Pattern-Mixture Models Identification Restriction Strategies For Longitudinal Data With Nonrandom Dropout

For the longitudinal study, due to obtain data needed for a long time, it may be because owe cooperation, action inconvenience or residence change of subject, inevitably appear missing data. Missing data mechanism can divided into three types, namely missing completely at random (MCAR), missing at random (MAR) and missing not at random (MNAR). In the presence of non-random dropout, the choices of the model mainly include selection models (SEM), pattern-mixture models (PMM), shared-parameter models (SPM) and varying coefficient models (VCM), which pattern-mixture models have gained considerable attention of the researchers. For the study to analyze the non-random missing data in longitudinal study, the issue that pattern-mixture models are by construction under-identified is gradually aroused people’s research interest.In order to solve the problem of under-identification in pattern-mixture models, this paper systematically elaborates three kinds of model identification restriction strategies that is complete case missing value restrictions (CCMV), neighboring case missing value restrictions(NCMV) and available case missing value restrictions (ACMV),and in this paper, a simulation proved study is implemented to describe the parameter estimations of model identification restriction strategies under various missing proportion and sample size. What’s more, combined with the national community hypertension standardized management case, we use the CCMV, NCMV and ACMV identification restriction to multiple imputed the missing hypertension follow-up data, and get their parameter estimates by the restricted maximum likelihood estimation method (REML); and a sensitivity analysis is proceeded through the analysis results of these three model identification restrictions which are compared to each other. The main results are as follows:1. Under the best suitable conditions, we can always get relatively stable and accurate parameter estimates from three model identification restriction strategies.The results of simulation study show that, when the missing proportion is fixed, along with the increasing of sample size, the parameter estimates of these three model identification restrictions are gradually close to the truth values and the standard errors of smaller and smaller; When the sample content reached200, the parameter estimates tend to be stable. When the sample size is fixed, along with the increasing of the missing proportion, the standard errors of the parameter estimates under these three model identification restrictions become larger and larger. When the missing proportion is small (less than about30%), the standard errors of CCMV restriction is small compared with the other two restrictions and the parameter estimates are closer to the truth values; However, when the missing proportion is large (greater than about60%), the standard errors of NCMV restriction is small compared with the other two restrictions and the parameter estimates are closer to the truth values; While under the other missing proportion, the standard errors of ACMV restriction is more small and the parameter estimates are relatively accurate.2. Viewing missing patterns as a stratification factor, using three model identification restrictions analyze the community hypertension standardized management data and integrate the results of each pattern, the explanation is more objective and accurate.The tendencies of the blood pressure values over time under missing patterns show that patients with higher systolic pressure and lower diastolic pressure are apt to missing. The results of each pattern indicated that the parameter estimates of these three identification restrictions are completely consistent under pattern3and pattern4, but inconformity for pattern1and pattern2. Moreover, integration results show that the parameter estimates under three restrictions are consistent. On the systolic pressure, using CCMV restriction, hypertension course of the disease and follow-up time are meaningful factors which affect the systolic pressure control effect of hypertension patients, while using NCMV and ACMV restrictions, hypertension course of the disease, overweight and follow-up time are meaningful factors which affect the systolic pressure control effect of community hypertension patients. On the diastolic pressure, these three identification restrictions imputed results show that age and follow-up time affect the diastolic pressure control effect of community hypertension patients.3. The comprehensive application of three identification restrictions can be used as the sensitivity analysis of the hypertension follow-up data.In this study, the analysis results of CCMV, NCMV and ACMV restrictions can be considered as the results of different sensitivity parameters. Regardless of the response variable as systolic or diastolic pressure, the parameter estimation results of PMM under three identification restrictions are basically the same, moreover, the blood pressure values over time tend to decrease and the slopes are closed and almost parallel. It is indicated that the missing data on hypertension can be imputed and estimated very well by using the PMM identification restrictions.