Evaluating Bayesian Methods for Predictive Models

The self-controlled case-series method (Farrington, 1995) compares rates of outcome events during times when a person is exposed to a drug versus outcome event rates during unexposed periods. In essence, each person serves as his/her own control. This feature naturally accounts for covariates that do not vary with time and means that only cases where a given event occurred are used in analysis, greatly reducing computation. The proposed work extends the current Bayesian multiple self-controlled case series in two ways. First, the current implementation uses the maximum of the posterior distribution as an estimate for the drug-effects. Though computationally efficient, this approach provides results that are only single-number summaries of the parameters. Using recent computational developments, however, we will implement a fully Bayesian approach where inference is done by sampling from the posterior distribution, thus generating uncertainty estimates for the parameters. Second, we will introduce hierarchical structure in the model based on associations between drugs and events. Multiple drugs of the same class can be modeled as having the same prior mean, for example, which encourages borrowing strength across similar drugs. Similarly, we can encourage sharing information across events or classes of events (musculoskeletal events, for example).