Leveraging randomized response frameworks to enhance sensitive data acquisition: implications for data regarding public health.

Traditional survey methods make it difficult to collect sensitive data, as respondents provide false information or deliberately refuse to answer. The current investigation presents innovative methods utilizing multi-stage randomized response models (MRDRMs) to tackle challenges in precisely quantifying sensitive numerical variables while safeguarding respondent anonymity. The MRDRMs framework, comprising two as well as three-stage mathematical models. To employ two randomized response mechanisms designed to improve privacy protection and estimation efficiency to address perceptions like social desirability and over-estimation, which are prevalent in sensitive public health data collection. The main problem addressed in this study is the difficulty of obtaining precise estimates of sensitive quantitative variables because respondents often hesitate to provide truthful answers due to privacy concerns, fear, and social desirability bias. The incorporation of substantial randomization stages enables the models to provide unbiased and precise estimates of means and sensitivity levels, thereby ensuring the reliability of the data while reducing the psychological strain on participants. Theoretical analysis, particularly simulations conducted using Monte Carlo methods, suggests that MRDRMs, in both two-stage and three-stage formats, significantly improve the precision and relative efficiency of estimates compared to conventional randomized response strategies. The empirical validation carried out via a cross-sectional survey in the districts of Faisalabad, Lahore, Multan, and Rawalpindi in Punjab, Pakistan, examined not sufficiently reported COVID-19 cases along with vaccine hesitancy, thereby affirming the practical significance of the MRDRMs methods. The findings demonstrate a substantial improvement in estimation accuracy accompanied by reduced variance compared to conventional approaches. The results highlighting the effectiveness of MRDRM-I and MRDRM-II as robust methods for sensitive data collection. The findings from this research highlight the potential of MRDRMs for enhancing the acquisition and evaluation regarding sensitive data, strengthening consistent, ethical, and tangible results in research related to public health. These improvements strengthen privacy protection and enhance the validity of responses in sensitive surveys, offering meaningful contributions to public health monitoring and evidence-based policy development at the global level. The proposed models can be applied in public health surveillance, epidemiological studies, social science research, and policy-sensitive domains requiring accurate and privacy-preserving data collection.