## Course summary - Beyond the Cox model - flexible parametric models and extensions

This day will consist of a series of lectures introducing flexible parametric survival models, illustration of the methods using real data, and demonstrations of how the methods are implemented in Stata. References will be provided for how the models can be estimates in SAS and R, but no demonstration will be provided.

Flexible parametric models, also known as Royston-Parmar models, combine the desired features of both the Cox model and parametric survival models. While the Cox model makes minimal assumptions about the form of the baseline hazard function, prediction of hazards and other related functions for a given set of covariates is hindered by this lack of assumptions; the resulting estimated curves are not smooth and do not hold information about what occurs between the observed failure times. Parametric models offer smooth predictions by assuming a functional form of the hazard, but often the assumed form is too structured for use with real data, especially if there exist significant changes in the shape of the hazard over time. Flexible parametric survival models provide researchers with the possibility to fit parametric models without imposing a restriction on the shape of the baseline hazard. Non-proportional hazards can be handled easily and because one has a parametric expression for the baseline cumulative hazard it is very easy to make smooth predictions of quantities of interest (e.g., hazard function, survivor function, expectation of life).

Topics include:

• A brief review of Cox Model & motivation of parametric models

• Flexible parametric survival models with proportional hazards.

• Flexible parametric survival models with time-dependent effects.

• Simple predictions: survival, hazard and contrasts (differences/ratios)

• Example applications

• Attained age as the-time scale

• Standardised survival curves and related measures.

• Other predictions (Restricted mean survival time / loss in expectation of life).

• Brief overview of further extensions:

- Competing risks (cause-specific and subhazard models).

- Random effect models.

- Using splines on the log-hazard scale.