Investigating alternative ways of estimating the prevalence of serious mental illness using the National Survey on Drug Use and Health

The National Survey on Drug Use and Health (NSDUH) uses two phases of data collection to estimate prevalences of serious mental illness (SMI). The first phase is the NSDUH itself, a large self-administered survey on substance use and mental health. In the second phase, the Mental Health Surveillance Survey (MHSS), a subsample of respondents is drawn from the NSDUH and clinically evaluated for SMI. A prediction model for clinically-evaluated SMI (the “gold standard”) is fitted in this MHSS subsample and the results applied to the entire NSDUH sample. Currently, an unadjusted (model-based) cut-point estimator is computed by classifying NSDUH respondents as having or not having SMI based on a fitted logistic model with two covariates, one based on psychological distress scores and the other based on functional impairment scores.

We investigated several potential alternatives to this estimator based on the same logistic-model fit to 2008 and 2009 NSDUH/MHSS data. These included an unadjusted probability estimator, which assigns a probability of having SMI to everyone in the NSDUH, and bias-adjusted (model-free) versions of the cut-point and probability estimators.

We measured the standard errors of the competing estimators using linearization and, where necessary, Fay's version of balanced repeated. When not biased, the unadjusted probability estimator always had the smallest standard error. Due to the added error from estimating the model parameters, the unadjusted cut-point estimator, although never biased, sometimes had more standard error than estimating from the MHSS subsample directly. It was more efficient at estimating differences across years or between subpopulations.