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. 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

Geoadditive hazard regression for interval censored survival times

The Cox proportional hazards model is the most commonly used method when analyzing the impact of covariates on continuous survival times. In its classical form, the Cox model was introduced in the setting of right-censored observations. However, in practice other sampling schemes are frequently encountered and therefore extensions allowing for interval and left censoring or left truncation are clearly desired. Furthermore, many applications require a more flexible modeling of covariate information than the usual linear predictor. For example, effects of continuous covariates are likely to be of nonlinear form or spatial information is to be included appropriately. Further extensions should allow for time-varying effects of covariates or covariates that are themselves time-varying. Such models relax the assumption of proportional hazards. We propose a regression model for the hazard rate that combines and extends the above-mentioned features on the basis of a unifying Bayesian model formulation. Nonlinear and time-varying effects as well as the baseline hazard rate are modeled by penalized splines. Spatial effects can be included based on either Markov random fields or stationary Gaussian random fields. The model allows for arbitrary combinations of left, right and interval censoring as well as left truncation. Estimation is based on a reparameterisation of the model as a variance components mixed model. The variance parameters corresponding to inverse smoothing parameters can then be estimated based on an approximate marginal likelihood approach. As an application we present an analysis on childhood mortality in Nigeria, where the interval censoring framework also allows to deal with the problem of heaped survival times caused by memory effects. In a simulation study we investigate the effect of ignoring the impact of interval censored observations