A Data Disclosure Policy for Count Data Based on the COM-Poisson Distribution

Count data arise in various organizational settings. When the release of such data is sensitive, organizations need information-disclosure policies that protect data confidentiality while still providing data access. In contrast to extant disclosure policies, we describe a new policy for count tables that is based on disclosing only the sufficient statistics of a flexible discrete distribution. This distribution, the COM-Poisson, well approximates Poisson counts but also under- and over-dispersed counts. The sufficient statistics mask the exact cell counts and often also the table size. Under the scenario of a data holding agency and a data snooper, we show that this policy has low disclosure risk with no loss of data utility: Usually, many count tables correspond to the disclosed sufficient statistics. Furthermore, these count tables are equally likely to be the undisclosed table. Finding these solutions requires solving a system of linear equations, which are underdetermined for tables with more than three cells, and can be computationally prohibitive for even small tables. We also consider cell-specific interval bounds, a commonly used disclosure limitation policy, and compare