Mathematical Programming Models for Balancing Data Quality and Confidentiality in Tabular Data

1. Mathematical Programming Model for Controlled Tabular Adjustment (CTA) Statistical agencies use different methods to protect the confidentiality of tabular data. The most widely used method, complementary cell suppression, suppresses both primary (sensitive) and secondary (non-sensitive cells) to assure confidentiality. Despite its popularity, it suffers from severe limitations. Complementary cell suppression problem is an NP-hard problem, and thereby computationally difficult to solve. It generates tables with missing data and many end users find it difficult to analyse the resulting data from a statistical point of view. For example, users cannot easily estimate means or variance from this data. Finally, published data protected by cell suppression can be susceptible to possible disclosure. Dandekar and Cox (2002) proposed controlled tabular adjustment (CTA) that overcomes many of the problems associated with traditional cell suppression and other perturbation methods. CTA assures confidentiality of the data by setting sensitive cells to either of their predefined protection limits and preserves table additivity by making the best mutual use of sensitive cell and non-sensitive cell adjustments. It can also control adjustment at the individual cell level. CTA has the ability of simultaneously satisfying different types of statistical goals. For example, Cox and Kelly (2003, 2004) demonstrate how CTA can be used to preserve univariate and bivariate properties of tabular data. The end result is that users receive clean, complete, and statistically accurate tabular data. Figure 1 shows a mixed integer-programming model for CTA.