ESTIMATING THE VARIANCE OF STANDARDIZED RATES OF RECURRENT EVENTS, WITH APPLICATION TO HOSPITALIZATIONS AMONG THE ELDERLY IN NEW-ENGLAND

Usual approaches for estimating the variance of a standardized rate ma y not be applicable to rates of recurrent events. Where individuals ar e prone to repeated health events, Greenwood and Yule (J R Stat Soc [A ], 1920;83:255-79) advocated use of the negative binomial distribution to account for departures from the assumption of randomness of recurr ent events required by the Poisson distribution. In this paper, the au thors implemented the negative binomial distribution in the computatio n of annual hospitalization rates within certain hospital market areas . Data used were from 1,549,915 New England residents aged 65 years or more who were enrolled in Medicare between October 1, 1988, and Septe mber 30, 1989, and who had 458,593 hospital admissions during that yea r. New England was partitioned into 170 hospital market areas ranging in population size from 162 to 70,821 elderly Medicare enrollees. The negative binomial distribution demonstrated substantially better fits than the Poisson distribution to the numbers of hospitalizations withi n hospital market areas. Estimated standard errors for indirectly stan dardized rates based on the negative binomial distribution were 25-51 percent higher than estimated standard errors that assumed an underlyi ng Poisson distribution. Using regression analysis to smooth overdispe rsion parameters across hospital market areas produced similar results . The approach described in this paper may be useful in estimation of confidence intervals for standardized rates of recurrent events when t hese events do not recur randomly.