Affectioan Of Random Effects In The Analysis Of Multi-centre Clinical Trials

ObjectivesTo study the application of random effects model in multi-center clinical trial, and do simulation to compare with traditional method(not considering the center effect or the center~* treatment interaction) and fixed effects model(center as fixed effect).To study how different designs affect the accuracy and precision of variance components estimation in small sample size unbalanced one-way random effects models.To examine which of the three procedures(SAS,S-PLUS,STATA) would give the most appropriate confidence interval for the case study and give a reference to the parameter estimation of the random effects model.MethodsFirstly,we use SAS to generate the value of the primary endpoint(treatment group and control group) for each patient,then we use PROC PLAN statement to allocate the patients into each center(block randomization),after that we use SAS PROC MIXED to do estimation and compare the results of the different models. Secondary,seven different design structures are simulated under various conditions with respect to sample size,number of random effects,and size of the intraclass correlation coefficient,and restricted maximum likelihood estimation(REML) is compared with Bayesian estimation of the variance components using PROC MIXED in SAS.Thirdly,we use SAS to generate the datasets,and 5000 independent replications were simulated such that there is a±0.6%precision when estimating the coverage probability with 95%confidence.Ninety-five percent approximate REML confidence limits for between class variance were obtained from the PROC MIXED, LME,and XTMIXED procedures under a PC Windows operating system.Default settings for the REML maximization algorithms were used for each of the procedures.ResultsIn the analysis of multi-center clinical trial,the treatment effect estimation is unbiased in the different models,the absolute value of the bias is between 0.01 and 0.03,and the value of MSE(mean square error) is between 0.001 and 0.003.REML estimates were more accurate compared to Bayesian estimates,but Bayesian interval estimates of the between-class variance were more precise than the REML interval estimates.For both methods,accuracy improved with larger sample sizes and more random effects.Estimation of the within-class variance was more accurate and precise compared to the estimation of the between-class variance.The results obtained when between group variance equals 1.5 indicate that the confidence limits PROC MIXED are not satisfactory,and either those from LME or XTMIXED should be used instead.Second,they explore how the intraclass correlation affect the three procedures,showing that at small intraclass correlations the differences between PROC MIXED and the other two procedures become more pronounced.Moreover,the lengths of the confidence intervals of all three procedures become more biased upward with small intraclass correlations. ConclusionsIn the analysis of multi-center clinical trial,the traditional analytical methods, such as fixed effect ANOVA model,this method treat the center as fixed effect and we can not make wider inference.But the object of the clinical trial is to make a wider inference to the whole population,and the random effects model can consider the relationship between the data,treat the center as random effect,give the right estimation and test.For small sample unbalanced designs with small to moderate ICC values,REML estimation is recommended in terms of bias and mean squared error.Bayesian estimation is favored when considering interval estimation.For a small sample one-way random effects model case study,the confidence limits for the between group variance obtained from PROC MIXED differed substantially with those from LME and XTMIXED.Finally,this brief note reminds us that although modern computing and available statistical software have made mixed effects modeling much more popular to applied researchers than a few decades ago, one must still guard against their naive use when estimating confidence limits for variance components.The comparison of results from different statistical software packages can be beneficial,and when results differ,as in our case study,small scale simulations can assist in examining the validity of the results.