Coping with extra Poisson variability in the analysis of factors influencing vaginal ring expulsions

The vaginal ring is one method of contraception currently under investigation and development by the Human Reproduction Programme of WHO. One factor that reduces its acceptability is that some women experience involuntary expulsions of the ring. WHO have collected prospective data on 1005 women from 19 centres worldwide to investigate various aspects of ring use including factors that might affect expulsions. For each subject the data include number of expulsions, age, parity, ponderal index, number of days of ring use and health care centre. To model the factors influencing expulsion, the number of expulsions was first considered as a Poisson variate with mean directly proportional to the log of the duration of ring use. Such a model gave a poor description of the data and it appeared that the number of expulsions was considerably over-dispersed for an assumed Poisson variate. This paper examines a variety of strategies for coping with the resulting lack of fit of the model. It turns out that a truncated Poisson model gives a better description of the expulsion data and that health care centre and parity influence the rates.