Robust Estimation Of Related Parameters For Longitudinal Medical Data

The longitudinal study is defined as repeated measurements over time, and it is different from the cross-sectional study in series of fixed points, whose basic purpose is to study the change of dependent variable over time and the influence factors of the change. In medical research, especially large clinical trials, we often meet this kind of data. There are lots of methods used to deal with longitudinal data. At present, people often use marginal model and the stochastic model. The optimal model is not determined by the data itself, but depends on the background and purpose of the study.This paper mainly focus on marginal model, and it dose not require the usual distribution assumptions .This feature leads to an estimation way known as "generalized estimating equations"(GEE). The regression parameters obtained by iterative method which can do well for generalized estimating equations is robust to the specification of within-individuals association,but not robust to outliers. Generalized estimation equations can also obtain correlation parameters. There are lots of ways to obtain correlation parameters. Here, we introduce moment estimation and quasi-least squares estimation(QLS) in details. The core of robust estimation equation is plugging Huber function into standardized residuals, which makes GEE robust to outliers and non-normal data, but it has a strong assumption– symmetry of error distribution..An limited simulation based on multiple normal distribution shows: Moment estimation of the correlation parameters always does not exist and QLS estimate is asymptotically unbiased. Regression parameters of QLS and moment estimation are both asymptotically unbiased. When outliers added in, robust GEE is better than ordinary GEE, but still exists bias. All the simulations are implemented in R software.As in other regression analysis situation, to longitudinal data, the first step is to judge whether there exists outliers. The example analysis confirmed that when outliers occur, the standard error of robust GEE estimation is obviously lower than that of ordinary GEE, and robust GEE can help to evaluate the influence degree of the abnormal points on results.