Semiparametric Model Averaging Prediction for Lifetime Data via Hazards Regression

Abstract Forecasting survival risks for time-to-event data is an essential task in clinical research. Practitioners often rely on well-structured statistical models to make predictions for patient survival outcomes. The nonparametric proportional hazards model, as an extension of the Cox proportional hazards model, involves an additive nonlinear combination of covariate effects for hazards regression and may be more flexible. When there are a large number of predictors, nonparametric smoothing for different variables cannot be simultaneously optimal using the conventional fitting program. To address such a limitation and still maintain the nonparametric flavour, we present a novel model averaging method to produce model-based prediction for survival outcome and our method automatically offers optimal smoothing for individual nonparametric functional estimation. The proposed semiparametric model averaging prediction (SMAP) method basically approximates the underlying unstructured nonparametric regression function by a weighted sum of low-dimensional nonparametric submodels. The weights are obtained from maximizing the partial likelihood constructed for the aggregated model. Theoretical properties are discussed for the estimated model weights. Simulation studies are conducted to examine the performance of SMAP under various evaluation criteria. Two real examples from genetic research studies motivated our work and are analysed by the proposed SMAP to produce new scientific findings.