Development of a three-stage randomized response model for sensitive surveys with a case study on drug consumption

Randomized response methods are commonly used in sensitive surveys to reduce response bias and to protect respondent confidentiality. However, existing randomized response models cannot achieve high estimation efficiency without sacrificing privacy. In this paper we propose a new three-stage randomization model to estimate the population proportion of a sensitive characteristic. The proposed model adds an extra stage of response, which allows the response mechanism to be more flexible and improves the precision of estimation. Expressions for variance and percentage relative efficiency (PRE) are derived to study the theoretical properties of the proposed model. Its performance is compared with the Warner, Huang, and Govardhana and Sarjinder randomized response models under different values of the sensitive proportion and different sample sizes. The simulation studies conducted on a large scale and the real drug consumption survey show that the proposed model always has lower variance and higher PRE than the existing models. The empirical results indicate that the proposed three-stage randomized response model is a more efficient and reliable framework for sensitive surveys while preserving the privacy of the respondents.