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Subgroup Analysis via Bayesian Hierarchical Modeling

Keith Goldfield ponders subgroup analysis:

Which got me thinking, of course, about subgroup analyses. In the context of a null hypothesis significance testing framework, it is well known that conducting numerous post hoc analyses carries the risk of dramatically inflating the probability of a Type 1 error – concluding there is some sort of effect when in fact there is none. So, if there is no overall effect, and you decide to look at a subgroup of the sample (say patients over 50), you may find that the treatment has an effect in that group. But, if you failed to adjust for multiple tests, than that conclusion may not be warranted. And if that second subgroup analysis was not pre-specified or planned ahead of time, that conclusion may be even more dubious.

If we use a Bayesian approach, we might be able to avoid this problem, and there might be no need to adjust for multiple tests. I have started to explore this a bit using simulated data under different data generation processes and prior distribution assumptions. It might all be a bit too much for a single post, so I am planning on spreading it out a bit.

Read on for two separate Bayesian model approaches to the problem. H/T R-Bloggers.