Improving the speed and accuracy when fitting flexible parametric survival models on the log-hazard scale

Flexible parametric survival models are an alternative to the Cox proportional hazards model and more standard parametric models for the modeling of survival (time-to-event) data. They are flexible in that spline functions are used to model the baseline and potentially complex time-dependent effects. In this talk, I will discuss using splines on the log-hazard scale. Models on this scale have some computational challenges because numerical integration is required to integrate the hazard function during estimation. The numerical integration is required for all individuals and for each call to likelihood/gradient/Hessian functions and can therefore be slow in large datasets. In addition, the models may have a singularity for the hazard function at t=0, which leads to precision issues. I will describe two recent updates to the stpm3 command that make these models faster to fit in large datasets and have improved accuracy for the numerical integration. First, the python option makes use of the mlad optimizer, which calls python, leading to major speed gains in large datasets. Second, there are different options for numerical integration of the hazard function, including tanh-sinh quadrature, which is now the default when the hazard function has a singularity at t=0. This leads to more accurate estimates compared with the more standard Gauss–Legendre quadrature. These speed and accuracy improvements make the use of these models more feasible in large datasets.