Sensitivity of Responder Effects to Different Thresholds and Control Group Means on Patient-Reported Outcomes: Varying Group Standard Deviations.

Limited research has been conducted to assess the sensitivity of responder effects (i.e., the difference in proportion of response between treatment and control groups) between interventions to different dichotomous threshold scores created from a continuous patient-reported outcome (PRO) (e.g., within-patient improvement of 10 or more points in PRO scores). We investigated the subject in several complementary ways: (1) local sensitivity in magnitude to measure the impact on responder effect to small changes in the threshold value; (2) sensitivity in direction to capture changes in the direction of responder effects with changes in the threshold; (3) average sensitivity in magnitude to measure the impact on responder effect to uncertainty in the threshold; and (4) the standard deviation (width) of Holland's hill (distribution of responder effects across threshold scores) to gauge the robustness of responder effects to different thresholds. We focused on normally distributed outcomes where within-group standard deviations may differ between intervention groups. Our findings indicate that, relative to equal group standard deviation, unequal group standard deviations give consistently higher levels of sensitivity for very small increases in the threshold value. For the case of no mean continuous treatment effect, responder analyses will generally misrepresent the direction of mean treatment effect when there is unequal group variability in the continuous PRO measure. By quantifying and elucidating subtle points on the sensitivity of responder effects-and the additional challenges on interpretation imposed by unequal group standard deviations-this article could be useful in the careful design, analysis, and interpretation of PRO studies.