A Toric Statistical Decision-Support Framework for Exact Inference from Sparse Public-Health Data

Sparse public-health tables are often released through margins, structural zeros, or suppression bounds. This study develops a toric statistical decision-support framework for stratified binary surveillance data and exact conditional procedures that preserve specified aggregate constraints. One quadratic move per stratum connects every fixed-margin fiber, while uncoupled cell bounds produce truncated hypergeometric factors. When the total diseased–exposed count is additionally fixed across strata, cross-stratum exchange moves connect the resulting non-factorizing fiber. A dynamic-programming recurrence evaluates the exact null distribution without enumerating all tables. In a reproducible four-stratum benchmark with 88 observations and 6,930 fixed-margin tables, the Mantel–Haenszel odds ratio is 2.540. The uncorrected Cochran–Mantel–Haenszel test gives p = 0.0401, whereas the exact probability-ordered test gives p = 0.0503. The differing decisions at the 5% significance level demonstrate that sparse-data asymptotics can alter a borderline public-health conclusion. The framework provides an interpretable computational basis for reliable decisions from sparse, structurally constrained, or partially suppressed surveillance information.