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Smooth backfitting has proven to have a number of theoretical and practicaladvantages in structured regression. Smooth backfitting projects the data downonto the structured space of interest providing a direct link between data andestimator. This paper introduces the ideas of smooth backfitting to survivalanalysis in a proportional hazard model, where we assume an underlyingconditional hazard with multiplicative components. We develop asymptotic theoryfor the estimator and we use the smooth backfitter in a practical application,where we extend recent advances of in-sample forecasting methodology byallowing more information to be incorporated, while still obeying thestructured requirements of in-sample forecasting.

Smooth backfitting of proportional hazards with multiplicative components