Estimation of the odds ratio in a proportional odds model with censored time-lagged outcome in a randomized clinical trial

In many randomized clinical trials of therapeutics for COVID-19, the primary outcome is an ordinal, categorical variable for which the final category is often death, which can be ascertained at the time of occurence. For the remaining categories, determination of into which of these categories a participant's outcome falls cannot be made until some ascertainment time that can be less than or equal to a pre-specified follow-up time. Interest focuses on the odds ratio (active agent vs. control) under the assumption of a proportional odds model. Although at the final analysis the outcome will be determined for all subjects, at an interim analysis, the status of some participants may not yet be determined; accordingly, the outcome from these subjects can be viewed as censored. A valid interim analysis can be based on data only from those subjects with full follow up; however, this approach is inefficient, as it does not exploit additional information that may be available on those who have not reached the follow-up time at the time of the interim analysis. Appealing to the theory of semiparametrics, we propose an estimator for the odds ratio in a proportional odds model with censored, time-lagged categorical outcome that incorporates such additional baseline and time-dependent information and demonstrate that it can result in considerable gains in efficiency relative to simpler approaches.