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A new non‐randomized model for analysing sensitive questions with binary outcomes
Author(s) -
Tian GuoLiang,
Yu JunWu,
Tang ManLai,
Geng Zhi
Publication year - 2007
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.2863
Subject(s) - randomized response , binary number , respondent , statistics , computer science , type i and type ii errors , binary data , set (abstract data type) , sample size determination , odds , likelihood ratio test , mathematics , logistic regression , estimator , arithmetic , political science , law , programming language
We propose a new non‐randomized model for assessing the association of two sensitive questions with binary outcomes. Under the new model, respondents only need to answer a non‐sensitive question instead of the original two sensitive questions. As a result, it can protect a respondent's privacy, avoid the usage of any randomizing device, and be applied to both the face‐to‐face interview and mail questionnaire. We derive the constrained maximum likelihood estimates of the cell probabilities and the odds ratio for two binary variables associated with the sensitive questions via the EM algorithm. The corresponding standard error estimates are then obtained by bootstrap approach. A likelihood ratio test and a chi‐squared test are developed for testing association between the two binary variables. We discuss the loss of information due to the introduction of the non‐sensitive question, and the design of the co‐operative parameters. Simulations are performed to evaluate the empirical type I error rates and powers for the two tests. In addition, a simulation is conducted to study the relationship between the probability of obtaining valid estimates and the sample size for any given cell probability vector. A real data set from an AIDS study is used to illustrate the proposed methodologies. Copyright © 2007 John Wiley & Sons, Ltd.