Advanced Analysis of Variance, Random Effects and Mixed Effects Models

In clinical trials it is common to assume a fixed effects research model. This means that the patients selected for a specific treatment are assumed to be homogeneous and have the same true quantitative effect and that the differences observed are residual, meaning that they are caused by inherent variability in biological processes, rather than some hidden subgroup property. If, however, we have reasons to believe that certain patients due to co-morbidity, co-medication, age or other factors will respond differently from others, then the spread in the data is caused not only by the residual effect but also by between patient differences due to some subgroup property. It may even be safe to routinely treat any patient effect as a random effect, unless there are good arguments no to do so. Random effects research models require a statistical approach different from that of fixed effects models.^1–3

With the fixed effects model the treatment differences are tested against the residual error, otherwise called the standard error. With the random effects models the treatment effects may be influenced not only by the residual effect but also by some unexpected, otherwise called random, factor, and so the treatment should no longer be tested against the residual effect. Because both residual and random effect constitute a much larger amount of uncertainty in the data, the treatment effect has to be tested against both of them.^4,5