The Extrapolation Performance of Survival Models for Data With a Cure Fraction: A Simulation Study

Objectives: Curative treatments can result in complex hazard functions. The use of standard survival models may result in poor extrapolations. Several models for data which may have a cure fraction are available, but comparisons of their extrapolation performance are lacking. A simulation study was performed to assess the performance of models with and without a cure fraction when fit to data with a cure fraction. Methods: Data were simulated from a Weibull cure model, with 9 scenarios corresponding to different lengths of follow-up and sample sizes. Cure and noncure versions of standard parametric, Royston-Parmar, and dynamic survival models were considered along with noncure fractional polynomial and generalized additive models. The mean-squared error and bias in estimates of the hazard function were estimated. Results: With the shortest follow-up, none of the cure models provided good extrapolations. Performance improved with increasing follow-up, except for the misspecified standard parametric cure model (lognormal). The performance of the flexible cure models was similar to that of the correctly specified cure model. Accurate estimates of the cured fraction were not necessary for accurate hazard estimates. Models without a cure fraction provided markedly worse extrapolations. Conclusions: For curative treatments, failure to model the cured fraction can lead to very poor extrapolations. Cure models provide improved extrapolations, but with immature data there may be insufficient evidence to choose between cure and noncure models, emphasizing the importance of clinical knowledge for model choice. Dynamic cure fraction models were robust to model misspecification, but standard parametric cure models were not

Generalised linear models for flexible parametric modelling of the hazard function

Background: Parametric modelling of survival data is important and reimbursement decisions may depend on the selected distribution. Accurate predictions require sufficiently flexible models to describe adequately the temporal evolution of the hazard function. A rich class of models is available among the framework of generalised linear models (GLMs) and its extensions, but these models are rarely applied to survival data. This manuscript describes the theoretical properties of these more flexible models, and compares their performance to standard survival models in a reproducible case-study. Methods: We describe how survival data may be analysed with GLMs and its extensions: fractional polynomials, spline models, generalised additive models, generalised linear mixed (frailty) models and dynamic survival models. For each, we provide a comparison of the strengths and limitations of these approaches. For the case-study we compare within-sample t, the plausibility of extrapolations and extrapolation performance based on data-splitting. Results: Viewing standard survival models as GLMs shows that many impose a restrictive assumption of linearity. For the case-study, GLMs provided better within-sample t and more plausible extrapolations. However, they did not improve extrapolation performance. We also provide guidance to aid in choosing between the different approaches based on GLMs and its extensions. Conclusions: The use of GLMs for parametric survival analysis can out-perform standard parametric survival models, although the improvements were modest in our case-study. This approach is currently seldom used. We provide guidance on both implementing these models and choosing between them. The reproducible case-study will help to increase uptake of these models

Generalized linear models for flexible parametric modeling of the hazard function

Background: Parametric modelling of survival data is important and reimbursement decisions may depend on the selected distribution. Accurate predictions require sufficiently flexible models to describe adequately the temporal evolution of the hazard function. A rich class of models is available among the framework of generalised linear models (GLMs) and its extensions, but these models are rarely applied to survival data. This manuscript describes the theoretical properties of these more flexible models, and compares their performance to standard survival models in a reproducible case- study. Methods: We describe how survival data may be analysed with GLMs and its extensions: fractional polynomials, spline models, generalised additive models, generalised linear mixed (frailty) models and dynamic survival models. For each, we provide a comparison of the strengths and limitations of these approaches. For the case-study we compare within-sample fit, the plausibility of extrapolations and extrapolation performance based on data-splitting. Results: Viewing standard survival models as GLMs shows that many impose a restrictive assumption of linearity. For the case-study, GLMs provided better within-sample fit and more plausible extrapolations. However, they did not improve extrapolation performance. We also provide guidance to aid in choosing between the different approaches based on GLMs and its extensions. Conclusions: The use of GLMs for parametric survival analysis can out-perform standard parametric survival models, although the improvements were modest in our case-study. This approach is currently seldom used. We provide guidance on both implementing these models and choosing between them. The reproducible case-study will help to increase uptake of these models

Multivariate Discount Weighted Regression and Local Level Models

In this paper we propose a multivariate discount weighted regression technique to give a tractable solution to the problem of variance estimation and forecasting for the multivariate local level model. We give the correspondence between discount regression and matrix normal dynamic linear models and we show that the local level model can be treated with discount regression techniques. We illustrate the proposed methodology with London metal exchange data consisting of aluminium spot and future contract closing prices. The proposed estimate of the noise covariance matrix suggests these data exhibit high cross-correlation, which is discussed in some detail