# Partial derivatives meta-analysis: pooled analyses when individual participant data cannot be shared

## TL;DR

This paper introduces a new method for combining data from multiple studies without sharing individual data, achieving results as strong as full data sharing.

## Contribution

The novel partial derivatives meta-analysis method enables gold-standard results using only aggregate data.

## Key findings

- Partial derivatives meta-analysis yields identical results to individual participant data pooling.
- The method allows post-hoc adjustments and stratifications without site-specific re-analysis.
- It maintains statistical power and flexibility even when individual data cannot be shared.

## Abstract

Joint analysis of data from multiple studies in collaborative efforts strengthens scientific evidence, with the gold standard approach being the pooling of individual participant data (IPD). However, sharing IPD often has legal, ethical, and logistic constraints for sensitive or high-dimensional data, such as in clinical trials, observational studies, and large-scale omics studies. Therefore, meta-analysis of study-level effect estimates is routinely done, but this compromises on statistical power, accuracy, and flexibility. Here we propose a novel meta-analytical approach, named partial derivatives meta-analysis, that is mathematically equivalent to using IPD, yet only requires the sharing of aggregate data. It not only yields identical results as pooled IPD analyses, but also allows post-hoc adjustments for covariates and stratification without the need for site-specific re-analysis. Thus, in case that IPD cannot be shared, partial derivatives meta-analysis still produces gold standard results, which can be used to better inform guidelines and policies on clinical practice.