Please read the following study:
Bonomi, L., Jiang, X., & Ohno-Machado, L. (2020).
Protecting patient privacy in survival analyses
. Journal of the American Medical Informatics Association, 27(3), 366–375.
Discuss your response to this survival analysis study. Do you have the same concerns as the researchers regarding the patient privacy issues when presenting actuarial/survival analysis tables? Do you have other suggestions regarding protecting patient privacy within a study?
Journal of the American Medical Informatics Association, 27(3), 2020, 366–375
Advance Access Publication Date: 21 November 2019
Research and Applications
Research and Applications
Protecting patient privacy in survival analyses
Luca Bonomi1, Xiaoqian Jiang2, and Lucila Ohno-Machado1,3
Department of Biomedical Informatics, UC San Diego Health, University of California, San Diego, La Jolla, California, USA,
School of Biomedical Informatics, University of Texas Health Science Center at Houston, Houston, Texas, USA, and 3Division of
Health Services Research and Development, VA San Diego Healthcare System, La Jolla, California, USA
Corresponding Author: Luca Bonomi, PhD, UCSD Health Department of Biomedical Informatics, University of California
San Diego, 9500 Gilman Dr., La Jolla, California 92093, USA; email@example.com
Received 15 July 2019; Revised 9 September 2019; Editorial Decision 6 October 2019; Accepted 18 October 2019
Objective: Survival analysis is the cornerstone of many healthcare applications in which the “survival” probability (eg, time free from a certain disease, time to death) of a group of patients is computed to guide clinical
decisions. It is widely used in biomedical research and healthcare applications. However, frequent sharing of
exact survival curves may reveal information about the individual patients, as an adversary may infer the presence of a person of interest as a participant of a study or of a particular group. Therefore, it is imperative to develop methods to protect patient privacy in survival analysis.
Materials and Methods: We develop a framework based on the formal model of differential privacy, which provides provable privacy protection against a knowledgeable adversary. We show the performance of privacyprotecting solutions for the widely used Kaplan-Meier nonparametric survival model.
Results: We empirically evaluated the usefulness of our privacy-protecting framework and the reduced privacy risk
for a popular epidemiology dataset and a synthetic dataset. Results show that our methods significantly reduce the
privacy risk when compared with their nonprivate counterparts, while retaining the utility of the survival curves.
Discussion: The proposed framework demonstrates the feasibility of conducting privacy-protecting survival
analyses. We discuss future research directions to further enhance the usefulness of our proposed solutions in
biomedical research applications.
Conclusion: The results suggest that our proposed privacy-protection methods provide strong privacy protections while preserving the usefulness of survival analyses.
Key words: data privacy, survival analysis, data sharing, Kaplan-Meier, actuarial
Survival analysis aims at computing the “survival” probability (ie,
how long it takes for an event to happen) for a group of observations that contain information about individuals, including time to
event. In medical research, the primary interest of survival analysis
is in the computation and comparison of survival probabilities
across patient groups (eg, standard of care vs. intervention), in
which survival may refer, for example, to the time free from the
onset of a certain disease, time free from recurrence, and time to
death. Survival analysis provides important insights, among other
things, on the effectiveness of treatments, identification of risk,
biomarker utility, and hypotheses testing.1–10 Survival curves aggregate information from groups of interest and are easy to generate, interpret, compare, and publish online. Although aggregate
data can be protected by different approaches, such as, rounding,11,12 binning,13 and perturbation,14 survival analysis models
have special characteristics that warrant the development of customized methods. Before describing our proposed solutions, we
briefly review how survival curves are derived and what their vulnerabilities are from a privacy perspective.
C The Author(s) 2019. Published by Oxford University Press on behalf of the American Medical Informatics Association.
All rights reserved. For permissions, please email: firstname.lastname@example.org
Journal of the American Medical Informatics Association, 2020, Vol. 27, No. 3
Survival analysis methods and privacy
Methods for survival analysis can be divided into 3 main categories:
parametric, semiparametric, and nonparametric models. Parametric
models rely on known probability distributions (eg, the Weibull distribution) to learn a statistical model. These models are less frequently
used than semi- or nonparametric methods, as their parametric
assumptions hardly apply in practice. Even though the released curves
exhibit a natural “smoothing,” studies have shown that the parameters of the model may reveal sensitive information.15 Semiparametric
methods are extremely popular for multivariate analyses and can be
used to identify important risk factors for the event of interest. As an
example, the Cox proportional hazards model16 only assumes a proportional relationship between the baseline hazard and the hazard attributed to a specific group (ie, it does not assume that survival
follows a known distribution, as is the case with parametric models).
Nonparametric models are frequently used to describe the survival
probability over time, without requiring assumptions on the underlying data distribution. Among those models, the Kaplan-Meier (KM)
product-limit estimators are frequent in the biomedical literature. As
an example, a search for PubMed articles using the term KaplanMeier retrieves more than 8000 articles each year, from 2013 to
2018. A search for actuarial returns about 500 articles per year. In
this article, we focus on the KM estimator and present results for the
actuarial model in the Supplementary Appendix. The KM method
generates a survival curve in which each event can be seen by a corresponding drop in the probability of survival. For example, Foldvary
et al4 used the KM method to analyze seizure outcomes for patients
who underwent temporal lobectomy for epilepsy. In contrast, in the
actuarial method,17,18 the survival probability is computed over prespecified periods of time (eg, 1 week, 1 month). For example, Balsam
et al19 used actuarial curves to describe the long-term survival for
valve surgery in an elderly population.
It is surprising that relatively little attention has been given so far
to the protection of individual privacy in survival analysis. Survival
analyses generate aggregated results that are unlikely to directly reveal identifying information (eg, name, SSN).20 However, a knowledgeable adversary, who observes survival analysis results over time,
may be able to determine whether a targeted individual participated
in the study and even if the individual belongs to a particular subgroup in the study, thus learning sensitive phenotypes. Several previous privacy studies have shown that sharing aggregated results may
lead to this privacy risk.15,21,22 For example, small values of counts
(eg, .05) and the differences between groups continue to be statistically significant.
We presented a differentially private framework that can be used to
release survival curves while protecting patient privacy. We demonstrated that our method significantly reduces the risk of a privacy
Journal of the American Medical Informatics Association, 2020, Vol. 27, No. 3
Figure 4. Inference error for the Kaplan-Meier (KM) survival curves for N ¼ 1000, 10000, and 100000 sampled patients obtained with the nonprivate (KM) and private (differentially private KM [DP-KM]) methods. Inference error for KM method and differently private solution (DP-KM) vs the privacy parameter (Þ; with (A) N
¼ 1000, (B) N ¼ 10000, and (C) N ¼ 100000.
Distributed survival analysis
Current research initiatives often rely on collaborative efforts, such
as the clinical data research network pSCANNER60 and equivalent
multicenter consortia. While our proposed methods are designed for
a centralized setting (ie, trusted aggregator), they could be adapted
to the distributed setting. Inspired by previous work,61 we can consider a protocol in which each institution perturbs the local stream
of time to events, while a central unit (not necessary trusted) aggregates and partitions the received streams.
Figure 5. Mean absolute error (MAE) of the differentially private Kaplan-Meier
(DP-KM) curve vs the privacy parameter (Þ; for N ¼ 1000; 10000; and 100000.
Achieving high utility under differential privacy is very challenging
in applications that require continual data releases. Recent works
have proposed extensions of the differential privacy model, in which
privacy is relaxed over time.48,49 Extending our privacy solutions to
satisfy those privacy relaxations would help improve the utility of
the released survival curves.
Solutions for other survival models
breach when compared with its nonprivate counterpart, while
retaining the utility of the survival curves. We discuss several future
In this work, we presented a preliminary study on privacyprotecting survival analyses based on the KM method (the actuarial
method is shown in the Supplementary Appendix). However, there
are many other types of survival models, including those based on
Journal of the American Medical Informatics Association, 2020, Vol. 27, No. 3
Figure 6. Survival curves for breast cancer patients in the Surveillance Epidemiology and End Results dataset for different groups. We sampled 2500 patients for
each group (ie, black, white, and others) who have been diagnosed since 2005. The curves obtained with the (A) nonprivate KM method and (B) differentially private curve (DP-KM).
Table 2. Kolmogorov-Smirnov test results for the Kaplan-Meier
0.37 (1.38 108)
0.21 (4.32 106)
0.48 (2.39 1014)
This work was supported by the National Heart, Lung, and Blood Institute
grant R01HL136835, and National Institute of General Medical Sciences
grant R01GM118609, and National Human Genome Research Institute
Values are the Kolmogorov-Smirnov statistic (P value).
Table 3. Kolmogorov-Smirnov test results for the DP-KM method
0.36 (2.95 108)a 0.23 (1.08 104)a
0.45, 1.15 1012)a
0.34 (1.29 109) 0.21 (4.34 103)
0.48 (6.45 1014)
0.38 (5.28 109)
0.28 (5.47 105) 0.49 (8.70 1015)
Values are the Kolmogorov-Smirnov statistic (P value). The test results
obtained on the curve produced by the differentially private Kaplan-Meier
DP: differentially private.
Differentially private curves are not statistically different from the original
ones (P > .05), and they preserve the separation between groups (P < .05). Cox proportional hazards,16 accelerated failure time,62 recurrent time-to-event data,63 and competing risk64 methods. Building on our results, we plan to develop new privacy methods for enabling other popular privacy-protecting survival analyses in the future. CONCLUSION Publication of survival curves is frequent in the biomedical literature and is becoming more frequent in websites. In this work, we studied the privacy risk in conducting survival analyses and proposed a differentially private framework for the KM product limit estimator. The differentially private curves generated by our framework prevent an adversary to infer the time to event for a particular target individual without a significant error (eg, 250 time units) while retaining the usefulness of the original nonprivate curves. LB developed the methods, contributed the majority of the writing, and conducted the experiments. XJ provided helpful comments on both methods and presentation. LO-M provided the motivation for this work, detailed edits, and critical suggestions. SUPPLEMENTARY MATERIAL Supplementary material is available at Journal of the American Medical Informatics Association online. CONFLICT OF INTEREST STATEMENT None declared. REFERENCES 1. Ohno-Machado L. Modeling medical prognosis: survival analysis techniques. J Biomed Inform 2001; 34 (6): 428–39. 2. Cortese G, Scheike TH, Martinussen T. Flexible survival regression modelling. Stat Methods Med Res 2010; 19 (1): 5–28. 3. Schwartzbaum JA, Hulka BS, Fowler JW, Kaufman DG, Hoberman D. The influence of exogenous estrogen use on survival after diagnosis of endometrial cancer. Am J Epidemiol 1987; 126 (5): 851–60. 4. Foldvary N, Nashold B, Mascha E. Seizure outcome after temporal lobectomy for temporal lobe epilepsy: a Kaplan-Meier survival analysis. Neurology 2000; 54 (3): 630. 5. Galon J, Costes A, Sanchez-Cabo F, et al. 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