Generating survival times with time-varying covariates using the Lambert W Function. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Ngwa, Julius S.; Cabral, Howard J.; Cheng, Debbie M.; Gagnon, David R.; LaValley, Michael P.; Cupples, L. Adrienne
• Is Part Of: Communications in statistics. Volume 51:Issue 1(2022)
• Page Start: 135
• Page End: 153
• Publication Date: 2022-01-02
• Subjects: Longitudinal and survival data -- Lambert W Function -- Time-varying covariates -- Two step approach -- Linear Mixed effects model; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2019.1648822
• Languages: English
• ISSNs: 0361-0918

Abstract

Abstract: Simulation studies provide an important statistical tool in evaluating survival methods, requiring an appropriate data-generating process to simulate data for an underlying statistical model. Many studies with time-to-event outcomes use the Cox proportional hazard model. While methods for simulating such data with time-invariant predictors have been described, methods for simulating data with time-varying covariates are sorely needed. Here, we describe an approach for generating data for the Cox proportional hazard model with time-varying covariates when event times follow an Exponential or Weibull distribution. For each distribution, we derive a closed-form expression to generate survival times and link the time-varying covariates with the hazard function. We consider a continuous time-varying covariate measured at regular intervals over time, as well as time-invariant covariates, in generating time-to-event data under a number of scenarios. Our results suggest this method can lead to simulation studies with reliable and robust estimation of the association parameter in Cox-Weibull and Cox-Exponential models.