Assessing treatment benefit with competing risks not affected by the randomized treatment.

Abstract

The comparison of overall survival curves between treatment arms will always be of interest in a randomized clinical trial involving a life-shortening disease. In some settings, the experimental treatment is only expected to affect the deaths caused by the disease, and the proportion of deaths caused by the disease is relatively low. In these settings, the ability to assess treatment-effect differences between Kaplan-Meier survival curves can be hampered by the large proportion of deaths in both arms that are unrelated to the disease. To address this problem, frequently displayed are cause-specific survival curves or cumulative incidence curves, which respectively censor and immortalize events (deaths) not caused by the disease. However, the differences between the experimental and control treatment arms for these curves overestimate the difference between the overall survival curves for the treatment arms and thus could result in overestimation of the benefit of the experimental treatment for the patients. To address this issue, we propose new estimators of overall survival for the treatment arms that are appropriate when the treatment does not affect the non-disease-related deaths. These new estimators give a more precise estimate of the treatment benefit, potentially enabling future patients to make a more informed decision concerning treatment choice. We also consider the case where an exponential assumption allows the simple presentation of mortality rates as the outcome measures. Applications are given for estimating overall survival in a prostate-cancer treatment randomized clinical trial, and for estimating the overall mortality rates in a prostate-cancer screening trial.