Survival Analysis: Latest Research in Copula, Cure, and Frailty Modeling

Chongliang Luo Chair
Washington University in St Louis
 
Tuesday, Aug 5: 10:30 AM - 12:20 PM
4116 
Contributed Papers 
Music City Center 
Room: CC-106C 

Main Sponsor

Biometrics Section

Presentations

A Semi-Parametric Marginal Cure Model for Long-Term Survivors

Cure rate models, or two-component mixture models for long-term survivors, are widely used in survival analysis. Most applications focus on interpreting covariate effects on the cure fraction and conditional hazard rate. However, it remains challenging to directly interpret their effects on overall survival outcomes, especially when covariates influence both components simultaneously. We propose a marginal cure rate model that provides a general framework for studying covariate effects from a marginal perspective, offering clearer interpretations. Using novel reparameterizations, we directly relate covariates to the marginal mean hazard rate. To enhance flexibility, we introduce a semi-parametric model based on Bernstein polynomials, relaxing the parametric baseline hazard assumption for the conditional hazard function. The performance of our approach is assessed through extensive simulations and illustrated using SEER liver cancer data. 

Keywords

Bernstein polynomials

Cure fraction

Cure rate model

Liver Cancer

SEER registry 

Co-Author(s)

Wei-Wen Hsu, University of Cincinnati
David Todem, Michigan State University
KyungMann Kim, University of Wisconsin-Madison

First Author

Jianfeng Chen, Kansas State University

Presenting Author

Wei-Wen Hsu, University of Cincinnati

Controlled Variable Selection in Generalized Odds Rate Mixture Cure Models for High-dimensional Data

When modeling a time-to-event outcome, a cured fraction exists when a subgroup of patients is immune to the event of interest. In such cases, rather than fitting a traditional survival model, a mixture cure model (MCM) is used. Additionally, when identifying genomic features associated with a time-to-event outcome, variable selection techniques for high-dimensional settings are needed. However, few variable selection methods exist for fitting MCMs to high-dimensional data. We developed a high-dimensional penalized generalized odds rate (GOR) MCM, which allows for identification of prognostic factors associated with both cure status and/or survival of uncured patients. We implemented the generalized monotone incremental forward stagewise algorithm to estimate the model complemented by the Model-X knockoffs framework to select important variables while controlling the false discovery rate. Through extensive simulations, we demonstrated empirical properties of our penalized GOR-MCM in comparison to alternative methods. In our acute myeloid leukemia application, we further showed controlled variable selection performance of our method in a real-world application setting. 

Keywords

survival analysis

cure fraction

variable selection

penalized

forward stagewise

false discovery rate 

Co-Author

Kellie Archer, The Ohio State University

First Author

Shuai Sun

Presenting Author

Shuai Sun

Semiparametric Analysis of Cure Rate Models using Soft Bayesian Additive Regression Tree

Many existing parametric and semi-parametric techniques for cure rate survival models struggle to adequately capture the complex effects of covariates. To address this limitation, adopting more flexible modelling approaches is crucial for improving the accuracy of survival predictions. Survival data often involve right-censored observations, which present additional challenges. To handle these complexities, we focus on Bayesian methodologies for survival prediction leveraging a novel approach called Soft Bayesian Additive Regression Trees (SBART). This method combines multiple trees into a unified framework using Bayesian principles. Using this method we discuss two distinct cases: one where the data is unclustered and another where the data exhibits a clustered structure. To enhance computational efficiency, we introduce a data augmentation scheme to support the Bayesian backfitting algorithm. We illustrate the advantage of our model by simulation study and analysis of Melanoma data from e1684 clinical trial and Florida Cancer Registry Data. 

Keywords

Bayesian additive regression trees

Survival analysis

Cure rate model

Semiparametric 

Co-Author

Debajyoti Sinha, Florida State University

First Author

Abhishek Mandal, Florida State University

Presenting Author

Abhishek Mandal, Florida State University

Individual Dynamic Prediction for Cure and Survival Based on Longitudinal Biomarkers

To optimize personalized treatment strategies and extend patients' survival times, it is critical to accurately predict patients' prognoses at all stages, from disease diagnosis to follow-up visits. The longitudinal biomarker measurements during visits are essential for this prediction purpose. Patients' ultimate concerns are cure and survival. However, in many situations, there is no clear biomarker indicator for cure. We propose a comprehensive joint model of longitudinal and survival data and a landmark cure model, incorporating proportions of potentially cured patients. The survival distributions in the joint and landmark models are specified through flexible hazard functions with the proportional hazards as a special case, allowing other patterns such as crossing hazard and survival functions. Formulas are provided for predicting each individual's probabilities of future cure and survival at any time point based on his or her current biomarker history. Simulations and a study of patients with chronic myeloid leukemia show that, with these comprehensive and flexible properties, the proposed cure models outperform standard cure models in terms of predictive performance. 

Keywords

Joint modeling

Landmarking

Non-proportional hazard function

Cure model

Predictive performance evaluation 

Co-Author(s)

Xuelin Huang, University of Texas MD Anderson Cancer Center
Ruosha Li, University of Texas School of Public Health
Alexander Tsodikov, University of Michigan
Kapil Bhalla, The University of Texas MD Anderson Cancer Center

First Author

Can Xie, The University of Texas MD Anderson Cancer Center

Presenting Author

Can Xie, The University of Texas MD Anderson Cancer Center

Multivariate generalized linear frailty models for clustered competing risk data

Competing risk data arises when the occurrence of one event prevents observation of another type of events. While competing risks are commonly encountered in biomedical research, failure to account for them can distort estimation of the effects of interest. A joint model for competing risks with shared random effects (frailty) could be useful to address this issue. In this study, we propose a joint modeling framework for analysis of clustered competing risk data, where the hazard for each competing risk event is assumed to be of the piecewise exponential form with a frailty shared between the events of individuals within each cluster. Based on the equivalence to Poisson regression likelihood, models of this approach can be fit under the framework of generalized linear mixed models. The performance of the proposed method was evaluated through an extensive simulation study. The proposed joint model showed stable estimation performance, even with a moderate correlation between the events, while univariate models not accounting for competing risks yielded considerable bias. The usefulness of the proposed method was demonstrated by application to real data from a clinical study. 

Keywords

survival analysis

competing risks

frailty

clustered survival data

biomedical data analysis 

Co-Author(s)

Kyoji Furukawa, Kurume University
Takeshi Emura, Institute of Statistical Mathematics

First Author

Ren Teranishi, Kurume Univeristy Graduate School of Medicine

Presenting Author

Kyoji Furukawa, Kurume University

Sample size calculations for nonproportional hazards utilizing the concept of Weighted Relative Time

Sample size calculations (SSC) for fixed two-arm randomized control trials (RCTs) with a survival endpoint have traditionally relied on the proportional hazards (PH) assumption or on the assumption of exponentially distributed survival times. When the PH assumption is not met, popular choices of SSC deploy the piecewise linear survival (Lakatos) approach or newer methods based on accelerated failure time (AFT) models that allow NPH. Recent advances in literature have shown how the concept of Relative Time (RT) using two different Weibull distributions can be used to handle the non-AFT and NPH scenarios. The main limitation of this method is that SSC is based on survival differences in the two arms at prespecified time points of interest. Here, we extend this method to conduct SSC comparing full survival curves using the concept of Weighted Relative Time (WRT). We consider two scenarios – early treatment effect, and delayed treatment effect and compare results to the Lakatos method and the logrank test with Fleming-Harrington weights. Simulations are conducted to assess the operation characteristics of the proposed method, and a real-life example is discussed. 

Keywords

nonproportional hazards

randomized control trial

sample size

survival endpoint

relative time

weighted approach 

First Author

Milind Phadnis, University of Kansas Medical Center

Presenting Author

Milind Phadnis, University of Kansas Medical Center