Guoyou Qin

Joint mean–covariance model in generalized partially linear varying coefficient models for longitudinal data

In longitudinal data analysis, efficient estimation of regression coefficients requires a correct specification of certain covariance structure, and efficient estimation of covariance matrix requires a correct specification of mean regression model. In this article, we propose a general semiparametric model for the mean and the covariance simultaneously using the modified Cholesky decomposition. A regression spline-based approach within the framework of generalized estimating equations is proposed to estimate the parameters in the mean and the covariance. Under regularity conditions, asymptotic properties of the resulting estimators are established. Extensive simulation is conducted to investigate the performance of the proposed estimator and in the end a real data set is analysed using the proposed approach.

Simultaneous mean and covariance estimation of partially linear models for longitudinal data with missing responses and covariate measurement error

Missing responses and covariate measurement error are very commonly seen in practice. New estimating equations are developed to simultaneously estimate the mean and covariance under a partially linear model for longitudinal data with missing responses and covariate measurement error. Specifically, a novel approach is proposed to handle measurement error by using independent replicate measurements. Compared with existing methods, the proposed method requires fewer assumptions. For example, it does not require to specify the distribution of the mismeasured covariate or the measurement error, and does not need a parametric model to estimate the probability of being observed or to impute the missing responses. Additionally, the proposed estimating equations are easy to implement in most popular statistical softwares by applying existing algorithms for standard generalized estimating equations. The asymptotic properties of the proposed estimators are established under regularity conditions, and simulation studies demonstrate desired properties. Finally, the proposed method is applied to data from the Lifestyle Education for Activity and Nutrition (LEAN) study. This data analysis confirms the effectiveness of the intervention in producing weight loss at month nine.

Robust estimation of the generalised partial linear model with missing covariates

In this paper, we propose robust estimation of the generalised partial linear model with covariates missing at random. The developed approach integrated the robust method and the method for dealing with missing data. Under some regularity conditions, we establish the asymptotic normality of the proposed estimator of the regression coefficients and show that the proposed estimator of the nonparametric function can achieve the optimal rate of convergence. It can be observed that the regression spline approach avoids some of the intricacies associated with the kernel method, and the robust estimation and inference can be carried out operationally as if a generalised linear model were used. Simulation studies are conducted to investigate the robustness of the proposed method. At the end, the proposed method is applied to a real data analysis for illustration.

Robust estimation of partially linear models for longitudinal data with dropouts and measurement error

Outliers, measurement error, and missing data are commonly seen in longitudinal data because of its data collection process. However, no method can address all three of these issues simultaneously. This paper focuses on the robust estimation of partially linear models for longitudinal data with dropouts and measurement error. A new robust estimating equation, simultaneously tackling outliers, measurement error, and missingness, is proposed. The asymptotic properties of the proposed estimator are established under some regularity conditions. The proposed method is easy to implement in practice by utilizing the existing standard generalized estimating equations algorithms. The comprehensive simulation studies show the strength of the proposed method in dealing with longitudinal data with all three features. Finally, the proposed method is applied to data from the Lifestyle Education for Activity and Nutrition study and confirms the effectiveness of the intervention in producing weight loss at month 9. Copyright

Variable selection for longitudinal data with high-dimensional covariates and dropouts

ABSTRACT A new variable selection approach utilizing penalized estimating equations is developed for high-dimensional longitudinal data with dropouts under a missing at random (MAR) mechanism. The proposed method is based on the best linear approximation of efficient scores from the full dataset and does not need to specify a separate model for the missing or imputation process. The coordinate descent algorithm is adopted to implement the proposed method and is computational feasible and stable. The oracle property is established and extensive simulation studies show that the performance of the proposed variable selection method is much better than that of penalized estimating equations dealing with complete data which do not account for the MAR mechanism. In the end, the proposed method is applied to a Lifestyle Education for Activity and Nutrition study and the interaction effect between intervention and time is identified, which is consistent with previous findings.

Robust estimation in linear regression models for longitudinal data with covariate measurement errors and outliers

Measurement errors and outliers commonly arise during the process of longitudinal data collection and ignoring them in data analysis can lead to large deviations in estimates. Therefore, it is important to take into account the effect of measurement errors and outliers in longitudinal data analysis. In this paper, a robust estimating equation method for analyzing longitudinal data with covariate measurement errors and outliers is proposed. Specifically, the biases caused by measurement errors are reduced via using the independence between replicate measurements and the biases caused by outliers are corrected via centralizing the observed covariate matrix. The proposed method does not require specifying the distributions of the true covariates, response and measurement errors. In practice, it can be easily implemented via the standard generalized estimating equations algorithms. The asymptotic normality of the proposed estimator is established under regularity conditions. Extensive simulation studies show that the proposed method performs better in handling measurement errors and outliers than several existing methods. For illustration, the proposed method is applied to a data set from the Lifestyle Education for Activity and Nutrition (LEAN) study.

A generalized partially linear mean-covariance regression model for longitudinal proportional data, with applications to the analysis of quality of life data from cancer clinical trials

Motivated by the analysis of quality of life data from a clinical trial on early breast cancer, we propose in this paper a generalized partially linear mean-covariance regression model for longitudinal proportional data, which are bounded in a closed interval. Cholesky decomposition of the covariance matrix for within-subject responses and generalized estimation equations are used to estimate unknown parameters and the nonlinear function in the model. Simulation studies are performed to evaluate the performance of the proposed estimation procedures. Our new model is also applied to analyze the data from the cancer clinical trial that motivated this research. In comparison with available models in the literature, the proposed model does not require specific parametric assumptions on the density function of the longitudinal responses and the probability function of the boundary values and can capture dynamic changes of time or other interested variables on both mean and covariance of the correlated proportional responses. Copyright

Quantile regression in longitudinal studies with dropouts and measurement errors

ABSTRACT Quantile regression models, as an important tool in practice, can describe effects of risk factors on the entire conditional distribution of the response variable with its estimates robust to outliers. However, there is few discussion on quantile regression for longitudinal data with both missing responses and measurement errors, which are commonly seen in practice. We develop a weighted and bias-corrected quantile loss function for the quantile regression with longitudinal data, which allows both missingness and measurement errors. Additionally, we establish the asymptotic properties of the proposed estimator. Simulation studies demonstrate the expected performance in correcting the bias resulted from missingness and measurement errors. Finally, we investigate the Lifestyle Education for Activity and Nutrition study and confirm the effective of intervention in producing weight loss after nine month at the high quantile.