Mixture randomized item-response modeling: a smoking behavior validation study

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Misleading response behavior is expected in medical settings where incriminating behavior is negatively related to the recovery from a disease. In the present study, lung patients feel social and professional pressure concerning smoking and experience questions about smoking behavior as sensitive and tend to conceal embarrassing or threatening information. The randomized item-response survey method is expected to improve the accuracy of self-reports as individual item responses are masked and only randomized item responses are observed. We explored the validation of the randomized item-response technique in a unique experimental study. Therefore, we administered a new multi-item measure assessing smoking behavior by using a treatment–control design (randomized response (RR) or direct questioning). After the questionnaire, we administered a breath test by using a carbon monoxide (CO) monitor to determine the smoking status of the patient. We used the response data to measure the individual smoking behavior by using a mixture item-response model. It is shown that the detected smokers scored significantly higher in the RR condition compared with the directly questioned condition. We proposed a Bayesian latent variable framework to evaluate the diagnostic test accuracy of the questionnaire using the randomized-response technique, which is based on the posterior densities of the subject's smoking behavior scores together with the breath test measurements. For different diagnostic test thresholds, we obtained moderate posterior mean estimates of sensitivity and specificity by observing a limited number of discrete randomized item responses
Original languageEnglish
Pages (from-to)4821-4837
JournalStatistics in medicine
Issue number27
Publication statusPublished - 10 Jun 2013


  • Randomized response
  • Classification probabilities
  • Diagnostic test accuracy
  • Mixture item response theory
  • Validation


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