Remarks on designs enriching for placebo non-responders.

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High response under placebo constitutes a concern in clinical studies, particularly in psychiatry. Discontinuation of placebo responders identified during a placebo run-in is often recommended to avoid failures of clinical trials in the presence of high placebo effects. Evidence for the benefit of this approach is ambiguous. We investigate under which conditions a placebo lead-in can be beneficial in the context of continuous data, assuming that the data in the placebo run-in and the treatment stage follow a bivariate normal distribution. Placebo responders are defined as patients with an effect during placebo lead-in which is larger than a pre-defined threshold on the absolute value or the absolute or relative change from baseline or a combination thereof. Data are less variable under either placebo or test treatment after placebo responders have been removed. Whether the effect of test over placebo increases or decreases after enrichment for placebo non-responders depends on the parameters of the distribution, in particular the covariance structure, and the threshold in the definition of placebo responders. The results apply in the continuous case, and the binary or ordinary case is not studied. The findings explain to some extent the ambiguity in the assessments of the usefulness of placebo lead-in periods in clinical trials; however, besides the clear statement on variability reduction, it is not straightforward to judge upfront whether placebo lead-in is useful. Concerns relating to the conduct and interpretation of results of such trials are mentioned.