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On the basis of model (2.1), the two fundamental issues in trial design to consider are as follows:

1 What levels of the design variable x to choose?

2 How many subjects should we recruit?

In this model, with x = 0 for the standard or control treatment, S, y₀ = β₀ and this represents the ‘true’ or population mean of this group, labelled μ_S. Alternatively, with x = 1, the sum y₁ = β₀ + β_Treat represents μ_T the population mean of group T. Thus, the difference, δ, between those receiving S and T, is y₁ − y₀ = β₀ + β_Treat − β₀ = β_Treat. From this β_Treat = μ_T − μ_S and β₀ = μ_S. Population means are estimated by sample means, in this case and so that the estimates of the parameters are b₀ = and b_Treat = − . The latter is the estimate of the true difference between treatments, δ = μ_T − μ_S.

In this example, Equation (2.1) describes the two‐group clinical trial of this chapter but, as we will see in other chapters, we can extend this model to describe more complex clinical trial designs although this basic type of equation encapsulates the essential structure of all our analyses.