Can synthetic data reproduce real-world findings in epidemiology? A replication study using adversarial random forests

Jan Kapar; Kathrin Günther; Lori Ann Vallis; Klaus Berger; Nadine Binder; Hermann Brenner; Stefanie Castell; Beate Fischer

q-bio.QMAug 19, 2025

Can synthetic data reproduce real-world findings in epidemiology? A replication study using adversarial random forests

Authors: Jan Kapar, Kathrin Günther, Lori Ann Vallis, Klaus Berger, Nadine Binder, Hermann Brenner, Stefanie Castell, Beate Fischer,

Organizations: Leibniz Institute for Prevention Research and Epidemiology—BIPS, Bremen, Germany · Faculty of Mathematics and Computer Science, University of Bremen, Bremen, Germany · Department of Human Health and Nutritional Sciences, University of Guelph, Guelph, Ontario, Canada · Institute of Epidemiology and Social Medicine, University of Münster, Münster, Germany · Institute of General Practice/Family Medicine, Faculty of Medicine and Medical Center, University of Freiburg, Freiburg Germany · Freiburg Center for Data Analysis, Modeling and AI, University of Freiburg, Freiburg, Germany · German Cancer Research Center (DKFZ), Heidelberg, Germany · Department of Epidemiology, Helmholtz Centre for Infection Research (HZI), Brunswick, Germany · Department of Epidemiology and Preventive Medicine, University of Regensburg, Regensburg, Germany · Institute for Occupational and Maritime Medicine (ZfAM), University Medical Center Hamburg-Eppendorf, Hamburg, Germany · Saarland Cancer Registry, Saarbrücken, Germany · Institute for Community Medicine, University Medicine Greifswald, Greifswald, Germany · Institute of Social Medicine, Epidemiology and Health Economics, Charité - Universitätsmedizin Berlin, Berlin, Germany · Institute of Clinical Epidemiology and Biometry, University of Würzburg, Würzburg, Germany · State Institute of Health I, Bavarian Health and Food Safety Authority, Erlangen, Germany · Max Delbrück Center for Molecular Medicine in the Helmholtz Association (MDC), Molecular Epidemiology Research Group, Berlin, Germany · Max Delbrück Center for Molecular Medicine in the Helmholtz Association (MDC), Biobank Technology Platform, Berlin, Germany · Charité - Universitätsmedizin Berlin, corporate member of Freie Universität Berlin and Humboldt-Universität zu Berlin, Berlin, Germany · IUF – Leibniz Research Institute for Environmental Medicine, Düsseldorf, Germany · Department of Environment and Health, School of Public Health, University of Bielefeld, Bielefeld, Germany · Institute for Medical Informatics, Biometry and Epidemiology, University Hospital of Essen, University of Duisburg-Essen, Germany · Center for Translational Oncology, University Hospital Regensburg, Regensburg, Germany · Bavarian Cancer Research Center (BZKF), Regensburg, Germany · Bremen Institute for Heart and Circulation Research (BIHKF), Bremen, Germany · Institute of Medical Epidemiology, Biometry, and Informatics, Profile Center Health Sciences, Faculty of Medicine, Martin-Luther-University Halle-Wittenberg, Halle, Germany · Department of Public Health, University of Copenhagen, Copenhagen, Denmark

Abstract

Synthetic data hold substantial potential to address practical challenges in epidemiology due to restricted data access and privacy concerns. However, many current methods suffer from limited quality, high computational demands, and complexity for non-experts. Furthermore, common evaluation strategies for synthetic data often fail to directly reflect statistical utility and measure privacy risks sufficiently. Against this background, a critical underexplored question is whether synthetic data can reliably reproduce key findings from epidemiological research while preserving privacy. We propose adversarial random forests (ARF) as an efficient and convenient method for synthesizing tabular epidemiological data. To evaluate its performance, we replicated statistical analyses from six epidemiological publications covering blood pressure, anthropometry, myocardial infarction, accelerometry, loneliness, and diabetes, from the German National Cohort (NAKO Gesundheitsstudie), the Bremen STEMI Registry U45 Study, and the Guelph Family Health Study. We further assessed how dataset dimensionality and variable complexity affect the quality of synthetic data, and contextualized ARF's performance by comparison with commonly used tabular data synthesizers in terms of utility, privacy, generalization, and runtime. Across all replicated studies, results on ARF-generated synthetic data consistently aligned with original findings. Even for datasets with relatively low sample size-to-dimensionality ratios, replication outcomes closely matched the original results across descriptive and inferential analyses. Reduced dimensionality and variable complexity further enhanced synthesis quality. ARF demonstrated favourable performance regarding utility, privacy preservation, and generalization relative to other synthesizers and superior computational efficiency.

Figures & tables

Publication	Data source	Research topic	$n$	$d$ (num/cat/lvls)	$n_{\text{NA}}$	$d_{\text{NA}}$	$\%_{\text{NA}}$
Schikowski et al. [ 36 ]	NAKO	Blood pressure	98 332	7 (5/2/4)	0	0	0
Fischer et al. [ 15 ]	NAKO	Anthropometry	101 557	12 (10/2/20)	97 903	9	34.43
Wienbergen et al. [ 43 ]	NAKO, BSR-U45	Myocardial infarction	1713	12 (3/9/24)	176	1	0.86
Breau et al. [ 3 ]	GFHS	Accelerometry	262	28 (25/3/34)	16	2	0.23
Berger et al. [ 1 ]	NAKO	Loneliness/COVID-19	113 527	47 (3/44/230)	0	0	0
Tanoey et al. [ 39 ]	NAKO	Type 1 diabetes	101 570	19 (7/12/42)	100 621	6	12.66

Table 1: Overview of publications and data used for synthetic data replications. The values for

n

partially deviate from the numbers given in the original publications due to participants withdrawing their consent for data usage in the respective cohort studies over time.

n

, number of rows/participants;

d

, dimensionality; num, number of numeric variables; cat, number of categorical variables; lvls, total number of categories (i.e., levels) across all categorical variables;

n_{\text{NA}}

, number of rows containing missing values;

d_{\text{NA}}

, number of variables containing missing values;

\%_{\text{NA}}

, percentage of missing values; NAKO, German National Cohort (NAKO Gesundheitsstudie); BSR-U45, Bremen STEMI Registry U45 Study; GFHS, Guelph Family Health Study

Figure 1: Replication of Figure 2 in Schikowski et al. [ 36 ] : differences of mean blood pressure values (in mmHg) using the mean of first and second measurement or the second measurement only by sex and age group (in years). Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are reported. avg., average; meas., measurement; MASD, mean absolute standardized difference; CIO, mean confidence interval overlap

Figure 2: Replication of Figure 5 in Fischer et al. [ 15 ] : subcutaneous and visceral abdominal adipose tissue thickness by sex. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are reported. In order to provide a clear comparability of the distributions despite the variability in the distribution of missing values in the synthetic data, the counts for the synthetic results were rescaled to match the total count of the real ones; WD, Wasserstein distance

Variable	Value cases	Value controls
Number of participants (n)	522 (485-560)	1191 (1153-1228)
	522 (486-560)	1191 (1153-1227)
Age (years) (median)	42 (42-43)	42 (41-42)
	41 (41-42)	41 (40-41)
Age (years) (1st quartile)	39 (38-39)	38 (37-38)
	38 (38-39)	37 (37-38)

Table 2: Replication of Table 1 in Wienbergen et al. [ 43 ] : Distribution of sociodemographic, lifestyle, and metabolic factors and family history of premature myocardial infarction according to cases and controls. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are printed in orange. n, number of participants; MI, myocaridal infarction; MASD, mean absolute standardized difference; CIO, mean confidence interval overlap

Figure 3: Replication of separate logistic regressions per variable, each adjusted for age, sex, country of birth, and years of school education, Table 2 in Wienbergen et al. [ 43 ] : associations between lifestyle and metabolic factors, as well as family history of premature MI and risk of early–onset MI. Median beta estimates and percentile-based 95% confidence intervals computed from the beta coefficient distribution across synthesis repetitions are reported for synthetic data. BMI, body mass index; MI, myocardial infarction; MASD, mean absolute standardized difference; mean CIO, confidence interval overlap

Figure 4: Replication of Figure 2 in Breau et al. [ 3 ] : calculated average valid wear time minutes per day spent in SED, LPA, and MVPA according to age-appropriate ActiGraph cutpoint sets by age group. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are reported. SED, sedentary behaviour; LPA, light physical activity; MVPA, moderate to vigorous physical activity; VA, vertical axis; VM, vector magnitude; MASD, mean absolute standardized difference; CIO, mean confidence interval overlap

Figure 5: Replication of multivariable linear regression, Table 3 in Berger et al. [ 1 ] , with general and task-specific synthesis: relationship between perceived loneliness and sociodemographic factors as well as symptoms of depression and anxiety among German National Cohort (NAKO Gesundheitsstudie) participants in May 2020. Median beta estimates and percentile-based 95% confidence intervals computed from the beta coefficient distribution across synthesis repetitions are reported for synthetic data. PHQ-9, nine-item Patient Health Questionnaire; GAD-7, Generalized Anxiety Disorder seven-item scale; MASD, mean absolute standardized difference; CIO, mean confidence interval overlap

Figure 6: Replication of univariable Cox regressions, Table 2 in Tanoey et al. [ 39 ] , with general and task-specific synthesis: type 1 diabetes univariable Cox regression estimates. Median beta estimates and percentile-based 95% confidence intervals computed from the beta coefficient distribution across synthesis repetitions are reported for synthetic data. C-section, caesarean section; MASD, mean absolute standardized difference; CIO, mean confidence interval overlap

Appendix figures & tables44 assets

Supplementary material from the paper’s appendix.

Appendix

Sex	Age group	Blood pressure measure	Avg. meas. 1/2 - meas. 2 (mean)
Male	20-24	Systolic	1.72 (1.51-1.91)
			1.61 (1.34-1.88)
		Diastolic	0.87 (0.73-1.02)
			0.87 (0.68-1.07)
	25-34	Systolic	1.26 (1.17-1.35)
			1.32 (1.21-1.45)

Appendix

Table B.1.1: Differences of mean blood pressure values (in mmHg) using the mean of first and second measurement or the second measurement only by sex and age group (in years). Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are printed in orange. avg., average; meas., measurement; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Figure B.1.1: Differences of mean blood pressure values (in mmHg) using the mean of first and second measurement or the second measurement only by sex and age group (in years). Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are reported. avg., average; meas., measurement; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Sex	Age group	Blood pressure measure	Aggregation	Value
Male	20-24	Systolic	Mean	126.22 (125.50-126.91)
				126.01 (125.09-126.97)
			SD	11.47 (10.91-12.00)
				11.22 (10.59-11.90)
		Diastolic	Mean	72.14 (71.64-72.65)
				72.39 (71.69-73.24)

Appendix

Table B.1.2: Distribution of systolic and diastolic blood pressure (second measurement; in mmHg) by sex and age group (in years). Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are printed in orange. SD, standard deviation; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Figure B.1.2: Distribution of systolic and diastolic blood pressure (second measurement; in mmHg) by sex and age group (in years). Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are reported. SD, standard deviation; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Sex	Age group	Hypertension status	Proportion using avg. meas. 1/2	Proportion using meas. 2
Male	20-24	Normotension	0.82 (0.79-0.84)	0.83 (0.81-0.85)
			0.83 (0.80-0.86)	0.84 (0.81-0.87)
		Hypertension known controlled	0.03 (0.02-0.04)	0.03 (0.02-0.04)
			0.03 (0.02-0.04)	0.03 (0.02-0.04)
		Hypertension known uncontrolled	0.02 (0.01-0.02)	0.01 (0.01-0.02)
			0.01 (0.01-0.02)	0.01 (0.01-0.02)

Appendix

Table B.1.3: Hypertension status by sex and age group using different definitions for the blood pressure values for scientific evaluations. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are printed in orange. avg., average; meas., measurement; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Variable	Sex	Age group	n	Mean	SD	10th percentile	50th perecentile	90th percentile
Height	Male	20-29	2899 (2798-2999)	180.75 (180.50-181.01)	7.14 (6.90-7.38)	171.90 (171.50-172.40)	180.70 (180.40-181.10)	189.90 (189.50-190.20)
			2210 (2044-2462)	180.19 (179.58-180.71)	7.31 (6.96-7.76)	170.98 (169.76-171.80)	180.30 (179.70-180.90)	189.38 (188.70-189.95)
		30-39	4168 (4048-4296)	180.66 (180.45-180.88)	7.15 (7.00-7.30)	171.50 (171.10-171.80)	180.60 (180.30-180.80)	189.60 (189.21-190.00)
			4933 (4572-5155)	179.95 (179.16-180.40)	7.47 (7.18-8.05)	170.40 (168.90-171.20)	180.00 (179.40-180.50)	189.30 (188.90-189.70)
		40-49	9431 (9241-9621)	179.83 (179.69-179.97)	7.14 (7.01-7.29)	170.80 (170.60-171.10)	179.90 (179.70-180.00)	188.80 (188.50-189.00)
			9799 (93312-10253)	179.17 (178.34-179.62)	7.45 (7.17-8.01)	169.70 (168.10-170.50)	179.30 (178.60-179.70)	188.50 (188.20-188.90)

Appendix

Table B.2.1: Distribution of anthropometric measurement parameters by sex and age group (in years). Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are printed in orange. n, number of participants; SD, standard deviation; BMI, body mass index; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Study centre	Height men (mean)	Height women (mean)
Augsburg	176.83 (176.63-177.03)	163.66 (163.48-163.84)
	176.64 (176.19-176.96)	164.34 (164.03-164.90)
Berlin Mitte	178.17 (177.90-178.45)	165.25 (165.02-165.47)
	177.67 (177.05-178.12)	165.53 (165.19-166.06)
Berlin Nord	177.60 (177.30-177.89)	164.70 (164.47-164.92)
	177.34 (176.70-177.77)	165.20 (164.84-165.86)

Appendix

Table B.2.2: Mean height (in cm) of participants by study centre and sex. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are printed in orange; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Sex	Age group	BMI group	Proportion
Male	20-29	Overweight	0.30 (0.28-0.31)
			0.30 (0.28-0.32)
		Obese	0.10 (0.09-0.11)
			0.09 (0.08-0.11)
	30-39	Overweight	0.39 (0.38-0.41)
			0.38 (0.37-0.40)

Appendix

Table B.2.3: Proportion of overweight and obese study participants by sex and age group (in years). Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are printed in orange. BMI, body mass index; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Figure B.2.1: Proportion of overweight and obese study participants by sex and age group (in years). Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are reported. BMI, body mass index; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Study centre	BMI men (mean)	BMI women (mean)
Augsburg	27.91 (27.78-28.05)	26.81 (26.66-26.97)
	27.93 (27.77-28.09)	26.84 (26.66-27.03)
Berlin Mitte	26.74 (26.59-26.90)	25.45 (25.27-25.62)
	26.90 (26.70-27.12)	25.57 (25.36-25.81)
Berlin Nord	27.71 (27.53-27.90)	26.41 (26.23-26.60)
	27.65 (27.45-27.86)	26.44 (26.23-26.66)

Appendix

Table B.2.4: Mean BMI (in kg/m²) of participants by study centre and sex. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are printed in orange. BMI, body mass index; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Figure B.2.2: Subcutaneous and visceral abdominal adipose tissue thickness by sex. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are reported. In order to provide a clear comparability of the distributions despite the variability in the distribution of missing values in the synthetic data, the counts for the synthetic results were rescaled to match the total count of the real ones; WD, Wasserstein distance

Variable	Value cases	Proportion cases	Value controls	Proportion controls
Number of participants (n)	522 (485-560)		1191 (1153-1228)
	522 (486-560)		1191 (1153-1227)
Age (years) (median)	42 (42-43)		42 (41-42)
	41 (41-42)		41 (40-41)
Age (years) (1st quartile)	39 (38-39)		38 (37-38)
	38 (38-39)		37 (37-38)

Appendix

Table B.3.1: Distribution of sociodemographic, lifestyle, and metabolic factors and family history of premature myocardial infarction according to cases and controls. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are printed in orange. n, number of participants; MI, myocaridal infarction; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Adj. level	Variable	Odds ratio	2.5%	97.5%
1	Smoking status: Former	1.00 (0.62-1.59)	0.63 (0.38-1.00)	1.60 (1.01-2.54)
		1.09 (0.68-1.66)	0.70 (0.43-1.07)	1.68 (1.08-2.58)
	Smoking status: Current	10.75 (7.87-15.80)	7.60 (5.61-10.79)	15.21 (10.98-23.13)
		8.66 (6.14-12.45)	6.25 (4.52-8.75)	12.02 (8.37-17.78)
	Alcohol consumption: 1x/month	1.04 (0.69-1.54)	0.70 (0.46-1.04)	1.53 (1.03-2.30)
		1.03 (0.70-1.55)	0.70 (0.48-1.06)	1.52 (1.02-2.28)

Appendix

Table B.3.2: Associations between lifestyle and metabolic factors, as well as family history of premature myocardial infarction and risk of early–onset myocardial infarction. Adj. level 1: adjusted for age, sex, country of birth, and years of school education; Adj. level 2: additionally adjusted for body mass index, smoking, and frequency of alcohol consumption; Adj. level 3: additionally adjusted for self–reported diabetes mellitus and hypertension. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are printed in orange. adj., adjustment; 2.5% and 97.5%, regression 95% confidence interval limits; BMI, body mass index; MI, myocardial infarction; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Figure B.3.1: Associations between lifestyle and metabolic factors, as well as family history of premature MI and risk of early–onset MI. Median beta estimates and percentile-based 95% confidence intervals computed from the beta coefficient distribution across synthesis repetitions are reported for synthetic data. BMI, body mass index; MI, myocardial infarction; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Subset	Adj. level	No. risk factors	Odds ratio	2.5%	97.5%
All	1	1	5.40 (3.08-12.42)	2.88 (1.80-5.20)	10.11 (5.28-29.45)
			4.40 (2.58-8.95)	2.48 (1.57-4.28)	7.81 (4.20-19.06)
		2+	43.81 (25.52-97.73)	23.27 (14.85-41.49)	82.48 (43.44-229.52)
			30.91 (17.28-64.17)	17.44 (10.68-30.29)	54.41 (28.09-139.38)
		1 unit increase	6.41 (5.25-8.16)	5.12 (4.26-6.40)	8.01 (6.47-10.39)
			5.32 (4.18-6.81)	4.33 (3.47-5.44)	6.53 (5.05-8.52)

Appendix

Table B.3.3: Joint associations of lifestyle and metabolic factors with risk of early–onset myocardial infarction, overall and by family history of premature myocardial infarction and sex. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are printed in orange. adj., adjustment; No., number; 2.5% and 97.5%, regression 95% confidence interval limits; BMI, body mass index; MI, myocardial infarction; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Variable	Everyone	Toddlers 1.5-2 yrs	Preschoolers 3-4 yrs	Preschoolers 3-6 yrs	School aged 5-6 yrs
Number of participants (n)	262 (262-262)	96 (80-111)	121 (105-136)	166 (151-182)	45 (34-57)
	262 (262-262)	84 (69-100)	143 (126-159.02)	178 (162-193)	35 (24-48)
Age (years) (mean)	3.62 (3.46-3.77)	2.26 (2.17-2.34)	3.96 (3.86-4.06)	4.40 (4.26-4.54)	5.58 (5.49-5.68)
	3.64 (3.50-3.78)	2.39 (2.30-2.47)	3.94 (3.84-4.03)	4.23 (4.12-4.36)	5.44 (5.34-5.54)
Age (years) (SD)	1.28 (1.20-1.35)	0.42 (0.38-0.45)	0.59 (0.54-0.64)	0.90 (0.83-0.96)	0.33 (0.27-0.37)
	1.10 (1.03-1.18)	0.38 (0.33-0.42)	0.56 (0.52-0.60)	0.79 (0.72-0.86)	0.30 (0.23-0.36)

Appendix

Table B.4.1: Characteristics of study population for the entire sample population and by age group. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are printed in orange. n, number of participants; SD, standard deviation; BMI, body mass index; HHI, household income; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Set of cutpoints	SED	LPA	MVPA
van Cauwenberghe	615.34 (607.77-623.08)	31.81 (30.92-32.68)	67.09 (64.70-69.44)
	614.10 (606.94-620.96)	31.88 (30.99-32.73)	67.22 (64.97-69.54)
Pate	574.95 (567.58-582.27)	48.54 (47.33-49.75)	90.75 (87.77-93.69)
	573.58 (566.89-579.93)	48.67 (47.47-49.84)	90.92 (88.07-93.83)
Puyau	574.95 (567.58-582.27)	93.60 (91.17-96.06)	45.69 (43.94-47.51)
	573.61 (566.97-580.11)	93.73 (91.37-96.15)	45.82 (44.07-47.61)

Appendix

Table B.4.2: Calculated average valid wear time minutes per day spent in SED, LPA, and MVPA according to the 10 different sets of ActiGraph cutpoints examined. Cutpoints were applied to the entire cohort. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are printed in orange. SED, sedentary behaviour; LPA, light physical activity; MVPA, moderate to vigorous physical activity; VA, vertical axis; VM, vector magnitude; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Figure B.4.1: Calculated average valid wear time minutes per day spent in SED, LPA, and MVPA according to the 10 different sets of ActiGraph cutpoints examined. Cutpoints were applied to the entire cohort. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are reported. SED, sedentary behaviour; LPA, light physical activity; MVPA, moderate to vigorous physical activity; VA, vertical axis; VM, vector magnitude; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Age group	Set of cutpoints	SED	LPA	MVPA
Toddlers (1.5-2 years)	Trost	491.66 (479.62-503.62)	107.73 (103.48-111.87)	82.01 (77.21-86.77)
		501.96 (488.56-513.23)	105.80 (101.54-110.26)	80.77 (76.03-85.99)
	Costa (VA)	477.97 (465.90-489.90)	132.69 (127.62-137.62)	70.75 (66.49-75.13)
		488.53 (475.31-499.88)	130.24 (125.12-135.73)	69.67 (65.49-74.12)
	Costa (VM)	449.33 (438.15-461.16)	157.79 (151.94-163.57)	74.28 (69.63-78.73)
		456.76 (443.80-468.22)	157.03 (151.06-163.17)	74.46 (69.94-79.37)

Appendix

Table B.4.3: Calculated average valid wear time minutes per day spent in SED, LPA, and MVPA according to age-appropriate ActiGraph cutpoint sets by age group. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are printed in orange. SED, sedentary behaviour; LPA, light physical activity; MVPA, moderate to vigorous physical activity; VA, vertical axis; VM, vector magnitude; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Figure B.4.2: Calculated average valid wear time minutes per day spent in SED, LPA, and MVPA according to age-appropriate ActiGraph cutpoint sets by age group. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are reported. SED, sedentary behaviour; LPA, light physical activity; MVPA, moderate to vigorous physical activity; VA, vertical axis; VM, vector magnitude; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Age group	Set of cutpoints	Proportion meeting PA guideline
Toddlers (1.5-2 years)	Trost	0.62 (0.53-0.72)
		0.59 (0.48-0.71)
	Costa (VA)	0.72 (0.62-0.80)
		0.70 (0.60-0.80)
	Costa (VM)	0.90 (0.83-0.95)
		0.88 (0.80-0.95)

Appendix

Table B.4.4: Percentage of sample meeting age-appropriate guidelines for physical activity according to age-appropriate ActiGraph cutpoints by age group. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are printed in orange. PA, physical activity; VA, vertical axis; VM, vector magnitude; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Figure B.4.3: Percentage of sample meeting age-appropriate guidelines for physical activity according to age-appropriate ActiGraph cutpoints by age group. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are reported. PA, physical activity; VA, vertical axis; VM, vector magnitude; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Variable	Value
Number of participants (n)	113527 (113527-113527)
	113527 (113527-113527)
	113527 (113527-113527)
Sex: Female (%)	51.75 (51.47-52.03)
	51.76 (51.45-52.05)
	51.76 (51.46-52.05)

Appendix

Table B.5.1: Characteristics of German National Cohort (NAKO Gesundheitsstude) participants taking part in the COVID survey in May 2020. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are reported, general synthesis replication results are printed in orange, task-specific synthesis replication results in violet. PHQ-9, nine-item Patient Health Questionnaire; GAD-7, Generalized Anxiety Disorder seven-item scale; SD, standard deviation; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Variable	Value	Value woman	Value men
Feeling of missing company of others (%)	79.88 (79.64-80.11)	83.49 (83.17-83.79)	76.00 (75.63-76.36)
	79.87 (79.63-80.10)	82.31 (81.91-82.72)	77.24 (76.79-77.69)
Feeling of being left out (%)	29.88 (29.62-30.16)	35.09 (34.70-35.47)	24.29 (23.92-24.67)
	29.88 (29.61-30.14)	34.11 (33.67-34.55)	25.34 (24.89-25.77)
Feeling of being socially isolated (%)	34.87 (34.61-35.15)	40.48 (40.07-40.89)	28.85 (28.47-29.22)
	34.87 (34.58-35.17)	39.28 (38.79-39.79)	30.14 (29.62-30.65)

Appendix

Table B.5.2: Relative frequency of loneliness and anxiety as well as depression and anxiety scores during pandemic measures in May 2020. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are printed in orange. PHQ-9, nine-item Patient Health Questionnaire; GAD-7, Generalized Anxiety Disorder seven-item scale; SD, standard deviation; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Variable	beta coefficient	2.5%	97.5%
(Intercept)	4.34 (4.27-4.41)	4.27 (4.20-4.34)	4.41 (4.34-4.48)
	4.30 (4.23-4.37)	4.24 (4.16-4.31)	4.37 (4.29-4.44)
	4.40 (4.32-4.49)	4.33 (4.25-4.41)	4.47 (4.39-4.56)
Age	0.00 (-0.00-0.00)	-0.00 (-0.00-0.00)	0.00 (0.00-0.00)
	-0.00 (-0.00-0.00)	-0.00 (-0.00–0.00)	0.00 (-0.00-0.00)
	0.00 (-0.00-0.00)	-0.00 (-0.00-0.00)	0.00 (-0.00-0.00)

Appendix

Table B.5.3: Relationship between perceived loneliness and sociodemographic factors as well as symptoms of depression and anxiety among German National Cohort (NAKO Gesundheitsstudie) participants in May 2020. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are reported, general synthesis replication results are printed in orange, task-specific synthesis replication results in violet. 2.5% and 97.5%, regression 95% confidence interval limits; PHQ-9, nine-item Patient Health Questionnaire; GAD-7, Generalized Anxiety Disorder seven-item scale; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Figure B.5.1: Relationship between perceived loneliness and sociodemographic factors as well as symptoms of depression and anxiety among German National Cohort (NAKO Gesundheitsstudie) participants in May 2020. Median beta estimates and percentile-based 95% confidence intervals computed from the beta coefficient distribution across synthesis repetitions are reported for synthetic data. PHQ-9, nine-item Patient Health Questionnaire; GAD-7, Generalized Anxiety Disorder seven-item scale; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Sex	Age group	Lonely participants (proportion)	Participants with increased loneliness (proportion)
Male	20-29	0.33 (0.32-0.35)	0.58 (0.57-0.60)
		0.33 (0.31-0.35)	0.57 (0.55-0.59)
	30-39	0.29 (0.28-0.30)	0.50 (0.48-0.51)
		0.30 (0.29-0.31)	0.51 (0.50-0.53)
	40-59	0.26 (0.25-0.26)	0.45 (0.44-0.46)
		0.26 (0.25-0.27)	0.46 (0.45-0.47)

Appendix

Table B.5.4: Proportion of lonely participants and of those, who felt more lonely during the pandemic than before, by sex and age group (in years). Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are printed in orange; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Figure B.5.2: Proportion of lonely participants and of those, who felt more lonely during the pandemic than before, by sex and age group (years). Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are reported; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Sex	Loneliness score	PHQ-9 score COVID survey (mean)	GAD-7 score COVID survey (mean)
Male	3	2.56 (2.51-2.61)	2.01 (1.96-2.05)
		2.38 (2.28-2.46)	1.87 (1.79-1.94)
	4	2.63 (2.59-2.67)	2.09 (2.06-2.13)
		2.65 (2.59-2.70)	2.11 (2.06-2.15)
	5	3.46 (3.39-3.53)	2.77 (2.71-2.83)
		3.62 (3.54-3.70)	2.93 (2.87-3.00)

Appendix

Table B.5.5: Relationship of drepression and anxiety symptoms with loneliness. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are printed in orange. PHQ-9, nine-item Patient Health Questionnaire; GAD-7, Generalized Anxiety Disorder seven-item scale; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Figure B.5.3: Relationship of depression and anxiety symptoms with loneliness. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are reported. PHQ-9, 9-item Patient Health Questionnaire; GAD-7, Generalized Anxiety Disorder seven-item scale; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Sex	Lonely	PHQ-9 score baseline examination (mean)	GAD-7 score baseline examination (mean)
Male	Yes	4.17 (4.10-4.24)	3.37 (3.31-3.42)
		4.19 (4.11-4.28)	3.42 (3.35-3.49)
	No	2.90 (2.87-2.93)	2.30 (2.27-2.32)
		2.93 (2.89-2.97)	2.33 (2.30-2.36)
Female	Yes	4.79 (4.73-4.84)	4.01 (3.96-4.06)
		4.76 (4.68-4.85)	3.98 (3.91-4.06)

Appendix

Table B.5.6: Baseline PHQ-9 and GAD-7 sum scores for lonely and non-lonely participants during the pandemic. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are printed in orange. PHQ-9, nine-item Patient Health Questionnaire; GAD-7, Generalized Anxiety Disorder seven-item scale; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Figure B.5.4: Baseline PHQ-9 and GAD-7 sum scores for lonely and non-lonely participants during the pandemic. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are reported. PHQ-9, nine-item Patient Health Questionnaire; GAD-7, Generalized Anxiety Disorder seven-item scale; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Variable	Agg.	No diabetes	Diabetes type 1	Diabetes type 2	Total
Number of participants (n)		94408 (94252-94569)	371 (331-410)	6574 (6420-6724)	101353 (101324-101381)
		94407 (94250-94562)	311 (270-351)	5847 (5477-6188)	100576 (100217-100884)
		94411 (94252-94563)	371 (333-412)	6571 (6429-6727)	101353 (101353-101353)
Sex: Male	n	43244 (42932-43555)	204 (175-233)	3602 (3489-3719)	47050 (46735-47362)
		43267 (42956-43586)	156 (130-183)	3164 (2942-3397)	46587 (46222-46949)
		43264 (42953-43555)	199 (171-227)	3588 (3477-3707)	47046 (46737-47346)

Appendix

Table B.6.1: Cohort description by diabetes category. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are reported, general synthesis replication results are printed in orange, task-specific synthesis replication results in violet. agg., aggregation; n, number of participants; prop., proportion; NA, indicator for missing values; BMI, body mass index; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Variable	Model	Age at diagnosis	Hazard ratio	2.5%	97.5%
Birth order: First	Univariable	0–40	0.83 (0.61-1.14)	0.61 (0.45-0.82)	1.12 (0.83-1.57)
			1.06 (0.72-1.63)	0.72 (0.49-1.04)	1.58 (1.05-2.56)
Birth order: Second			0.69 (0.50-0.96)	0.50 (0.36-0.69)	0.94 (0.69-1.34)
			0.97 (0.65-1.51)	0.65 (0.44-0.98)	1.44 (0.95-2.37)
Birth order: $>$ =Third			0.66 (0.45-0.96)	0.46 (0.30-0.67)	0.95 (0.66-1.38)
			0.97 (0.63-1.51)	0.63 (0.41-0.96)	1.48 (0.95-2.39)

Appendix

Table B.6.2: Type 1 diabetes risk estimates from Cox regression models with all cases, onset age 0–15 years (n = 100) and onset age 16–40 years (n = 271). Full models adjusted for paternal diabetes, maternal diabetes, migration background, premature birth, birth weight and being breastfed history. Reduced models adjusted for paternal diabetes, maternal diabetes and migration background. All models were stratified by birth year. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are printed in orange. n, number of participants; 2.5% and 97.5%, regression 95% confidence interval limits; C-section, caesarean section; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Variable	Hazard ratio	2.5%	97.5%
Birth order: First	0.83 (0.61-1.14)	0.61 (0.45-0.82)	1.12 (0.83-1.57)
	1.06 (0.72-1.63)	0.72 (0.49-1.04)	1.58 (1.05-2.56)
	0.84 (0.62-1.17)	0.62 (0.46-0.85)	1.14 (0.85-1.61)
Birth order: Second	0.69 (0.49-0.96)	0.50 (0.36-0.69)	0.94 (0.68-1.35)
	0.97 (0.65-1.51)	0.65 (0.44-0.98)	1.44 (0.95-2.37)
	0.70 (0.51-0.97)	0.51 (0.37-0.70)	0.97 (0.71-1.35)

Appendix

Table B.6.3: Type 1 diabetes univariable Cox regression estimates. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are reported, general synthesis replication results are printed in orange, task-specific synthesis replication results in violet. 2.5% and 97.5%, regression 95% confidence interval limits; C-section, caesarean section; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Figure B.6.1: Type 1 diabetes univariable Cox regression estimates. Median beta estimates and percentile-based 95% confidence intervals computed from the beta coefficient distribution across synthesis repetitions are reported for synthetic data. C-section, caesarean section; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Sex	Age at diagnosis	Therapy	n
Male	0-15	With insulin	36 (25-48)
			15 (8-24)
			42 (28-56)
		Unknown	13 (6-21)
			6 (2-12)
			12 (6-20)

Appendix

Table B.6.4: Numbers of type 1 diabetes cases by sex, age at diagnosis (in years) and therapy. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are reported, general synthesis replication results are printed in orange, task-specific synthesis replication results in violet. n, number of participants; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Figure B.6.2: Numbers of participants with type 1 diabetes by sex, age at diagnosis (in years) and therapy. Percentile-based 95% bootstrap confidence intervals are reported for original data results. Median and percentile-based 95% confidence intervals of synthetic data results are reported. n, number of participants; MASD, mean absolute standardized difference; CIO, confidence interval overlap

Publication	Key variables	Target variable
Schikowski et al. [ 36 ]	Age , Sex	Hypertension
Fischer et al. [ 15 ]	Age , Sex , Height , Weight , Study Center	VAT
Wienbergen et al. [ 43 ]	Age , Sex , BMI , Education , Birth Germany	EOMI
Breau et al. [ 3 ]	Age , Sex , Weight , Height , Ethnicity	Income Household
Berger et al. [ 1 ]	Age , Sex , Study Center , Education	Suicidal Ideation
Tanoey et al. [ 39 ]	Age , Sex , Height , Migration Background	Diabetes

Appendix

Table C.1.1: Overview of key and target variables for each publication used for attribtute inference attacks. VAT, visceral adipose tissue; EOMI, early-onset myocardial infarction

Figure C.1.1: Utility (MASD) for downstream descriptive analyses from Schikowski et al. [ 36 ] ( Figure 1 ) and Breau et al. [ 3 ] ( Figure 4 ) vs. privacy risk MIA/AIA. Comparison of ARF performance (downstream utility: MASD; privacy risk: MIA & AIA performance) across five minimum node sizes and five alternative synthesizers. Mean values over five synthesizer training repetitions are reported. ARF, adversarial random forests; MASD, mean absolute standardized difference; MIA, membership inference attack; TPR@FPR=0.01, attack true positive rate at a false positive rate of

0.01

; AIA, attribute inference attack; AUROC, area under the receiver operating characteristic curve, Fig, figure; mns, minimum node size of random forest

Figure C.1.2: Utility (WD) for downstream multivariate distribution analysis from Fischer et al. [ 15 ] ( Figure 2 ) vs. privacy risk MIA/AIA. Comparison of ARF performance (downstream utility: WD; privacy risk: MIA & AIA performance) across five minimum node sizes and five alternative synthesizers. Mean values over five synthesizer training repetitions are reported. WD, multivariate Wasserstein distance; MASD, mean absolute standardized difference; MIA, membership inference attack; TPR@FPR=0.01, attack true positive rate at a false positive rate of

0.01

; AIA, attribute inference attack; AUROC, area under the receiver operating characteristic curve, Fig, figure; mns, minimum node size of random forest

Figure C.1.3: Utility (CIO) for downstream regression analyses from Wienbergen et al. [ 43 ] ( Figure 3 ), Berger et al. [ 1 ] ( Figure 5 ) and Tanoey et al. [ 39 ] ( Figure 6 ) vs. privacy risk MIA/AIA. Comparison of ARF performance (downstream utility: CIO; privacy risk: MIA & AIA performance) across five minimum node sizes and five alternative synthesizers. Mean values over five synthesizer training repetitions are reported. CIO, mean confidence interval overlap; MIA, membership inference attack; TPR@FPR=0.01, attack true positive rate at a false positive rate of

0.01

; AIA, attribute inference attack; AUROC, area under the receiver operating characteristic curve, Fig, figure; mns, minimum node size of random forest

Figure C.2.1: Distributional similarity (WD Syn-Test) vs. privacy risk MIA. Comparison of ARF performance (distributional similarity: WD Syn-Test; privacy risk: MIA performance) across five minimum node sizes and five alternative synthesizers. Mean values over five synthesizer training repetitions are reported. WD Syn-Test, multivariate Wasserstein distance between synthetic and test data not used for synthesizer training; MIA, membership inference attack; TPR@FPR=0.01, attack true positive rate at a false positive rate of

0.01

; mns, minimum node size of random forest

Figure C.3.1: Synthesis runtime for Breau et al. [ 3 ] and Berger et al. [ 1 ] . Synthesis runtime comparison (synthesizer training and sampling in seconds) for ARF and five alternative synthesizers. Median, minimum, and maximum values over five synthesizer repetitions are reported. ARF, adversarial random forests with minumum node size of two (default); n, number of training samples; d, dimensionality

Synthetic Tabular Data Generation

Synthetic tabular data generation creates artificial records that preserve useful feature relationships while limiting exposure of sensitive data.

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Evaluating quality in synthetic data generation for large tabular health datasets
Apr 17, 2026Jean-Baptiste Escudié, Benjamin Barnes, Stefan Meisegeier +3Healthcare Synthetic Tabular Data Generation
Centre for Artificial Intelligence in Public Health Research, Robert Koch Institute · German Centre for Cancer Registry Data, Robert Koch Institute · Medical Informatics, Berlin Institute of Health at Charité - Universitätsmedizin Berlin
Synthetic but Not Realistic: The Evaluation Challenge in Generative Modelling for Structured Electronic Medical Records
Jun 8, 2026Nicholas I-Hsien Kuo, Blanca Gallego, Louisa JormSynthetic Tabular Data Generation Electronic Health Records
Centre for Big Data Research in Health, the University of New South Wales, Sydney, Australia
From Statistical Fidelity to Clinical Consistency: Scalable Generation and Auditing of Synthetic Patient Trajectories
Mar 6, 2026Guanglin Zhou, Armin Catic, Motahare Shabestari +4Synthetic Data Generation Synthetic Clinical Data Generation
The University of Queensland, Brisbane, QLD, Australia · The University of New South Wales, Sydney, NSW, Australia · Shahid Sadoughi University of Medical Sciences and Health Services, Yazd, Iran +1

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Evaluating quality in synthetic data generation for large tabular health datasets

Jean-Baptiste Escudié, Benjamin Barnes, Stefan Meisegeier, Klaus Kraywinkel+2

Centre for Artificial Intelligence in Public Health Research, Robert Koch Institute · German Centre for Cancer Registry Data, Robert Koch Institute · Medical Informatics, Berlin Institute of Health at Charité - Universitätsmedizin Berlin

Healthcare Synthetic Tabular Data Generation Synthetic Data Evaluation Synthetic Clinical Data Generation

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There is no consensus in the field of synthetic data on concise metrics for quality evaluations or benchmarks on large health datasets, such as historical epidemiological data. This study presents an evaluation of seven recent models from major machine learning families. The models were evaluated using four different datasets, each with a distinct scale. To ensure a fair comparison, we systematically tuned the hyperparameters of each model for each dataset. We propose a methodology for evaluating the fidelity of synthesized joint distributions, aligning metrics with visualization on a single plot. This method is applicable to any dataset and is complemented by a domain-specific analysis of the German Cancer Registries' epidemiological dataset. The analysis reveals the challenges models face in strictly adhering to the medical domain. We hope this approach will serve as a foundational framework for guiding the selection of synthesizers and remain accessible to all stakeholders involved in releasing synthetic datasets.

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Synthetic Tabular Data Generation

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