Statistical evaluation of relationships between analgesic dose and ordered ratings of pain relief over an eight-hour period.

Statistical considerations are discussed for the application of alternative methods to a clinical trial involving repeated ordinal ratings and multiple dosage levels of active drugs. Analyses included summary measures traditionally employed in studies of acute pain: sum of pain intensity differences from baseline, total pain relief, and total pain half gone. Estimators and confidence intervals of relative potency are developed for univariate and multivariate situations, using weighted least squares analysis with mean response and variances from Taylor series linearizations. The estimates from these methods are compared to those from traditional methods, such as ordinary least squares regression and Fieller's method for confidence intervals, as well as those from more recent developments, such as generalized estimating equations and sample survey data regression. A double-blind, two-center, randomized clinical trial of acute pain relief comparing placebo with two analgesics, each at two dosage levels, over an 8-hr period serves as an illustrative example for these techniques and comparisons.