Identifying subpopulations that may be sensitive to the specific treatment is an important step toward precision medicine. On the other hand, longitudinal data with dropouts is common in medical research, and subgroup analysis for this data type is still limited. In this paper, we consider a single‐index threshold linear marginal model, which can be used simultaneously to identify subgroups with differential treatment effects based on linear combination of the selected biomarkers, estimate the treatment effects in different subgroups based on regression coefficients, and test the significance of the difference in treatment effects based on treatment‐subgroup interaction. The regression parameters are estimated by solving a penalized smoothed generalized estimating equation and the selection bias caused by missingness is corrected by a multiply robust weighting matrix, which allows multiple missingness models to be taken account into estimation. The proposed estimator remains consistent when any model for missingness is correctly specified. Under regularity conditions, the asymptotic normality of the estimator is established. Simulation studies confirm the desirable finite‐sample performance of the proposed method. As an application, we analyze the data from a clinical trial on pancreatic cancer.
Aim: We aimed to develop a new signature based on immune-related genes to predict prognosis and response to immune checkpoint inhibitors in patients with triple-negative breast cancer (TNBC). Materials & methods: Single-sample gene set enrichment was used to develop an immune-based prognostic signature (IPRS) for TNBC patients. We conducted multivariate Cox analysis to evaluate the prognosis value of the IPRS. Result: An IPRS based on 66 prognostic genes was developed. Multivariate Cox analysis indicated that the IPRS was an independent factor for prognosis. PD-1, PD-L1, PD-L2 and CTLA4 gene expression was higher in the low-risk group, suggesting IPRS could predict the response to immune checkpoint inhibitors. Conclusion: The IPRS might be a reliable signature to predict TNBC patients’ prognosis and response to immune checkpoint inhibitors, but needs prospective validation.
Background Estimating the average effect of a treatment, exposure, or intervention on health outcomes is a primary aim of many medical studies. However, unbalanced covariates between groups can lead to confounding bias when using observational data to estimate the average treatment effect (ATE). In this study, we proposed an estimator to correct confounding bias and provide multiple protection for estimation consistency. Methods With reference to the kernel function-based double-index propensity score (Ker.DiPS) estimator, we proposed the artificial neural network-based multi-index propensity score (ANN.MiPS) estimator. The ANN.MiPS estimator employed the artificial neural network to estimate the MiPS that combines the information from multiple candidate models for propensity score and outcome regression. A Monte Carlo simulation study was designed to evaluate the performance of the proposed ANN.MiPS estimator. Furthermore, we applied our estimator to real data to discuss its practicability. Results The simulation study showed the bias of the ANN.MiPS estimators is very small and the standard error is similar if any one of the candidate models is correctly specified under all evaluated sample sizes, treatment rates, and covariate types. Compared to the kernel function-based estimator, the ANN.MiPS estimator usually yields smaller standard error when the correct model is incorporated in the estimator. The empirical study indicated the point estimation for ATE and its bootstrap standard error of the ANN.MiPS estimator is stable under different model specifications. Conclusions The proposed estimator extended the combination of information from two models to multiple models and achieved multiply robust estimation for ATE. Extra efficiency was gained by our estimator compared to the kernel-based estimator. The proposed estimator provided a novel approach for estimating the causal effects in observational studies.
Subgroup analysis has become an important tool to characterize the treatment effect heterogeneity, and finally towards precision medicine. On the other hand, longitudinal study is widespread in many fields, but subgroup analysis for this data type is still limited. In this article, we study a partial linear varying coefficient model with a change plane, in which the subgroups are defined based on linear combination of grouping variables, and the time‐varying effects in different subgroups are estimated to capture the dynamic association between predictors and response. The varying coefficients are approximated by basis functions and the group indicator function is smoothed by kernel function, which are included in the generalized estimating equation for estimation. Asymptotic properties of the estimators for the varying coefficients, the constant coefficients and the change plane coefficients are established. Simulations are conducted to demonstrate the flexibility, efficiency and robustness of the proposed method. Based on the Standard and New Antiepileptic Drugs study, we successfully identify a subgroup in which patients are sensitive to the newer drug in a specific period of time.
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