ItemContinuous threshold models with two-way interactions in survival analysis(Wiley, 2020-07-28) Liu, S.; Chen, B. E.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. ItemResidual Bootstrap Test for Interactions in Biomarker Threshold Models with Survival Data(Springer, 2017-12-20) Gavanji, Parisa; Chen, Bingshu E.; Jiang, WenyuMany new treatments in cancer clinical trials tend to benefit a subset of patients more. To avoid unnecessary therapies and failure to recognize beneficial treatments, biomarker threshold models are often used to identify this subset of patients. We are interested in testing the treatment-biomarker interaction effects in a threshold model with biomarker but an unknown cut point. The unknown cut point causes irregularity in the model, and the traditional likelihood ratio test cannot be applied directly. A test for biomarker-treatment interaction effects is developed using a residual bootstrap method to approximate the distribution of the proposed test statistic. We evaluate the residual bootstrap and the permutation methods through extensive simulation study and find that the residual bootstrap method gives accurate test size, while the permutation method cannot control type $I$ error sometimes in the presence of main treatment effects. The proposed residual bootstrap test can be used to explore potential treatment-by-biomarker interaction in clinical studies. The findings can be applied to guide the follow-up trial design using biomarker as a stratification factor. We apply the proposed residual bootstrap method to data from Breast International Group (BIG) 1-98 randomized clinical trial and show that patients with high Ki-67 level may benefit more from Letrozole treatment. ItemBayesian inference for treatment-biomarker interaction in clinical trials(2016-02-02) Chen, Bingshu E.; Jiang, W.; Tu, DongshengSome baseline patient factors, such as biomarkers, are useful in predicting patients’ responses to a new therapy. Identification of such factors is important in enhancing treatment outcomes, avoiding potentially toxic therapy that is destined to fail and improving the cost-effectiveness of treatment. Many of the biomarkers, such as gene expression, are measured on a continuous scale. Threshold of biomarker is often needed to define sensitive subset for making easy clinical decisions. A novel hierarchical Bayesian method is developed to make statistical inference simultaneously on the threshold and the treatment effect restricted on the sensitive subset defined by the biomarker threshold. In the proposed method, the threshold parameter is treated as a random variable that takes values with certain probability distribution. The observed data are used to estimate parameters in the prior distribution for the threshold, so that the posterior is less dependent on the prior assumption. The proposed Bayesian method is evaluated through simulation studies. Compared to the existing approaches such as the profile likelihood method, which makes inference about the threshold parameter using the bootstrap, the proposed method provides better finite sample properties in term of the coverage probability of 95% credible interval. The proposed method is also applied to a clinical trial of prostate cancer with the serum prostatic acid phosphatase (AP) biomarker. ItemAlcohol: a recently identified risk factor for breast cancer(Canadian Medical Association, 2003-04-29) Aronson, Kristan J.