A bivariate regression model with correlated mixed responses.

Bray, Ross A.
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In the dissertation we consider a bivariate model for associated binary and continuous responses such as those in a clinical trial where both safety and efficacy are observed. We designate a marginal and conditional model that allows for the association between the responses by including the marginal response as an additional predictor of the conditional response. We use a Bayesian approach to model the bivariate regression model using a hierarchical prior structure. Simulation studies indicate that the model provides good point and interval estimates of regression parameters across a variety of parameter configurations, with smaller binary event probabilities offering particular challenges. For example, as the probability of an adverse event decreases, we find that the marginal posterior variances increase for the binary safety response regression coefficients, but not for the conditional efficacy response coefficients. Potential problems with induced priors are briefly considered. We implement an asymptotic higher order approximation in order to obtain parameter estimates and confidence intervals via a simulation study. In comparison, the frequentist intervals are slightly more narrow than the Bayesian intervals (using vague priors), but the latter have far superior coverage. Finally, we implement a Bayesian sample size determination method while controlling an operating characteristic of the model, the family-wise error rate. We find that there is a savings in power afforded by use of the multiplicity adjustment when simultaneously testing multiple hypotheses. Simulation results indicate that multiplicity adjustments improve the power of the model when compared to the overly conservative Bonferroni adjustment. We also see an improvement in power through the effective use of prior information.

Bayesian statistics., Asymptotic confidence intervals., Bayesian sample size determination., Correlated mixed responses.