Testing microbiologic response to antiinfective medications with incomplete data

Clinical trials of antiinfective medications often require estimates of the proportions of patients, n, who are free of disease-causing pathogens at the end of treatment, as well as the proportions of all pathogens that have been eradicated. Each patient is infected with several species of pathogens, but the response to study medication for some of these pathogens may be unknown because some specimens were lost or because the patient received nonstudy medication that was known to be effective against these species. This paper develops a statistical model that estimates pi for each treatment and that accounts for the unknown pathogen responses as well as overdispersion of the remaining responses due to within-patient effects. The data are modeled with the Poisson distribution for the numbers of pathogen species per patient and the beta-binomial model for pathogen eradication. The Poisson and beta-binomial parameters are estimated through maximum likelihood estimation, and the treatment difference in the pi valves and its standard error are estimated by transforming the underlying parameters. Confidence intervals based on these estimates are constructed to test the hypothesis of noninferiority of the test treatment.