Extrapolating sparse gold standard cause of death designations to characterize broader catchment areas

The Child Health and Mortality Prevention Surveillance (CHAMPS) Network is designed to elucidate and track causes of under-5 child mortality and stillbirth in multiple sites in sub-Saharan Africa and South Asia using advanced surveillance, laboratory and pathology methods. Expert panels provide an arguable gold standard determination of underlying cause of death (CoD) on a subset of child deaths, in part through examining tissue obtained via minimally invasive tissue sampling (MITS) procedures. We consider estimating a population-level distribution of CoDs based on this sparse but precise data, in conjunction with data on subgrouping characteristics that are measured on the broader population of cases and are potentially associated with selection for MITS and with cause-specific mortality. We illustrate how estimation of each underlying CoD proportion using all available data can be addressed equivalently in terms of a Horvitz-Thompson adjustment or a direct standardization, uncovering insights relevant to the designation of appropriate subgroups to adjust for non-representative sampling. Taking advantage of the functional form of the result when expressed as a multinomial distribution-based maximum likelihood estimator, we propose small-sample adjustments to Bayesian credible intervals based on Jeffreys or related weakly informative Dirichlet prior distributions. Our analyses of early data from CHAMPS sites in Kenya and Mozambique and accompanying simulation studies demonstrate the validity of the adjustment approach under attendant assumptions, together with marked performance improvements associated with the proposed adjusted Bayesian credible intervals. Adjustment for non-representative sampling of those validated via gold standard diagnostic methods is a critical endeavor for epidemiologic studies like CHAMPS that seek extrapolation of CoD proportion estimates.