What Is the Numerical Nature of Pain Relief?

Pain relief, or a decrease in self-reported pain intensity, is frequently the primary outcome of pain clinical trials. Investigators commonly report pain relief in one of two ways: using raw units (additive) or using percentage units (multiplicative). However, additive and multiplicative scales have different assumptions and are incompatible with one another. In this work, we describe the assumptions and corollaries of additive and multiplicative models of pain relief to illuminate the issue from statistical and clinical perspectives. First, we explain the math underlying each model and illustrate these points using simulations, for which readers are assumed to have an understanding of linear regression. Next, we connect this math to clinical interpretations, stressing the importance of statistical models that accurately represent the underlying data; for example, how using percent pain relief can mislead clinicians if the data are actually additive. These theoretical discussions are supported by empirical data from four longitudinal studies of patients with subacute and chronic pain. Finally, we discuss self-reported pain intensity as a measurement construct, including its philosophical limitations and how clinical pain differs from acute pain measured during psychophysics experiments. This work has broad implications for clinical pain research, ranging from statistical modeling of trial data to the use of minimal clinically important differences and patient-clinician communication.