A Proportional Odds Beta-Binomial Model for Evaluating the Effect of Treatment in Cross-Over Studies with Baseline Covariates: An Application to Condom Failure Data

Abstract

Cross-over trials with correlated Bernoulli outcomes are common designs. In condom functionality studies, for example, an indicator of condom failure is reported for each sex act using standard or experimental condoms. Two popular analysis methods for such data are Generalized Estimating Equations and logit-normal random effects models. An alternative random effects model, the beta-binomial, is commonly used in contexts involving only between-cluster effects. The flexibility of the beta distribution and the interpretation of random effects as cluster-specific failure probabilities make it appealing, and we consider an extension of the model to account for within-cluster treatment effects using proportional odds assumptions.

Keywords:

• Beta-binomial
• Condom failure
• Cross-over

Mathematics Subject Classification:

• Primary 62J02
• Secondary 62-07

Acknowledgments

An earlier version of this article was submitted by N. Cheung Hall to the Department of Biostatistics, The University of North Carolina at Chapel Hill, in partial fulfillment of the MPH degree. Funding for this research was supported in part by funds from the United States Agency for International Development (USAID) cooperative agreement GPO-A-OO-05-00022-00. The views expressed in this article, however, do not necessarily reflect those of the funding agency. The authors wish to thank Rosalie Dominik and Pai-Lien Chen for helpful comments and suggestions on improving the manuscript.

Notes

^aWith logit-link and independent working correlation matrix.

^aCouples used an average of 3.82 latex and 3.76 experimental condoms, with a maximum of 4 per type.

^aEstimate of mean couple-specific failure probability for latex type (for beta-binomial model) or population average failure probability for latex type (for GEE analysis). Parameter not in logit-normal model.

^bOdds ratio for condom failure, experimental versus latex condom type.

^cWith independent working correlation matrix.

^aWith independent working correlation matrix.

^†Assuming 250 couples using 5 control and 5 experimental condoms, with 2500 replicates per condition.

^aFor nominal α = 0.05 level test of H 0: OR = 1 vs. H 1: OR ≠ 1 using default Z- and T-statistics in SAS v9.

^bCouple-specific control condom failure probability sampled from Beta distribution with mean of 0.02 and dispersion parameter chosen to provide a correlation of 0.15 between condom uses.

^cRandom effect sampled from normal (−5.9, 4.9) distribution, corresponding to a mean control condom failure probability of ∼0.02 and a correlation of ∼0.15 between control condom uses.

^dUsing independent working correlation matrix.