基于Fréchet边界条件的广义估计方程

A Modified Generalized Estimating Equation Based on Fréchet Bounds

在广义估计方程(GEE)的框架下,引入二进制变量的Fréchet边界条件,解决广义估计方程在工作相关系数不在可行区间内的情况下,其估计值产生偏差的问题.在Fréchet边界内运用拟似然独立准则QIC选取最佳工作相关系数估计值,保证估计值的有效性,并结合马尔科夫链模型的极大似然估计值对分析结果进行验证.对Ham-D数据的分析表明,在GEE框架下考虑变量的Fréchet边界条件将改变对药物效果显著性的错误推断,其结果与马尔科夫链模型的分析结果一致.

In order to solve the problem that the generalized estimating equations （GEE） generate errone-ous estimates and lead to incorrect inferential results when the working correlation estimate is out of feasi-ble bounds, the Fréchet bounds of binary variables are introduced in this study under the quasi-likelihood framework. To ensure that the estimate is within the feasible bounds, we use quasi-likelihood under the independence model criterion （QIC） to select the best working correlation coefficient estimates within the Fréchet bounds and then use the Markov chain model to verify the results. The analysis of HAM-D data shows that when the Frfichet bounds are not considered, the inferential results may be erroneous. Taking these bounds into account will ensure a correct analysis and may change the inferential results. Therefore, Fréchet bounds are important when GEE is used to analyze binary longitudinal data.