Comparison of a time-varying covariate model and a joint model of time-to-event outcomes in the presence of measurement error and interval censoring: application to kidney transplantation

Kristen R Campbell,Jane Gralla,Scott Davis,Gary K Grunwald,James Cooper,Elizabeth Juarez-Colunga

doi:10.1186/s12874-019-0773-1

Abstract

BackgroundTacrolimus (TAC) is an immunosuppressant drug given to kidney transplant recipients post-transplant to prevent antibody formation and kidney rejection. The optimal therapeutic dose for TAC is poorly defined and therapy requires frequent monitoring of drug trough levels. Analyzing the association between TAC levels over time and the development of potentially harmful de novo donor specific antibodies (dnDSA) is complex because TAC levels are subject to measurement error and dnDSA is assessed at discrete times, so it is an interval censored time-to-event outcome.MethodsUsing data from the University of Colorado Transplant Center, we investigated the association between TAC and dnDSA using a shared random effects (intercept and slope) model with longitudinal and interval censored survival sub-models (JM) and compared it with the more traditional interval censored survival model with a time-varying covariate (TVC). We carried out simulations to compare bias, level and power for the association parameter in the TVC and JM under varying conditions of measurement error and interval censoring. In addition, using Markov Chain Monte Carlo (MCMC) methods allowed us to calculate clinically relevant quantities along with credible intervals (CrI).ResultsThe shared random effects model was a better fit and showed both the average TAC and the slope of TAC were associated with risk of dnDSA. The simulation studies demonstrated that, in the presence of heavy interval censoring and high measurement error, the TVC survival model underestimates the association between the survival and longitudinal measurement and has inflated type I error and considerably less power to detect associations.ConclusionsTo avoid underestimating associations, shared random effects models should be used in analyses of data with interval censoring and measurement error.

Highlights

Tacrolimus (TAC) is an immunosuppressant drug given to kidney transplant recipients post-transplant to prevent antibody formation and kidney rejection
To analyze the association between TAC and de novo donor specific antibodies (dnDSA), we propose a shared random effects model and compare it with a traditional interval censored survival model treating TAC as a time-varying covariate
Spline terms for time were tested, but Deviance Information Criterion (DIC) and WatanabeAkaike information criterion (WAIC) indicated that a linear trend was sufficient

Summary

Introduction

Tacrolimus (TAC) is an immunosuppressant drug given to kidney transplant recipients post-transplant to prevent antibody formation and kidney rejection. There are nearly 100,000 patients on the U.S kidney transplant waiting list, with 13 people dying every day while awaiting this life-saving therapy [1]. The antibodies that mediate this rejection process, de novo donor-specific antibodies (dnDSA), have been established as an early biomarker for post-transplant adverse kidney events and patients are screened for dnDSA at regular intervals at most centers around the country [3, 4]. The majority of centers in the U.S (93%) use Tacrolimus (TAC) as the backbone of their immunosuppression protocols [5], but the drug has a narrow and poorly defined therapeutic range that varies by patient

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Conclusion