Variant Poisson Item Count Technique with Non-Compliance †

In this article, we propose a variant Poisson item count technique (VPICT) that explicitly accounts for respondent non-compliance in surveys involving sensitive questions. Unlike the existing Poisson item count technique (PICT), the proposed VPICT (i) replaces the sensitive item with a triangular model that combines the sensitive and an additional non-sensitive item; (ii) utilizes data from both control and treatment groups to estimate the prevalence of the sensitive characteristic, thereby improving the accuracy and efficiency of parameter estimation; and (iii) limits the occurrence of the floor effect to cases where the respondent neither possesses the sensitive characteristic nor meets the non-sensitive condition, thus protecting a subset of respondents from privacy breaches. The method introduces a mechanism to estimate the rate of non-compliance alongside the sensitive trait, enhancing overall estimation reliability. We present the complete methodological framework, including survey design, parameter estimation via the EM algorithm, and hypothesis testing procedures. Extensive simulation studies are conducted to evaluate performance under various settings. The practical utility of the proposed approach is demonstrated through an application to real-world survey data on illegal drug use among high school students.