Reverse Time-to-Death as Time-Scale in Time-to-Event Analysis for Studies of Advanced Illness and Palliative Care

Incidence of adverse outcome events rises as patients with advanced illness approach end-of-life. Exposures that tend to occur near end-of-life, for example, use of wheelchair, oxygen therapy and palliative care, may therefore be found associated with the incidence of the adverse outcomes. We propose a concept of reverse time-to-death (rTTD) and its use for the time-scale in time-to-event analysis based on partial likelihood to mitigate the time-varying confounding. We used data on community-based palliative care uptake (exposure) and emergency department visits (outcome) among patients with advanced cancer in Singapore to illustrate. We compare the results against that of the common practice of using time-on-study (TOS) as time-scale. Graphical analysis demonstrated that cancer patients receiving palliative care had higher rate of emergency department visits than non-recipients mainly because they were closer to end-of-life, and that rTTD analysis made comparison between patients at the same time-to-death. In analysis of a decedent cohort, emergency department visits in relation to palliative care using TOS time-scale showed significant increase in hazard ratio estimate when observed time-varying covariates were omitted from statistical adjustment (% change-in-estimate = 16.2%; 95% CI 6.4% to 25.6%). There was no such change in otherwise the same analysis using rTTD (% change-in-estimate = 3.1%; 95% CI -1.0% to 8.5%), demonstrating the ability of rTTD time-scale to mitigate confounding that intensifies in relation to time-to-death. A similar pattern was found in the full cohort. Simulations demonstrated that the proposed method had smaller relative bias and root mean square error than TOS-based analysis. In conclusion, use of rTTD as time-scale in time-to-event analysis provides a simple and robust approach to control time-varying confounding in studies of advanced illness, even if the confounders are unmeasured.