Analysis of Clustered, Interval-Censored Survival Data

Prostate Specific Antigen (PSA) is a widely accepted marker of prostate cancer recurrence. Genitourinary surgeons and oncologists are particularly interested in whether a surgery using robotic device improves times to PSA recurrence compared to non-robotic surgery for removing the cancerous prostate. Such survival times, as time to PSA recurrences, are typically interval-censored between consecutive clinical inspections. In addition, success of medical devices and technologies often depends on factors such as experience and skill level of medical service providers, thus leading to clustering of these survival times. We present three novel methods for median regression of clustered interval-censored survival data. The first method is based on transform-both-sides model with Gaussian random effects to account for within-cluster association. Our second method ensures marginal Laplace distribution for the transformed log-survival times with a Gaussian copula to accommodate clustering. The third method, obtained as a special case of the second model, has Laplace distribution for the marginal log-survival times with Gaussian copula for within-cluster association. We provide Frequentist and Bayesian analysis for the three competing models with a comprehensive comparison among them based on model properties and computational ease. Popular parametric and semiparametric hazards regression models for clustered survival data are inappropriate and inadequate when the unknown effects of different covariates and clustering are complex. This calls for a flexible modeling framework to yield efficient survival prediction. Moreover, for some survival studies involving time to occurrence of some asymptomatic events, survival times are typically interval censored between consecutive clinical inspections. In this article, we propose a robust semiparametric model for clustered interval-censored survival data under a paradigm of Bayesian ensemble learning, called Soft Bayesian Additive Regression Trees or SBART (Linero and Yang, 2018), which combines multiple sparse (soft) decision trees to attain excellent predictive accuracy. We develop a novel semiparametric hazards regression model by modeling the hazard function as a product of a parametric baseline hazard function and a nonparametric component that uses SBART to incorporate clustering, unknown functional forms of the main effects, and interaction effects of various covariates. In addition to being applicable for left-censored, right-censored, and interval-censored survival data, our methodology is implemented using a data augmentation scheme which allows for existing Bayesian backfitting algorithms to be used. We illustrate the practical implementation and advantages of our method via simulation studies and an analysis of a prostate cancer surgery study where dependence on the experience and skill level of the physicians leads to clustering of survival times. We conclude by discussing our method's applicability in studies involving high dimensional data with complex underlying associations.