Data from the SURVAYA study^25,26 (clinicaltrials.gov NCT05379387) was re-used with permission from the sponsor. SURVAYA was a population-based cross-sectional cohort study amongst AYA cancer patients registered in the Netherlands Cancer Registry (NCR). SURVAYA included AYAs that had been treated either in a Dutch academic medical centre or in the Netherlands Cancer Institute, and were registered in the NCR between 1999 to 2015; Amsterdam AMC, Netherlands Cancer Institute, and Utrecht UMC supplied treatment-related data up to 2014. The principal instruments in SURVAYA were validated health-related Quality of Life (QoL) questionnaires^27–30, which were linked to clinical attributes from the NCR. Details are provided in the original study publications^25,26. In total, there were 950 variables, some of which contained unstructured text.

We limited ourselves only to variables selected by Saris et al. (2022) for logistic regression models of negative body image among AYAs²⁵. As per the original research, participants that had filled in less than half of the body image-related questionnaire items were excluded. We imputed missing values using multiple imputation by chained equations. Age at diagnosis was left in as a privacy concealment challenge for attribute inference, since certain cancer diagnoses are widely known to be exceptionally rare among younger AYAs. The pre-processed training data, hereafter referred to as the original dataset (OD), consisted of 3735 AYAs with 21 variables (37 after a one-hot encoding of categories) – see Supplementary material S1.

Training and generating experiments are illustrated in Figure 1. The OD was sampled without replacement to produce smaller training datasets of sizes 3600, 3350, …, down to 600 subjects, resulting in a total of 14 distinct training sets.

We tested four SD generator architectures from the Synthetic Data Vault (SDV)⁹ Python library. Two of these were machine learning (ML)-based architectures that used strictly parametric statistical models. The first was a speed-optimised Gaussian copula generator (hereafter “Fast ML”) and the other was a classical Gaussian copula generator (hereafter “Gaussian Copula”). Two non-parametric architectures were based on deep-learning (DL) neural networks; a Conditional Tabular Generative Adversarial Network (CTGAN)¹² and a Conditional Generative Adversarial Network incorporating Differential Privacy (DP-CGAN)¹⁰. The DP-CGAN was not part of SDV’s current library, but was built on top of existing SDV-library modules.

In the Fast ML architecture, each of the aforementioned subsets of the OD were used for training, thus resulting in 14 separately trained Fast ML generators. This process was then repeated entirely for the Gaussian Copula, CTGAN, and DP-CGAN architectures, thus always resulting in 14 separately trained generators within each of the four selected architectures.

Each architecture used default (hyper-)parameters for training specified by its developers. We limited our experiments only to the default hyper-parameters, without fine-tuning and no grid search for these experiments. All architectures were supplied with the metadata of the OD as required in the documentation^10,31. Hyper-parameters per architecture and variable metadata are provided in supplementary material S2 and S3, respectively.

From each of the separately trained generators (thus 4 architectures x 14 training OD subsets per architecture = 56 unique generators), we generated SD of varying samples sizes ranging from 100 up to 39100 artificial subjects, in increments of 1000. Thus, for each uniquely trained generator, we derived 40 distinct sets of SD (56 generators x 40 sets of SD per generator = 2240 SD sets in total).

Actionability was assessed by comparing a selected SD set, from a given generator, to the corresponding OD training set used to train that generator. For instance, a SD set of 5100 samples generated with a Fast ML generator that was trained using a set of 3735 real subjects was compared to those specific 3735 real subjects.

Veracity of SD was quantified in terms of precision, density, recall, and coverage^32–34. The precision metric quantifies the proportion of individual subjects in the SD that fall within a minimum number of neighbouring subjects (k) found in the OD. The density corrects for outliers in precision by scoring the number of samples inside the densely overlapping regions. Recall describes the proportion of OD samples that lay close to the SD’s samples. Finally, coverage corrects for outliers in recall by building the radii with the OD’s samples, rather than the SD’s samples. A schematic overview of the veracity metrics’ mechanism is provided in supplementary material S4. The metrics were computed using the prdc Python library with a constant k = 5.

Utility was examined by checking if a given SD reproduced the same logistic regression coefficients as the original paper by Saris et al.²⁵, for generative architectures that had been trained using all of 3735 real subjects. For each generator, we selected an SD output size of 3100 for the comparison of odds ratios (ORs) with Saris et al. The regression analyses were conducted using Python libraries; Statsmodels for regression analysis and scikit-learn for an optimism-adjusted (through random under-sampling) concordance-statistic as area-under receiver-operator curve score.

Privacy concealment was assessed with two metrics. First, a measure of the minimum Hamming distance¹⁰ between any ‘synthetic’ subject in a given SD to any ‘real’ subject in the OD used to train the corresponding generator. Second, we estimated an attribute inference probability using seemingly innocent information that might be obtained by through public channels. We limited the test variables to age in nearest whole year, type of cancer and romantic partnership status, which we assumed would be easily gleaned from social media. We then assumed that an attacker would infer a sensitive and not easily known attribute, i.e., an AYA’s self-perception of sexual attractiveness (a primary outcome in SURVAYA). The attribute inference attack was simulated using a Correct Attribution Probability algorithm (CAP)³⁵.