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.