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A Bayesian subgroup analysis using collections of ANOVA models
Author(s) -
Liu Jinzhong,
Sivaganesan Siva,
Laud Purushottam W.,
Müller Peter
Publication year - 2017
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.201600064
Subject(s) - covariate , categorical variable , frequentist inference , bayesian probability , prior probability , posterior probability , mathematics , statistics , subgroup analysis , model selection , computer science , bayesian inference , confidence interval
We develop a Bayesian approach to subgroup analysis using ANOVA models with multiple covariates, extending an earlier work. We assume a two‐arm clinical trial with normally distributed response variable. We also assume that the covariates for subgroup finding are categorical and are a priori specified, and parsimonious easy‐to‐interpret subgroups are preferable. We represent the subgroups of interest by a collection of models and use a model selection approach to finding subgroups with heterogeneous effects. We develop suitable priors for the model space and use an objective Bayesian approach that yields multiplicity adjusted posterior probabilities for the models. We use a structured algorithm based on the posterior probabilities of the models to determine which subgroup effects to report. Frequentist operating characteristics of the approach are evaluated using simulation. While our approach is applicable in more general cases, we mainly focus on the 2 × 2 case of two covariates each at two levels for ease of presentation. The approach is illustrated using a real data example.