Assessing the Causal Effect of Treatment Dosages in the Presence of Self-Selection

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. When subjects on the control arm cannot obtain treatment, these principal strata are fully observed on treatment, but remain latent on control. Adverse event information can be used to identify the tolerated dose level in the control arm.