Using post‐outcome measurement information in censoring‐by‐death problems

Summary Many clinical studies on non‐mortality outcomes such as quality of life suffer from the problem that the non‐mortality outcome can be censored by death, i.e. the non‐mortality outcome cannot be measured if the subject dies before the time of measurement. To address the problem that this censoring by death is informative, it is of interest to consider the average effect of the treatment on the non‐mortality outcome among subjects whose measurement would not be censored under either treatment or control, which is called the survivor average causal effect (SACE). The SACE is not point identified under usual assumptions but bounds can be constructed. The previous literature on bounding the SACE uses only the survival information before the measurement of the non‐mortality outcome. However, survival information after the measurement of the non‐mortality outcome could also be informative. For randomized trials, we propose a set of ranked average score assumptions that make use of survival information before and after the measurement of the non‐mortality outcome which are plausibly satisfied in many studies and we develop a two‐step linear programming approach to obtain the closed form for bounds on the SACE under our assumptions. We also extend our method to randomized trials with non‐compliance or observational studies with a valid instrumental variable to obtain bounds on the complier SACE which is presented in on‐line supplementary material. We apply our method to a randomized trial of the effect of mechanical ventilation with lower tidal volume versus traditional tidal volume for acute lung injury patients. Our bounds on the SACE are much shorter than the bounds that are obtained by using only the survival information before the measurement of the non‐mortality outcome.