A Measure of Disclosure Risk for Microdata

Protection against disclosure is important for statistical agencies releasing microdata files from sample surveys. Estimates of simple measures of disclosure risk can provide useful evidence to support decisions about release. We propose a new measure of disclosure risk: the probability that a unique match between a microdata record and a population unit is correct. We argue that this measure has at least two advantages. First, we suggest that it may be a more realistic measure of risk than two measures currently used with census data. Second, we show that it may be estimated consistently from sample data without making strong modelling assumptions. This is a surprising finding, in its contrast to the properties of the two ‘similar’ established measures. As a result, this measure has potentially useful applications to sample surveys. Moreover, we propose a simple variance estimator and show that it is consistent. We also show that the measure and its estimation may be extended to allow for misclassification of identifying variables and to allow for certain complex sampling schemes. We present a numerical study based upon 1991 census data for some 450,000 enumerated individuals in one area of Great Britain. We show that the theoretical results on the properties of the point estimator of the measure of risk and its variance estimator hold to a good approximation for these data.