PCORI Methodology Standards:
Academic Curriculum
© 2016 Patient-Centered Outcomes Research Institute. All Rights Reserved.
Module 3: Subgroup Analysis
Category 5: Heterogeneity of
Treatment Effects
Prepared by Ravi Varadhan, PhD
Chenguang Wang, PhD
Presented by Ravi Varadhan, PhD
Subgroup Analysis
 We focus on the setting of a randomized clinical trial of treatment Z for response Y
with K categorical baseline variables or factors, X1,...,XK
 What we will discuss also applies to nonexperimental settings, but possibly with some
additional considerations, such as confounded treatment assignment
 It is supposed a priori that any of these factors could be a source of HTE (selection of
these factors is a critical issue, which will be discussed in another module)
 There are two types of subgroups:
 Univariate
 Multivariate
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Univariate Subgroup Analysis
 Each subgroup is defined on the basis of a single baseline variable
 For example:
• Men and women
• Smokers and nonsmokers
• Normal, overweight, and obese individuals
 HTE is examined separately for each subgrouping variable
 Note that the subgroups are not mutually exclusive
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Subgroup-Specific
Treatment
Effects
Source: Antman, E. M., Morrow, D. A., McCabe, C.
H., et al. (2006). Enoxaparin versus unfractionated
heparin with fibrinolysis for ST-elevation
myocardial infarction. The New England Journal of
Medicine, 354(14), 1477–1488.
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Procedure
Diagram With
Gender Subgroup
Factor
Limitation:
Comparisons are
indirect, and
stratification
reduces power
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One-by-One Interaction Testing (OBO)
g(E[Y|X]) = 01 + 11Z + 1X1 + 1X1 * Z
⋮
g(E[Y|X]) = 0K + 1KZ + KXK + KXK * Z
 Remarks:
 A proper way to test for HTE
 XK assumed to be binary
 Bonferroni correction for type I error inflation
 Increases type I error without adjustment for multiplicity
 Adjustment for multiplicity decreases power K
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Univariate Subgroup Analysis
 Univariate subgroup analysis is the most popular approach and is reported in most
Phase 3 clinical trials
 Evaluate whether the treatment is consistent across univariate subgroups
 The subgroups are not mutually exclusive, and therefore, subgroup-specific treatment
effects are correlated
 Subgroups are also more similar to each other because they differ in only one
characteristic, which reduces likelihood of detecting HTE
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Multivariate Subgroup Analysis
 Each subgroup is defined on the basis of multiple baseline variables
 For example:
• Men—smoker
• Women—smoker
• Men—nonsmoker
• Women—nonsmoker
 These are mutually exclusive subgroups, and therefore, the raw subgroup effects are
independent
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Multivariate Subgroup Analysis
 Our interest lies in understanding how the effect of treatment Z on Y varies jointly
according to baseline characteristics
 We can define the treatment effect within any given stratum x = {x1, ··· , xK} as
follows:
(x) = g(E[Y|Z = 1, X = x]) – g(E[Y|Z = 0, X = x])
… where E[.] denotes the expectation (mean) of Y,
and g(.) is a link function denoting the scale in
which the treatment effect is quantified
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Multivariate Subgroup Analysis
 Commonly used treatment effect scales are:
 Identity link:
• g(x) = x
 Log link:
• g(x)= log(x)
 Logit link:
x
• g x = log (
)
1–x
 Curse of dimensionality severely limits the number of characteristics
 Some type of modeling becomes necessary to share information across subgroups
 We will discuss Bayesian approaches in another module
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Reading List

Berry, D. A. (1990). Subgroup analyses. Biometrics, 46(4), 1227–1230.

Fleming, T. R. (2010). Clinical trials: discerning hype from substance. Annals of Internal Medicine,
153(6), 400–406. http://doi.org/10.7326/0003-4819-153-6-201009210-00008

Jones, H. E., Ohlssen, D. I., Neuenschwander, B., Racine, A., & Branson, M. (2011). Bayesian
models for subgroup analysis in clinical trials. Clinical Trials (London, England), 8(2), 129–143.
http://doi.org/10.1177/1740774510396933

Rothwell, P. M., ed. (2007). Treating Individuals: From Randomised Trials to Personalised
Medicine. Edinburgh; New York: Elsevier.

Varadhan, R., Segal, J. B., Boyd, C. M., Wu, A. W., & Weiss, C. O. (2013). A framework for the
analysis of heterogeneity of treatment effect in patient-centered outcomes research. Journal of
Clinical Epidemiology, 66(8), 818–825. http://doi.org/10.1016/j.jclinepi.2013.02.009
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