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arXiv · 2610.07877

State-space representation of early-life child mortality dynamics: linking event history analysis and orbit-based models

Wendy Lefotlha·David Sherwell·Maria Vivien Visaya
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Abstract

Understanding early-life child mortality requires methods that capture both statistically significant risk factors and the structure of individual life trajectories. Event History Analysis (EHA) estimates associations between covariates and mortality risk but may obscure rare or high-dimensional configurations of risk. Orbit Theory (OT) represents individuals as exact trajectories in a combinatorial state space, preserving full multivariate structure. We analyse longitudinal data across 12 variables for 31,081 children from the Agincourt Health and Demographic Surveillance System (South Africa, 1998-2008) using both methods. We show three things EHA alone cannot. First, maternal migration is structurally pivotal in the transition dynamics leading to child death despite being statistically non-significant in EHA. Second, maternal refugee status, while statistically significant, generates no trajectory dynamics and is correctly excluded from any structural reduction. Third, a three-variable subsystem (child status, mother status, mother migration) recovers EHA's principal findings within a reduced state space of at most 48 states while exposing small high-risk clusters invisible to regression-based analysis. Maternal death is the dominant EHA predictor; maternal migration organises 87% of the observable sequential transitions into child-death states. These are not contradictory: maternal death rarely appears as a preceding state because its role is terminal rather than sequential. Early-life mortality can be read at two levels simultaneously - statistically, through effect estimates, and structurally, through observed transitions.

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Wendy Lefotlha, David Sherwell, Maria Vivien Visaya. 2026-10-06. State-space representation of early-life child mortality dynamics: linking event history analysis and orbit-based models. https://arxiv.org/abs/2610.07877

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