Two sensitive characteristics and their overlap with two questions per card

Area of Science:

• Statistics
• Survey Methodology
• Biostatistics

Background:

• Accurate data collection on sensitive topics is crucial in medical and social sciences.
• Existing randomized response models face challenges in balancing privacy protection and estimation accuracy.

Purpose of the Study:

• To develop a new, unique unrelated question randomized response model.
• To provide unbiased estimators for sensitive characteristics and their overlap.
• To assess the privacy protection and efficiency of the proposed model.

Main Methods:

• Development of a novel randomized response model where each card contains two questions (either both sensitive or both unrelated).
• Derivation of unbiased estimators for prevalence and overlap of sensitive characteristics.
• Computation of variance expressions, relative efficiency, and relative privacy protection.
• Verification of estimator variances against Cramer-Rao lower bounds.

Main Results:

• The proposed model ensures respondent privacy through its unique question pairing.
• Unbiased estimators for sensitive characteristics and their overlap were developed.
• The model demonstrates competitive relative efficiency and privacy protection compared to existing methods.
• Variance expressions were derived and validated, with estimators for conditional proportion, relative risk, and correlation coefficient also discussed.

Conclusions:

• The developed randomized response model offers enhanced privacy protection.
• The model provides unbiased and validated estimators for sensitive data analysis.
• The proposed method is valuable for medical and social science studies requiring sensitive data collection.