Smooth Backfitting of Proportional Hazards With Multiplicative Components

Smooth backfitting has proven to have a number of theoretical and practical advantages in structured regression. By projecting the data down onto the structured space of interest smooth backfitting provides a direct link between data and estimator. This article introduces the ideas of smooth backfitting to survival analysis in a proportional hazard model, where we assume an underlying conditional hazard with multiplicative components. We develop asymptotic theory for the estimator. In a comprehensive simulation study, we show that our smooth backfitting estimator successfully circumvents the curse of dimensionality and outperforms existing estimators. This is especially the case in difficult situations like high number of covariates and/or high correlation between the covariates, where other estimators tend to break down. We use the smooth backfitter in a practical application where we extend recent advances of in-sample forecasting methodology by allowing more information to be incorporated, while still obeying the structured requirements of in-sample forecasting. Supplementary materials for this article are available online.