Application Of Bayesian Statistics Model In The Elderly Health Management Study

ObjectiveBayesian statistics has been recognized and concerned by more and more researchers, but the domestic research on Bayesian statistics is still weak. The objective of this study was to introduce the Bayesian statistics and its applications. The main theories cover non-informative prior, informative prior, skeptical prior, enthusiastic prior, eliciting prior distributions from multiple experts, Bayesian mixed model, and sensitivity analysis theory. By using of empirical research method, this study conducted the empirical analysis for Bayesian model in the evaluation of self-rated intervention effect of elderly health management in a community in Nanjing. In addition, this study expounded the methods for the acquisition of expert opinion and the process of Bayesian mixed model Constructing. Sensitivity analysis for prior distribution will enable us to arrive at more comprehensive conclusions. The present study also provided the theory base for the studies about Bayesian prior distribution and Bayesian mixed model.MethodsObjective to comprehensively present the Bayesian prior distribution theory and the theory of Bayesian mixed model by reviewing literatures at home and abroad. By using of empirical research method, this paper conducted the empirical analysis for prior elicited from expert opinion and Bayesian mixed model in the evaluation of self-rated intervention effect of elderly health management. Utilizing investigation emotional function data, constructed variance analysis model by non-informative prior and informative prior elicited from multiple experts and compared the results between Bayesian and frequentist analysis. Bayesian mixed model construction in this research mainly with non-informative prior. In addition, Bayesian sensitivity analysis has the main concern of sensitivity to the prior distribution. A frequentist analysis used the SAS procedure MIXED yielded MLEs. By the R2OpenBUGS package in RStudio 0.98 is able to call OpenBUGS 3.22 software for model building, compiling and iterative, summarize inferences and convergence in a table and graph, and save the simulations in arrays for easy access in RStudio software.ResultsAccording to the empirical results, we got the following conclusions:there were no differences in demographic characteristics between management group and control group, as in the result of frequentist analysis; the results of Baseline analysis using non-informative prior showed there was significant difference between management group and control group on emotional function dimensions, and the scores of physical function and emotional function in the control group was better than that of the management group, as in the result of frequentist analysis(F=10.014,.P=0.002<0.05); looking at the posterior estimates derived using the non-informative prior and three types of experts priors,we noticed that the posterior estimates obtained by different types of priors were similar, and all · results showed that there was no significant difference between management group and control group on the difference baseline-six months intervention of emotional dimensions, the 95% credible interval included zero, as in the result of frequentist analysis(F=0.057,P=0.881>0.05); the posterior estimates derived using the non-informative prior and three types of experts priors,we founded that the posterior estimates obtained by different types of priors were similar, and all results showed that there was significant difference between management group and control group on the difference baseline-24 months intervention of emotional function dimensions, the 95% credible interval didn’t included zero, the traditional statistical result also showed that there was significant difference among the two groups (F=8.427, P=0.004<0.05).The result of the Multilevel model utilizing emotional function dimensions data indicated that the estimated mean of slope-time and slope-group time interaction were-0.0085 and 0.016,had statistical significance (P< 0.001).The residual of level 1 was 0.605.Looking at the random effects, we found that the intercept variance was statistically significant. The results of the Bayesian mixed model indicated that the estimated posterior mean of slope-time was-0.0085(95% CI:-0.0165,-0.0008) and the estimated posterior mean of slope-group time interaction was 0.0160(95%CY: 0.0063,0.0257),and fixed effects parameters were statistically significant. The random effects results indicated that the estimated posterior mean of intercept variance was large, suggesting that the random intercepts account for much of the variability in the data. There was also evidence of variability in the random slopes account for the variability in the data although this was small.Sensitivity analysis showed that ANOVA model of emotional function dimensions posterior estimates obtained by different types of priors, including non-informative prior, three types of experts priors, skeptical priors and enthusiastic priors, were similar. Bayesian mixed model of emotional function dimensions results showed that fixed effects parameters posterior estimates obtained by non-informative prior, skeptical priors and enthusiastic priors, were similar, the random effects variance parameters posterior estimates obtained by non-informative prior, skeptical priors and enthusiastic priors had great differences, but otherwise did not affect our conclusions about the effect of intervention. In addition, the Bayesian residual analysis results showed that the model fitted the observations well.ConclusionThe results of Baseline analysis using non-informative prior were in agreement with the results of frequentist analysis in this study. The different methods of eliciting from expert opinion will obtain prior distribution with different distribution parameters, which will exert different influences on the estimated posterior distribution. Sensitivity analysis prior distribution using skeptical prior and enthusiastic prior informative is essential to come to a general conclusion. The results show that the sensitivity of simple model to prior distribution parameters was lower than that of the complex statistical model. The results of Bayesian mixed model using non-informative prior were in agreement with the results of frequentist analysis in this study, but the residual of level 1 of Bayesian mixed model was getting smaller. Bayesian mixed models also incorporates prior information to statistical inference and can easily get an intuitive display of the results directly. Therefore, Bayesian statistics is discussed as a recommendable method.