Analyzing a Randomized Cancer Prevention Trial with a Missing Binary Outcome, an Auxiliary Variable, and All-or-None Compliance

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Abstract
The Prostate Cancer Prevention Trial is a randomized chemoprevention trial designed to compare the effect of daily finasteride versus placebo on prostate cancer determined by biopsy. Investigators have scheduled a biopsy at the end of the trial in 7 years or following a positive prostate-specific antigen (PSA) on annual screening. The analysis will need to adjust for two likely complications. First, some subjects will not receive a biopsy, depending in part on whether or not they had a positive PSA. The indicator of positive PSA is called an auxiliary variable, which is a variable observed after randomization and prior to outcome. Second, starting soon after randomization, some subjects randomized to finasteride will stop taking their tablets, and some subjects randomized to placebo will obtain finasteride outside of the trial. This type of noncompliance is called all-or-none. To adjust for these complications, we formulate the appropriate likelihoods and obtain closed-form maximum likelihood estimates and variances. Without these adjustments, estimates may be biased, two-sided type I errors above nominal levels, and coverage of confidence intervals below nominal levels.

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