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Data sets with missing values bring great challenges to k-means clustering (KMC). At present, most studies focus on KMC data with low missing ratio while few studies on KMC data with high missing ratio. The current imputation methods have the following problems when dealing with the KMC data: (1) the error between imputation value and original true value is large, which leads to the poor imputation precision; (2) the imputation results have a great influence on the clustering results, which reduce the accuracies of the clustering results. We propose a novel imputation method, to deal with the problems, called as trimmed scores regression (TSR), which obtains an imputation estimator from a regression equation with a trimmed score matrix, and a novel cluster with k-means method. Compared with other imputation methods in numerical analysis, the TSR method exhibits better performance.

The Generalized Estimating Equations (GEE) method is one of the most commonly used statistical methods for the analysis of longitudinal data in epidemiological studies. A working correlation structure for the repeated measures of the outcome variable of a subject needs to be specified by this method. However, statistical criteria for selecting the best correlation structure and the best subset of explanatory variables in GEE are only available recently because the GEE method is developed on the basis of quasi-likelihood theory. Maximum likelihood based model selection methods, such as the widely used Akaike Information Criterion (AIC), are not applicable to GEE directly. Pan (2001) proposed a selection method called QIC which can be used to select the best correlation structure and the best subset of explanatory variables. Based on the QIC method, we developed a computing program to calculate the QIC value for a range of different distributions, link functions and correlation structures. This program was written in Stata software. In this article, we introduce this program and demonstrate how to use it to select the most parsimonious model in GEE analyses of longitudinal data through several representative examples.