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arxiv: 2604.06499 · v1 · submitted 2026-04-07 · 📊 stat.AP · stat.ML

Equivalence Testing Under Privacy Constraints

Savita Pareek , Luca Insolia , Roberto Molinari , St\'ephane Guerrier This is my paper

Pith reviewed 2026-05-10 17:52 UTC · model grok-4.3

classification 📊 stat.AP stat.ML
keywords differential privacyequivalence testingTOST proceduresimulation calibrationmeansproportionsprivacy-preserving statisticstype I error control
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The pith

A simulation-calibrated procedure performs equivalence tests for means and proportions while satisfying differential privacy.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops DP-TOST, a single framework that adds calibrated noise to standard equivalence test statistics so that individual data remain private. Because the exact distribution of the noisy statistic is intractable, the method uses repeated simulations to set critical values that keep the type I error rate at the nominal level. Numerical checks show that power approaches the power of ordinary non-private equivalence tests once the privacy budget or the sample size becomes large enough. The construction applies equally to tests for means and for proportions, which matters for settings such as hospital comparisons or laboratory calibration where both privacy and equivalence decisions are required.

Core claim

DP-TOST conducts differentially private equivalence testing of means and proportions by injecting noise into the usual two one-sided test statistics and calibrating rejection thresholds via simulation so that the finite-sample type I error stays at the nominal alpha while power converges to the non-private benchmark as the privacy parameter or sample size increases.

What carries the argument

DP-TOST is a simulation-based calibration procedure that adds differential-privacy noise to the equivalence test statistic and determines critical values from Monte Carlo draws under the null.

If this is right

  • Equivalence testing for means and proportions can be performed on sensitive data without exceeding the nominal type I error rate.
  • Power of the private test increases toward the power of the corresponding non-private test as the privacy budget grows or as sample size increases.
  • The same simulation-calibration approach works uniformly for both continuous means and binary proportions.
  • The framework supplies a practical tool for privacy-preserving analyses in domains that require both statistical equivalence decisions and individual-level confidentiality.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same noise-injection-plus-simulation strategy could be adapted to other two-sided or one-sided tests that currently lack private versions.
  • Multi-site studies could adopt DP-TOST to compare treatment effects across institutions while releasing only the noisy summary statistics.
  • Computational cost of the required simulations grows with desired precision, creating a practical trade-off between privacy strength and run time that users must manage.

Load-bearing premise

Simulation-based calibration must produce a sufficiently accurate approximation to the finite-sample distribution of the noisy test statistic.

What would settle it

A set of repeated simulations under the boundary null hypothesis in which the empirical rejection rate substantially exceeds the nominal alpha for any fixed privacy budget and sample size would falsify the type I error claim.

Figures

Figures reproduced from arXiv: 2604.06499 by Luca Insolia, Roberto Molinari, Savita Pareek, St\'ephane Guerrier.

Figure 1
Figure 1. Figure 1: Empirical test size (y-axis) as a function of the sample size (x-axis) for the non-private TOST and DP [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Empirical probability of rejecting H0 (y-axis) as a function of the true difference in proportions (x-axis) for the non-private TOST and DP-TOST with different privacy budgets ϵ. Each column corresponds to a fixed value of π1 ∈ {0.5, 0.65, 0.8} and each row represents a given sample size n ∈ {200, 400, 800}. Vertical dashed lines denote the equivalence margins c0 = 0.1, and the horizontal dashed line repre… view at source ↗
Figure 3
Figure 3. Figure 3: Empirical test size (y-axis) as a function of the half-width [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Empirical probability of rejecting H0 (y-axis) as a function of the true difference in means (x-axis) for the non-private TOST and DP-TOST with different privacy budgets ϵ. Each column corresponds to a different data clamping scheme, and each row represents a given sample size n ∈ {200, 400, 800}. Vertical dashed lines denote the equivalence margins c0 = 0.5, and the horizontal dashed line represents the n… view at source ↗
Figure 5
Figure 5. Figure 5: Kernel density estimates of log-transformed CD4 T-cell counts at week 20 (CD4 [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Decision agreement for equivalence testing of ”Off-Treat” proportions between the non-private TOST and [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Decision agreement for equivalence testing of mean log-transformed CD4 counts (CD4 [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
read the original abstract

Protecting individual privacy is essential across research domains, from socio-economic surveys to big-tech user data. This need is particularly acute in healthcare, where analyses often involve sensitive patient information. A typical example is comparing treatment efficacy across hospitals or ensuring consistency in diagnostic laboratory calibrations, both requiring privacy-preserving statistical procedures. However, standard equivalence testing procedures for differences in proportions or means, commonly used to assess average equivalence, can inadvertently disclose sensitive information. To address this problem, we develop differentially private equivalence testing procedures that rely on simulation-based calibration, as the finite-sample distribution is analytically intractable. Our approach introduces a unified framework, termed DP-TOST, for conducting differentially private equivalence testing of both means and proportions. Through numerical simulations and real-world applications, we demonstrate that the proposed method maintains type-I error control at the nominal level and achieves power comparable to its non-private counterpart as the privacy budget and/or sample size increases, while ensuring strong privacy guarantees. These findings establish a reliable and practical framework for privacy-preserving equivalence testing in high-stakes fields such as healthcare, among others.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript proposes DP-TOST, a unified framework for differentially private equivalence testing of means and proportions. It relies on simulation-based calibration to approximate the finite-sample null distribution of the noisy test statistic under differential privacy mechanisms (since the distribution is analytically intractable), and claims that the procedure maintains type-I error at the nominal level while achieving power comparable to the non-private TOST as the privacy budget or sample size grows, with demonstrations via numerical simulations and real-world applications.

Significance. If the simulation calibration can be shown to deliver reliable type-I error control, the work supplies a practical extension of equivalence testing to privacy-constrained settings, which is relevant for healthcare and other sensitive domains. It correctly builds on standard DP primitives rather than introducing ad-hoc mechanisms, and the empirical results suggest the power loss is modest for moderate privacy budgets. The absence of analytical error bounds on the Monte Carlo step, however, leaves the central guarantee on an empirical footing.

major comments (1)
  1. The claim of nominal type-I error control (abstract and methods) rests entirely on Monte Carlo approximation of the null distribution of the DP-perturbed test statistic. The manuscript provides no simulation count, Monte Carlo standard-error estimates, or convergence diagnostics for the calibrated critical values or p-value thresholds. This is load-bearing because the privacy noise renders the distribution intractable, and without reported precision on the approximation the control is only empirically suggested, especially near the equivalence boundary or for small ε and n where noise dominates sampling variability.
minor comments (2)
  1. The abstract states that simulations 'show type-I error control' but does not specify the range of ε, δ, n, or equivalence margins examined; adding a brief table or sentence summarizing the simulation grid would improve reproducibility.
  2. Notation for the privacy mechanism (e.g., Laplace or Gaussian noise scale) and the exact form of the calibrated rejection region should be stated explicitly in the main text rather than deferred to supplementary material.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive and detailed review. We appreciate the recognition of DP-TOST as a practical extension of equivalence testing to privacy-constrained settings. We agree that the Monte Carlo calibration step requires more explicit reporting to support the type-I error claims and have prepared revisions accordingly.

read point-by-point responses

  1. Referee: The claim of nominal type-I error control (abstract and methods) rests entirely on Monte Carlo approximation of the null distribution of the DP-perturbed test statistic. The manuscript provides no simulation count, Monte Carlo standard-error estimates, or convergence diagnostics for the calibrated critical values or p-value thresholds. This is load-bearing because the privacy noise renders the distribution intractable, and without reported precision on the approximation the control is only empirically suggested, especially near the equivalence boundary or for small ε and n where noise dominates sampling variability.

    Authors: We agree that the manuscript should provide greater transparency on the Monte Carlo procedure used to calibrate critical values and p-value thresholds. In the revised manuscript we will explicitly state the number of Monte Carlo replications employed for each calibration, report Monte Carlo standard-error estimates for the resulting quantiles, and include convergence diagnostics (e.g., stability checks across increasing replication counts). These additions will be placed in the Methods section and highlighted in the simulation results, with particular attention to the regimes of small ε and n. While analytical error bounds on the Monte Carlo approximation remain intractable given the privacy-induced noise, the expanded reporting will make the empirical foundation of the type-I error control fully reproducible and quantifiable. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper constructs DP-TOST by combining standard differential privacy mechanisms (e.g., noise addition) with simulation-based calibration to handle the analytically intractable finite-sample null distribution of the test statistic. This is a standard, non-circular technique for Monte Carlo testing rather than a self-definitional loop or a fitted parameter renamed as a prediction. Type-I error control is asserted via numerical simulations, but the core derivation relies on established DP primitives and does not reduce to its own inputs by construction, self-citation chains, or imported uniqueness results. The approach is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the intractability of the finite-sample distribution under privacy noise and on the ability of simulation calibration to restore error control.

axioms (1)
  • domain assumption The finite-sample distribution of the test statistic is analytically intractable under differential privacy
    Explicitly stated in the abstract as the reason for using simulation-based calibration.

pith-pipeline@v0.9.0 · 5486 in / 1175 out tokens · 38433 ms · 2026-05-10T17:52:10.962403+00:00 · methodology

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Reference graph

Works this paper leans on

59 extracted references · 59 canonical work pages

  1. [1]

    D. J. Schuirmann. A comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of average bioavailability.Journal of Pharmacokinetics and Biopharmaceutics, 15(6):657–680, 1987

    work page 1987

  2. [2]

    C. Metzler. Bioavailability – a problem in equivalence.Journal of Pharmaceutical Sciences, 30:309–317, 1974

    work page 1974

  3. [3]

    W. J. Westlake. Use of confidence intervals in analysis of comparative bioavailability trials.Journal of Pharma- ceutical Sciences, 61(8):1340–1341, 1972

    work page 1972

  4. [4]

    W. J. Westlake. Symmetrical confidence intervals for bioequivalence trials.Biometrics, 32:741–744, 1976

    work page 1976

  5. [5]

    Food and Drug Administration

    U.S. Food and Drug Administration. Bioequivalence studies with pharmacokinetic endpoints for drugs submitted under an ANDA. Technical report, Center for Drug Evaluation and Research (CDER), Silver Spring, MD, USA,

    work page

  6. [6]

    Accessed: 2025-10-17

    URLhttps://www.fda.gov/media/87219/download. Accessed: 2025-10-17

    work page 2025

  7. [7]

    Guideline on the investigation of bioequivalence

    European Medicines Agency. Guideline on the investigation of bioequivalence. Technical report, Committee for Medicinal Products for Human Use (CHMP), London, UK, 2010. URLhttps://www.ema.europa.eu/en/ documents/scientific-guideline/guideline-investigation-bioequivalence-rev1_en.pdf. Ac- cessed: 2025-10-17

    work page 2010

  8. [8]

    M13a: Bioequivalence for immediate-release solid oral dosage forms

    International Council for Harmonisation of Technical Requirements for Pharmaceuticals for Human Use (ICH). M13a: Bioequivalence for immediate-release solid oral dosage forms. Technical report, ICH, Geneva, Switzer- land, 2024. URLhttps://www.ich.org/page/m13-bioequivalence. Accessed: 2025-10-17

    work page 2024

  9. [9]

    Annex 6: Multisource (generic) pharmaceutical products: Guide- lines on registration requirements to establish interchangeability

    World Health Organization. Annex 6: Multisource (generic) pharmaceutical products: Guide- lines on registration requirements to establish interchangeability. Technical Report 992, World Health Organization, Geneva, Switzerland, 2017. URLhttps://www.who.int/docs/ default-source/medicines/norms-and-standards/guidelines/regulatory-standards/ trs992-annex6-wh...

    work page 2017

  10. [10]

    not different

    Myles W. O’Brien and Derek S. Kimmerly. Is “not different” enough to conclude similar cardiovascular re- sponses across sexes?American Journal of Physiology-Heart and Circulatory Physiology, 322(3):H355–H358, 2022

    work page 2022

  11. [11]

    Wehrle, T

    F.M. Wehrle, T. Bartal, M. Adams, D. Bassler, C.F. Hagmann, O. Kretschmar, G. Natalucci, and B. Latal. Similarities and differences in the neurodevelopmental outcome of children with congenital heart disease and children born very preterm at school entry.The Journal of Pediatrics, 250:29–37.e1, 2022

    work page 2022

  12. [12]

    Sansone, L.G

    P. Sansone, L.G. Giaccari, C. Aurilio, F. Coppolino, M.B. Passavanti, V . Pota, and M.C. Pace. Comparative efficacy of tapentadol versus tapentadol plus duloxetine in patients with chemotherapy-induced peripheral neu- ropathy.Cancers, 14:4002, 2022

    work page 2022

  13. [13]

    Branscheidt, N

    M. Branscheidt, N. Ejaz, J. Xu, M. Widmer, M.D. Harran, J.C. Cort ´es, T. Kitago, P. Celnik, C. Hernandez- Castillo, J. Diedrichsen, A. Luft, and J.W. Krakauer. No evidence for motor-recovery-related cortical connectivity changes after stroke using resting-state fmri.Journal of Neurophysiology, 127:637–650, 2022

    work page 2022

  14. [14]

    Lakens, A.M

    D. Lakens, A.M. Scheel, and P.M. Isager. Equivalence testing for psychological research: A tutorial.Advances in Methods and Practices in Psychological Science, 1:259–269, 2018

    work page 2018

  15. [15]

    F. Feri, C. Giannetti, and P. Guarnieri. Risk-taking for others: An experiment on the role of moral discussion. Journal of Behavioral and Experimental Finance, 37:100735, 2023. 15 A PREPRINT

    work page 2023

  16. [16]

    Aggarwal, J

    M. Aggarwal, J. Allen, A. Coppock, D. Frankowski, S. Messing, K. Zhang, J. Barnes, A. Beasley, H. Hantman, and S. Zheng. A 2 million-person, campaign-wide field experiment shows how digital advertising affects voter turnout.Nature Human Behaviour, pages 1–10, 2023

    work page 2023

  17. [17]

    Sureshkumar, R

    H. Sureshkumar, R. Xu, N. Erukulla, A. Wadhwa, and L. Zhao. “snap on” or not? a validation on the measure- ment tool in a virtual reality application.Journal of Digital Imaging, 35:692–703, 2022

    work page 2022

  18. [18]

    M. Meyners. Equivalence Tests - A Review.Food Quality and Preference, 26:231–245, 2012

    work page 2012

  19. [19]

    Leday, Jasper Engel, Jack H

    Gwena ¨el G.R. Leday, Jasper Engel, Jack H. V ossen, Ric C.H. de V os, and Hilko van der V oet. Multivariate equivalence testing for food safety assessment.Food and Chemical Toxicology, 170:113446, 2022

    work page 2022

  20. [20]

    A method for determining equivalence in industrial applications.Quality Engineering, 14(3):375–380, 2002

    Scott J Richter and Carri Richter. A method for determining equivalence in industrial applications.Quality Engineering, 14(3):375–380, 2002

    work page 2002

  21. [21]

    Investigation of ideal-ct device equivalence: Are all devices equal?Transportation Research Record, 2676(5):1–12, 2022

    Nathan Moore, Richard Steger, Benjamin Bowers, and Adam Taylor. Investigation of ideal-ct device equivalence: Are all devices equal?Transportation Research Record, 2676(5):1–12, 2022

    work page 2022

  22. [22]

    Mazzolari, S

    R. Mazzolari, S. Porcelli, D.J. Bishop, and D. Lakens. Myths and methodologies: The use of equivalence and non-inferiority tests for interventional studies in exercise physiology and sport science.Experimental Physiology, 107:201–212, 2022

    work page 2022

  23. [23]

    T. Tango. Equivalence test and confidence interval for the difference in proportions for the paired-sample design. Statistics in Medicine, 17(8):891–908, 1998

    work page 1998

  24. [24]

    J. J. Chen, Y . Tsong, and S.H. Kang. Tests for equivalence or noninferiority between two proportions.Drug Information Journal, 34:569–578, 2000

    work page 2000

  25. [25]

    Wellek.Testing Statistical Hypotheses of Equivalence and Noninferiority

    S. Wellek.Testing Statistical Hypotheses of Equivalence and Noninferiority. CRC Press, Boca Raton, FL, 2nd edition, 2010

    work page 2010

  26. [26]

    Chapman and Hall/CRC, New York, 2nd edition, 2017

    Scott D Patterson and Byron Jones.Bioequivalence and Statistics in Clinical Pharmacology. Chapman and Hall/CRC, New York, 2nd edition, 2017

    work page 2017

  27. [27]

    Berger and J.C

    R.L. Berger and J.C. Hsu. Bioequivalence trials, intersection-union tests and equivalence confidence sets.Sta- tistical Science, 11(4):283–319, November 1996

    work page 1996

  28. [28]

    ElSayed, A

    Z. ElSayed, A. Abdelgawad, and N. Elsayed. Cybersecurity and frequent cyber attacks on IoT devices in health- care: Issues and solutions.arXiv preprint arXiv:2501.11250, 2025

    work page arXiv 2025

  29. [29]

    Solove and W

    D.J. Solove and W. Hartzog. The great scrape: The clash between scraping and privacy.California Law Review, 113:1521–1580, 2025

    work page 2025

  30. [30]

    Data privacy laws and compliance: A comparative review of the eu gdpr and usa regulations.Computer Science & IT Research Journal, 5(3):528–543, 2024

    Seun Solomon Bakare, Adekunle Oyeyemi Adeniyi, Chidiogo Uzoamaka Akpuokwe, and Nkechi Emmanuella Eneh. Data privacy laws and compliance: A comparative review of the eu gdpr and usa regulations.Computer Science & IT Research Journal, 5(3):528–543, 2024

    work page 2024

  31. [31]

    Homer, S

    N. Homer, S. Szelinger, M. Redman, D. Duggan, W. Tembe, J. Muehling, J. V . Pearson, D. A. Stephan, S. F. Nelson, and D. W. Craig. Resolving individuals contributing trace amounts of dna to highly complex mixtures using high-density snp genotyping microarrays.PLoS Genetics, 4(8):1–9, 2008

    work page 2008

  32. [32]

    Narayanan and V

    A. Narayanan and V . Shmatikov. Robust de-anonymization of large sparse datasets. InProceedings of the 2008 IEEE Symposium on Security and Privacy (SP 2008), pages 111–125, Oakland, CA, USA, 2008. Proceedings of the IEEE Symposium on Security and Privacy

    work page 2008

  33. [33]

    M. Gotz, A. Machanavajjhala, G. Wang, X. Xiao, and J. Gehrke. Publishing search logs – a comparative study of privacy guarantees.IEEE transactions on knowledge and data engineering, 24(3):520–532, 2012

    work page 2012

  34. [34]

    C. Dwork. Differential privacy. In M. Bugliesi, B. Preneel, V . Sassone, and I. Wegener, editors,Automata, Languages and Programming, volume vol 4052 ofLecture Notes in Computer Science, pages 1–12, Berlin, Heidelberg, 2006. Springer. doi: 10.1007/11787006 1. URLhttps://doi.org/10.1007/11787006_1

    work page doi:10.1007/11787006 2006

  35. [35]

    Dwork and A

    C. Dwork and A. Roth. The algorithmic foundations of differential privacy.Foundations and Trends in Theoret- ical Computer Science, 9(3–4):211–407, 2014

    work page 2014

  36. [36]

    Karwa and S

    V . Karwa and S. Vadhan. Finite sample differentially private confidence intervals. InProceedings of the 9th Innovations in Theoretical Computer Science Conference (ITCS 2018), pages 44:1–44:9, Dagstuhl, Germany,

    work page 2018

  37. [37]

    Finite Sample Differentially Private Confidence Intervals

    Innovations in Theoretical Computer Science Conference (ITCS), Schloss Dagstuhl–Leibniz-Zentrum f¨ur Informatik. doi: 10.4230/LIPIcs.ITCS.2018.44. URLhttps://doi.org/10.4230/LIPIcs.ITCS.2018.44

    work page doi:10.4230/lipics.itcs.2018.44 2018

  38. [38]

    J. A. Awan and A. Slavkovi ´c. Differentially private inference for binomial data.Journal of Privacy and Confi- dentiality, 10(1), 2020. 16 A PREPRINT

    work page 2020

  39. [39]

    Fiducial matching: Differentially private inference for categorical data.arXiv preprint arXiv:2507.11762, 2025

    Ogonnaya Michael Romanus, Younes Boulaguiem, and Roberto Molinari. Fiducial matching: Differentially private inference for categorical data.arXiv preprint arXiv:2507.11762, 2025

    work page arXiv 2025

  40. [40]

    Gaboardi, H

    M. Gaboardi, H. Lim, R. Rogers, and S. Vadhan. Differentially private chi-squared hypothesis testing: Goodness of fit and independence testing. InProceedings of the 33rd International Conference on Machine Learning (ICML), pages 2111–2120. Proceedings of The 33rd International Conference on Machine Learning, PMLR, 2016

    work page 2016

  41. [41]

    Aliakbarpour, I

    M. Aliakbarpour, I. Diakonikolas, and R. Rubinfeld. Differentially private identity and equivalence testing of discrete distributions. InProceedings of the 35th International Conference on Machine Learning (ICML 2018), pages 169–178, Stockholm, Sweden, 2018. International Conference on Machine Learning (ICML), PMLR. URLhttps://proceedings.mlr.press/v80/al...

    work page 2018

  42. [42]

    Omer and O

    D. Omer and O. Sheffet. Differentially private equivalence testing for continuous distributions and applications. InProceedings of the 38th Conference on Neural Information Processing Systems (NeurIPS 2024), Vancouver, Canada, 2024. Proceedings of the 38th Conference on Neural Information Processing Systems (NeurIPS)

    work page 2024

  43. [43]

    S. Orso, M. Karemera, M.-P. Victoria-Feser, and S. Guerrier. An accurate percentile method for parametric inference based on asymptotically biased estimators.arXiv preprint, 2024

    work page 2024

  44. [44]

    Gourieroux, A

    C. Gourieroux, A. Monfort, and E. Renault. Indirect inference.Journal of Applied Econometrics, 8(S1):S85– S118, 1993

    work page 1993

  45. [45]

    S. M. Hammer, D. A. Katzenstein, M. D. Hughes, H. Gundacker, R. T. Schooley, R. H. Haubrich, W. K. Henry, M. M. Lederman, J. P. Phair, M. Niu, et al. A trial comparing nucleoside monotherapy with combination therapy in hiv-infected adults with cd4 cell counts from 200 to 500 per cubic millimeter.New England Journal of Medicine, 335(15):1081–1090, 1996

    work page 1996

  46. [46]

    Equivalence testing for binomial random variables: Which test to use?The American Statistician, 55(4):279–287, November 2001

    Lawrence Barker, Henry Rolka, Deborah Rolka, and Cedric Brown. Equivalence testing for binomial random variables: Which test to use?The American Statistician, 55(4):279–287, November 2001

    work page 2001

  47. [47]

    Dinur and K

    I. Dinur and K. Nissim. Revealing information while preserving privacy. InProceedings of the twenty-second ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems, pages 202–210. PODS ’03: Proceedings of the 22nd ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems, 2003

    work page 2003

  48. [48]

    and Smith, A

    C. Dwork, F. McSherry, K. Nissim, and A. Smith. Calibrating noise to sensitivity in private data analysis. In S. Halevi and T. Rabin, editors,Theory of Cryptography Conference, volume vol 3876 ofLecture Notes in Computer Science, pages 265–284, Berlin, Heidelberg, 2006. Springer. doi: 10.1007/11681878 14. URL https://doi.org/10.1007/11681878_14

    work page doi:10.1007/11681878 2006

  49. [49]

    Alabi and S

    D. Alabi and S. Vadhan. Hypothesis testing for differentially private linear regression. InAdvances in Neu- ral Information Processing Systems 35 (NeurIPS 2022), pages 14196–14209. Advances in Neural Information Processing Systems 35 (NeurIPS), 2022

    work page 2022

  50. [50]

    Simulation-based bias correction methods for complex models.Journal of the American Statistical Association, 114(525):146–157, 2019

    St ´ephane Guerrier, Elise Dupuis-Lozeron, Yanyuan Ma, and Maria-Pia Victoria-Feser. Simulation-based bias correction methods for complex models.Journal of the American Statistical Association, 114(525):146–157, 2019

    work page 2019

  51. [51]

    Juraska, P

    M. Juraska, P. B. Gilbert, X. Lu, M. Zhang, M. Davidian, and A. A. Tsiatis.speff2trial: Semiparametric Efficient Estimation for a Two-Sample Treatment Effect, 2025. URLhttps://github.com/mjuraska/speff2trial. R package version 1.0.5

    work page 2025

  52. [52]

    N. P. Terry. Protecting patient privacy in the age of big data.UMKC Law Review, 81:385–415, 2012

    work page 2012

  53. [53]

    Masood, Y

    I. Masood, Y . Wang, A. Daud, N. R. Aljohani, and H. Dawood. Towards smart healthcare: Patient data privacy and security in sensor-cloud infrastructure.Wireless Communications and Mobile Computing, 2018, 2018

    work page 2018

  54. [54]

    W. Xia, W. Liu, Z. Wan, Y . V orobeychik, M. Kantarcioglu, S. Nyemba, E. W. Clayton, and B. A. Malin. Enabling realistic health data re-identification risk assessment through adversarial modeling.Journal of the American Medical Informatics Association, 28(4):744–752, 2021

    work page 2021

  55. [55]

    S. A. Battistini Garcia, M. Zubair, and N. Guzman. Cd4 cell count and hiv. InStatPearls [Internet], Treasure Island (FL), January 2025. StatPearls [Internet], StatPearls Publishing

    work page 2025

  56. [56]

    W. Liu, Y . Zhang, H. Yang, and Q. Meng. A survey on differential privacy for medical data analysis.Annals of Data Science, pages 1–15, 2023

    work page 2023

  57. [57]

    Hauschke, V

    D. Hauschke, V . Steinijans, and I. Pigeot.Bioequivalence Studies in Drug Development: Methods and Applica- tions. John Wiley & Sons, Ltd, Chichester, UK, 2007

    work page 2007

  58. [58]

    Hoffelder, R

    T. Hoffelder, R. G ¨ossl, and S. Wellek. Multivariate equivalence tests for use in pharmaceutical development. Journal of Biopharmaceutical Statistics, 25(3):417–437, 2015. 17 A PREPRINT

    work page 2015

  59. [59]

    Pallmann and T

    P. Pallmann and T. Jaki. Simultaneous confidence regions for multivariate bioequivalence.Statistics in Medicine, 36(29):4585–4603, 2017. 18

    work page 2017