Generating Synthetic Pharmacometric Data: A Review of the Methods, and Where synpmx Fits

Andrew Stein

Synthetic datasets in pharmacometrics (PMX) are useful for open-source software development, AI-assisted software development, teaching, and external collaborations. Several different approaches exist for generating them, and they optimize for genuinely different things — which means the question is never “which method is best” but “best at what.”

This article surveys the four generation families in use, explains why differential privacy sits across all of them rather than inside one, and says where synpmx fits. Its companion, the checking review, is a tutorial on the other literature — the one about checking synthetic data once it exists, which is a separate field with its own vocabulary, and which is easy to reinvent badly if you have not read it. Current as of August 2026.

Mechanistic simulation

Trial simulation has long been the standard approach within pharmacometrics, using tools like rxode2 or mrgsolve. A structural pharmacokinetic (PK) or pharmacodynamic (PD) model, a set of parameters with between-subject variance, and a trial design produce as many virtual subjects as you like.

Strengths

• No patient record is read, provided the model is public (see below)
• Mechanistically interpretable: every feature of the output traces to a model assumption you chose
• Unlimited dataset size, and any design you can describe

Limitations

• Simulations often lack the irregularities of operational clinical datasets: unexpected dosing histories, protocol deviations, and inconsistent observation schedules. These mechanisms can be built in, but doing so makes the simulation considerably more complex, and accurate models of the deviation processes are themselves hard to develop
• The output is only as good as the model, and a wrong structural assumption produces confidently wrong data

The privacy claim deserves care, because it is often overstated. Simulation is perfectly private only when the model it simulates from is public. A model fitted to the trial you are trying to protect carries information about those patients in its parameter estimates, and publishing simulations from it is a release of that information, not an alternative to one. This distinction is why synpmx separates a mode that reads no data at all from modes that read data under a budget.

Copulas: realistic covariates to simulate from

A structural model needs covariates to simulate on — age, body weight, renal function, liver function, laboratory values, disease characteristics — and drawing each one independently from its own marginal distribution produces patients who do not exist: 45 kg adults with the creatinine clearance of a 90 kg one.

A copula solves this by separating a joint distribution into two parts that can be handled independently: the marginal distribution of each variable on its own, and the dependence structure linking them. Fit the dependence structure on real data, keep the marginals, and you can then draw whole covariate vectors in which the relationships between variables are realistic even though no vector belongs to a real patient. Zwep and colleagues developed this for virtual patient simulation, and Guo and colleagues for realistic virtual adult populations.

The important thing about copula methods, for the purposes of this survey, is what they produce: one row per virtual patient — a covariate vector, not a longitudinal profile. They do not compete with mechanistic simulation, they supply its input. A published copula also travels well: it can be shared without the underlying data, which is what makes the combination a genuinely strong option for a fully synthetic study.

Deep generative models

Recent advances in machine learning have introduced deep generative models for synthetic PK/PD data generation. Methods explored include generative adversarial networks (GANs), TimeGAN for sequences, variational autoencoders (VAEs), diffusion models, and probabilistic autoregressive networks. Jiang and colleagues benchmark several of these on PK/PD data; Gadgil and colleagues apply diffusion models to virtual populations and pharmacometric simulation.

These models aim to reproduce the statistical properties of longitudinal PK datasets while maintaining realistic relationships among patients and observations.

Strengths

• Flexible nonlinear modeling with no structural assumption imposed in advance
• Learn dependence structures nobody specified, including ones nobody noticed
• Actively developed, with a large methods literature to draw on

Limitations

• Fidelity is an aim rather than a result. Where it has been measured in pharmacometrics the answer is mixed: Jiang and colleagues find performance varies substantially by method and scenario, and Woillard and colleagues found TVAE clearly behind CT-GAN and AVATAR on the same data
• Data-hungry in a field whose cohorts are often 12 to 200 subjects
• In the pharmacometric applications published so far, the input is usually a simulated dataset or a simplified longitudinal concentration profile rather than an operational trial dataset.

Sequential conditional models: synthpop and tabular tools

Outside pharmacometrics, the most widely used synthetic-data approach is neither mechanistic nor deep. The synthpop R package (Nowok, Raab and Dibben) synthesizes a table column by column: choose an order for the variables, model each one conditional on the variables already synthesized — usually with a classification and regression tree (CART) — and draw from that fitted conditional. Repeat until every column is synthetic.

It is the default tool in official statistics and social science, and deserves to be better known in this field. The same niche is occupied by the tabular deep-learning tools — CT-GAN and TVAE, from the Synthetic Data Vault project — which Woillard and colleagues benchmark against AVATAR.

Strengths

• No distributional assumptions, and mixed variable types handled natively
• Fast, mature, well documented, and equipped with its own utility and disclosure diagnostics
• Sequential conditioning preserves relationships between columns by construction

Limitations

• It is built for rectangular, one-row-per-unit data. A pharmacometric event table is not that: it has many rows per subject, ordered in time, with a grammar in which EVID, AMT, CMT, and DV mean different things on different rows
• Synthesizing such a table column by column treats each row as an independent unit. That destroys the within-subject trajectory and readily produces illegal event sequences — an observation before the first dose, a dosing row carrying a measurement, a subject whose times do not increase

You can flatten a study to one row per subject and synthesize that successfully — which is exactly what Woillard and colleagues do, on 253 patients with a single measurement each. What you cannot do that way is keep the longitudinal endpoint, which for pharmacometrics is the data.

Schema-only synthesis: FakeDataR

Take the conditioning step out of column-by-column synthesis and the result is a different kind of tool: a table with the right shape and no relationships inside it. The FakeDataR package (Ahmed, CRAN 0.2.2) does this on purpose. It reproduces a dataset’s schema — column names, types, factor levels, value ranges, and missingness — and fills it with values drawn one column at a time. Categorical columns resample the observed levels by empirical frequency, or take generic labels Category A, Category B. Numeric columns are drawn uniformly between the observed minimum and maximum, or resampled from the observed values with replacement.

The target is the large language model (LLM) workflow. llm_bundle() writes the fake table, a scrubbed schema, and a README prompt into a single zip archive, so a model can be handed the shape of a dataset without the dataset. FakeDataR will also build a fake table directly from a structured query language (SQL) database schema, reading no rows at all, which is a stronger privacy position than any method in this article: there is no input record to protect.

What that costs is every relationship. Columns are drawn independently, so a 45 kg subject with the creatinine clearance of a 90 kg one is the expected output rather than a defect, and the copula problem described above is not addressed but skipped. There is no notion of a subject, so an event table loses its within-subject trajectory, its time ordering, and the link between a dosing row and the observations that follow it. In the uniform-range mode the shape of each distribution is discarded while the minimum and the maximum, which are real values belonging to the two most extreme patients, are carried through to the output.

FakeDataR states these limits itself: no formal privacy guarantee, no guaranteed statistical fidelity, and not a substitute for the original data in statistical modeling. Its documented uses are demonstrations, tutorials, bug reports, and testing. That makes it the closest thing in this survey to synpmx’s own motivation — developing code, and using AI coding tools, without the real study present — reached by a different route. A schema-shaped placeholder is enough to draft a query or file a reproducible bug report. It is not enough to develop a dataset assembly script, a diagnostic plot, or model-run plumbing, because those fail on the event grammar and a placeholder has none.

Record-based blending

Another class of algorithms generates synthetic records directly from existing ones, by blending or sampling among neighboring individuals within the original dataset. The original method here is AVATAR, due to Guillaudeux and colleagues, in which each synthetic record is built from the local neighborhood of real records. “AVATAR” is a method name rather than an initialism. Destere and colleagues benchmark a modified AVATAR against differentially private alternatives on a population PK model, and Woillard and colleagues include a simplified AVATAR in the pharmacogenetics comparison above.

Strengths

• High realism, because the output is made of real data rather than of a model of it
• Empirical distributions and complex, unmodeled relationships are preserved without anyone having to notice them first
• Works at small cohort sizes, where deep methods struggle

Limitations

• No formal privacy guarantee. Protection is a set of mechanisms whose coverage must be argued and measured, not a bound that can be stated
• Real datasets contain operational characteristics that identify people on their own — actual dosing times, actual amounts, observation schedules, protocol deviations — and blending measurement values does nothing about any of them. These require separate masking
• The output is assembled from real trajectories, so it inherits the source data’s handling obligations wherever it goes

Differential privacy is a guarantee, not a family

Differential privacy (DP) is frequently listed alongside the approaches above, which is a category error worth undoing. DP is not a way of generating data. It is a property a release mechanism can have: a bound, epsilon, on how much the presence or absence of any single individual can change the distribution of what is released. Any of the families above either has such a bound or does not.

Three things follow that matter in practice.

• It is the only claim that survives a determined recipient. Every other protection in this article is an argument about what an attacker is likely to manage. DP is a statement about what is possible.
• It composes, and it is spent. Two releases from the same data cost the sum of their epsilons. A budget is a finite resource, which is why it is allocated deliberately across the quantities being released.
• It is not free. The guarantee is purchased with noise, and at pharmacometric cohort sizes the price is steep. A study of 12 subjects cannot hide one subject cheaply.

The practical consequence is that DP and record-based realism sit at opposite ends of one axis, and choosing between them is a question about where the data is going rather than about which method is better. Destere and colleagues measure exactly this tradeoff. synpmx treats it as the primary design decision; the reasoning is in the privacy article, with the formal argument and the cohort-size feasibility analysis alongside it.

Where synpmx fits

synpmx generates event-based pharmacometric datasets — dosing and measurement tables with the schema, event grammar, and rough behavior of a real study — for software development, package testing, reproducible examples, educational materials, AI-assisted programming, and workflow validation.

The emphasis is on the structural characteristics that software encounters when processing real trial data. Concretely, that means a synthetic dataset should contain the patient who missed the week-4 visit, had a dose interrupted and restarted, and withdrew at week 12 — because the assembly script, the diagnostic plot, and the model-run plumbing all have to survive that patient, and a clean simulation never contains them.

It is in the record-based family, and inherits its problems

The default method, synpmx_avatar(), is record-based blending, and every limitation listed in that section applies to it. What distinguishes the package is not escaping those limitations but treating them as the specification.

• Values are protected by blending across at least k = 5 donors with no donor exceeding max_donor_weight = 0.50 of any avatar
• Observation times are coarsened onto the declared protocol grid, which is what turns a cohort of individually identifiable sampling schedules into a shared one
• A pattern of attended visits held by fewer than two real patients is refused rather than copied, so no avatar has one person’s history of absences
• Structurally extreme subjects are screened out of the anchor pool, and donors are never blended across routes of administration
• Every one of these mechanisms reports what it actually did on the run, in counts, so the argument is auditable rather than asserted

The mechanisms are specified in the AVATAR algorithm article, measured across eight public datasets in the evaluation, and the questions to ask of any generated dataset — from any method — are in the checks article.

The modes across the families

The package’s generation modes do not all sit in the same family. Choosing among them is a privacy decision, not a technical preference. The four carrying a privacy position are tabulated here; synpmx_pca() makes no formal claim and belongs beside AVATAR.

Mode	Family	Formal guarantee
synpmx_avatar()	Record-based blending	None; mechanisms, measured
synpmx_prior()	Mechanistic simulation from a public model	epsilon = 0 — no data is read
synpmx_calibrated()	Mechanistic, with magnitude corrected under a budget	(epsilon, delta) DP
synpmx_empirical()	Statistical, rebuilt from DP summaries	(epsilon, delta) DP

Family	Primary goal	Typical methods
Mechanistic	Simulate the biology	mrgsolve, rxode2, copulas for covariates
Statistical	Match the observed distributions	GANs, diffusion models, synthpop, CT-GAN
Structural	Preserve how the dataset behaves	AVATAR-style blending on event tables

Mechanistic methods are indispensable for simulation studies. Statistical methods excel at reproducing distributions and supporting data sharing. What neither is built to do is keep the event table intact — the dosing history, the irregular visit, the multiple endpoints on one grid, the deviation — because for their purposes those are nuisance rather than signal. For software engineering and methodological development they are relevant.

synpmx fills the gap between mechanistic simulation and statistical synthetic data generation.
It is built for developing software against realistic data, not for estimating parameters from it.

References

• Jiang Y, García-Durán A, Losada IB, Girard P, Terranova N. Generative models for synthetic data generation: application to pharmacokinetic/pharmacodynamic data. J Pharmacokinet Pharmacodyn. 2024. doi: 10.1007/s10928-024-09935-6.

• Gadgil PK, Poojari SM, Ramanathan M. Diffusion models for virtual populations and pharmacometric simulations. J Pharmacokinet Pharmacodyn. 2026;53(5):45.

• Zwep LB, Guo T, Nagler T, Knibbe CAJ, Meulman JJ, van Hasselt JGC. Virtual Patient Simulation Using Copula Modeling. Clin Pharmacol Ther. 2024;115(4):795-804. doi: 10.1002/cpt.3099.

• Guo T, et al. Generation of realistic virtual adult populations using a model-based copula approach. J Pharmacokinet Pharmacodyn. 2024. doi: 10.1007/s10928-024-09929-4.

• Nowok B, Raab GM, Dibben C. synthpop: Bespoke creation of synthetic data in R. Journal of Statistical Software. 2016;74(11):1-26. doi: 10.18637/jss.v074.i11.

• Xu L, Skoularidou M, Cuesta-Infante A, Veeramachaneni K. Modeling tabular data using conditional GAN. Advances in Neural Information Processing Systems 32 (NeurIPS 2019). 2019:7335-7345. (CT-GAN and TVAE, from the Synthetic Data Vault project.)

• Ahmed Z. FakeDataR: Privacy-Preserving Synthetic Data for ‘LLM’ Workflows. R package version 0.2.2, published 2025-10-06. CRAN, documentation.

• Guillaudeux M, Rousseau O, Petot J, et al. Patient-centric synthetic data generation, no reason to risk re-identification in biomedical data analysis. npj Digital Medicine. 2023;6. doi: 10.1038/s41746-023-00771-5.

• Destere A, Lombardi R, Labriffe M, et al. Can synthetic data overcome the privacy and fidelity bottleneck in Pharmacometrics? A comparative benchmark using a daptomycin population pharmacokinetic model. medRxiv preprint, posted June 2, 2026. doi: 10.64898/2026.05.30.26354512.

• Woillard JB, Benoist C, et al. To be or not to be, when synthetic data meet clinical pharmacology: A focused study on pharmacogenetics. CPT Pharmacometrics Syst Pharmacol. 2025. doi: 10.1002/psp4.13240.

• Dwork C, Roth A. The Algorithmic Foundations of Differential Privacy. Foundations and Trends in Theoretical Computer Science. 2014;9(3-4). doi: 10.1561/0400000042.