Probabilistic models to analyze psychiatric contacts

Abstract

SummaryObjective – To present three probabilistic models (Poisson, negative binomial, Waring) to analyze the distribution of the number of contacts of patients followed using a psychiatric case register. Design – Longitudinal to obtain the distribution of the number of contacts (during 91 days following that of the first contact) observed on patients followed using the South-Verona Psychiatric Case Register during the period 1/1/79-31/12/91. Results – There were a total number of 6913 contacts on 3454 subjects. The chi-square test for the goodness of fit yields a significant result both for the Poisson distribution (3580 with 6 degrees of freedom, p < 0.001) and for the negative binomial distribution (65.47 with 18 degrees of freedom, p < 0.001); on the other hand a non significant result was obtained for the Waring distribution (25.31 with 19 degrees of freedom, p = 0.151). Conclusions – The Poisson distribution gave a very poor fit for the distribution of contacts. The negative binomial distribution could be employed to analyze the pattern of contacts when the right tail of the distribution is not important. The Waring distribution is the best of the three presented. Moreover, the variance of the Waring distribution can be decomposed in three components: a random component, a component which accounts for endogenous factors and another component which accounts for esogenous factors. Therefore the Waring distribution is useful when one wants to make comparisons between psychiatric case registers of the same country or of different countries.