Pediatric Pain, Predictive Inference, and Sensitivity Analysis

The understanding, prevention, and treatment of pain is of great importance to medical science. Children were asked to immerse their hands in cold water until they were unable to tolerate the pain of the cold. The length of time that they kept their hands immersed is a measure of pain tolerance. Two factors were studied. One factor is a child's Coping Style (CS) with the pain (attenders pay attention to the pain, distracters think of other things), and it was assessed at a baseline trial. The other factor is Treatment (TMT), one of three counseling interventions (a null intervention, counseling to attend, or counseling to distract), and was randomly applied prior to the response. The covariate is a baseline measure of pain tolerance prior to the intervention. Distracters, taught to distract, tolerated the pain much better than any other group. No strategy improved attenders' pain tolerance. This article analyzes this data from a predictive Bayesian viewpoint. The assumption of constant variance is not met on the original scale, and some of the data is censored; furthermore, the censoring model is unknown. Simultaneous transformation of the response and baseline is used to search for a scale where the variance is constant. Predictive inference is used to provide interpretable inferences. A sensitivity analysis is used to determine whether the treatment of the censored data matters. Without the sensitivity analysis, we are left wondering whether the conclusions rest on a true underlying treatment effect or on cases of questionable quality. In spite of a devil's-advocate effort to produce an alternative model which leads to contradictory conclusions, no such model was found.