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?

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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?

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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?

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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?

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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?

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Simple Bayesian Models

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Simple Shrinkage

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Simple Shrinkage

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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

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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

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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

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Regression

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These models and a number of other Bayesian regression models can be implemented

using BEANZ software

BEANZ

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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

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