Continuous threshold models with two-way interactions in survival analysis |
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Authors: | Shuo Shuo Liu Bingshu E Chen |
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Institution: | 1. Department of Statistics, The Pennsylvania State University, University Park, PA, U.S.A;2. Canadian Cancer Trials Group and Department of Public Health Sciences, Queen's University, Kingston, Ontario, Canada |
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Abstract: | Proportional hazards model with the biomarker–treatment interaction plays an important role in the survival analysis of the subset treatment effect. A threshold parameter for a continuous biomarker variable defines the subset of patients who can benefit or lose from a certain new treatment. In this article, we focus on a continuous threshold effect using the rectified linear unit and propose a gradient descent method to obtain the maximum likelihood estimation of the regression coefficients and the threshold parameter simultaneously. Under certain regularity conditions, we prove the consistency, asymptotic normality and provide a robust estimate of the covariance matrix when the model is misspecified. To illustrate the finite sample properties of the proposed methods, we simulate data to evaluate the empirical biases, the standard errors and the coverage probabilities for both the correctly specified models and misspecified models. The proposed continuous threshold model is applied to a prostate cancer data with serum prostatic acid phosphatase as a biomarker. |
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Keywords: | Asymptotic statistics change-point rectified linear unit single-index model subset two-way interaction effect survival analysis threshold model |
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