Varying Coefficient Models For Longitudinal Data With Continuous Nonrandom Dropout

Dropout is a common occurrence in longitudinal studies because of the longer observation time. The dropout is termed "nonrandom dropout" if the missingness process depends on the unobserved outcomes. Nowadays, pattern mixture models is common used for nonrandom dropout. However, the pattern mixture models only take several missing time points into account, and the distribution of missing time is consider as discrete distribution. In actual research, we sometimes can’t get data as the planned times because of various reasons, such as the objects are too busy or go out, which lead to the dropout can occur at any time of the survey, not just at the planned time. In this situation, the pattern mixed models are helplessness.Focusing on the longitudinal studies which include nonrandom missingness and the continuous distribution dropout time, we develop a general framework of varying coefficient model based on the pattern mixture model with the Bayesian penalized splines function, which considers the model parameters such as regression coefficient and variance components as the functions of dropout time. Because of the dropout time distribution is unspecified, the model parameters depend on the dropout time through unspecified smooth functions.In this study, a simulation study verifies the parameter estimation’s accuracy of varying coefficient models under various missing proportion and sample size. Then the proposed model is applied to longitudinal data of community hypertension standardization management, the mainly results are showed as follows.1. Varying coefficient model can get the accurate parameter estimates under various sample size and missing proportion.The result of simulation study indicates that, when the missing proportion is fixed, the parameter estimates are more closed to the truth value with the increasing of sample size. When the sample size reaches more than300, the parameter estimates tend to be stable, moreover, the standard error becomes smaller with the increasing of sample size. When the sample size is fixed, the missing proportion have little affect with the parameter estimates, which means that under various missing proportion, the model can always get the parameter estimates closed to the simulation truth values. However, the standard error becomes larger with the increasing of missing proportion.2. The varying coefficient model can explain the data of community hypertension standardization management subjectively and reasonably.The results of community hypertension standardization management indicate that the intercept and the regression coefficients such as the age parameter, the sex parameter and so on are all changed over dropout time. In other word, patients who are early dropouts and those later dropouts have the different model parameters. On the systolic pressure, the main effect of age is decreasing as dropout time increases, and the values are negative, which dipicts that those later dropouts have more obvious downtrend. The main effect of sex is increasing as dropout time increase and the values are positive, which states that the control effect of systolic pressure in male patients is better than that of the female patients. On diastolic pressure, the main effect of hypertension course is increasing as dropout time increase, and the values are positive, which states that the hypertension course has less effect to early dropouts, but to the later dropouts, the diastolic pressure is much higher when the hypertension course is longer.33、 The sensitivity analysis confirms further that the varying coefficient models is suitable to this data and the result can be explained reasonably.When constructing the varying coefficient model, it is assumed that there are the same parameter estimates between the observed data and the unobserved data. However, this assumption cannot be identified by the observed data, so the sensitivity analysis is needed, which can verify if the conclusion is similar when we lengthen the observed time. The sensitivity analysis results of both gender in four communities state that:when a=5and a=10, the blood pressure estimates are close to the VCM estimates,which state that the VCM is suitable to this data and the result can be explained reasonably.In conclusion, this study proposed a varying coefficient model for longitudinal data with nonrandom dropout including the principle, the methods, the computer programming and the implement in community hypertension standardization management and sensitivity analysis. The VCM is built with Bayesian penalized splines function based on the pattern mixture pattern. In the varying coefficient models, the model parameters such as regression coefficients and variance components are the functions of dropout time. It overcomes the shortage of pattern mixture model that the dropout time is discrete distribution, and solves the problem that dropout is continuous time. So it is the optimum selection to deal with the longitudinal data of continuous time with nonrandom dropout.