Releasing confidential microdata as synthetic data

In SynthesizerPlus: Synthetic Data Generation with Copulas, Evaluation and Multi-Format I/O

knitr::opts_chunk$set(collapse = TRUE, comment = "#>", fig.width = 7,
                      fig.height = 4, dpi = 72, out.width = "100%")

Statistical offices and survey organisations hold microdata — census records, labour force or household budget surveys — that cannot be published because individuals could be identified and their confidential answers disclosed. A synthetic version of the file, generated from a model fitted to the confidential data, can be released instead: it reproduces the statistical structure, but its records are not real persons.

This vignette goes through such a release step by step, and shows how to choose how much noise is introduced, by looking at disclosure risk and analytical utility together.

library(SynthesizerPlus)
library(ggplot2)

The confidential file

census_sim is a simulated census-like file with 5000 persons (it contains no real data, so the example can be shared). It has a direct identifier, demographic variables that an intruder could know about a person (key variables or quasi-identifiers), and confidential variables.

str(census_sim)
keys <- c("age", "sex", "region", "household_size")   # what an intruder may know
sensitive <- c("income", "education")                 # what must be protected

Step 1: how risky would releasing the real data be?

disclosure_risk() measures the two classical risks.

• Identity disclosure: records that are unique on the key variables can be recognised. replicated_uniques is the share of these unique key combinations that also occur exactly once in the released file.
• Exact copies: synthetic records identical to a real record on all variables except the direct identifier (ignore = "person_id").
• Attribute disclosure: an intruder who knows a person's keys looks up the matching records in the released file and guesses the sensitive values (most frequent category, or median for numeric variables, correct if within 10%). This is the correct attribution probability (CAP). It is compared with a baseline guess that uses no microdata at all.

risk_real <- disclosure_risk(census_sim, census_sim, keys = keys, target = sensitive,
                             ignore = "person_id")
risk_real

A third of the persons are unique on four harmless-looking variables, and for them the intruder would learn income and education with certainty.

Step 2: a synthetic file

The synthesizer is fitted to the confidential file. The direct identifier is declared in id_cols (it is replaced by new, meaningless identifiers), and the model is stratified by employment and sex, because income depends strongly on employment status.

fit <- fit_synthesizer(census_sim, id_cols = "person_id",
                       by = c("employment", "sex"), knots = 500)
syn <- generate(fit, seed = 1)
head(syn)
disclosure_risk(census_sim, syn, keys = keys, target = sensitive,
                ignore = "person_id")

The correct attribution probabilities fall to — or below — the baseline: knowing a person's age, sex, region and household size and looking them up in the synthetic file tells the intruder no more about their income or education than general statistics do. Even the replicated uniques are mostly coincidences, since synthetic key combinations are generated at random; no synthetic record is a copy of a real one.

The argument knots = 500 stores each continuous distribution through 500 quantiles instead of all 5000 observed values, so that the fitted model itself contains no individual values.

Step 3: near-copies and the amount of noise

Fully synthetic data already protect against attribute disclosure. The remaining risk is that some synthetic records happen to be very close to a real person — close enough to be taken as that person. dcr() measures it: close_share is the share of synthetic records that are closer to a real record than 95% of the real persons are to their nearest real neighbour. If synthetic records are no closer to real persons than real persons are to each other, close_share is about 5%; clearly larger values signal near-copies.

conf <- census_sim[-1]                 # without the identifier
dcr(conf, syn[-1], max_rows = 1500, seed = 1)$close_share

For the model above, the share is at the chance level: no noise is needed. Near-copies appear when the model is too detailed for the data, for example when it is stratified into many small groups. The model below splits the 5000 persons into 64 strata and treats all numeric variables with up to 60 distinct values as discrete:

detailed <- fit_synthesizer(census_sim, id_cols = "person_id",
                            by = c("region", "employment", "sex"),
                            min_stratum_size = 5, discrete_threshold = 60)

The amount of noise is set with closeness (noise level = 1 − closeness): lower closeness smooths numeric values, re-draws some categories and weakens the dependence. To see what it buys, we compute for several noise levels the risk (close_share) and the utility of a typical analysis — a regression of income on demographic variables, compared with the same regression on the real data through the overlap of the confidence intervals (mean overlap, negative values counted as 0; 1 = identical inference). Results are averaged over four synthetic files per setting; the utility estimates still vary by about ±0.03 from one set of files to another.

model <- income ~ age + sex + education + employment
risk_utility <- function(fit, closeness, seeds = 1:4) {
  v <- sapply(seeds, function(sd) {
    s <- generate(fit, closeness = closeness, seed = sd)
    c(dcr(conf, s[-1], max_rows = 1500, seed = 1)$close_share,
      mean(pmax(ci_overlap(census_sim, s, model)$overlap, 0)))
  })
  data.frame(noise = 1 - closeness, risk = mean(v[1, ]), utility = mean(v[2, ]))
}
ru <- do.call(rbind, lapply(c(1, 0.95, 0.9, 0.85, 0.8, 0.7), function(cl) {
  cbind(model = "detailed (64 strata)", risk_utility(detailed, cl))
}))
ru <- rbind(ru, cbind(model = "stratified by employment x sex", risk_utility(fit, 1)))
ru[-1] <- round(ru[-1], 3)
ru

ggplot(ru, aes(risk, utility, colour = model)) +
  geom_path(data = ru[ru$model != ru$model[nrow(ru)], ], colour = "#c3c2b7") +
  geom_point(size = 3) +
  geom_text(aes(label = paste("noise", noise)), vjust = -1, size = 3,
            colour = "#52514e", show.legend = FALSE) +
  geom_vline(xintercept = 0.05, linetype = "dashed", colour = "#898781") +
  scale_x_reverse(expand = expansion(mult = 0.08)) +
  scale_y_continuous(expand = expansion(mult = c(0.08, 0.15))) +
  scale_colour_manual(values = c("#eb6834", "#2a78d6"), name = NULL) +
  labs(x = "disclosure risk: share of near-copies (axis reversed: right is safer)",
       y = "utility: mean CI overlap", title = "Risk-utility map") +
  theme_minimal(base_size = 10) +
  theme(legend.position = "top", panel.grid.minor = element_blank())

This risk–utility map (Duncan and Stokes, 2004) is the basis of the release decision: right is safer, up is more useful. It shows two things.

• For the over-detailed model, noise works as intended: as the noise level increases, the share of near-copies falls towards the chance level (dashed line) — and the utility falls with it.
• The well-specified model is the better starting point: without any noise it is already at the chance level of near-copies, with about the same utility as the detailed model without noise, and clearly more utility than the noisy versions of the detailed model that reach the same level of risk. Pushing the detailed model slightly below the chance level is possible, but costs most of its utility. The first lever for privacy is therefore the model (not too many small strata, knots, a sensible discrete_threshold); noise is the second lever, to be used in small, calibrated amounts.

Step 4: set the noise to meet a risk threshold

Suppose the release rule says that at most 6% of synthetic records may be near-copies of real persons, and the detailed model has to be used (for instance because analysts need region-by-employment detail). calibrate_closeness() accepts any risk measure as a function and finds the smallest amount of noise that meets the rule:

near_copies <- function(real, synthetic) {
  dcr(real[-1], synthetic[-1], max_rows = 1500, seed = 1)$close_share
}
cal <- calibrate_closeness(detailed, census_sim, target = 0.06, metric = near_copies,
                           grid = c(0.7, 0.8, 0.9, 1), refine = 2)
cal
release <- generate(detailed, closeness = cal$closeness, seed = 2026)

The noise level to report with the release is 1 - cal$closeness.

Step 5: check the released file

Before release, verify that the file still supports the intended analyses and that the risk is acceptable for a new random file:

ci_overlap(census_sim, release, model)[, c("term", "estimate_real",
                                           "estimate_synthetic", "overlap")]
disclosure_risk(census_sim, release, keys = keys, target = sensitive,
                ignore = "person_id")
dcr(conf, release[-1], max_rows = 1500, seed = 2)$close_share

plot_marginals(conf, release[-1], vars = c("age", "income", "household_size"))

The marginal distributions and the employment effects survive, but the effects of age and education on income are clearly attenuated. This is the price of the noise shown on the risk–utility map; if these effects matter for the users of the file, the better choice is the less detailed model, which meets the same risk threshold without noise.

Targeted noise

Noise does not have to be the same for all variables. With perturbation() it can be concentrated where it is needed — for instance on the confidential income and on the key variables age and household size — while the other variables and the dependence structure are left untouched. (Variables used in by define the strata and cannot be perturbed.)

targeted <- perturbation(noise = c(income = 0.5, age = 0.3), swap = c(household_size = 0.2))
rel2 <- generate(detailed, perturb = targeted, seed = 1)
c(risk = near_copies(census_sim, rel2),
  utility = mean(pmax(ci_overlap(census_sim, rel2, model)$overlap, 0)))

Good practice

• Choose a model that does not over-fit before adding noise; check the risk on the risk–utility map.
• Remove or replace direct identifiers (id_cols).
• Release the synthetic data, never the fitted model: unless knots is used, the model stores the observed values of continuous variables.
• Avoid very small strata (min_stratum_size), which can reproduce small groups too faithfully.
• Report the noise level and the risk and utility measures.
• Synthetic data generated this way have no formal privacy guarantee such as differential privacy. The measures above are empirical; they depend on the chosen key variables and on what an intruder may know. Review them with the disclosure control experts of your organisation.

References

Duncan, G. T. and Stokes, S. L. (2004). Disclosure risk vs. data utility: the R-U confidentiality map as applied to topcoding. Chance, 17(3), 16–20.

Nowok, B., Raab, G. M. and Dibben, C. (2016). synthpop: Bespoke creation of synthetic data in R. Journal of Statistical Software, 74(11), 1–26.

Taub, J., Elliot, M., Pampaka, M. and Smith, D. (2018). Differential correct attribution probability for synthetic data: an exploration. In Privacy in Statistical Databases, LNCS 11126, 122–137.

SynthesizerPlus documentation built on Oct. 16, 2026, 5:10 p.m.