Exchangeable Versus Age- structured Priors in Small-Area Estimation of Adult Mortality From Sibling Survival Histories

Sibling survival histories provide adult mortality estimates for countries lacking civil registration, but age-sex disaggregation often leaves cells sparse. Analysts routinely smooth these estimates using either an exchangeable prior, which borrows strength across all cells, or an age-structured prior, which borrows from neighboring ages, a choice rarely justified explicitly. We compared empirical Bayes, Bayesian IID, and age-structured (RW2) smoothing of visibility-corrected estimates from the 2024 Nigeria and 2016 Nepal Demographic and Health Surveys, chosen for contrasting sparsity (37–93 versus 8–30 effective deaths per cell), plus a simulation under known ground truth. In Nigeria's denser cells, the two priors agreed closely; in Nepal's sparser cells, six of 14 diverged materially, four female age groups showed nominally significant divergence, and three remained significant after adjustment for multiple comparisons. Raw sparsity did not predict which cells diverged: simulations show divergence instead reflects genuine local departures from the broader age pattern, which age-structured priors recover more faithfully than exchangeable priors, at a modest cost that includes spreading artificial input distortions to neighboring cells. Empirical Bayes intervals also badly undercovered when the true pattern was smooth. We recommend routine reporting of exchangeable-versus-structured divergence as a standard part of small-area demographic estimation.