Bayesian approaches to correcting bias in epidemiological data.

Bias in parameter estimation of count data is a common concern. The concern is even greater when all counts are not recorded. Failing to adjust for underreported data can lead to incorrect parameter estimates. A Bayesian Poisson regression model to account for underreported data has previously been developed. We expand this model by using a multilevel Poisson regression. In our model we consider the case where the probability of reporting is the same for all groups, and the case where there are multiple reporting probabilities. In both situations we show the importance of accounting for underreporting in the analysis. Another common source of bias in parameter estimation is missing data. In particular, we consider missing data in follow-up studies aimed to estimate the rate of a particular event. If we ignore the missing data, then both the overall event rates and the uncertainty in the model parameters will be underestimated. To address this problem we will extend an already existing Bayesian model for missing data in follow-up studies to two multilevel models. One model uses an overdispersion term to account for excess variability in the data. The second model uses random intercepts and slopes. The last topic that we consider is a meta-analysis comparison. We are interested in the performance of the methods for safety signal evaluation of rare events. This topic is of particular interest due to the recent FDA guidance for assessing cardiovascular risk in diabetes drugs. We consider three methods based on the Cox proportional hazards model, including a Bayesian approach. A formal comparison of the methods is conducted using a simulation study. In our simulation we model two treatments and consider several scenarios.