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Pediatric Anesthesia. 2021;31:539–547. wileyonlinelibrary.com/journal/pan | 539© 2021 John Wiley & Sons Ltd
1 | INTRODUC TION
Quality improvement (QI) is the framework used to systematically improve the way health care is delivered to patients. QI entails iter- ative efforts to reduce process variation and improve outcomes for patients and healthcare organizations. Commitment from multiple individuals in a local team and key stakeholders within an organi- zation is required to achieve a sustainable QI process.1 In order to achieve improvement, a change is necessary.
The key to identifying changes that result in improvement lies in measurement. Measurement is second nature to healthcare provid- ers who measure elements of patient care. Vital signs, blood chemis- tries, and patient outcomes are just a few data points collected and analyzed in everyday work. Throughout training, healthcare provid- ers are trained to evaluate these data with statistical studies (mean and standard deviations, t tests, regression analysis, etc.) when there is a desire to determine whether a process leads to improved out- comes. While powerful, this type of statistical analysis relies on data collected at static points in time and does not allow for rapid deter- mination of change that can be used in day- to- day management of patient care. Data measurement for QI relies on continuous data col- lection and dynamic processing of data using run charts or statistical
process control (SPC) charts. These charts provide a real- time inter- pretation of data against time to enable teams to determine whether changes in process or outcomes are moving in the desired direction.2 The measures in QI are distinctive from the measures used in re- search (Supportive Table S1). In research, the possibility of type I and II errors arise because of the intrinsic nature of hypothesis testing. On the other hand, in QI, a healthcare improvement is performed and a hypothesis is not specifically tested. The improvement in health care made during a project may be readily attributable to a change in practice or a bundle of practices, but the exact cause of improvement may not be determined.
In this review, we will describe the basics of measurement in QI and the use of run charts and SPC charts with practical examples.
2 | MAIN ARTICLE
The science of QI follows an improvement model which is a graphi- cal representation of a simple, yet powerful tool. This improve- ment model is used as a framework to guide QI work and is used by the Institute for Healthcare Improvement (IHI).3 The model for improvement is made up of three fundamental questions that drive
Received: 9 October 2020 | Revised: 12 February 2021 | Accepted: 16 February 2021
DOI: 10.1111/pan.14163
E D U C A T I O N A L R E V I E W
Statistics in quality improvement: Measurement and statistical process control
Heather A. Wolfe1 | April Taylor2 | Rajeev Subramanyam1
1Division of Anesthesiology and Critical Care Medicine, The Children’s Hospital of Philadelphia, The University of Pennsylvania Perelman School of Medicine, Philadelphia, PA, USA 2Department of Pediatrics, The Children’s Hospital of Philadelphia, Philadelphia, PA, USA
Correspondence Heather A. Wolfe, 3401 Civic Center Blvd, Wood Building Room 6040, Philadelphia, PA 19104, USA. Email: [email protected]
Editor: Andrew Davidson
Abstract Data are used in healthcare quality improvement endeavors to measure and deter- mine whether the changes made in the course of the work have made the desired impact. The methods used to analyze data in quality improvement differ slightly from those used in classical statistics. Run charts and statistical process control charts are the most common types of graphical representations used to visualize data collected for quality improvement. This review provides a basic introduction to measurement in quality improvement and explains the use of run charts and statistical process control charts with real- life examples.
K E Y W O R D S healthcare quality evaluation, process assessment, quality improvement, quality improvement Statistics, statistical process control
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the improvement: 1) What are we trying to accomplish? 2) How will we know that a change is an improvement? and 3) What change can we make that will result in improvement? These three funda- mental questions are combined with the cyclical process of action and learning known as the plan- do- study- act (PDSA) cycle or the Shewhart cycle in order to drive improvement.4 The PDSA cycle is also referred to as the Deming cycle or as the PDCA (plan- do- check- act) cycle. Although randomized controlled trials are considered the standard in research methodology, most of our knowledge is be- lieved to come to us through PDSA cycles.5 The cyclical nature of these PDSA models builds upon small, iterative changes in behavior, and the outcomes from these changes are analyzed before deter- mining whether the change leads to improvement. A single PDSA cycle can be tested sequentially for the same change strategy by using the rule of starting small and scaling up. A rule of thumb of testing one, and then five and 25 and so forth could be used. This sequential change strategy from the same PDSA cycle can be repre- sented using PDSA ramps.
An example of a PDSA ramp is provided in a project on infusion pump medication errors during anesthesia in a radiology suite.6 If there is evidence that the change strategy could work, learn- ing from this should be incorporated for the next tests of change (Adapt). If the change leads to improvement, the strategy worked and should be kept (Adopt). After multiple tests if the testing strat- egy was not successful, it should be eliminated (Abandon). The goal of a PDSA ramp is to build each cycle from sequential test- ing, implementing, and either adapting, adopting, or abandoning a change strategy. It is important that teams are willing to abandon new processes that do not lead to improvement and avoid seeing it as a failure. Abandoning when appropriate conserves time and other valuable resources.
2.1 | Measurement
For QI, the major components of measurement are as follows: 1) determining and defining key processes or outcomes; 2) collecting relevant and appropriate amount of data; and 3) analyzing and inter- preting these data.
2.1.1 | Why should we measure?
Measurement is the key to improvement and is important at every step of ensuring safe and effective patient care. A surgeon may approach an anesthesiologist to ask that they do an improvement project to improve on- time starts in the operating room (OR). An improvement team is assembled and analyzes the process for on- time starts, and multiple ideas are put forth to solve the problem. The team then measures on- time starts for two weeks to gather baseline data and finds that 95% of the time cases are starting on time. It is likely the problem that was put forth may have been based on one or two deviations in case starting time and not the
majority of case starts. Observation is imperative to understand processes that occur in the hospital. Observation is frequently documented as data collected for various safety or operational reasons (on- time starts, surgical site infection rates, staff burn- out rates, etc.). There are many types of data that are useful in supporting improvement efforts: continuous measurements (eg, blood pressure), counts or classification of observations (eg, num- ber of arterial line insertion attempts or insertion attempts suc- cessful/not successful), or documentation of people's thinking and feeling, ratings, and rankings.3
2.1.2 | What are we measuring?— Process, outcome, and balancing metrics
“Every system is perfectly designed to get the results that it does.” This famous quote in quality and business improvement highlights some of the keys to measurement in system improvement. What is a system? It can be a healthcare system, an OR, or the system used in a hospital to fill prescriptions. The system contains the people and the steps they take every day to perform any myriad of tasks. An OR that starts 50% of its cases late is designed to produce 50% late starts. Although not designed on purpose, it functions to give similar results. The system that produces these late starts may be made up of “processes” that lead to that “outcome.”
Every system can be broken down into small steps or maps that can explain the processes that comprise it. For example, the system that makes late OR starts may look like this: patient ar- rival → check- in → preoperative activities → transport to OR → anesthesia start. Any step along the way can contribute to late start time. Improvement projects typically involve three types of measures: process measures, outcome measures, and balancing measures. In simplistic terms, the steps along the way can often be considered “process measures” in QI and the item of concern to improve can be considered an “outcome measure.” Process measures are measures of the steps in a process that lead to a specific outcome (either positively or negatively). An outcome measure is generally the target of the project and can be patient- centric (decrease harm rates) or healthcare personnel- centric (cli- nician medication choice). A QI project's primary aim could either be a process measure or an outcome measure. Incorporation of a change during a QI project could move the primary aim in a favor- able direction; however, it could move another unrelated variable in an unfavorable direction and potentially cause a system imbal- ance. To measure such imbalance in a metric, a balancing mea- sure is incorporated into most projects to monitor for favorable or unfavorable changes. Balancing measures could also reflect other favorable changes that are not the primary outcome, for example, reducing time to care may favorably (or unfavorably) impact pa- tient satisfaction.
In the example of on- time case starts in the operating room, a process measure may be on- time patient arrival to preoperative area and the outcome measure may be on- time case starts. On the other
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hand, if the patient were asked to come in many hours prior to their timed surgical procedure to ensure on- time starts, this may decrease patient satisfaction as they now have an incredibly long wait time. Patient satisfaction in this scenario could be measured as a “balanc- ing measure.”
Unrealistic goals can have a negative impact on stakeholders’ morale and could run a high possibility of failure in achieving the results. For instance, in the scenario above, if the team decided to go forward with the goal of 100% on- time case starts, although ideal, they would be unlikely to attain that goal. In health care, emergen- cies arise both on the patient and healthcare personnel's side of care and 100% is sometimes not attainable.
The SMART (Specific, Measurable, Actionable, Relevant, Timely) aim is a useful acronym to help teams in setting achiev- able goals. Goals can be set based on available standards (local, na- tional, or international). In the above example on late case starts, a hospital that is planning to improve their on- time case starts could potentially survey other similar hospitals to determine the average delay times to plan their own goal. If these data are not available either through publication or through other modalities, levels of reliability could be used. Reliability is measured as the inverse of the failure rate of the system. Most US healthcare organizations function at 10−1 reliability, in other words a defect rate of 1 in 10 or 10%. Applying this concept to QI, level 1 reliability is 90% goal (failure rate of 1 in 10), level 2 reliability is 95% goal (failure rate of 5 in 100), and level 3 reliability 99% goal (failure rate of 5 in 1000).7
We will explain the three measures (process, outcome, and bal- ancing) with another example of a QI project in which the author RS was the team lead.6 The project had a goal to reduce the medication errors related to infusion pumps related to pediatric anesthesia in the radiology suite. The “SMART Aim” for this project was to have two- person verification of infusion pump programming prior to medication administration 90% of the time by a prespecified time period. The secondary aim was the reduction in medication errors related to administration of infusion pump medications. The sec- ondary aim was an outcome measure and was a result of change in the primary process measure. Since the two- person verification required minimal additional time in the patient flow (although fully justified in view of safety), any delays in case starts were measured as the balancing measure.
2.2 | Analyzing variation
Time- series data are the classic representation of measurements in a QI project. Displaying data over time provides an important means to identify the presence of both random and nonrandom patterns in the data. Two common graphical displays used to summarize time- series QI data include the run chart and the SPC chart (or “con- trol chart”). Both charts are used to monitor a process to identify trends and can be used for process, outcome, and balancing met- rics. Both plot data over time (eg, days, weeks, quarters) and depict a centerline.
2.2.1 | Run chart
A run chart is a time- series plot using a median as the centerline, and the process/outcome measurements over time (Figure 1).8,9 The median is chosen in order to use probability rules based on the fact that the median is not influenced by extreme values and is the point in which half of the data will lie above and half below the center- line.10 Run charts are simpler than SPC charts to construct and may be easier for novice QI teams to create and analyze.
2.2.2 | Statistical process control charts
A SPC chart also depicts data over time but adds statistical informa- tion derived from the data. A typical SPC chart shown in Figure 2 plots the measurements of a quality characteristic from a process over time with the centerline representing the mean of the process measurements. Additionally, the chart includes upper and lower control limits (UCL and LCL). The control limits, typically set at three- standard deviations from the mean, are derived from the process data with the width of the control limits inversely proportional to the sample size.11
SPC charts are generally classified into two types: variables con- trol charts and attributes control charts (Table 1). Variables control charts depict data based on a continuous scale of measurement (eg, time, weight, volume), whereas attributes control charts are used for count or classification data (eg, yes/no, pass/fail).12 All of the charts listed in Table 1 can be created using a traditional statistical program such as SAS® software (SAS Institute, Inc.), STATA (StataCorp, LLC), SPSS® Statistics (IBM Corp.), or Minitab® (Minitab, Inc.) or QI- specific software packages such as QIMacros® (KnowWare International, Inc.) or SPC for Excel (BPI Consulting, LLC). Chart selection begins with the type of data (Figure 3). For continuous data, an x- chart is used for a sample size of one (eg, an individual measurement) and an x- bar chart for sample sizes >1. Using the infusion pump project example6 pre- viously described, the balancing measure of delayed procedure start times could also be tracked as the average number of minutes late by week, month, or some other interval using an x- bar chart.
For count and classification data, the three most common control charts used in healthcare are the c- , u- , and p- charts. To distinguish between these three charts, consider the following example using the medication administration project previously described. The secondary aim was the reduction in medication errors related to administration of infusion pump medications. There are numerous ways to measure and track these medication errors. One could measure the number of medication errors per patient during their anesthetic. Alternatively, one could measure whether the patient had at least one medical error during their anesthetic. The former would be best displayed as a c- chart (if the sample size is consistent) or u- chart (if the sample size is variable) as it counts the number of medication errors. The latter would be best displayed using a p- chart as we have moved from a count of individual medication errors to a classification per patient anesthetic encounter of yes/no medication error (Figure 3).
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Both run charts and SPC charts help providers determine the type of variation that exists in data; however, SPC charts provide more an- alytical power with the addition of the control limits to better assess nonrandom patterns or special vs. common cause variation, an essen- tial component of QI that we describe below. Development of both types of charts begins with gathering enough data to establish a base- line. These data could represent either retrospective or prospective collection; however, they should include data prior to the introduction of any interventions to allow special cause rules to be applied. For run charts, a median line is mapped over the run chart data once ten or more data points are gathered. For SPC charts, this is generally 12– 20 data points to account for seasonal or secular trends in the data.8,11,12
2.2.3 | Common cause vs. special cause variation
Common cause variation is random variability that exists intrinsic to the system. This type of variation is to be expected and indicates a stable (healthcare) measure. In the initial example of anesthesiolo- gist improving on- time starts to OR cases, some will start two min- utes early, some 15 min late, but it is very unlikely that an OR ever starts 100% of cases exactly on time in every case. There is an aver- age start time, for example, ten minutes after scheduled start time, and the majority of the data points will hover around that start time.
As long as no action is taken to improve or worsen the start time, the data will continue to randomly vary around this centerline.
On the other hand, special cause variation is an unexpected change that occurs due to changes in the system, and in the context of QI, is often considered desirable to achieve the predetermined aim of the project. In a QI project, if the intervention has resulted in improvement, a favorable nonrandom pattern indicating sustained change is expected.13 The presence of special cause variation is used to evaluate the effectiveness of interventions by careful and system- atic measurements. The occurrence of any special cause variation is appropriately annotated in the run or the control chart. The special cause variation will create a new mean (control chart) or median (run chart) when the variation coincides temporally with a plausible ex- planation that was part of the change initiated.
In the OR example above, if the QI team initiated a daily huddle in the hopes of having equipment available earlier in the day and the centerline in their data shifted to reliably having cases start five minutes after the planned start of the case, then we would con- sider the variation in the data to have special cause. Since it was temporally related to the intervention by the team, the variation is likely due to that intervention. The explanation of special cause is important to rule out accidental causes for the variation (eg, prob- lems with data collection, staffing changes, etc.). For example, if the team did not document the start time until fifty minutes after the
F I G U R E 1 Run chart rules showing the median and the process/outcome measurements over time. Figure shows four run chart rules: shift, trend, astronomical point based on IHI rules, and alternating points of 14 or more consecutive data points. Time is represented on the x- axis and the data from SMART aim on y- axis8,9
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case actually began, that would not be special cause. Special cause variation is interpreted based on rules which are discussed later in the article.
Many providers at this point in the discussion of measures and variation may think, “What is wrong with collecting before and after data and calculating means or medians and using standard statistical
F I G U R E 2 Statistical process control charts showing the measurements of a quality characteristic from a process over time with the centerline representing the mean of the process measurements14
Chart type Use Example
Variable charts
x- chart Individual measurement Number of anesthesia serious adverse events. Number of medication errors.
x- bar Continuous measurement; average
Anesthesia or surgery duration. Duration of nerve block placement.
Attribute charts
p- chart Dichotomous variable; proportion
Proportion of patients who experience an adverse event (eg, percentage of laryngospasm in the operating room).
c- chart Count of an event with more than one event possible per patient.
Number of anesthesia serious adverse events/ patient.
Number of medication errors/patient.
u- chart Rate of an event with more than one event possible per patient. Rate is adjusted per a common sampling denominator size.
Number of medication errors per 1000 anesthesia events.
TA B L E 1 Statistical process control chart types
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methods to compare the groups?” For instance, with the previous example of implementing a two- person verification to prevent med- ication errors in infusion medications, the two following patterns are possible during the QI project. In the first example, an initial improve- ment in medication errors with reversion toward the previous level is seen; however, the second example shows a sustained decline in medication errors. The averages from the periods both before and after the intervention are the same; however, the second example is clearly preferable (Figure 4). By displaying data over time, run charts and SPC charts are able to provide practitioners with more detailed information and trends.
2.2.4 | Run chart interpretation
Probability rules are used to determine whether data points above or below the centerline are observed changes are due to chance (common cause variation) or likely related to the intervention (spe- cial cause variation). At least ten data points are required in order to create a median line in order to reliably apply the following rules: shifts, trends, runs, astronomical points, and alternating points. Figure 1 describes these rules and their definitions that determine special cause variation in run charts.
2.2.5 | Statistical process control chart interpretation
One of the most basic rules used in the interpretation of a SPC chart is any point outside of the 3- standard deviation limits. Three- standard deviation limits have been shown to work empirically in practice— minimizing both overcorrecting and undercorrecting. For normally distributed data, the probability of all x points being within the limits is 0.9974 (in other words, 99% of the data are within three standard deviations for mean). Therefore in 1956, Western Electric introduced three additional rules to increase the sensitivity of de- tecting nonrandom patterns of change due to an intervention (in the case of the QI project) or instability if a process is in a monitoring stage.
1. Two out of three consecutive points beyond 2- standard deviation 2. Four out of five points more than 1- standard deviation from the
centerline, and 3. Eight consecutive points on one side of the centerline (eight- point
rule)
Over time, additional rules have been added with the most common rules used in health care illustrated in Figure 2.14 These
F I G U R E 3 Chart selection tool
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probability- based rules are indicative of nonrandom or special cause variation. Generally speaking, if only common cause or normal ran- dom variation were observed, we would expect our process mea- surements to vary randomly above and below the centerline with 0.5 above and below that line equally. As an example of nonrandom variation, using the eight- point rule, we can calculate the probability of that event occurring as 0.0036. Many rules, such as the eight- point rule, require a significant amount of time to determine an improvement. As such, Wheeler and colleagues have proposed an alternative aggregate- point rule suggesting improvement using four or five points.15
2.2.6 | What type of variation do we want to see in a QI project— random or nonrandom?
The answer is— it depends! If a project is undertaking active QI inter- ventions, nonrandom variation is the goal. Nonrandom variation in the direction of the QI target represents progress toward the goal, whereas random variation would suggest that there has not been a change due to the intervention(s). In contrast, QI projects that are in a maintenance or sustain phase display random variation appropri- ately. Once a QI project has achieved its targeted performance and no new interventions are introduced, the data return to a normal
F I G U R E 4 Differing patterns with same average values. Panel 4A: The averages from the periods both before and after the intervention are the same; however, the example in panel 4C is clearly preferable. Panel 4B: An initial improvement with reversion toward the previous level is seen. Panel 4C: A sustained decline in medication errors
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pattern but with a new re- calculated baseline and ideally reduced overall variability (Figure 5).11
2.2.7 | Design
The design for a QI project should follow SQUIRE 2.0 guidelines.16 The SQUIRE 2.0 guidelines provide a framework for describing QI projects and encourage teams to report in- depth the steps they took to develop a project, and describe PDSA cycles completed and rel- evant outcomes. Outcomes from QI efforts at publication are best displayed in run or SPC charts which are able to be created by health- care teams without significant statistical backgrounds. Before/after retrospective studies are not recommended for reasons discussed in this article of the importance of trends over time.
3 | SUMMARY
Measurement is key to any successful QI project. Process, outcome, and balancing metrics are determined by the improvement team at the beginning of the project. Data for these measures can be plotted over time in either run charts or SPC charts. Probabilities or statistical rules are applied to determine whether special cause
variation is present to explain a change or whether only common cause variation is present. The analysis of special cause variation is used by QI teams to determine whether actions from PDSA cy- cles have moved the data in a favorable or unfavorable direction. Understanding the basics of the use of data in QI is a foundation for all healthcare workers who seek to improve the care provided to patients.
4 | REFLEC TIVE QUESTIONS
1. How do we use data when evaluating quality improvement projects?
Measurement of process, outcome, and balancing metrics are key in a quality improvement project to determine whether the changes made during PDSA cycles are producing the change desired by the team. Data are measured and displayed over time in run charts and/ or statistical process control charts.
2. What types of variability occur in data? Special cause variation is unnatural variation that occurs in data
that is due to external factors. Common cause variation is natural variation in data that is inherent to the process being measured.
3. Why are control charts used to measure change in quality im- provement projects?
F I G U R E 5 Trial limits, intervention period, and re- calculated limits
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Statistical process control charts use rigorous statistical methods to identify common cause and special cause variation. They allow im- provement teams to continuously evaluate their data, and determine whether changes made to a process are leading to desired outcomes.
ACKNOWLEDG EMENTS The authors would like to thank Kristin McNaughton, MHS, for as- sistance with editing.
CONFLIC T OF INTERE S T Dr. Subramanyam has research funding from Masimo Foundation, Irvine, CA. Dr. Subramanyam is an Associate Editor for Pediatric Anesthesia. Dr. Wolfe has received a speaking honoraria fee from Zoll Medical Foundation in 2018.
DATA AVAIL ABILIT Y S TATEMENT Data sharing is not applicable to this article as no new data were cre- ated or analyzed in this study.
ORCID Heather A. Wolfe https://orcid.org/0000-0002-2760-6286 Rajeev Subramanyam https://orcid.org/0000-0003-4221-5790
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SUPPORTING INFORMATION Additional supporting information may be found online in the Supporting Information section.
How to cite this article: Wolfe HA, Taylor A, Subramanyam R. Statistics in quality improvement: Measurement and statistical process control. Pediatr Anesth. 2021;31:539–547. https://doi. org/10.1111/pan.14163
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