A SAS analyst fits PROC GENMOD to count data representing hospital readmissions per patient. The output shows significant overdispersion (deviance/DF = 3.2). Which distribution family should replace Poisson to better handle overdispersion?

C is correct because Poisson regression assumes mean = variance, but deviance/DF >> 1 indicates overdispersion (variance > mean). The negative binomial distribution includes an extra dispersion parameter allowing variance to exceed the mean, making it appropriate for overdispersed count data. In PROC GENMOD, specify DIST=NEGBIN. A (binomial) is for proportion/count-out-of-total data, not open-ended counts. B (gamma) is for continuous positive values, not counts. D (normal with log link) is a log-linear model that does not constrain to integer counts.