A new non‐randomized model for analysing sensitive questions with binary outcomes

Abstract

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.

A Survey Design for a Sensitive Binary Variable Correlated with Another Nonsensitive Binary Variable

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Tian et al (2007) introduced a so-called hidden sensitivity model for evaluating the association of two sensitive questions with binary outcomes. However, in practice, we sometimes need to assess the association between one sensitive binary variable (e.g., whether or not a drug user, the number of sex partner being ⩽1 or >1, and so on) and one nonsensitive binary variable (e.g., good or poor health status, with or without cervical cancer, and so on).

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Bayesian randomized item response modeling for sensitive measurements

“…Also, two-stage RR methods requiring two randomizing devices (e.g., Kim & Elam, 2005;Kim & Warde, 2005;Mangat, 1994) and optional randomized response methods (e.g., Chaudhuri & Mukerjee, 1985;Chaudhuri & Saha, 2005;Saha, 2007) were developed to reduce the sampling variance. Many authors explored RR techniques handling two sensitive characteristics at the same time (e.g., Christofides, 2005;Tian, Yu, Tang, & Geng, 2007). Methods not requiring direct answers to sensitive questions among others were addressed by Kuk (1990), Christofides (2003) and Tian et al (2007).…”

“…Many authors explored RR techniques handling two sensitive characteristics at the same time (e.g., Christofides, 2005;Tian, Yu, Tang, & Geng, 2007). Methods not requiring direct answers to sensitive questions among others were addressed by Kuk (1990), Christofides (2003) and Tian et al (2007).…”

“…In the method of hidden sensitivity (HS) described by Tian et al (2007), two sensitive questions (e.g. a question on drug abuse history and a question on AIDS history) with binary outcomes are handled simultaneously.…”

“…The methods were developed in the late 70's (Takahasi & Sakasegawa, 1977) and have received increased attention in the past five years. Related developments are the hidden sensitivity method (Tang, Tian, Tang, & Liu, 2009;Tian et al, 2007), the triangular method (Tan, Tian, & Tang, 2009;Tian, Tang, Liu, Tan, & Tang, 2011;Yu, Tian, & Tang, 2008), the crosswise method (Jann, Jerke, & Krumpal, 2012;Yu et al, 2008), the method of single sample count (Petróczi et al, 2011), and the unmatched count technique (Coutts & Jann, 2011). The techniques are usually claimed to be free from the limitations of the randomized approach and to increase the relative efficiency and the degree of privacy protection.…”