Background: 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. 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.
Methods: By 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.
Results: Our 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.
Conclusions: We 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.
Keywords: Distributed analysis; Modified Poisson regression; Multi-center studies; Odds ratio; Privacy protection; Risk ratio.