The use of restricted cubic splines to approximate complex hazard functions in the analysis of time-to-event data: a simulation study

If interest lies in reporting absolute measures of risk from time-to-event data then obtaining an appropriate approximation to the shape of the underlying hazard function is vital. It has previously been shown that restricted cubic splines can be used to approximate complex hazard functions in the context of time-to-event data. The degree of complexity for the spline functions is dictated by the number of knots that are defined. We highlight through the use of a motivating example that complex hazard function shapes are often required when analysing time-to-event data. Through the use of simulation, we show that provided a sufficient number of knots are used, the approximated hazard functions given by restricted cubic splines fit closely to the true function for a range of complex hazard shapes. The simulation results also highlight the insensitivity of the estimated relative effects (hazard ratios) to the correct specification of the baseline hazard.