Structure estimation of binary graphical models on stratified data: Application to the description of injury tables for victims of road accidents

Ballout, Nadim; Viallon, Vivian · 2019 · Crossref

DOI: 10.1002/sim.8138

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Summary

This paper addresses the challenge of estimating the conditional dependence structure of binary graphical models across multiple predefined population strata. The authors motivate this work with an application in road safety, where understanding associations among injuries suffered by victims is crucial for care services and diagnostics. Since injury patterns vary by road user type (e.g., pedestrians, car occupants), the problem requires estimating separate graphical models for each stratum while accounting for potential homogeneity in injury associations across groups. Standard methods that estimate each stratum independently fail to leverage shared structures and cannot reliably identify heterogeneities. To solve this, the authors propose two new approaches that combine the SepLogit method—which estimates Ising model parameters via multiple $\ell_1$-penalized logistic regressions—with penalties designed for stratified regression data. The first method, Fused-SepLogit, employs a generalized fused lasso penalty that shrinks parameter estimates across strata toward each other, encouraging equality where appropriate. The second method, DataShared-SepLogit, uses an additive decomposition of parameters into a common component and stratum-specific deviations, shrinking estimates toward a weighted median. Both methods include strategies (MIN and MAX) to resolve asymmetries in edge selection across the $K$ graphs. The authors evaluate these proposals through simulation studies comparing them against independent estimation (Indep-SepLogit) and an existing multiplicative decomposition approach (Guo et al., 2015). Simulations varied the number of variables ($p=10$ and $p=40$), strata ($K=3$ and $K=4$), and levels of heterogeneity ($\rho$). Performance was measured by accuracy in recovering the support of the parameter matrices (Acc.S) and accuracy in identifying heterogeneities between strata (Acc.H). Results showed that both Fused-SepLogit and DataShared-SepLogit generally outperformed Indep-SepLogit, particularly when heterogeneity was low. Crucially, the proposed methods significantly outperformed both Indep-SepLogit and Guo et al.’s approach in identifying heterogeneities (Acc.H), demonstrating that the existing multiplicative approach is ill-suited for detecting differences between strata. The significance of this work lies in providing robust statistical tools for analyzing stratified binary data where both shared structures and group-specific differences are of interest. By enabling accurate identification of heterogeneities, these methods allow clinicians and researchers to distinguish between universal injury associations and those specific to certain victim groups. The paper concludes with an application to a French registry of road accident victims, illustrating how these models can describe injury tables according to road user type, thereby supporting better diagnostic protocols and care resource allocation.

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