Mixed model-based inference in geoadditive hazard regression for interval-censored survival times

Mixed model-based estimation of additive or geoadditive regression models has become popular throughout recent years. It provides a unified and modular framework that facilitates joint estimation of nonparametric covariate effects and the corresponding smoothing parameters. Therefore, extensions of mixed model-based inference to a Cox-type regression model for the hazard rate are considered, allowing for a combination of general censoring schemes for the survival times and a flexible, geoadditive predictor. In particular, the proposed methodology allows for arbitrary combinations of right, left, and interval censoring as well as left truncation. The geoadditive predictor comprises time-varying effects, nonparametric effects of continuous covariates, spatial effects, and potentially a number of extensions such as cluster-specific frailties or interaction surfaces. In addition, all covariates are allowed to be piecewise constant time-varying. 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. Estimation is based on a reparametrization of the model as a variance component mixed model. The variance parameters, corresponding to inverse smoothing parameters, can then be determined using an approximate marginal likelihood approach. An analysis on childhood mortality in Nigeria serves as an application, where the interval censoring framework additionally allows to deal with the problem of heaped survival times. The effect of ignoring the impact of interval-censored observations is investigated in a simulation study.