Evaluation of Viable Dynamic Treatment Regimes in a Sequentially Randomized Trial of Advanced Prostate Cancer

We present new statistical analyses of data arising from a clinical trial designed to compare two-stage dynamic treatment regimes (DTRs) for advanced prostate cancer. The trial protocol mandated that patients were to be initially randomized among four chemotherapies, and that those who responded poorly were to be rerandomized to one of the remaining candidate therapies. The primary aim was to compare the DTRs' overall success rates, with success defined by the occurrence of successful responses in each of two consecutive courses of the patient's therapy. Of the one hundred and fifty study participants, forty seven did not complete their therapy per the algorithm. However, thirty five of them did so for reasons that precluded further chemotherapy; i.e. toxicity and/or progressive disease. Consequently, rather than comparing the overall success rates of the DTRs in the unrealistic event that these patients had remained on their assigned chemotherapies, we conducted an analysis that compared viable switch rules defined by the per-protocol rules but with the additional provision that patients who developed toxicity or progressive disease switch to a non-prespecified therapeutic or palliative strategy. This modification involved consideration of bivariate per-course outcomes encoding both efficacy and toxicity. We used numerical scores elicited from the trial's Principal Investigator to quantify the clinical desirability of each bivariate per-course outcome, and defined one endpoint as their average over all courses of treatment. Two other simpler sets of scores as well as log survival time also were used as endpoints. Estimation of each DTR-specific mean score was conducted using inverse probability weighted methods that assumed that missingness in the twelve remaining drop-outs was informative but explainable in that it only depended on past recorded data. We conducted additional worst-best case analyses to evaluate sensitivity of our findings to extreme departures from the explainable drop-out assumption.