristics

Stroke admissions Regional emergency stroke admissions standardised by age and gender HSCIC

Stroke mortality Regional stroke mortality standardised by age and gender HSCIC

All SMR All age standardised mortality ratio (SMR) HSCIC

Median wage Regional full-time weekly median wage ONS; ASHE

Inequality Ratio of 10th and 90th percentile full time weekly wage ONS; ASHE

No qualifications Regional population with no qualifications (%) NOMIS

402 M. Ali et al.

123

Table 5 In- and out-sample fit measures

In-sample fit Out-sample fit

AIC BIC LOOCV k-fold

(1) (2) (3) (4)

Models

Model 1 2195.83 2236.35 9.314 9.319

Model 2 2147.44 2195.23 9.204 9.091

Model 3 2131.69 2175.86 8.562 8.405

Model 4 2096.64 2140.80 8.531 8.268

Table 6 Linear mixed effects regression results

Models

(1) (2) (3) (4)

(Intercept) 44.361 (5.706)*** -7.571 (23.684) 14.724 (23.185) -4.762 (21.197)

Beds -0.003 (0.002) -0.000 (0.002) -0.002 (0.002) -0.002 (0.002)

Day case theatres -0.117 (0.263) -0.371 (0.264) -0.172 (0.262) -0.231 (0.236)

Nurse-to-bed ratio 5.490 (1.567)*** 2.175 (1.701) 2.259 (1.648) 1.916 (1.525)

Neurology 0.168 (0.108) 0.015 (0.110) 0.067 (0.109) 0.036 (0.097)

Neurophysiology 0.311 (0.650) 0.340 (0.649) 0.392 (0.638) 0.291 (0.579)

Neurosurgery -0.087 (0.147) 0.001 (0.145) -0.019 (0.143) -0.026 (0.128)

Teaching 1.849 (1.549) 1.580 (1.533) 1.555 (1.504) 1.164 (1.331)

Foundation trust 2.487 (1.226)** 3.332 (1.209)*** 1.445 (1.223) 1.884 (1.117)*

ASU 1.524 (1.937) 1.576 (1.875) -0.370 (1.830)

RSU 1.066 (1.761) 0.388 (1.739) 0.625 (1.676)

CSU 3.795 (2.181)* 2.172 (2.145) 0.129 (2.100)

SUTC 2.461 (1.011)** 2.639 (0.977)*** 2.748 (0.935)***

Specialist 5.172 (1.136)*** 3.935 (1.132)*** 1.899 (1.150)

ESD 1.876 (1.314) 1.842 (1.275) 0.925 (1.233)

NeuroClinic 3.149 (2.128) 4.709 (2.071)** 3.437 (1.996)*

PatientViews -1.408 (1.904) -2.614 (1.897) -2.639 (1.817)

Report 0.909 (1.174) 1.088 (1.139) 1.115 (1.092)

Stroke admissions -0.000 (0.000) -0.000 (0.000) -0.000 (0.000)

Stroke mortality 0.141 (0.129) 0.200 (0.124) 0.230 (0.116)**

No qualifications 0.086 (0.332) -0.355 (0.336) -0.177 (0.302)

Median wage 0.084 (0.024)*** 0.036 (0.025) 0.057 (0.023)**

Neurosurgeons per region 0.019 (0.026) 0.047 (0.026)* 0.021 (0.023)

Year dummy 6.574 (1.250)*** 4.831 (1.178)***

Organisation score 0.331 (0.050)***

AIC 2222.923 2231.788 2205.433 2199.928

BIC 2295.973 2322.657 2299.844 2265.798

Num. obs. 303 303 303 303

*** p\0:001, ** p\0:01, * p\0:05, � p\0:1. Table 6 shows linear mixed effects results corresponding to the four tree models. The dependent variable is the quality score and explanatory variables are lagged 1

year. Column 1 includes hospital characteristics, human capital factors, teaching and foundation trust status,

and primary variables reflecting the quality of the organisation of the process of stroke care. Column 2 adds

a set of external variables and column 3 adds the year dummy. Column 4 substitutes the composite

organisational measure for the primary organisation features of the process of stroke care

Hospital heterogeneity: what drives the quality of health care 403

123

Table 7 Correlated random effects results

Models

(1) (2) (3) (4)

(Intercept) 42.975 (5.950)*** 6.059 (30.758) 11.222 (30.751) -19.008 (26.751)

Beds 0.017 (0.017) 0.009 (0.015) 0.008 (0.015) -0.000 (0.014)

Day case theatres -0.439 (1.207) -0.102 (1.047) -0.230 (1.037) -0.647 (1.005)

Nurse-to-bed ratio 4.794 (3.921) 0.669 (3.601) 0.552 (3.562) -1.196 (3.400)

Neurology -0.648 (0.736) -1.001 (0.680) -0.913 (0.674) -0.994 (0.655)

Neurophysiology 1.669 (3.573) -0.294 (3.128) -0.367 (3.094) -0.085 (3.017)

Neurosurgery 0.794 (1.129) 0.207 (1.041) 0.189 (1.029) 0.053 (1.002)

Teaching 1.761 (1.556) 1.032 (1.538) 1.467 (1.547) 1.110 (1.342)

Foundation trust 2.614 (1.238)** 1.600 (1.257) 1.716 (1.252) 1.675 (1.122)

ASU 1.599 (1.957) -0.140 (1.862) -0.198 (1.849)

RSU 1.107 (1.772) 0.809 (1.708) 0.664 (1.699)

CSU 3.716 (2.197)* 0.143 (2.123) 0.026 (2.111)

SUTC 2.389 (1.026)** 2.559 (0.963)*** 2.580 (0.956)***

Specialist 5.394 (1.161)*** 2.575 (1.172)** 2.308 (1.170)*

ESD 2.000 (1.323) 1.216 (1.244) 1.152 (1.235)

NeuroClinic 3.364 (2.155) 4.069 (2.020)** 3.302 (2.035)

PatientViews -1.099 (1.920) -2.051 (1.851) -2.378 (1.844)

Report 0.683 (1.187) 0.674 (1.121) 0.839 (1.116)

Beds (mean) -0.021 (0.017) -0.011 (0.015) -0.010 (0.015) -0.003 (0.014)

Day case theatres (mean) 0.349 (1.241) -0.112 (1.085) 0.072 (1.077) 0.409 (1.033)

Nurse-to-bed ratio (mean) 1.431 (4.314) 3.191 (4.091) 3.294 (4.054) 3.770 (3.824)

Neurology (mean) 0.825 (0.743) 1.099 (0.691) 1.004 (0.684) 1.035 (0.663)

Neurophysiology (mean) -1.424 (3.634) 0.653 (3.197) 0.785 (3.163) 0.203 (3.073)

Neurosurgery (mean) -0.881 (1.139) -0.255 (1.049) -0.238 (1.038) -0.094 (1.010)

Stroke admissions 0.030 (0.016)* 0.022 (0.016) 0.015 (0.015)

Stroke mortality -1.470 (0.958) -1.209 (0.955) -0.855 (0.918)

No qualifications -0.288 (0.366) -0.322 (0.365) -0.029 (0.320)

Median wage 0.067 (0.105) -0.225 (0.169) -0.133 (0.158)

Neurosurgeons per region -0.038 (0.201) -0.224 (0.216) -0.197 (0.208)

Stroke admissions (mean) -0.030 (0.016)* -0.022 (0.016) -0.015 (0.015)

Stroke mortality (mean) 1.715 (0.974)* 1.416 (0.973) 1.064 (0.933)

Median wage (mean) -0.025 (0.109) 0.256 (0.168) 0.194 (0.157)

Neurosurgeons per region (mean) 0.077 (0.202) 0.268 (0.218) 0.206 (0.209)

Year dummy 11.414 (5.220)** 10.570 (4.746)**

Organisation score 0.029 (0.083)

Organisation score (mean) 0.449 (0.104)***

AIC 2222.916 2226.488 2218.599 2202.447

BIC 2317.328 2352.433 2348.008 2307.439

Num. obs. 303 303 303 303

*** p\0:001, ** p\0:01, * p\0:05, � p\0:1. Table 7 shows correlated random effects results for the four models. Each time-varying explanatory variable appears once in its original form and once as a within-group (hospital) average. The coefficients of the variables reflect fixed

effects estimates. We control for both hospital and time fixed effects in column 3 and column 4 by adding the year dummy

404 M. Ali et al.

123

Table 8 Fixed effects model (time)

Models

(1) (2) (3)

Beds -0.004 (0.002)** -0.002 (0.002) -0.002 (0.002)

Day case theatres -0.045 (0.235) -0.189 (0.237) -0.246 (0.221)

Nurse-to-bed ratio 4.267 (1.446)*** 2.944 (1.567)* 2.201 (1.472)

Neurology 0.189 (0.096)** 0.072 (0.097) 0.037 (0.091)

Neurophysiology 0.302 (0.577) 0.359 (0.570) 0.267 (0.539)

Neurosurgery -0.069 (0.130) -0.020 (0.128) -0.031 (0.119)

Teaching 2.193 (1.381) 1.710 (1.359) 1.181 (1.242)

Foundation trust 1.405 (1.138) 1.772 (1.160) 2.042 (1.074)*

ASU -0.755 (1.857) -0.245 (1.836)

RSU 1.605 (1.628) 0.632 (1.627)

CSU 0.958 (2.073) 0.668 (2.033)

SUTC 2.902 (0.952)*** 3.261 (0.936)***

Specialist 2.381 (1.158)** 2.047 (1.147)*

ESD 1.248 (1.236) 1.248 (1.225)

NeuroClinic 2.893 (1.998) 4.110 (1.985)**

PatientViews -1.171 (1.779) -2.386 (1.808)

Report 1.338 (1.100) 1.197 (1.084)

Stroke admissions -0.000 (0.000) -0.000 (0.000)

Stroke mortality 0.216 (0.125)* 0.238 (0.115)**

No qualifications -0.347 (0.306) -0.154 (0.284)

Median wage 0.036 (0.023) 0.059 (0.021)***

Neurosurgeon per region 0.045 (0.023)* 0.018 (0.021)

Organisation score 0.359 (0.049)***

R2 0.191 0.244 0.297

Adj. R2 0.179 0.225 0.281

Num. obs. 303 303 303

*** p\0:001, ** p\0:01, * p\0:05, � p\0:1. Column 1 includes the internal drivers of clinical quality of the process of stroke care. Column 2 adds potential external drivers. Column 3 replaces the individual

organisational variables with the composite measure of organisational quality. All the three models control

for time fixed effects

Hospital heterogeneity: what drives the quality of health care 405

123

Table 9 Correlated random effects results: rescaled clinical and organisational quality scores

Models

(1) (2) (3) (4)

(Intercept) -9.850 (11.11) -53.01 (20.19)*** -50.61 (27.51)* -55.67 (26.95)**

Beds -0.003 (0.002)* -0.002 (0.002) -0.001 (0.002) -0.002 (0.002)

Day case theatres -0.125 (0.204) -0.228 (0.207) -0.352 (0.266) -0.228 (0.207)

Nurse-to-bed ratio 2.358 (1.475) 1.853 (1.408) 1.116 (1.538) 1.864 (1.415)

Neurology 0.070 (0.079) 0.035 (0.079) -0.023 (0.137) 0.037 (0.079)

Neurophysiology 0.320 (0.453) 0.297 (0.419) -0.067 (0.617) 0.294 (0.420)

Neurosurgery -0.044 (0.116) -0.024 (0.100) 0.029 (0.112) -0.026 (0.101)

Teaching 1.414 (1.330) 1.163 (1.300) 1.514 (1.518) 1.186 (1.322)

Foundation trust 1.248 (0.994) 1.849 (1.015)* 1.811 (1.115) 1.841 (1.019)*

Stroke admissions -0.000 (0.000) -0.000 (0.000) -0.000 (0.000) -0.000 (0.000)

Stroke mortality 0.084 (0.105) 0.228 (0.122)* 0.204 (0.138) 0.237 (0.136)*

No qualifications -0.422 (0.321) -0.182 (0.301) -0.173 (0.309) -0.189 (0.306)

Neurosurgeons per region 0.060 (0.015)*** 0.022 (0.020) 0.028 (0.038) 0.028 (0.038)

Median wage 0.056 (0.020)*** 0.060 (0.032)* 0.060 (0.031)*

Organisation score 0.297 (0.048)*** 0.325 (0.049)*** 0.313 (0.053)*** 0.326 (0.049)***

London -1.042 (5.961)

Year dummy -0.502 (0.965) -1.668 (1.020) -1.540 (1.323) -1.782 (1.246)

R 2 0.230 0.250 0.143 0.250

Adj. R 2 0.218 0.237 0.134 0.236

Num. obs. 303 303 265 303

*** p\0:01, ** p\0:05, * p\0:1. The dependent variable in all the models is the change in the quality of the process of stroke care obtained by taking out the within-hospital mean of the variable from the variable. Similarly, the table replaces the composite organisational score with the

change in the variable obtained by taking out the within-hospital mean of the variable. Column 3 excludes data relating to London hospitals.

Column 4 includes the London dummy, using the full data

Table 10 Fixed effects models: organisation score

Models

(1) (2) (3) (4)

Beds 0.017 (0.012) 0.018 (0.012) 0.018 (0.012) 0.016 (0.012)

Day case theatres 1.112 (0.790) 0.930 (0.795) 0.963 (0.798) 1.004 (0.788)

Nurse-to-bed ratio 5.238 (2.987)* 6.486 (3.079)** 6.301 (3.106)** 5.519 (3.086)*

Neurology -0.260 (0.576) -0.084 (0.585) -0.112 (0.588) -0.202 (0.582)

Neurophysiology 1.554 (2.918) 1.857 (2.912) 1.851 (2.924) 1.209 (2.901)

Neurosurgery -0.558 (0.904) -0.423 (0.904) -0.483 (0.904) -0.099 (0.909)

Teaching 0.540 (10.373) 0.490 (10.327) 0.466 (10.357) 0.865 (10.227)

Foundation trust -2.747 (1.847) -1.354 (2.044) -1.718 (2.026) -0.764 (2.045)

Median wage -0.034 (0.028) 0.358 (0.176)**

R 2 0.055 0.051 0.064 0.076

Adj. R 2 0.026 0.024 0.029 0.035

Num. obs. 342 342 342 342

*** p\0:001, ** p\0:01, * p\0:05, � p\0:1. The dependent variable is the composite organisational measure, all explanatory variables are lagged for 1 year, and the coefficients are all fixed effects estimates.

Column 1 controls for hospital fixed effects while column 2 controls for hospital and time fixed effects.

Columns 3 and 4 add weekly median wage. The columns respectively control for individual fixed effects

and both individual and time fixed effects. Column 5 adds the lag of the dependent variable and controls for

individual and time fixed effects

406 M. Ali et al.

123

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