Doubly robust estimation of generalized partial linear models for longitudinal data with dropouts

Subgroup analysis for longitudinal data based on a partial linear varying coefficient model with a change plane

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.

Multiply robust subgroup analysis based on a single-index threshold linear marginal model for longitudinal data with dropouts

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.

Robust estimation of models for longitudinal data with dropouts and outliers

Missing data and outliers usually arise in longitudinal studies. Ignoring the effects of missing data and outliers will make the classical generalized estimating equation approach invalid. The longitudinal cohort study of rheumatoid arthritis patients was designed to investigate whether the Health Assessment Questionnaire score was associated with baseline covariates and changed with time. There exist dropouts and outliers in the data. In order to analyze the data, we develop a robust estimating equation approach. To deal with the responses missing at random, we extend a doubly robust method. To achieve robustness against outliers, we utilize an outlier robust method, which corrects the bias induced by outliers through centralizing the covariate matrix in the estimating equation. The doubly robust method for dropouts is easy to combine with the outlier robust method. The proposed method has the property of robustness in the sense that the proposed estimator is not only doubly robust against model misspecification for dropouts when there is no outlier in the data, but also robust against outliers. Consistency and asymptotic normality of the proposed estimator are established under regularity conditions. A comprehensive simulation study and real data analysis demonstrate that the proposed estimator does have the property of robustness.

A multiple robust propensity score method for longitudinal analysis with intermittent missing data

Longitudinal data are very popular in practice, but they are often missing in either outcomes or time-dependent risk factors, making them highly unbalanced and complex. Missing data may contain various missing patterns or mechanisms, and how to properly handle it for unbiased and valid inference still presents a significant challenge. Here, we propose a novel semiparametric framework for analyzing longitudinal data with both missing responses and covariates that are missing at random and intermittent, a general and widely encountered situation in observational studies. Within this framework, we consider multiple robust estimation procedures based on innovative calibrated propensity scores, which offers additional relaxation of the misspecification of missing data mechanisms and shows more satisfactory numerical performance. Also, the corresponding robust information criterion on consistent variable selection for our proposed model is developed based on empirical likelihood-based methods. These advocated methods are evaluated in both theory and extensive simulation studies in a variety of situations, showing competing properties and advantages compared to the existing approaches. We illustrate the utility of our approach by analyzing the data from the HIV Epidemiology Research Study.