Evaluation of alternative statistical models for crossover studies to demonstrate caffeine adjuvancy in the treatment of tension headache

Abstract

This paper discusses alternative statistical models for the analysis of six crossover studies to determine whether better relief of tension headache occurs from treatment with an analgesic plus caffeine (C) than with the analgesic alone (A) or with placebo (P). Each patient in these crossover studies randomly received a pair of distinct medications in such a way as to treat the first two of four headaches with the initial medication in the pair and to treat the third and fourth headaches with the last medication in the pair. In order to have greater power for the C versus A comparison, three times as many patients were randomly assigned to the A:C and C:A sequence groups as to the A:P, C:P, P:A, and P:C sequence groups.

An issue of statistical interest for these crossover studies is the extent to which the possibility of unequal carryover effects of the three medications influences the roles of alternative models for data analysis and the interpretation of results. When carryover effects for all three medications are equal, univariate analysis of variance for the difference scores between the average response for the first two headaches and the average response for the third and fourth headaches for each patient provides nearly the same power for pairwise treatment comparisons as more comprehensive multivariate methods for all four headaches. However, for comparisons concerning carryover effects and for treatment comparisons with adjustment for carryover effects, multivariate methods encompassing all four headaches jointly can provide greater power than univariate analysis for difference scores, particularly when there is low intraclass correlation for responses within the same patient. Another noteworthy role for multivariate methods in situations with potentially unequal carryover effects is their capacity to clarify whether multiple types of carryover effects occur across the second, third, and fourth headaches in the respective sequence groups.

Multivariate models with alternative specifications of carryover effects are fit to the data from the six crossover studies to compare C, A, and P by weighted least squares. The role of potential variation among centers is addressed in these analyses by the use of stratified proportional means over centers, means of center means, and means ignoring centers. The primary focus of attention in the respective analyses is the evaluation of treatment comparisons with and without adjustment for potential differences among carryover effects of the treatments. Comparisons among carryover effects are assessed as well, but they mainly serve a background purpose since the principal issue is the extent to which findings for treatment comparisons are similar across alternative ways of accounting for potential carryover effects.

For all models, the average predicted response across all headaches treated with C was significantly better than that for A or P. For models that adjusted treatment effects for carryover effects in a statistically efficient way, the adjusted direct treatment effect of C was significantly better than that of A or P. Thus, the superiority of C over A found robust support from models both with and without adjustment for potential differences among carryover effects of the treatments.

Keywords:

• Caffeine adjuvancy
• Carryover effects
• Crossover designs
• Multivariate linear models
• Tension headache
• Weighted least squares