Gaining Power and Precision by Using Model-based Weights in the Analysis of Late Stage Cancer Trials with Substantial Treatment Switching

In randomised controlled trials of treatments for late-stage cancer, it is common for control arm patients to receive the experimental treatment around the point of disease progression. This treatment switching can dilute the estimated treatment effect on overall survival and impact the assessment of a treatment's benefit on health economic evaluations. The rank-preserving structural failure time model of Robins and Tsiatis (Comm. Stat., 20:2609-2631) offers a potential solution to this problem and is typically implemented using the logrank test. However, in the presence of substantial switching, this test can have low power because the hazard ratio is not constant over time. Schoenfeld (Biometrika, 68:316-319) showed that when the hazard ratio is not constant, weighted versions of the logrank test become optimal. We present a weighted logrank test statistic for the late stage cancer trial context given the treatment switching pattern and working assumptions about the underlying hazard function in the population. Simulations suggest that the weighted approach can lead to large efficiency gains in either an intention-to-treat or a causal rank-preserving structural failure time model analysis compared with the unweighted approach. Furthermore, violation of the working assumptions used in the derivation of the weights only affects the efficiency of the estimates and does not induce bias or inflate the type I error rate. The weighted logrank test statistic should therefore be considered for use as part of a careful secondary, exploratory analysis of trial data affected by substantial treatment switching.