The Strategy Of Joint Bivariate Modeling And Implementation

Background:In many medical studies, the outcomes of interset are usually several. Modeling on different dependent variables repectively is choosed in most of Analytic process,especially when the types of dependent variables are different.In fact,in case of modeling related dependent variables, this method has low statistical efficiency and may get a contradictory conclusion.As a result,it is reasonable to put the correlation between dependent variables into consideration, which is the basis of parameter estimation.Methods:In multicentered clinical trials, it is requested to put the effect into consideration, according to cluster effect caused by the design and the way of randomization.For exemple, the data of SBP and DBP can be collected by different follow up, which means every patient has several values of blood pressure. To analyse this data, it is required to considerate not only the correlation of values in every follow up but the correlation between SBP and DBP. Another example is the data of the patients in multicentered clinical trial with the values of HBA1 c, FBG and other safety indexs.As for these kinds of data, the effect of every center and the correlation of outcomes should be considered.It differs with the correlation of repeated measures, while the correlation between different types of outcomes is supposed to be considerated.Content:This study is based on the theory of joint modeling focusing on the data with multiple dependent variables.And it ueses the multicentered clinical trial example to explore how to do bivariate regression and how to apply this method.What is more, this study uses copula function to join the two dependent variables. The overall results shows that this method can be used to explore the information concealed in the data and its statitical efficiency is much higher. In addition, in the analysis of regression with mixed typed dependent variables, it calculates explicitly the joint probability distribution,which makes the process of modeling much more flexible and general.Results:The study shows that the ICC should be used to test the homogeneity of the data in different center.This article realized the estimation and hypothesis testing of the stucture of variance/covariance by SAS.The reasonable estimation toward the hypothesis provides the basis for the strategy of joint modeling with two dependent variables.Facing the joint modeling of two variables with the same distribution,it is necessary to put the correlation into consideration firstly.On condition that they are normal distribution, coefficient of correlation is reanable to discribe the correlation between the variables.If they are binary distribution, it is acceptable to use contingency coefficient to represent the relationship of two dependent variables with the same binary distribution.This study uses the multicentered data of diabetes patients to test the effect of correlation between variables and analyse the center effect. And the software of MLWin is used to complete the parameter estimation and test the difference of effect between different dependent variables. Further more, it suggests that joint model not only provides more information than singular model but improves the statistical efficiency.In addition, it verifies the advantages and feasibility of multivariate multilevel model to solve the problem of correlated data.When the two dependent variables are different distribution, the problem that it is so hard to find the theoretical distribution is tough in regression analysis.The study introduces copula function to join two different distributions,which provides the possibility to do the regression analysis with the precisely distribution function.By SAS NLMIXED prcedure,the parameter estimation is finished successfully.The result shows the comprehensive effect of the drug and safety. And the criteria to choose the copula function is that scatter plot of simulated data combined with the index of Goodness of Fit.We try five copula functions to fit the model and build the likehood function tentatively. The outcome shows that gumble copula and normal copula are usually the optimal copula function.Furthermore,the feasibility of regression analysis of complex distribution based copula function is proved. And the comparison of algorithm, majorization of the estimation process can be done in the future.Conclusion:In clinical data,ignoring the correlation of outcome variables will induce mistaken conclusion.How to describe this correlation, how to explore the effect toword multiple dependent variables and how to judge the comprehensive effect of a independnt varibale are urgent issues to be solved. And the joint modeling strategy is one of the ways to cope with these problems. The application of copula function has its own unique superiority, broadening the scope of regression. It will be highlighted in the future research with great prospect of study and application.