In some randomized clinical trials, patients may die before the measurement time point of their outcomes. Even though randomization generates comparable treatment and control groups, the remaining survivors often differ significantly in background variables that are prognostic to the outcomes. This is called the truncation by death problem. Under the potential outcomes framework, the only well-defined causal effect on the outcome is within the subgroup of patients who would always survive under both treatment and control. Because the definition of the subgroup depends on the potential values of the survival status that could not be observed jointly, without making strong parametric assumptions, we cannot identify the causal effect of interest and consequently can only obtain bounds of it. Unfortunately, however, many bounds are too wide to be useful. We propose to use detailed survival information before and after the measurement time point of the outcomes to sharpen the bounds of the subgroup causal effect. Because survival times contain useful information about the final outcome, carefully utilizing them could improve statistical inference without imposing strong parametric assumptions. Moreover, we propose to use a copula model to relax the commonly-invoked but often doubtful monotonicity assumption that the treatment extends the survival time for all patients.
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.
more » « less- NSF-PAR ID:
- 10397394
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Volume:
- 78
- Issue:
- 1
- ISSN:
- 1369-7412
- Page Range / eLocation ID:
- p. 299-318
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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