A Gamma-frailty proportional hazards model for bivariate interval-censored data

Correlated survival data naturally arise from many clinical and epidemiological studies. For the analysis of such data, the Gamma-frailty proportional hazards (PH) model is a popular choice because the regression parameters have marginal interpretations and the statistical association between the failure times can be explicitly quantified via Kendall's tau. Despite their popularity, Gamma-frailty PH models for correlated interval-censored data have not received as much attention as analogous models for right-censored data. In this work, a Gamma-frailty PH model for bivariate interval-censored data is presented and an easy to implement expectation-maximization (EM) algorithm for model fitting is developed. The proposed model adopts a monotone spline representation for the purposes of approximating the unknown conditional cumulative baseline hazard functions, significantly reducing the number of unknown parameters while retaining modeling flexibility. The EM algorithm was derived from a data augmentation procedure involving latent Poisson random variables. Extensive numerical studies illustrate that the proposed method can provide reliable estimation and valid inference, and is moreover robust to the misspecification of the frailty distribution. To further illustrate its use, the proposed method is used to analyze data from an epidemiological study of sexually transmitted infections.