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Recent years, large scale clinical data like patient surveys and medical record data are playing an increasing role in medical data science. These large-scale clinical data, collectively referred to as "real-world data (RWD)". It is expected to be widely used in large-scale observational studies of specific diseases, personal medicine or precise medicine, finding the responder of drugs or treatments. Applying RWD for estimating heterogeneous treat ment effect (HTE) has already been a trending topic. HTE has the potential to considerably impact the development of precision medicine by helping doctors make more informed precise treatment decisions and provide more personalized medical care. The statistical models used to estimate HTE is called treatment effect models. Powers et al. proposed a some treatment effect models for observational study, where they pointed out that the bagging causal MARS (BCM) performs outstanding compared to other models. While BCM has excellent performance, it still has room for improvement. In this paper, we proposed a new treatment effect model called shrinkage causal bagging MARS method to improve their shared basis conditional mean regression framework based on the following points: first, we estimated basis functions using transformed outcome, then applied the group LASSO method to optimize the model and estimate parameters. Besides, we are focusing on pursing better interpretability of model to improve the ethical acceptance. We designed simulations to verify the performance of our proposed method and our proposed method superior in mean square error and bias in most simulation settings. Also we applied it to real data set ACTG 175 to verify its usability, where our results are supported by previous studies., Comment: 19 pages, 9 figures

Multivariable predictive models are important statistical tools for providing synthetic diagnosis and prognostic algorithms based on multiple patients' characteristics. Their apparent discriminant and calibration measures usually have overestimation biases (known as 'optimism') relative to the actual performances for external populations. Existing statistical evidence and guidelines suggest that three bootstrap-based bias correction methods are preferable in practice, namely Harrell's bias correction and the .632 and .632+ estimators. Although Harrell's method has been widely adopted in clinical studies, simulation-based evidence indicates that the .632+ estimator may perform better than the other two methods. However, there is limited evidence and these methods' actual comparative effectiveness is still unclear. In this article, we conducted extensive simulations to compare the effectiveness of these methods, particularly using the following modern regression models: conventional logistic regression, stepwise variable selections, Firth's penalized likelihood method, ridge, lasso, and elastic-net. Under relatively large sample settings, the three bootstrap-based methods were comparable and performed well. However, all three methods had biases under small sample settings, and the directions and sizes of the biases were inconsistent. In general, the .632+ estimator is recommended, but we provide several notes concerning the operating characteristics of each method.