Competing risks regression under random signs censoring using pseudo-values

In medical research, investigators are often interested in estimating marginal survival distributions of latent failure times in the presence of competing risks. However, marginal survival functions are not identifiable without further assumption. Previous studies have shown that by incorporating the random signs censoring (RSC) principle, we can estimate marginal survival functions and that the RSC principle is verifiable from the observed data.\ud \ud In this study, we proposed under the RSC principle an estimator of covariate effect on marginal survival function using time-dependent pseudo-values created from inverse-probability-censoring-weighted (IPCW) Kaplan-Meier estimates. A generalized linear regression model of pseudo-values can then be built, from which the covariate effects and marginal survival at any given time can be estimated by solving the corresponding generalized estimating equations. Time-dependent covariates are easy to incorporate in our method. We also derived robust standard errors of the estimators, examined the asymptotic properties, and developed a graphical representation for changes in covariate effects over time. \ud \ud We evaluated the finite-sample performance of the estimator and the corresponding marginal survival estimators via simulation studies. In applications of the proposed method, we identified potential risk factors of pretransplantation survival for pediatric patients with end-stage liver diseases and estimated their 90-day pretransplantation survival graphically. Effects of time-varying covariates were estimated and the covariate effects against time were also examined graphically. Public Health Significance: Our proposed method is easier for statisticians to implement and the analysis results are easier for medical professionals to interpret. The proposed method allows medical researchers to incorporate repeatedly measured covariates as well as constant covariates and evaluate time-varying covariate effects in the presence of competing risks, which eliminates certain biases in estimating marginal survival and in turn can contribute to better policy or regulatory decisions.\u