Raking mortality rates across cause, population group and geography with variance estimation

Abstract

Raking adjusts observations in contingency tables to match known marginals, reconciling estimates across models with different granularities in survey inference and global health. A key use case is the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD), which estimates mortality rates and other health metrics at multiple scales and can produce inconsistent tables (e.g., subregion totals that do not sum to regional totals). GBD outputs include uncertainty (standard deviations or confidence intervals), but variance estimation for raked values is typically obtained by computationally intensive Monte Carlo methods that pass thousands of samples through the full raking procedure. In this paper, we propose a variance estimation approach that, at the cost of a single solve, achieves nearly the same variance estimates as these Monte Carlo techniques. We also introduce a convex optimization framework that unifies raking extensions, including differential weights, alternative distance measures that enforce bounds, feasibility checks, raking to margins as hard constraints or aggregate observations, and handling missing data. We illustrate the general approach and uncertainty computation on a large-scale 3D mortality estimation use case that reconciles estimates across race, county, and cause.