Marginalized Conditional Linear Model For Longitudinal Binary Data With Continuous Informative Dropout

Longitudinal study is the same individual repeated over a longer period of time. With the change of medical model,longitudinal data analysis method of community medicine, psychology and public health has attracted researchers attention.Because of a long time study,the object of observation often lose interest in the study or withdrew from the study due to reasons such as condition deteriorated, leading to the missing data.For the longitudinal binary data with non-random missing, selection model,shared parameter model and pattern mixture models are the most commonly used methods.These models only take missing time points into account. In the survery, objects can not complete investigation at the stipulated time,which raise a new topic for the dropout occur at any time of the survey.Focusing on the longitudinal binary data which include nonrandom missingness and the continuous distribution dropout time in the longitudinal study. Based on the pattern mixture model principle, we develop a marginalized conditional linear model with Bayesian function and method, and complete software code.Model consideres marginal mean,conditional mean and correlation structure separately, model parameters as the linear or quadratic function of dropout time.Marginal conditional linear model not only considers the relationship between covariates and response variable,also considering the relationship between response variable and dropout time in the analysis of longitudinal binary data with missing not at random. It overcomes the problem of pattern mixture model that the dropout time is discrete distribution, and solves the problem that dropout occur at any time of the survey.It makes full use of the information provided by the lack of time for each individual.It not only reflects the dynamic change trend, but also shows the differences between different individuals.In order to solve the problem of theoretical research and application of marginal conditional linear model,the paper proposes a simulated study under different sample size and missing proportion.Model is applied to longitudinal data of community hypertension standardization management.Setting different sensitivity parameters for sensitivity analysis. The main results are as follows:1. Marginal conditional linear model can get the accurate parameter estimates under different sample size and missing proportion.Simulation study under a missing proportion is10%-90%and sample size is30-1000.The result indicates that, when sample size is fixed, the standard error becomes bigger with missing proportion increasing;when the missing proportion is fixed, the parameter estimates are more closed to the truth values and the standard error become smaller with the increasing of sample size. When the sample size is less than300,parameter estimates tend to be unstable, when the sample size reaches more than300,parameter estimates closed to the simulation truth values.So the marginal conditional linear model can get the accurete parameter estimates for longitudinal binary data which include nonrandom missingness.2. Marginal conditional linear model can explain the longitudinal binary data of community hypertension standardization management objectively and accurately.Building marginal conditional linear model with the data of taiyuan community hypertension standardization management.The results indicate that the age parameter and BMI parameter changed over dropout time.Patients who are early dropouts and those later dropouts have the different model parameters.The main effect of age is increasing as dropout time increase and the values are positive,which states that the older patients who are later dropouts with abnormal blood pressure values.BMI parameter is increasing as dropout time increase,which indicates that overweight patients who are later dropouts with abnormal blood pressure values. Center parameter unchanged over dropout time. Compared with the center1,blood pressure control effect of center3is well, then center4and center2are poor.3. Sensitivity analysis confirms that the marginal conditional linear model is suitable to this data and the result can be explained reasonably.Set different sensitivity parameters based on sex of centerl and center2Different sensitivity parameter values are a1=0and a2=2;a1=2and a2=0; a1=2and a2=2.The sensitivity analysis results state that:the blood pressure estimates of man and woman are very similar with different sensitivity parameters. Sensitivity analysis further confirms that the marginal conditional linear model is suitable to the data with missing not at random and the result can be explained reasonably.4. WinBUGS software can easily solve Bayesian inferences with complex models and distribution problemsThe instance shows that WinBUGS can not only be used to intuitively describ,also give the Gibbs sampling dynamic map of parameters. It makes sampling results more intuitive, and can easily get the mean of parameter posterior distribution and95%confidence interval. However,due to the WinBUGS software demanding the format of the data and the data storage space is limited.It is very hard to analysis directly in WinBUGS when there are a large amount of data.Call the WinBUGS software package by R code and complete the analysis of community hypertension data. Program of marginal conditional linear mode is easy to complete under the combination of WinBUGS and SAS software. The results are explained more reasonably.