Survival models for right censored breast cancer data: theory, application and comparison

Abstract

Background: Censoring frequently occurs in disease data analysis, which is a key characteristic of time to failure modeling. Typically, time to failure studies are conducted through non-parametric and semi-parametric modelling techniques. Parametric models provide more efficient estimates, but are seldomly used, because of some of the limitations and assumptions which need to be fulfilled to apply them. The aim of this study is to illustrate the theoretical and application limitations and performance of different flexible and standard parametric models to evaluate the prognostic value for mortality risk of breast cancer after recurrence among women. Methods: This article describes the theoretical properties of flexible parametric models and compares their performances to standard parametric models, by studying mortality in women diagnosed with breast cancer. We describe how time to failure data may be analyzed with nonlinear flexible models. In this regard, we apply fractional polynomials, spline models, piecewise exponential models, and piecewise exponential additive mixed models. We also illustrate properties of standard parametric models. All analyses have been conducted with multiple covariates to identify significant predictors. Information criteria have been used to evaluate performances of models. Results: Fractional polynomial and spline-based generalized additive models work well in capturing local fluctuations. Parameter estimation with a piecewise exponential additive mixed model (PAMM) as an extension of the piecewise exponential modelling (PEM) approach automatically penalizes model complexity, which is very helpful to avoid over fitting. Conclusions: Flexible parametric time to failure models are more efficient than standard parametric time to failure models. By incorporating time dependent covariates, PAMM is a good approach to perform in-depth studies of predictors over different finite intervals of follow-up time. Until now, this approach is rarely used in time to failure right censored studies.