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Whatever the type of trial, it is usually convenient to think of the underlying structure of the design in terms of a statistical model. This model encapsulates the question we are intending to answer. Once the model is specified, the object of the corresponding clinical trial (and hence the eventual analysis) is to estimate the parameters of this model as precisely as is reasonable.

Suppose in a particular trial, we wish to compare two treatments, Standard (S) and Test (T). We can use an indicator variable to identify the treatment received by a patient, by setting x = 0 and x = 1 for the two treatments respectively. If the outcome of interest is a continuous variable, y, then this is related to the treatment or intervention by the linear regression equation

(2.1)

In this equation, β₀ and β_Treat are constants and are termed the parameters of the model. Here, β_Treat is the coefficient which represents the magnitude of the difference between the treatments and so to determine its value is the major focus for the clinical trials. In contrast, ε represents the noise (or error) and this is assumed to be random and have an independent Normal distribution with mean value 0 across all subjects recruited to the trial and standard deviation (SD), σ. The object of a trial would be to estimate β₀ and β_Treat, and we write such estimates as b₀ and b_Treat to distinguish them from the corresponding parameters.