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PCORI Methodology Standards:
Academic Curriculum
© 2016 Patient-Centered Outcomes Research Institute. All Rights Reserved.
Prepared by Ravi Varadhan, PhD
Chenguang Wang, PhD
Presented by Ravi Varadhan, PhD
Module 5: Bayesian Models for HTE
Analysis (Advanced)
Category 5: Heterogeneity of Treatment Effects
In Bayesian analysis, all unknown parameters (e.g., main effects, interaction effects)
are treated as random variables, and observed data {X, Z, Y} are considered to be fixed
In the more popular frequentist approaches, the unknown parameters are fixed, and
the observed data are a particular instance of a random process
Bayesian methods require specification of prior beliefs for the unknown parameters, in
the form of prior probability distributions
What Is a Bayesian HTE Analysis?
3
Like frequentist methods, Bayesian methods require a statistical model for the data-
generating process
Using Bayes’ rule, the prior distributions and data-generating model are combined to
produce updated, posterior distributions for the unknown parameters
Powerful computational tools are often used (e.g., Markov Chain Monte Carlo
techniques) to generate samples of unknown parameters from the posterior
distribution
Summaries of the posterior distribution comprise the main results of a Bayesian
analysis
What Is a Bayesian HTE Analysis?
4
The phrase heterogeneity of treatment effects implies an underlying distribution of
treatment effects
Thus, a Bayesian framework is natural
A Bayesian analysis does not emphasize whether a statistical procedure for detecting
HTE is significant or not—an arbitrarily dichotomous decision
A Bayesian approach emphasizes estimation of the magnitude of HTE
Why Consider Bayesian HTE Analysis?
5
Bayesian approach can exploit prior knowledge to increase the precision of subgroup-
specific effects
Typically, model-based Bayesian estimates will have less uncertainty than estimates
from separate analyses of subgroups (e.g., raw subgroup-specific effects)
By sharing information across subgroups, according to the model, the Bayesian
approach will stabilize the raw estimate by pulling it back (“shrinkage”) toward the
overall treatment effect
This produces estimates with lower mean-squared error
Why Consider Bayesian HTE Analysis?
6
Bayes’ approach supports simple and direct probability statements about subgroup-
specific effects
For example, we can ask:
“What is the probability that treatment A is better than treatment B for women?”
or
“Do men benefit more from treatment A than women?”
Such summaries can be readily understood by patients and other stakeholders
Frequentist approach, however, permits statements only about the likelihood of
observed data, under the hypothesized value of the effects
Why Consider Bayesian HTE Analysis?
7
Simple Bayesian Models
8
Simple Shrinkage
9
Simple Shrinkage
10
Simple Shrinkage
Adapted from: Efron, B., & Morris, C. (1977). Stein’s paradox in statistics. Scientific American, 236(5), 119–127. 11
Simple Shrinkage
Adapted from: Efron, B., & Morris, C. (1977). Stein’s paradox in statistics. Scientific American, 236(5), 119–127.
A. Raw subgroup
effects
12
Simple Shrinkage
Adapted from: Efron, B., & Morris, C. (1977). Stein’s paradox in statistics. Scientific American, 236(5), 119–127.
A. Raw subgroup
effects
B. Variance of raw
subgroup effect
13
Simple Shrinkage
Adapted from: Efron, B., & Morris, C. (1977). Stein’s paradox in statistics. Scientific American, 236(5), 119–127.
A. Raw subgroup
effects
B. Variance of raw
subgroup effect
C. Subgroup effects
after shrinkage
14
Regression
15
These models and a number of other Bayesian regression models can be implemented
using BEANZ software
BEANZ
16
Berry, D. A. (1990). Subgroup analyses. Biometrics, 46(4), 1227–1230.
Dixon, D. O., & Simon, R. (1991). Bayesian subset analysis. Biometrics, 47(3), 871–881.
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
Spiegelhalter, D. J., Abrams, K. R., & Myles, J. P. (2004). Bayesian Approaches to Clinical Trials
and Health-Care Evaluation. John Wiley & Sons.
Reading List
17