The Negative Binomial Model and the Denominator Problem in a Rural Family Practice

Much accurate health services and epidemiologic research in primary care is impeded by an inability to determine or estimate practice size in many countries. While the number of patients attending a practice is known, the number of non-attending members is not. Much of the work aimed at solving the denominator problem has focused on mathematical models for estimating the non-attenders. Of these, the negative binomial distribution of illness episodes received considerable early attention because of its success in British general practices. Enthusiasm for the negative binomial distribution waned when its application in non-capitated practices was largely unsuccessful. However, these American studies contained major biases, particularly in terms of independent knowledge of practice size and the potential for frequent usage of other primary care services. The negative binomial distribution was re-evaluated in a rural Canadian practice where there was only limited opportunity for external service utilization and where the practice's patient list had been subjected to separate validation. It fits well with the distribution of illness episodes in each of two consecutive 12-month periods and provided accurate estimates of practice size. It did not function well with the distribution of patient visits. This observation regarding the negative binomial distribution is discussed in the context of further searches for a solution to the denominator problem.