Improved Generalized Estimating Equations For Incomplete Longitudinal Binary Data

Objective:Longitudinal study is a very common method to explore and explain the phenomenon of the complete development process about something. In the intervention effect evaluation about medical research,due to the continuous research and the objects of study in poor cooperation, etc., longitudinal binary data often exist missing data problems. If missing data were not be taken into consideration, replaced with directly modeling of longitudinal data, there would be potentially biased estimates of the model parameters.According to the longitudinal study of cardiac rehabilitation in patients with acute coronary syndrome in CCU, this paper aims to explore the performance of weighted generalized estimating equations(WGEEs), multiple imputation based on generalized estimating equations(MI-GEEs) and generalized estimating equations(GEEs) in terms of handling dropouts that are missing at random(MAR).Methods:Aimed at comparing the performance of the above methods, the methods are compared on simulation study and example analysis. The longitudinal binary data are generated from a logistic regression model, under different sample sizes. The incomplete data are created for three different dropout rates. The methods are evaluated in terms of bias, precision and mean square error in case where data are subject to MAR dropout.Combined heart rehabilitation about ACS patients in a cardiovascular specialist hospital of Shanxi province, 211 cases were randomly assigned to intervention group with secondary prevention of cardiac rehabilitation intervention and control groups with conventional treatment. To evaluate cardiac rehabilitation of individual comprehensive intervention model for secondary prevention of acute coronary patients in cardiac rehabilitation, the monitoring data of myocardial enzyme spectrum and myocardial infarction markers were collected.Results:1. Improved GEE method performed better than standard GEE In longitudinal binary random missing data, and MI-GEE showed the best.Simulation results show that the improved approaches both WGEE and MI-GEE performed better than the standard GEE in the longitudinal binary missing data, and MI-GEE showed the best. The sample size and proportion affect the performance of the above methods in handling dropouts that are missing at random(MAR). As the sample size increases, the effect of three methods improved. Along with the increase of the proportion of missing, three methods of handling missing data capacity has declined.2. MI-GEE is the effective model for dichotomous random missing data.Both simulation analysis and case studies show that, MI-GEE using multiple imputation of data sets conduct GEE analysis, making full use of missing information contains information, can reasonably analyze and evaluate the effectiveness of intervention.Standards GEE analysis parameter estimation results of comprehensive intervention on anxious patients with coronary cardiac rehabilitation effect and no difference in the conventional therapy group, obviously masking effect of the intervention, not reasonable analysis case study. WGEE can be used to handle missing data and parameter estimation of bias can be reduced to a certain extent, but MI-GEE still had some shortcomings.3.Secondary prevention of acute coronary cardiac rehabilitation in patients with individualized comprehensive intervention model to be effective.The case of ACS patients in cardiac rehabilitation shown that, MI-GEE methods to take full advantage of lack of data, it is reasonable analysis and evaluation for secondary prevention of cardiac rehabilitation of individual comprehensive intervention model for the CCU acute effect of Crown. Results show that the two groups of patients with acute pro BNP and c Tn I positive rates between the two groups are different, and therapeutic effect of comprehensive intervention group was better than conventional therapy, and rehabilitation treatment of prolonged effect more obvious. Making monitoring index pro BNP and c Tn I binary can be more rational analysis and interpretation of cardiac rehabilitation.Conclusions:For the longitudinal binary data with missing at random, two improved forms of GEE(WGEE and MI-GEE) performed obviously better than the standard GEE, and the bias of parameter estimation using MI-GEE is the smallest, and MI-GEE performed best. MI-GEE is a powerful method for dichotomous data with MAR, can be used to guide the evaluation of patients with ACS rehabilitation of individual comprehensive intervention model for secondary prevention effect. Early in patients with acute cardiac rehabilitation mode of individualized intervention is an effective measure, secondary prevention of cardiac rehabilitation intervention model can be incorporated into the treatment of patients with ACS clinical pathways.