Abstract
For any particular psychological instrument, published normative distributions have been derived in one to at most a few specific "reference" populations. Here a method is provided for estimating a normative distribution pertinent to the specific population being evaluated in a randomized clinical trial. Normative quantiles are obtained using quantile regression, a method chosen for its flexibility in that no assumptions are made about the parametric form (e.g., Gaussian) of the normative distribution to be estimated. Outcome is regressed on disease severity for the τth quantile using that sample of consented participants who were not randomized because they fell below the trial's disease severity entry criterion. The τth quantile of the normative distribution is then estimated by the intercept of this fitted regression function, which corresponds to severity of zero. Additional covariates that explain variation in outcome may be included to permit adjustment for shifts in their distributions between the randomized and non-randomized samples. The method is illustrated using data on a depression instrument (GRID Hamilton Rating Scale for Depression) and a neurocognitive instrument (CogScreen Pathfinder Number) from a multicenter clinical trial in sleep apnea patients.