Survival analyses generate aggregated results that are unlikely to directly reveal identifying information (eg, name, SSN). It is surprising that relatively little attention has been given so far to the protection of individual privacy in survival analysis. For example, Balsam et al 19 used actuarial curves to describe the long-term survival for valve surgery in an elderly population. 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, Foldvary et al 4 used the KM method to analyze seizure outcomes for patients who underwent temporal lobectomy for epilepsy. The KM method generates a survival curve in which each event can be seen by a corresponding drop in the probability of survival. In this article, we focus on the KM estimator and present results for the actuarial model in the Supplementary Appendix. A search for actuarial returns about 500 articles per year. As an example, a search for PubMed articles using the term Kaplan-Meier retrieves more than 8000 articles each year, from 2013 to 2018. Among those models, the Kaplan-Meier (KM) product-limit estimators are frequent in the biomedical literature. Nonparametric models are frequently used to describe the survival probability over time, without requiring assumptions on the underlying data distribution. As an example, the Cox proportional hazards model 16 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). 15 Semiparametric methods are extremely popular for multivariate analyses and can be used to identify important risk factors for the event of interest. Even though the released curves exhibit a natural “smoothing,” studies have shown that the parameters of the model may reveal sensitive information. These models are less frequently used than semi- or nonparametric methods, as their parametric assumptions hardly apply in practice. Parametric models rely on known probability distributions (eg, the Weibull distribution) to learn a statistical model.
Methods for survival analysis can be divided into 3 main categories: parametric, semiparametric, and nonparametric models. Before describing our proposed solutions, we briefly review how survival curves are derived and what their vulnerabilities are from a privacy perspective. 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. 1–10 Survival curves aggregate information from groups of interest and are easy to generate, interpret, compare, and publish online.
Survival analysis provides important insights, among other things, on the effectiveness of treatments, identification of risk, biomarker utility, and hypotheses testing.
#UNITE PRIVATE NETWORKS AND COX FREE#
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. 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. 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.
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