Use of the Beta‐Binomial Distribution to Model the Effect of Policy Changes on Appropriateness of Hospital Stays

Health services research data often consist of clusters of binary observations, such as serial observations of patients over the course of a hospital stay, that exhibit within‐cluster homogeneity. This paper demonstrates the use of the beta‐binomial regression model to investigate important questions that relate to health services research and cannot be answered by using standard logistic regression methods. The use of beta‐binomial models not only allows for the assessment of different probabilities according to covariates, but also permits the estimation of the degree of clustering. Application of beta‐binomial models to 750 and 633 hospital stays in 1988 and 1990 in a tertiary care hospital showed that the stays were shorter in 1990 but that a day of a stay in 1990 was more likely to be inappropriate. However, the models also showed that the propagation of inappropriateness within a stay was less in 1990 than in 1988. This analysis demonstrates the need to use relevant models for the study of complex relationships between policies affecting both the length of stay and the efficiency of hospital utilization.