Estimating the functional form of a continuous covariate's effect on survival time
Several methods for estimating the functional form of the effect of one continuous covariate are investigated in the framework of the Cox proportional hazards model. In particular, prespecified as well as data-driven risk functions are considered: Using the former (e.g. restricted cubic splines, the categorisation of the continuous covariate by fixed cutpoints) the general functional form is given in advance, the data are used for estimating the parameters of these functions only. With data-driven risk functions (e.g. the categorisation by data-driven cutpoints, fractional polynomials) the functional form is estimated from the data, too. All methods are extended by adapting bootstrap aggregating (bagging). The approaches are illustrated with the data of a breast cancer study. Assessment is performed by a simulation study considering typical risk functions. Altogether fractional polynomials performed best. Furthermore, it could be shown that bagging is able to improve the estimation of risk functions, if the underlying method does not describe the true effect correctly in the original data.
proportional hazards model risk function bootstrap aggregating model building