[Paper Review] Covariate Microaggregation for Logistic Regression: An Application for Analysis of Confidential Data

Paramita Saha‐Chaudhuri|arXiv (Cornell University)|Mar 17, 2016

Privacy-Preserving Technologies in Data22 references3 citations

TL;DR

This paper proposes Pooled Logistic Regression (PoLoR), a privacy-preserving method for analyzing binary disease outcomes in distributed health data networks. By microaggregating covariates into pools before sharing aggregate-level data with a central analysis center, PoLoR enables consistent estimation of logistic regression parameters—such as odds ratios—without exposing individual-level information, while maintaining compatibility with standard statistical software and enabling model selection via likelihood ratio tests.

ABSTRACT

In the recent past, electronic health records and distributed data networks emerged as a viable resource for medical and scientific research. As the use of confidential patient information from such sources become more common, maintaining privacy of patients is of utmost importance. For a binary disease outcome of interest, we show that the techniques of microaggregation (equivalent to specimen pooling) and \underline{Po}oled \underline{Lo}gistic \underline{R}egression (PoLoR) could be applied for analysis of large and/or distributed data while respecting patient privacy. PoLoR is exactly the same as standard logistic regression, but instead of using individual covariate level, the analysis uses microaggregated covariate level when microaggregation is conditional on the outcome status. Aggregate levels of covariates can be passed from the nodes of the network to the analysis center without revealing individual-level microdata and can be used very easily with standard softwares for estimation of disease odds ratio associated with a set of categorical or continuous covariates. Microaggregation of covariates allows for consistent estimation of the parameters of logistic regression model that can include confounders and transformation of exposure. Additionally, since the microdata can be accessed within nodes, effect modifiers can be accommodated and consistently estimated. For analysis of confidential health data, covariate microaggregation for logistic regression will provide a practical and straightforward alternative to more complicated existing options.

Motivation & Objective

• To address the challenge of analyzing confidential patient data in distributed health data networks while preserving patient privacy.
• To develop a practical, computationally efficient alternative to complex privacy-preserving methods for logistic regression with binary outcomes.
• To enable estimation of odds ratios and model parameters using only aggregate covariate levels, avoiding individual-level data sharing.
• To support model selection and standard error estimation using familiar statistical tools despite data privacy constraints.
• To demonstrate that microaggregation of covariates maintains parameter consistency and reduces data dimensionality in big data settings.

Proposed method

• Microaggregation of covariates is applied at each data node, grouping individuals into pools of size g to create aggregate-level covariate values.
• The pooled covariate data—derived from individual-level data within each node—are shared with the central analysis center, not individual records.
• A standard logistic regression model is fitted on the aggregate-level covariates, equivalent to PoLoR, which produces consistent parameter estimates.
• The method supports both continuous and categorical covariates, including transformations and confounder adjustment.
• Model selection and inference are performed using standard likelihood ratio tests and robust standard errors, ensuring validity.
• The approach is scalable and maintains privacy by ensuring no individual-level data leave the nodes, with only aggregate summaries exchanged.

Experimental results

Research questions

• RQ1 Can microaggregation of covariates enable consistent estimation of logistic regression parameters in a distributed data network without exposing individual-level data?
• RQ2 How does the choice of pool size g affect the bias and precision of odds ratio estimates in PoLoR?
• RQ3 Can PoLoR support model selection and standard error estimation using conventional statistical software and methods?
• RQ4 Is PoLoR applicable to both continuous and categorical covariates, including transformed exposures and confounders?
• RQ5 What are the asymptotic properties of PoLoR estimators, and how do they depend on the number of pools rather than individuals?

Key findings

• PoLoR produces consistent estimates of logistic regression coefficients and odds ratios when using microaggregated covariate levels instead of individual-level data.
• For the colon cancer dataset, PoLoR with pool sizes g = 3 and g = 4 yielded log OR estimates close to those from standard logistic regression, with only minor differences in standard errors.
• The method maintains model validity, allowing for likelihood ratio tests and standard error estimation using conventional software.
• A pool size between 5 and 20 provides a reasonable balance between privacy protection and estimation bias, with g > 40 leading to increased bias due to regression to the mean.
• PoLoR is scalable and suitable for big data and resource-constrained environments due to reduced data dimensionality and single-pass estimation.
• The approach is not intended for repeated updates; adding new records requires re-pooling and re-analysis from scratch.