How serious is bias in effect estimation in randomised trials with survival data given risk heterogeneity and informative censoring?

It is often assumed that randomisation will prevent bias in estimation of treatment effects from clinical trials, but this is not true of the semiparametric Proportional Hazards model for survival data when there is underlying risk heterogeneity. Here, a new formula is proposed for estimation of this bias, improving on a previous formula through ease of use and clarity regarding the role of the mid-study cumulative hazard rate, shown to be an important factor for the bias magnitude. Informative censoring (IC) is recognised as a source of bias. Here, work on selection effects among survivors due to risk heterogeneity is extended to include IC. A new formula shows that bias in causal effect estimation under IC has two sources: one consequent on heterogeneity and one from the additional impact of IC. The formula provides new insights not previously shown: there may less bias under IC than when there is no IC and even, in principle, zero bias. When tested against simulated data, the new formulae are shown to be very accurate for prediction of bias in Proportional Hazards and accelerated failure time analyses which ignore heterogeneity. These data are also used to investigate the performance of accelerated failure time models which explicitly model risk heterogeneity ('frailty models') and G estimation. These methods remove bias when there is simple censoring but not with informative censoring when they may lead to overestimation of treatment effects. The new formulae may be used to help researchers judge the possible extent of bias in past studies. Copyright (C) 2017 John Wiley & Sons, Ltd.