On Consistency in Multi-Question Negative Surveys with Application to Healthcare Data Collection

The negative survey could preserve the privacy of individuals when collecting sensitive information, which has received wide attention. The existing reconstruction methods of negative surveys are usually designed for the single question negative surveys. Although the reconstruction methods of single question negative surveys could also be applied to multiquestion negative surveys after minor modifications, the consistency between the joint distribution and the marginal distributions in the multiquestion reconstructed results has never been considered. In this paper, the concept of consistency in the multiquestion reconstructed results is defined. Then the consistency of the reconstructed results obtained by two typical reconstruction methods, i.e., NStoPS and NStoPS-I, is analyzed. Furthermore, a novel reconstruction method for multiquestion negative survey is proposed, which could return consistent and reasonable multiquestion reconstructed results. Finally, the simulated experimental results on collecting healthcare data also illustrate that the performance of our method is excellent in terms of accuracy.