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Abstract:
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Failure-time data with long-term survivors are frequently encountered in clinical investigations and they are often analyzed with mixture cure rate models. Existing model selection procedures for mixture cure rate models do not readily discriminate nonlinear effects in the selected variables. Herein, we consider variable selection in partially linear cure rate models consisting of both linear and nonlinear components. We propose a new procedure based on the Least Absolute Shrinkage and Selection Operators (LASSO) to determine the model composition of mixture cure rate models. Specifically, we partition each variable into linear and nonlinear parts, where the nonlinear part is modeled by coefficients of cubic-B spline bases. The procedure differs from the existing variable selection methods in its ability to discover hidden nonlinear structures in the independent variables. To implement, we compute maximum likelihood estimates using an Expectation Maximization (EM) algorithm. We conduct extensive simulation studies to assess the operating characteristics of the proposed methods. We illustrate our method by analyzing data from a real clinical study.
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