General and specific utility measures for synthetic data

TL;DR

This paper develops and compares measures for evaluating the quality of synthetic data, focusing on general distribution similarity and specific analysis results, with theoretical derivations and practical examples.

Contribution

It adapts the pMSE utility measure for synthetic data, derives its distribution under correct model use, and compares it with other specific utility measures.

Findings

The asymptotic distribution of pMSE is derived for synthetic data.

Simulation confirms the theoretical distribution of the utility measure.

Comparison shows different utility measures provide complementary insights.

Abstract

Data holders can produce synthetic versions of datasets when concerns about potential disclosure restrict the availability of the original records. This paper is concerned with methods to judge whether such synthetic data have a distribution that is comparable to that of the original data, what we will term general utility. We consider how general utility compares with specific utility, the similarity of results of analyses from the synthetic data and the original data. We adapt a previous general measure of data utility, the propensity score mean-squared-error (pMSE), to the specific case of synthetic data and derive its distribution for the case when the correct synthesis model is used to create the synthetic data. Our asymptotic results are confirmed by a simulation study. We also consider two specific utility measures, confidence interval overlap and standardized difference in summary statistics, which we compare with the general utility results. We present two examples examining this comparison of general and specific utility to real data syntheses and make recommendations for their use for evaluating synthetic data.