The importance of avoiding time-dependent bias when testing the prognostic value of an intervening event — Two acute cellular rejection examples in intestinal transplantation

Abstract

In testing the prognostic value of the occurrence of an intervening event (clinical event that occurs posttransplant), 3 proper statistical methodologies for testing its prognostic value exist (time-dependent covariate, landmark, and semi-Markov modeling methods). However, time-dependent bias has appeared in many clinical reports, whereby the intervening event is statistically treated as a baseline variable (as if it occurred at transplant). Using a single-center cohort of 445 intestinal transplant cases to test the prognostic value of first acute cellular rejection (ACR) and severe (grade of) ACR on the hazard rate of developing graft loss, we demonstrate how the inclusion of such time-dependent bias can lead to severe underestimation of the true hazard ratio (HR). The (statistically more powerful) time-dependent covariate method in Cox’s multivariable model yielded significantly unfavorable effects of first ACR (P < .0001; HR = 2.492) and severe ACR (P < .0001; HR = 4.531). In contrast, when using the time-dependent biased approach, multivariable analysis yielded an incorrect conclusion for the prognostic value of first ACR (P = .31, HR = 0.877, 35.2% of 2.492) and a much smaller estimated effect of severe ACR (P = .0008; HR = 1.589; 35.1% of 4.531). In conclusion, this study demonstrates the importance of avoiding time-dependent bias when testing the prognostic value of an intervening event.