Estimating treated prevalence and service utilization rates: assessing disparities in mental health

There is considerable public concern about health disparities among different cultural/racial/ethnic groups. Important process measures that might reflect inequities are treated prevalence and the service utilization rate in a defined period of time. We have previously described a method for estimating N, the distinct number who received service in a year, from a survey of service users at a single point in time. The estimator is based on the random variable 'time since last service', which enables the estimation of treated prevalence. We show that this same data can be used to estimate the service utilization rate, E(J), the mean number of services in the year. If the sample is typical with respect to the time since last visit, the MLE of E(J) is asymptotically unbiased. Confidence intervals and a global test of equality of treated prevalence and service utilization rates among several groups are given. A data set of outpatient mental health services from a county in New York State for which the true values of the parameters are known is analyzed as an illustration of the methods and an appraisal of their accuracy.