Normal approximation for Bayesian models with non-sampling bias.

Bayesian sample size determination can be computationally intensive for mod- els where Markov chain Monte Carlo (MCMC) methods are commonly used for in- ference. It is also common in a large database where the unmeasured confounding presents. We present a normal theory approximation as an alternative to the time consuming MCMC simulations in sample size determination for a binary regression with unmeasured confounding. Cheng et al. (2009) develop a Bayesian approach to average power calculations in binary regression models. They then apply the model to the common medical scenario where a patient's disease status is not known. In this dissertation, we generate simulations based on their Bayesian model with both binary and normal outcomes. We also use normal theory approximation to speed up such sample size determination and compare power and computational time for both.