Analysis of time‐dependent covariates in a regressive relative survival model

Abstract

Relative survival is a method for assessing prognostic factors for disease-specific mortality. However, most relative survival models assume that the effect of covariate on disease-specific mortality is fixed-in-time, which may not hold in some studies and requires adapted modelling. We propose an extension of the Esteve et al. regressive relative survival model that uses the counting process approach to accommodate time-dependent effect of a predictor's on disease-specific mortality. This approach had shown its robustness, and the properties of the counting process give a simple and attractive computational solution to model time-dependent covariates. Our approach is illustrated with the data from the Stanford Heart Transplant Study and with data from a hospital-based study on invasive breast cancer. Advantages of modelling time-dependent covariates in relative survival analysis are discussed.

Use of Remote Monitoring Is Associated With Lower Risk of Adverse Outcomes Among Patients With Implanted Cardiac Defibrillators

“…13 In this model, RPM activation was a time-varying covariate to account for differences in the time from ICD implantation to first RPM transmission. The model accounted for clustering of the patients within hospitals through the inclusion of a hospitalspecific random effect that has a multiplicative effect on the baseline hazard function.…”

“…13 In the model, rehospitalizations were considered as potentially recurrent events and accounted for the same factors used in the survival analyses. In the rehospitalization models, patients were censored at the time point of last follow-up or death.…”

Restrictive access to clopidogrel and mortality following coronary stent implantation

“…This method also accounted for adherence and duration of treatment. [21][22][23] We also assessed adherence to nonrestricted cardiovascular drugs by calculating the percentage of days on the same drug class during the follow-up period. Discrete data are presented as percentage, and continuous data are presented as mean (standard deviation [SD]) and median (25th-75th percentile) when nonnormally distributed.…”

Survival Data Analysis with Time-Dependent Covariates Using Generalized Additive Models

“…By adding x l 4 〈 d 〉 as one of time-dependent covariate for the liver transplantation, one can test the significance of liver transplantation. The covariate for liver transplantation is taken as a binary variable (codes 0 before liver transplantation, 1 at liver transplantation) as shown in Giorgi and Gouvernet [16] and Crowley [37]. Table 6 shows the three types for the combination of “censored” and “liver transplantation.” Table 7 shows the values of covariates for liver-transplanted patient #5.…”

“…The proportional hazard model (2) used the time-fixed values of covariates as shown in Dickson et al [1]. The estimates of hazard ratio by relative survival regression model [16] with time-dependent covariates are compared with that of Cox proportional hazard model. A new approach [17, 18] is proposed with PBC data, aiming to capture nonlinear patterns of bilirubin time courses and their relationship with survival time of patients.…”