Applications Of Mixed Models In Clinical Trials

Analysis of variance and regression analysis have been the mainstay of statistical modeling for many years. These techniques usually have as a basic assumption that the residual or error terms are independently and identically distributed. Mixed models are an important new approach to modeling which allows us to relax the independence assumption and take into account more complicated data structures in a flexible way. There are many benefits to be gained from using mixed models. In some situations the benefits will be an increase in the precision of our estimates. In others, we will be able to make wider inferences. We will sometimes be able to use a more appropriate model, which will give us greater insight into what underpins the structure of the data.Many clinical trials are organized on a multi-centre basis, usually because there are an inadequate number of suitable patients in any single centre. The analysis of multi-centre trials often ignores the centers from which the data are obtained, making the implicit assumption that all centers are identical to one another. This assumption may sometimes be dangerously misleading. Mixed models can provide an insightful analysis of such a trial by allowing for the extent to which treatment effects differ from centre to centre. Even when the difference betweentreatments can be assumed to be identical in all centers, a mixed model can improve the precision of the treatment estimates by taking appropriate account of the centers in the analysis. In addition, the response to treatment is often assessed as a series of observations over time in a clinical trial. A mixed model analysis of such a study does not require complete data from all subjects. This results in more appropriate estimates of the effect of treatment and their standard errors. The mixed model also gives a wide variety of ways in which the successive observations are correlated with one another.ObjectivesThe purpose of this article is to demonstrate the process and usefulness of the mixed models by comparing it with the traditional statistical methods such as general linear models, repeated measures analysis of variance for analysis of a longitudinal dataset and a multi-center clinical trial dataset And we fit the random effects model, covariance pattern models, random coefficients models and generalized linear mixed models respectively, at the same time, we demonstrate the results in detail and make some explanations, comparisons as well.MethodsThe data considered were taken from a clinical trial of treatments for HBV in 144 patients, in which a baseline and three post-randomization measurements of outcomes were taken.As for quantitative dependent variables, fixed effects model can be fitted with GLM procedure in SAS, while mixed model can be fitted with MIXED procedure. But for categorical dependent variables, we made the chi square test and logistic regression for fitting fixed effects model (generalized linear models), and used the GLIMMIX procedure to fit generalized linear mixed models. What's more, Monte Carlo simulation was carried out by SAS macro RMNC.ResultsTake prothrombin activity (PTA) for example, we first used fixed effects model and discovered that there was a significant difference between A and B group with the p value of 0.0431;And even if the centre effect was controlled, the result did not change very much. Then random effects model was fitted and it also indicated there was a significant difference between the two groups, with the P value of 0.0414;in addition, it also showed that the centre effect variance component estimate was 69.53 while the residual variance component was 300.88, which indicated the variance of the dependent variable was mainly caused by patient effects not by center effects. What's more, we found that the outliers in the data would influence the results of random effects model greatly. But whether the number of observations will affect the results should be explored further.As for the repeated measures data in the clinical trial, we used the covariance pattern model to analyze serum total protein, and found when the covariance pattern was compound symmetry (CS), the model fitted the best. Then we used this covariance pattern to make other parameters estimates, and found that mere was no significant difference between A and B group, with the P value of 0.2845.Thirdly, to discuss the random coefficients model, we compared it with the repeated measures analysis of variance (RMAOV) in analyzing alanine aminotransferase (ALT) of the 144 patients in the same clinical trial. The repeated measures analysis of variance was used to compare group means on a dependent variable across repeated measurements of time. Time is often refened to as the within-subjects factor, whereas a fixed or nonchanging variable (e.g., treat) is referred to as the between-subjects factor. In this study, we compared differences in the ALT (dependent variable) across time (within-subjects factor) by treat and center (between-subjects factors). As a result, the repeated measures analysis of variance indicated that the P value for treatment effect was 0.0961, at the same time, the linear random coefficients model indicated that there was no significant difference between the two groups, with the P value of 0.9042. But thepolynomial random coefficients model indicated that there might be non-linear trend between alanine aminotransferase (ALT) and time.Finally, we took the adverse event for example to demonstrate the SAS procedure of GLIMMIX. The generalized linear model indicated mere was no significant difference between the two groups, and the generalized linear mixed model made the similar results with the P value of 0.1170. In addition, the generalized linear mixed model can take the center effect as random effects, so the results obtained can be inferenced and applied more reasonablely to other centers.ConclusionsMixed models take account of the covariance structure or interdependence of the data, whereas more conventional fixed effects methods assume that all observations are independent Therefore, mixed models may provide results that are more appropriate to the study design.The MIXED procedure of the SAS System provides a rich selection of covariance structures through the RANDOM and REPEATED statements. Modeling the covariance structure is a major hurdle in the use of the MIXED procedure. However, once the covariance structure is modeled, inference about fixed effects proceeds essentially as when using the GLM procedure. And the same comment applies to the GLIMMIX procedure of the SAS system.But traditional statistical models are simple and can be used easily;what's more, its results can be interpreted much easily, so it is acceptable for most people, especially for non-statistician. Certainly, traditional statistical models are less accurate and flexible.All in all, there is no single "correct" model in most situations and in fact models are rarely completely adequate. So the job of the statistical modeller is to choose that model which most closely achieves the objectives of the study.