Contributions to the theory and practice of prior elicitation in biopharmaceutical research.

In this dissertation, we consider modeling problems in biopharmaceutical research, much of which is motivated by industry colleagues. Expert opinion is necessary in many applications of survival analysis, especially in exploratory and early phase research. We develop methods for eliciting informative priors using expert knowledge on observable survival time summaries in the proportional hazards model. In problems with small sample sizes and censoring, incorporating information from historical studies can enhance statistical inference. To this end, we present methods for selecting a critical parameter in the power prior using operational assessments of such choices, such as FDA guidance and prior effective sample size. We investigate the consequences of misspecified information in prior elicitations and create a mathmatical framework and graphical guide with which to understand the effects. Finally, we investigate the effect of various non-informative priorchoices on the between-trial heterogeneity in a logistic regression network meta-analysis.