In clinical trials a fixed effects research model assumes that the patients selected for a specific treatment have the same true quantitative effect and that the differences observed are residual error. If, however, we have reasons to believe that certain patients respond differently from others, then the spread in the data is caused not only by the residual error but also by between-patient differences. The latter situation requires a random effects model.
To explain random effects models in analysis of variance and to give examples of studies qualifying for them.
If in a particular study the data are believed to be different from one assessing doctor to the other, and if we have no prior theory that 1 or 2 assessing doctors produced the highest scores, but rather expect there may be heterogeneity in the population of doctors at large, then a random effects model will be appropriate. For that purpose between-doctor variability is compared to within-doctor variability. If the data of 2 separate studies of the same new treatment are analyzed simultaneously, it will be safe to consider an interaction effect between the study number and treatment efficacy. If the interaction is significant, a random effects model with the study number as random variable, will be adequate. For that purpose the treatment effect is tested against the interaction effect. In a multicenter study the data are at risk of interaction between centers and treatment efficacy. If this interaction is significant, a random effects model with the health center as random variable, will be adequate. The treatment effect is tested not against residual but against the interaction. If in a crossover study a treatment difference is not observed, this may be due to random subgroup effects. A post-hoc random effects model, with patients effect as random variable, testing the treatment effect against treatments x patients interaction, will be appropriate.
Random effects research models enable the assessment of an entire sample of data for subgroup differences without need to split the data into subgroups. Clinical investigators, in general, are hardly aware of this possibility and, therefore, wrongly assess random effects as fixed effects leading to a biased interpretation of the data.
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