Flexible parametric modelling of the hazard function in breast cancer studies

Abstract

In cancer research, study of the hazard function provides useful insights into disease dynamics, as it describes the way in which the (conditional) probability of death changes with time. The widely utilized Cox proportional hazard model uses a stepwise nonparametric estimator for the baseline hazard function, and therefore has a limited utility. The use of parametric models and/or other approaches that enables direct estimation of the hazard function is often invoked. A recent work by Cox et al. [6] has stimulated the use of the flexible parametric model based on the Generalized Gamma (GG) distribution, supported by the development of optimization software. The GG distribution allows estimation of different hazard shapes in a single framework. We use the GG model to investigate the shape of the hazard function in early breast cancer patients. The flexible approach based on a piecewise exponential model and the nonparametric additive hazards model are also considered.

Flexible estimation of survival curves conditional on non‐linear and time‐dependent predictor effects

“…Future research should systematically compare different flexible approaches for modeling NL or TD covariate effects, based on, for example, penalized smoothing splines , restricted cubic splines , fractional polynomials , or the weighted residuals . Finally, further simulation studies should involve systematic comparisons of our estimates with other flexible models, which estimate survival probabilities conditional on NL and/or TD effects .…”

“…In contrast, the ‘TD model’ limited flexible modeling of covariate effects to TD effects, while imposing the linearity of the association between each continuous predictor and the log hazard. Both NL models and TD models have been considered by several authors, using different flexible modeling techniques. In our analyses, either TD or NL effects were estimated with regression splines using equations and .…”

“…Several authors have proposed different methods to combine estimation of the baseline hazard with flexible modeling of covariate effects , including flexible models developed specifically for relative survival analyses of cancer registry data . The number of alternative methods developed in these publications reflects the importance of the problem, while the diversity of the proposed approaches reflects the complexity of the analytical and conceptual challenges involved.…”