多反应变量重复测量资料的协方差类型模型应用及SAS实现

Application of covariance pattern model for multivariate repeated measures data and implementation of SAS

目的 探讨协方差类型模型在多反应变量的重复测量资料分析中的应用方法 为了评价盐酸吡格列酮片治疗2型糖尿病的有效性,以安慰剂为对照,对240例2型糖尿病患者的空腹血糖和餐后2 h血糖重复观测数据进行多反应变量的协方差类型模型分析,对模型的固定效应参数矩阵作最小二乘估计并进行组间比较,同时给出误差效应的方差协方差矩阵,利用SAS中的MIXED过程得以实现结果 2组空腹血糖和餐后2 h血糖的总体差别有统计学意义（P〈0.01）;各时间点的差异有统计学意义（P〈0.01）;反应变量类别和时间的交互作用有统计学意义（P〈0.05）,说明空腹血糖和餐后2 h血糖随时间的变化趋势有所不同;分组和时间的交互作用有统计学意义（P〈0.01）,说明2组血糖随时间的变化趋势有所不同.得到固定效应的有关参数的估计值,并给出了曲线图.用药后患者的空腹血糖和餐后2 h血糖随时间变化而变化,且2组曲线的变化趋势是不相同的.试验组曲线随时间迅速下降,而安慰剂组曲线随时间变化非常平缓结论 多反应变量的协方差类型模型可以处理有随机缺失数据的资料,并允许每个观察对象观察次数和观察时间不同,通过指定非独立数据的方差协方差矩阵结构,直接对相关性结构建模.模型不仅考虑了每个反应变量多次重复测量结果之间的相关性,也考虑了各个反应变量之间的相关性,可有效地进行重复测量资料的动态变化趋势分析,统计结论更为可信.

Objective Applying covariance pattern model to analyze the multivariate repeated measurement data. Methods In order to assess the effectiveness of Pioglitazone hydrochloride for Type II Diabetes mellitus, 240 patients with Type II Di- abetes mellitus were arranged to randomly take 2 kinds of medicine, Pioglitazone hydrochloride or placebo. Both fasting plasma glucose and 2 h plasma glucose repeated measurement data were analyzed by covariance pattern model. The fixed effect parameters matrix of model coefficients were estimated by using least squares estimation method, the effects between treatment groups were compared and the variance-covariance matrices was also estimated. Corresponding analysis methods were programmed with MIXED procedure of SAS software. Results There was statistically significant difference between the 2 groups of fasting plasma glucose and 2 h plasma glucose overall （ P〈 0.01 ） ; There was statistically significant difference among different time points （ P 〈 0.01 ） ; The interaction effects of response variables category and time was statistically significant （P〈0.05）, it indicats that the trend changing with time was different between fasting plasma glucose and 2 h plasma glucose. The interaction effects of group and time was statistically significant （P〈0.01）, it indicats that the trend of blood sugar changing with time was different between the 2 groups. Estimated parameters with fixed effect were obtained and graphs were drawn. Both fasting plasma glucose and 2 h plasma glucose changed with time after treatment and the trends between 2 groups were different. Curve of treatment group fell rapidly over time, and curve of placebo group was very gentle changing with time. Conclusion The covariance pattern model for the multivariate repeated measurement data can handle the materials with random missing data, and allow different observed times and observation time for each observation object. It can directly build the model on the correlation structure through specifying the variance-covariance matrices of the dependent data. The model consider not only the correlation between multiple repeated measurements of each response variable, but also the correlation of all the response variables. The model can effectively analyze the dynamic change trend of multivariate repeated measurement data, so the statistical conclusion is more credible.