Journal Analysis - Landmark analysis: A primer - Critique

EDITORIAL

Landmark analysis: A primer

Charity J. Morgan, PhDa

a Department of Biostatistics, University of Alabama at Birmingham, Birmingham, AL, UK

Received Jan 2, 2019; accepted Jan 2, 2019

doi:10.1007/s12350-019-01624-z

In the survival analysis setting, landmark analysis

refers to the practice of designating a time point

occurring during the follow-up period (known as the

landmark time) and analyzing only those subjects who

have survived until the landmark time. 1 A comprehen-

sive overview of the landmark analysis method and its

use has been provided by Dafni. 2 To understand why

landmark analysis is sometimes necessary, consider the

following hypothetical example.

A study is conducted in which all subjects were

treated at baseline and then followed for a period of

several years. During follow-up, a subset of subjects

were found to respond favorably to treatment, with

response times varying among responders.

Figure 1 displays the response times for three

hypothetical subjects during the first six months of the

study. The dashed lines represent the time during which

the subject has not responded to treatment; for subjects

that respond to treatment, solid lines are used to denote

the time during which the subject has responded. After

six months, Subject 1 has not responded. Subjects 2 and

3 responded to treatment after 1.6 and 2.9 months,

respectively.

Study investigators might be interested in deter-

mining whether the responders had a significantly longer

survival times than non-responders. A naive (and

incorrect) approach would be to classify Subject 1 as a

non-responder and Subjects 2 and 3 as responders and

then use standard survival analysis methods, such as

Kaplan-Meier estimation or Cox proportional hazard

modeling, to compare the survival of these two groups

following treatment. Such an approach effectively

assumes that Subjects 2 and 3 responded to treatment

immediately. However, at baseline (i.e., the time of

treatment), responder status is unknown for all subjects.

That is, Subjects 2 and 3 begin the study as non-re-

sponders and do not become responders until later in

follow-up. Assuming otherwise ignores the fact that

responders, by definition, are guaranteed to survive at

least until the time of response; this error is known as the

guarantee-time bias or the immortal time bias. 3,4

Landmark analysis may be used to avoid this type

of bias. Under this approach, a landmark time is selected

and any subjects who were lost to follow-up or died

prior to this time are excluded from further analysis. For

the remaining subjects, subjects who have responded by

the landmark time are classified as responders. Any

subject who has not responded by the landmark time is

classified as a non-responder, even if that subject later

responds to treatment.

Figure 2 provides two examples of this process. In

Figure 2A, a landmark time of two months post-treat-

ment is chosen. Subjects 1 and 2 are then classified as

non-responders because neither subject has responded to

treatment at that time. Note that even though Subject 2

will later go on to respond to treatment, to avoid the

guarantee-time bias, Subject 2 must be considered to be

a non-responder due to his or her status at the landmark

time. Subject 3 responded to treatment prior to the

landmark time and is thus classified as a responder. As

can be seen in Figure 2B, selecting a different landmark

time (here, four months post-treatment) may change the

classification of some subjects. In this example, the later

landmark allows Subject 2 enough time to respond to

treatment, leading to this subject being placed in the

responder group.

Once the landmark has been chosen, any ineligible

subjects have been excluded, and subjects have been

classified according to their status at the landmark time,

the usual survival analysis methods are applied. The

results of these methods are interpreted as usual, with

the important caveat that conclusions are only general-

izable to subjects who have survived until the landmark

time.

While landmark analysis was originally proposed to

evaluate the association between treatment response and

survival, 1

or to allow for groupings based on any

Reprint requests: Charity J. Morgan, PhD, Department of Biostatistics,

University of Alabama at Birmingham, 1720 Second Avenue South,

Birmingham, AL 35294-0022, UK; [email protected]

J Nucl Cardiol 2019;26:391–3.

1071-3581/$34.00

Copyright � 2019 American Society of Nuclear Cardiology.

391

covariate whose value is not known at baseline, this

method does not necessarily need to be used for a group

comparison. In some cases, it may be of interest to

simply compare the survival experience both before and

after the landmark (see Figure 3).

Results can vary according to the landmark time, so

the choice of landmark is a critically important consid-

eration. Because events occurring prior to the landmark

time are excluded from the analysis, choosing a later

landmark will result in a smaller sample size and

therefore lower statistical power. The earlier the land-

mark time, the more likely late responders are to be

misclassified as non-responders (as with Subject 2 in

Figure 2A). To avoid bias, the landmark should be

chosen before data analysis begins and ideally should

correspond to a clinically meaningful period of time. 2

When the choice of landmark time is not obvious, the

data should be analyzed using multiple landmark times

in order to determine the sensitivity of the findings to the

choice of landmark. 3

An alternative to landmark analysis is a Cox pro-

portional hazards model that allows the value of the

covariate indicating treatment response to vary over

time. 5 This extension of the Cox model allows the entire

follow-up period to be considered (rather than only the

post-landmark time) and does not require any subjects or

events to be excluded from analysis. Furthermore,

Dafni 2 notes that this approach would avoid both the

problem of selecting a landmark time and any misclas-

sification errors. However, interpretation of the results

from these models can be difficult. 6 Further discussion

of time-varying Cox models may be found in Fisher and

Lin. 6

Application of the landmark analysis method is

straightforward and yields easily interpretable results.

Nevertheless, the choice of landmark time must be

carefully considered and sensitivity analyses should be

utilized whenever there are multiple landmark times

under consideration. For settings where an appropriate

landmark cannot be determined or where results are

overly sensitive to the choice of landmark, a Cox model

with time-varying covariates provides a feasible

alternative.

Figure 2. Classification of hypothetical subjects according to status at landmark. Subjects are classified as either responders (red) or non-responders (blue) based on their status at the landmark time.

Figure 1. Response times for three hypothetical subjects. Time of response indicated with a square. Dashed lines represent time the subject has not responded to treatment; solid lines denote the time during which the subject has responded.

392 Morgan Journal of Nuclear Cardiology� Landmark analysis: A primer March/April 2019

Disclosure

The author has no conflicts of interest to disclose.

References

1. Anderson JR, Cain KC, Gelber RD. Analysis of survival by tumor

response. J Clin Oncol 1983;1:710-9.

2. Dafni U. Landmark analysis at the 25-year landmark point. Circ

Cardiovasc Qual Outcomes 2011;4:363-71.

3. Buyse M, Piedbois P. On the relationship between response to

treatment and survival time. Stat Med 1996;15:2797-812.

4. Gleiss A, Oberbauer R, Heinze G. An unjustified benefit: Immortal

time bias in the analysis of time-dependent events. Transpl Int

2018;31:125-30.

5. Cox DR. Regression models and life-tables. J R Stat Soc Ser B

1972;34:187-220.

6. Fisher LD, Lin DY. Time-dependent covariates in the Cox

proportional-hazards regression model. Annu Rev Public Health

1999;20:145-57.

Publisher’s Note Springer Nature remains neutral with regard to

jurisdictional claims in published maps and institutional affiliations. Figure 3. Kaplan-Meier estimates of survival before and after the landmark time.

Journal of Nuclear Cardiology� Morgan 393 Volume 26, Number 2;391–3 Landmark analysis: A primer