Power of the Wilcoxon-Mann-Whitney test for non-inferiority in the presence of death-censored observations

Abstract

In clinical trials with patients in a critical state, death may preclude measurement of a quantitative endpoint of interest, and even early measurements, for example for intention-to-treat analysis, may not be available. For example, a non-negligible proportion of patients with acute pulmonary embolism will die before 30 day measurements on the efficacy of thrombolysis can be obtained. As excluding such patients may introduce bias, alternative analyses, and corresponding means for sample size calculation are needed. We specifically consider power analysis in a randomized clinical trial setting in which the goal is to demonstrate noninferiority of a new treatment as compared to a reference treatment. Also, a nonparametric approach may be needed due to the distribution of the quantitative endpoint of interest. While some approaches have been developed in a composite endpoint setting, our focus is on the continuous endpoint affected by death-related censoring, for which no approach for noninferiority is available. We propose a solution based on ranking the quantitative outcome and assigning worst rank scores to the patients without quantitative outcome because of death. Based on this, we derive power formulae for a noninferiority test in the presence of death-censored observations, considering settings with and without ties. The approach is illustrated for an exemplary clinical trial in pulmonary embolism. The results there show a substantial effect of death on power, also depending on differential effects in the two trial arms. Therefore, use of the proposed formulae is advisable whenever there is death to be expected before measurement of a quantitative primary outcome of interest.

Keywords: censoring by death; combined endpoints; global rank test; noninferiority; pulmonary embolism.