Assessing the Causal Effect of Treatment Dosages in the Presence of Self-Selection
Michael R. Elliott, University of Michigan, Department of Biostatistics 
*Xin Gao, University of Michigan, Department of Biostatistics 

Keywords: Causal Modeling, Potential Outcome, Principal Stratification, Drug Satety

To make drug therapy as effective as possible, patients are often put on an escalating dosing schedule. But patients may choose to take a lower dose because of side effects. Thus even in a randomized trial, the dose level received is a post-randomization variable, and comparison with the control group may no longer have a causal interpretation. Hence we use the potential outcomes framework to define pre-randomization “principal strata” from the joint distribution of doses selected under control and treatment arms, with the goal of estimating the effect of treatment within the subgroups of the population who will select a given set of dose levels. We utilize a Bayesian framework incorporating a Markov chain Monte Carlo algorithm to analyze a randomized clinical study on painful bladder syndrome, and compare the results from our proposed model with traditional approaches. Simulation results show that the estimates of interests in our proposed causal model have correct coverage.