Pseudo-Observations for Bivariate Survival Data

TL;DR

This paper extends the pseudo-observations method to bivariate survival data with right censoring, enabling covariate effect estimation on joint survival probabilities and related quantities.

Contribution

It introduces a generalized approach for bivariate survival data, demonstrating consistency and asymptotic normality of the estimators using two nonparametric joint survival estimators.

Findings

Method produces consistent, asymptotically normal estimates.

Enables covariate effect estimation on joint survival probabilities.

Validated through simulations and real data analysis.

Abstract

The pseudo-observations approach has been gaining popularity as a method to estimate covariate effects on censored survival data. It is used regularly to estimate covariate effects on quantities such as survival probabilities, restricted mean life, cumulative incidence, and others. In this work, we propose to generalize the pseudo-observations approach to situations where a bivariate failure-time variable is observed, subject to right censoring. The idea is to first estimate the joint survival function of both failure times and then use it to define the relevant pseudo-observations. Once the pseudo-observations are calculated, they are used as the response in a generalized linear model. We consider two common nonparametric estimators of the joint survival function: the estimator of Lin and Ying (1993) and the Dabrowska estimator (Dabrowska, 1988). For both estimators, we show that our bivariate pseudo-observations approach produces regression estimates that are consistent and asymptotically normal. Our proposed method enables estimation of covariate effects on quantities such as the joint survival probability at a fixed bivariate time point, or simultaneously at several time points, and consequentially can estimate covariate-adjusted conditional survival probabilities. We demonstrate the method using simulations and an analysis of two real-world datasets.