Type Ⅱ Combination Questionnaire Model: A New Survey Design For A Totally Sensitive Binary Variable Correlated With Another Nonsensitive Binary Variable

Recently, Yu et al.(2013) introduced a combination questionnaire model to investi-gate the association between one sensitive binary variable and another non-sensitive binaryvariable. However, in practice, we sometimes need to assess the association between onetotally sensitive binary variable (e.g., the number of sex partner being3or>3, theannual income being$25000or>$25000, and so on) and one non-sensitive binaryvariable (e.g., good or poor health status, with or without cervical cancer, and so on). Toour knowledge, the survey design for addressing this issue and relevant statistical methodsare not available. By sufciently utilizing the information contained in the non-sensitivebinary variable, in this paper we propose a new survey design, called Type II combinationquestionnaire model, which consists of a four-category parallel questionnaire and a sup-plemental direct questionnaire. Likelihood-based methods including maximum likelihoodestimates, asymptotic and bootstrap confdence intervals of parameters of interest are de-rived. A likelihood ratio test is provided to test the association between the two binaryrandom variables. Bayesian methods are also presented. Simulation studies are performedand a cervical cancer data set in Atlanta is used to illustrate the proposed methods.