Variable selection and nonlinear effect discovery in partially linear mixture cure rate models

Abstract

Survival data with long-term survivors are common in clinical investigations. Such data are often analyzed with mixture cure rate models. Existing model selection procedures do not readily discriminate nonlinear effects from linear ones. Here, we propose a procedure for accommodating nonlinear effects and for determining the cure rate model composition. The procedure is based on the Least Absolute Shrinkage and Selection Operators (LASSO). Specifically, by partitioning each variable into linear and nonlinear components, we use LASSO to select linear and nonlinear components. Operationally, we model the nonlinear components by cubic B-splines. The procedure adds to the existing variable selection methods an ability to discover hidden nonlinear effects in a cure rate model setting. To implement, we ascertain the maximum likelihood estimates by using an Expectation Maximization (EM) algorithm. We conduct an extensive simulation study to assess the operating characteristics of the selection procedure. We illustrate the use of the method by analyzing data from a real clinical study.

Keywords:

• Mixture cure rate models
• LASSO
• cubic B-splines
• variable selection

Acknowledgments

The authors thank the Editor, the Associate Editor, and the Reviewers for their many constructive comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Wanzhu Tu  http://orcid.org/0000-0002-4236-9135

Additional information

Notes on contributors

Abdullah Al Masud

Abdullah Al Masud, Ph.D. is a biostatistician, a recent graduate from Department of Biostatistics, Indiana University, Indianapolis, IN. He is currently practicing in bio-pharmaceutical industry. He is interested in clinical trial design and model selection issues.

Zhangsheng Yu

Zhangsheng Yu, Ph.D. is a biostatistician, Professor of Biostatistics at Shanghai Jiao Tong University, Shanghai, China. Dr. Yu is primarily interested in survival analysis, medical image analysis.

Wanzhu Tu

Wanzhu Tu, Ph.D. is an applied statistician. He is Professor of Biostatistics, Department of Biostatistics, Indiana University School of Medicine, Indianapolis, IN. He is interested in the use of nonparametric and semiparametric techniques in various statistical models.