Robust analysis of longitudinal data with nonignorable missing responses

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 © 2016 John Wiley & Sons, Ltd.

Estimation of response from longitudinal binary data with nonignorable missing values in migraine trials

In migraine trials pain relief responses from a headache at specific time points and sustained pain relief response over a period of time are important efficacy measures. When there are missing records of individual time point pain scores and/or headache recurrences during a migraine trial, the common approach used in practice to estimate the sustained response is statistically inconsistent even if the data are missing completely at random. Methods dealing with nonignorable longitudinal missing data usually assume certain models for the missing mechanism which can not be checked as they involve unobserved data. Taking advantage of the specific definition of the 'sustained pain relief' response, we propose two estimating methods based on intuitive imputation, which do not require model assumptions on the missing probability or specification of the correlation structure among the longitudinal observations. The consistency of the proposed methods is discussed in theory and their empirical performances are assessed through intensive simulation studies. The simulation results show that the proposed methods perform well in terms of reducing bias and mean square error except in several extreme cases which are unlikely to happen in real trials. The application of the proposed methods is illustrated in a real data analysis.