Survey Methodology
Investigating alternative estimators for the prevalence of serious mental illness based on a two-phase sample

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by Phillip S. Kott, Dan Liao, Jeremy Aldworth, Sarra L. Hedden, Joseph C. Gfroerer, Jonaki Bose and Lisa ColpeNote 1

  • Release date: June 21, 2018
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Abstract

A two-phase process was used by the Substance Abuse and Mental Health Services Administration to estimate the proportion of US adults with serious mental illness (SMI). The first phase was the annual National Survey on Drug Use and Health (NSDUH), while the second phase was a random subsample of adult respondents to the NSDUH. Respondents to the second phase of sampling were clinically evaluated for serious mental illness. A logistic prediction model was fit to this subsample with the SMI status (yes or no) determined by the second-phase instrument treated as the dependent variable and related variables collected on the NSDUH from all adults as the model’s explanatory variables. Estimates were then computed for SMI prevalence among all adults and within adult subpopulations by assigning an SMI status to each NSDUH respondent based on comparing his (her) estimated probability of having SMI to a chosen cut point on the distribution of the predicted probabilities. We investigate alternatives to this standard cut point estimator such as the probability estimator. The latter assigns an estimated probability of having SMI to each NSDUH respondent. The estimated prevalence of SMI is the weighted mean of those estimated probabilities. Using data from NSDUH and its subsample, we show that, although the probability estimator has a smaller mean squared error when estimating SMI prevalence among all adults, it has a greater tendency to be biased at the subpopulation level than the standard cut point estimator.

Key Words:      Bias; Bias-corrected estimator; Domain; Survey-sampling theory; Asymptotic.

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How to cite

Kott, P.S., Liao, D., Aldworth, J., Hedden, S.L., Gfroerer, J.C., Bose, J. and Colpe, L. (2018). Investigating alternative estimators for the prevalence of serious mental illness based on a two-phase sample. Survey Methodology, Statistics Canada, Catalogue No. 12-001-X, Vol. 44, No. 1. Paper available at https://www150.statcan.gc.ca/n1/pub/12-001-x/2018001/article/54928-eng.htm.

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ISSN : 1492-0921

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Survey Methodology publishes articles dealing with various aspects of statistical development relevant to a statistical agency, such as design issues in the context of practical constraints, use of different data sources and collection techniques, total survey error, survey evaluation, research in survey methodology, time series analysis, seasonal adjustment, demographic studies, data integration, estimation and data analysis methods, and general survey systems development. The emphasis is placed on the development and evaluation of specific methodologies as applied to data collection or the data themselves. All papers will be refereed. However, the authors retain full responsibility for the contents of their papers and opinions expressed are not necessarily those of the Editorial Board or of Statistics Canada.

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Published by authority of the Minister responsible for Statistics Canada.

© Her Majesty the Queen in Right of Canada as represented by the Minister of Industry, 2018

Use of this publication is governed by the Statistics Canada Open Licence Agreement.

Catalogue No. 12-001-X

Frequency: Semi-annual

Ottawa

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Table of contents

Abstract - Article main page
Section 1. Introduction
Section 2. Some estimators
Section 3. The MHSS subsample
Section 4. Some concluding remarks
References

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