Fig. 1: Data simulated with variable placebo response and additive (constant) treatment effect.

Treatment effect and measurement error were simulated on a zero-to-one scale, using a cutoff for response dichotomization of 0.55 (depicted by the horizontal black line) and with parameter values selected to achieve response rates similar to those reported by Gomeni, Hopkins, Bressole-Gomeni, and Fava [1] (~33% “D−P−”, ~25% “D+P−”, ~42% “D+P+”, delineated graphically by vertical grey lines). The probability of placebo response is known exactly in the simulation and increases from left to right, but the magnitude of the treatment effect is identical for all patients, corresponding to the fixed vertical distance between the two sigmoidal lines. As such, the additive nature of the simulated treatment effect is consistent with the meta-analytic findings of Whitlock, Woodward, and Alexander [5]. The figure therefore illustrates that, even if the probability of placebo response could be computed exactly on the basis of baseline and screening data, it would convey no value for trial enrichment. (This situation is, of course, unchanged when the probability of placebo response is instead estimated by an artificial neural net.) Moreover, the figure illustrates why the “D+P−” designation in itself is a misleading artifact of dichotomization and does not constitute a meaningful target for trial enrichment, since it identifies patients whose scores are near the boundary for dichotomization rather than patients with greater magnitudes of treatment effect. R code to generate this plot and the simulated data underlying it is provided as supplemental material.