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Recurrent event data with a terminal event commonly arise in many longitudinal follow‐up studies. This article proposes a class of dynamic semiparametric transformation models for the marginal mean functions of the recurrent events with a terminal event, where some covariate effects may be time‐varying. An estimation procedure is developed for the model parameters, and the asymptotic properties of the resulting estimators are established. In addition, relevant significance tests are suggested for examining whether or not covariate effects vary with time, and a model checking procedure is presented for assessing the adequacy of the proposed models. The finite sample performance of the proposed estimators is examined through simulation studies, and an application to a medical cost study of chronic heart failure patients is provided. [ABSTRACT FROM AUTHOR]

Background: In biomedical and epidemiological studies, gene-environment (G-E) interactions play an important role in the etiology and progression of many complex diseases. In ultra-high-dimensional survival genomic data, two common approaches (marginal and joint models) are proposed to determine important interaction biomarkers. Most existing methods for detecting G-E interactions (marginal Cox model and marginal accelerated failure time model) are limited by a lack of robustness to contamination/outliers in response outcome and prediction biomarkers. In particular, right-censored survival outcomes and ultra-high-dimensional feature space make relevant feature screening even more challenging. Methods: In this paper, we utilize the non-parametric Kendall’s partial correlation method to obtain pure correlation to determine the importance of G-E interactions concerning clinical survival data under a marginal modeling framework. Results: A series of simulated scenarios are conducted to compare the performance of our proposed method (Kendall’s partial correlation) with some commonly used methods (marginal Cox’s model, marginal accelerated failure time model, and censoring quantile partial correlation approach). In real data applications, we utilize Kendall’s partial correlation method to identify G-E interactions related to the clinical survival results of patients with esophageal, pancreatic, and lung carcinomas using The Cancer Genome Atlas clinical survival genetic data, and further establish survival prediction models. Conclusions: Overall, both simulation with medium censoring level and real data studies show that our method performs well and outperforms existing methods in the selection, estimation, and prediction accuracy of main and interacting biomarkers. These applications reveal the advantages of the non-parametric Kendall’s partial correlation approach over alternative semi-parametric marginal modeling methods. We also identified the cancer-related G-E interactions biomarkers and reported the corresponding coefficients with p-values.