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The coding of the treatment effect

In the single-trial setting (see Chapter 3), the coding of the treatment effect (using e.g., -1/1, 1/0 or any other coding scheme) is essentially irrelevant. The same holds in the multiple-trial setting when models are considered in which treatment occurs as a fixed effect only. Indeed, in these scenarios, all treatment coding choices lead to an equivalent model fit and the parameters are connected by simple linear transformations.

In contrast, the choice for a 0/1 or -1/1 coding for treatment is relevant and impacts the results when mixed-effects models are used. Indeed, a 1/0 coding, for a positive-definite D matrix, forces the variability in the experimental arm to be greater than or equal to the variability in the control arm. A -1/1 coding on the other hand ensures that the same components of variability operate in both treatment arms (Burzykowski, Molenberghs, and Buyse, 2005; Molenberghs et al., 2010). In practice, both situations may be relevant and it is of importance to illicit views from the study investigators regarding the appropriate treatment coding scheme.

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