A Bayesian model for estimating the effects of drug use when drug use may be under-reported

Authors

  • Garnett P. McMillan,

    Corresponding author
    1. Behavioral Health Research Center of the Southwest, A Center of the Pacific Institute for Research and Evaluation, Albuquerque, NM, USA and
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  • Edward Bedrick,

    1. Department of Mathematics and Statistics at the University of New Mexico, Albuquerque, NM, USA
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  • Janet C'deBaca

    1. Behavioral Health Research Center of the Southwest, A Center of the Pacific Institute for Research and Evaluation, Albuquerque, NM, USA and
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Garnett P. McMillan, Behavioral Health Research Center of the Southwest, A Center of the Pacific Institute for Research and Evaluation, 612 Encino Pl NE, Albuquerque, NM 87102, USA. E-mail: gmcmillan@bhrcs.org

ABSTRACT

Aims  We present a statistical model for evaluating the effects of substance use when substance use might be under-reported. The model is a special case of the Bayesian formulation of the ‘classical’ measurement error model, requiring that the analyst quantify prior beliefs about rates of under-reporting and the true prevalence of substance use in the study population.

Design  Prospective study.

Setting  A diversion program for youths on probation for drug-related crimes.

Participants  A total of 257 youths at risk for re-incarceration.

Measurements  The effects of true cocaine use on recidivism risks while accounting for possible under-reporting.

Findings  The proposed model showed a 60% lower mean time to re-incarceration among actual cocaine users. This effect size is about 75% larger than that estimated in the analysis that relies only on self-reported cocaine use. Sensitivity analysis comparing different prior beliefs about prevalence of cocaine use and rates of under-reporting universally indicate larger effects than the analysis that assumes that everyone tells the truth about their drug use.

Conclusion  The proposed Bayesian model allows one to estimate the effect of actual drug use on study outcome measures.

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