A Flexible Partially Linear Single Index Proportional Hazards Regression Model for Multivariate Survival Data

We address the problem of survival regression modelling with multivariate responses and nonlinear covariate effects. Our model extends the proportional hazards model by introducing several weakly-parametric elements: the marginal baseline hazard functions are expressed as piecewise constants, association is modelled with copulas, and nonlinear covariate effects are handled by a single-index structure using a spline. The model permits a full likelihood approach to inference, making it possible to obtain individual-level survival or hazard function estimates. Performance of the new model is evaluated through simulation studies and application to the Busselton health study data. The results suggest that the proposed method can capture nonlinear covariate effects well, and that there is benefit to modeling the association between the correlated responses.