Privacy-protecting estimation of adjusted risk ratios using modified Poisson regression in multi-center studies

Di Shu,Jessica G Young,Sengwee Toh

doi:10.1186/s12874-019-0878-6

Di Shu, Jessica G Young + Show 1 more

Open Access

https://doi.org/10.1186/s12874-019-0878-6

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Abstract

BackgroundMulti-center studies can generate robust and generalizable evidence, but privacy considerations and legal restrictions often make it challenging or impossible to pool individual-level data across data-contributing sites. With binary outcomes, privacy-protecting distributed algorithms to conduct logistic regression analyses have been developed. However, the risk ratio often provides a more transparent interpretation of the exposure-outcome association than the odds ratio. Modified Poisson regression has been proposed to directly estimate adjusted risk ratios and produce confidence intervals with the correct nominal coverage when individual-level data are available. There are currently no distributed regression algorithms to estimate adjusted risk ratios while avoiding pooling of individual-level data in multi-center studies.MethodsBy leveraging the Newton-Raphson procedure, we adapted the modified Poisson regression method to estimate multivariable-adjusted risk ratios using only summary-level information in multi-center studies. We developed and tested the proposed method using both simulated and real-world data examples. We compared its results with the results from the corresponding pooled individual-level data analysis.ResultsOur proposed method produced the same adjusted risk ratio estimates and standard errors as the corresponding pooled individual-level data analysis without pooling individual-level data across data-contributing sites.ConclusionsWe developed and validated a distributed modified Poisson regression algorithm for valid and privacy-protecting estimation of adjusted risk ratios and confidence intervals in multi-center studies. This method allows computation of a more interpretable measure of association for binary outcomes, along with valid construction of confidence intervals, without sharing of individual-level data.

Highlights

Multi-center studies can generate robust and generalizable evidence, but privacy considerations and legal restrictions often make it challenging or impossible to pool individual-level data across data-contributing sites
Log-binomial regression can directly estimate adjusted risk ratios without requiring the rare disease assumption, but it is susceptible to non-convergence issues when the maximum likelihood estimators lie near the boundary of the parameter space [9, 10]
As a solution to these challenges, Zou [12] proposed a modified Poisson regression approach that allows direct estimation of adjusted risk ratios even when the rare disease assumption is not met. This approach avoids the convergence issues typically observed in log-binomial regression and, unlike conventional Poisson regression, provides consistent variance estimates and confidence intervals with the correct nominal coverage

Summary

Introduction

Multi-center studies can generate robust and generalizable evidence, but privacy considerations and legal restrictions often make it challenging or impossible to pool individual-level data across data-contributing sites. Log-binomial regression can directly estimate adjusted risk ratios without requiring the rare disease assumption, but it is susceptible to non-convergence issues when the maximum likelihood estimators lie near the boundary of the parameter space [9, 10]. Shu et al BMC Medical Research Methodology (2019) 19:228 space This approach provides consistent estimates of adjusted risk ratios but incorrect estimates of the variance because it relies on a Poisson distributed, rather than binomially distributed, outcome. As a solution to these challenges, Zou [12] proposed a modified Poisson regression approach that allows direct estimation of adjusted risk ratios even when the rare disease assumption is not met This approach avoids the convergence issues typically observed in log-binomial regression and, unlike conventional Poisson regression, provides consistent variance estimates and confidence intervals with the correct nominal coverage

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