Generalized Linear Models for Flexible Parametric Modeling of the Hazard Function

Kearns, Benjamin; Stevenson, Matt; Triantafyllopoulos, Kostas; Manca, Andrea

doi:10.1177/0272989x19873661

Cited by 34 publications

(28 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There is a growing awareness that such models may not be sufficiently flexible to accurately capture the complex hazard patterns that may arise in practice [ 3 , 4 ]. There are several more-advanced survival models which may give improved fit to the observed data [ 5 ]. However, it is unclear if improved within-sample fit will lead to improved extrapolation performance, and there is dearth of comparative studies which include these flexible emerging practice models.…”

Section: Introductionmentioning

confidence: 99%

Comparing current and emerging practice models for the extrapolation of survival data: a simulation study and case-study

Kearns

Stevenson

Triantafyllopoulos

et al. 2021

BMC Med Res Methodol

Self Cite

View full text Add to dashboard Cite

Background Estimates of future survival can be a key evidence source when deciding if a medical treatment should be funded. Current practice is to use standard parametric models for generating extrapolations. Several emerging, more flexible, survival models are available which can provide improved within-sample fit. This study aimed to assess if these emerging practice models also provided improved extrapolations. Methods Both a simulation study and a case-study were used to assess the goodness of fit of five classes of survival model. These were: current practice models, Royston Parmar models (RPMs), Fractional polynomials (FPs), Generalised additive models (GAMs), and Dynamic survival models (DSMs). The simulation study used a mixture-Weibull model as the data-generating mechanism with varying lengths of follow-up and sample sizes. The case-study was long-term follow-up of a prostate cancer trial. For both studies, models were fit to an early data-cut of the data, and extrapolations compared to the known long-term follow-up. Results The emerging practice models provided better within-sample fit than current practice models. For data-rich simulation scenarios (large sample sizes or long follow-up), the GAMs and DSMs provided improved extrapolations compared with current practice. Extrapolations from FPs were always very poor whilst those from RPMs were similar to current practice. With short follow-up all the models struggled to provide useful extrapolations. In the case-study all the models provided very similar estimates, but extrapolations were all poor as no model was able to capture a turning-point during the extrapolated period. Conclusions Good within-sample fit does not guarantee good extrapolation performance. Both GAMs and DSMs may be considered as candidate extrapolation models in addition to current practice. Further research into when these flexible models are most useful, and the role of external evidence to improve extrapolations is required.

show abstract

Section: Introductionmentioning

confidence: 99%

Comparing current and emerging practice models for the extrapolation of survival data: a simulation study and case-study

Kearns

Stevenson

Triantafyllopoulos

et al. 2021

BMC Med Res Methodol

Self Cite

View full text Add to dashboard Cite

show abstract

“…First, we only examined seven commonly used parametric survival models [2]. There are other models that could be applied, as well as more flexible models such as spline-based models and fractional polynomials [19][20][21][22]. Further research into the impact on extrapolation uncertainty of using these models would be beneficial.…”

Section: Discussionmentioning

confidence: 99%

How Uncertain is the Survival Extrapolation? A Study of the Impact of Different Parametric Survival Models on Extrapolated Uncertainty About Hazard Functions, Lifetime Mean Survival and Cost Effectiveness

et al. 2019

Self Cite

View full text Add to dashboard Cite

Background and Objective The extrapolation of estimated hazard functions can be an important part of cost-effectiveness analyses. Given limited follow-up time in the sample data, it may be expected that the uncertainty in estimates of hazards increases the further into the future they are extrapolated. The objective of this study was to illustrate how the choice of parametric survival model impacts on estimates of uncertainty about extrapolated hazard functions and lifetime mean survival. Methods We examined seven commonly used parametric survival models and described analytical expressions and approximation methods (delta and multivariate normal) for estimating uncertainty. We illustrate the multivariate normal method using case studies based on four representative hypothetical datasets reflecting hazard functions commonly encountered in clinical practice (constant, increasing, decreasing, or unimodal), along with a hypothetical cost-effectiveness analysis. Results Depending on the survival model chosen, the uncertainty in extrapolated hazard functions could be constant, increasing or decreasing over time for the case studies. Estimates of uncertainty in mean survival showed a large variation (up to sevenfold) for each case study. The magnitude of uncertainty in estimates of cost effectiveness, as measured using the incremental cost per quality-adjusted life-year gained, varied threefold across plausible models. Differences in estimates of uncertainty were observed even when models provided near-identical point estimates. Conclusions Survival model choice can have a significant impact on estimates of uncertainty of extrapolated hazard functions, mean survival and cost effectiveness, even when point estimates were similar. We provide good practice recommendations for analysts and decision makers, emphasizing the importance of considering the plausibility of estimates of uncertainty in the extrapolated period as a complementary part of the model selection process.

show abstract

“…Further details on model specification (for the noncured component) are provided in a previous publication. 15 A total of 4 types of cure fraction model were included. For these, the correct background mortality was provided for the cured group.…”

Section: Methodsmentioning

confidence: 99%

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

et al. 2021

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Generalized Linear Models for Flexible Parametric Modeling of the Hazard Function

Cited by 34 publications

References 32 publications

Comparing current and emerging practice models for the extrapolation of survival data: a simulation study and case-study

Comparing current and emerging practice models for the extrapolation of survival data: a simulation study and case-study

How Uncertain is the Survival Extrapolation? A Study of the Impact of Different Parametric Survival Models on Extrapolated Uncertainty About Hazard Functions, Lifetime Mean Survival and Cost Effectiveness

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

Contact Info

Product

Resources

About