Length of stay in the intensive care unit (ICU) is a common outcome measure in randomized trials of ICU interventions. Because many patients die in the ICU, it is difficult to disentangle treatment effects on length of stay from effects on mortality; conventional analyses depend on assumptions that are often unstated and hard to interpret or check. We adapt a proposal from Rosenbaum that addresses concerns about selection bias and makes its assumptions explicit. A composite outcome is constructed that equals ICU length of stay if the patient was discharged alive and indicates death otherwise. Given any preference ordering that compares death with possible lengths of stay, we can estimate the intervention's effects on the composite outcome distribution. Sensitivity analyses can show results for different preference orderings. We discuss methods for constructing approximate confidence intervals for treatment effects on quantiles of the outcome distribution or on proportions of patients with outcomes preferable to various cutoffs. Strengths and weaknesses of possible primary significance tests (including the Wilcoxon-Mann-Whitney rank sum test and a heteroskedasticity-robust variant due to Brunner and Munzel) are reviewed. An illustrative example reanalyzes a randomized trial of an ICU staffing intervention.
Keywords: Brunner–Munzel test; Mann–Whitney U-test; Wilcoxon rank sum test; bootstrap confidence intervals; censoring by death; intensive care unit; length of stay; nonparametric Behrens–Fisher problem; quantile treatment effects; rank tests.