In randomized trials with follow-up, outcomes such as quality of life may be undefined for individuals who die before the follow-up is complete. methods for individuals with acute respiratory distress syndrome. denotes the treatment variable in a randomized trial that is binary, for example, = 1 indicates treated and = 0 indicates the control condition. Let be an outcome of interest that is measured after some follow-up period. Let be an indicator of whether the individual is alive when the outcome is measured, with = 1 indicating alive and = 0 indicating dead. For individuals who died (= 0), the outcome is undefined. For each individual, we can also consider Dimethylfraxetin IC50 counterfactual outcomes or potential outcomes (25, 26) corresponding to what would have happened had an individual been in the treatment arm other than the one to which he or she was assigned. Let = 1 and = 0, respectively. In actuality, we observe only one of = 1, and we observe = 0. We have no way of observing the other potential outcome. However, at least hypothetically, we can conceive of what the survival status would have been for each individual under each of the 2 possible treatment scenarios. Likewise, we let for each individual under treatment = 1 and = 0, respectively. The variables would be undefined. A crude comparison of the outcome among the treated and the controls would consist of, for example, comparing the means of in each treatment arm Dimethylfraxetin IC50 among those who in fact survived: Note that E[= 1, = 1] is estimated by the sample mean of among those surviving in the treated group, and E[= 0, = 1] is estimated by the sample mean of among those surviving in the control arm. As noted at the Dimethylfraxetin IC50 beginning Dimethylfraxetin IC50 of this paper, the simple crude contrast given above is not a fair comparison because the group that survived without Sox17 treatment may be healthier overall than those who survived with treatment. The control condition may have resulted in unhealthy individuals dying but for whom treatment would have kept alive. These less healthy individuals who would have died under the control condition but survived under treatment are included in the average outcomes (e.g., QOL) when examining the treated individuals who survived but would not be included in the average when examining the controls who survived. The crude comparison above effectively compares outcomes for different populations, not for the same population comparing different treatments. A simple example demonstrating why a different approach is needed is given in Appendix 1. As an alternative to the crude measure, one can assess the principal strata effect or SACE. This is defined below as in prior literature (1, 7, 8). Definition 1: The principal strata effect or SACE is defined as the effect of treatment among the subpopulation that would have survived under either Dimethylfraxetin IC50 treatment arm: The SACE compares the outcome under the treated versus the control condition but among only the subpopulation that would have survived irrespective of which treatment arm they were assigned. A subpopulation such as this one that is defined by reference to potential outcomes under 2 different treatment scenarios is referred to as a principal stratum (7). By restricting the comparison to the subpopulation that would have survived under either treatment arm, we circumvent the problem with the crude comparison that, for the treatment group, we include potentially less healthy individuals who would have died if they had been in the control arm. Trying to identify and estimate the SACE from data is subject to the challenge that we do not know which individuals would have survived under either treatment arm. In the next section, we describe a very simple method that can be used to try to assess the SACE. The analysis is facilitated by what is sometimes referred to as a monotonicity assumption: Assumption 1 (monotonicity): For all individuals, is randomized and that the monotonicity assumption (assumption 1) holds; then, where = E[= 1, = 1] C E[= 0, = 1]. The result states that, to obtain the SACE, one can use the crude difference in outcomes between the treated and control conditions among those who survived, E[| =1, = 1] C E[| = 0, = 1], and then subtract the sensitivity analysis parameter . The sensitivity analysis parameter is set by the investigator according to what is thought plausible. The sensitivity analysis parameter can be varied over a range of plausible values.