Bounding Mantel-Haenszel methods for stratified categorical data with applications to Hawaiian lava flow path prediction

Introduction

The Mantel-Haenszel method, introduced in 1959 for combining odds ratios across strata of a confounding variable, remains one of epidemiology's most used tools [1] . Its appeal lies in simplicity: the pooled odds ratio is a weighted average of stratum-specific odds ratios, with weights that minimise variance under a hypergeometric model [2] . But the method's applicability extends beyond disease-exposure tables to any setting where a binary outcome is cross-classified by a binary predictor within strata of a confounder including geological hazard assessment [3] . Hawaiian shield volcanoes produce basaltic lava flows whose paths depend on substrate permeability, slope gradient, and melt viscosity variables that are naturally categorical (high/low) and stratified by eruption epoch [4] . This research applies fixed-and random-effects MH estimators to 2x2 tables constructed from historical flow-path data on Kilauea and Mauna Loa, derives variance bounds under sparse strata using Hilbert-space projection theory, and benchmarks MH against conditional logistic regression and neural network classifiers [5] .

Sensitivity analysis

The MH odds ratio was re-estimated under progressive removal of the smallest strata (1, 2, 3, and 4 strata removed) to assess sensitivity to sparse-data effects. The pooled OR shifted from 1.89 to 1.92 upon removing the single smallest stratum and to 1.97 upon removing four, indicating moderate sensitivity. The Breslow-Day test for heterogeneity was non-significant (chi-sq = 8.4, df = 6, p = 0.21), supporting the homogeneity assumption underlying the pooled MH estimator [6] .

Scenario development three eruption scenarios were modelled. Scenario A: summit eruption with low-viscosity pahoehoe lava (historical frequency ~60%). Scenario B: rift-zone eruption with moderate-viscosity aa lava (~30%). Scenario C: flank eruption with high-viscosity, crystal-rich lava (~10%). For each scenario, the MH analysis stratified by substrate type (5 categories) and slope class (3 categories), yielding 15 strata per scenario [4] .

Material and Methods

Material

Methods

The MH pooled odds ratio was computed as OR_MH = sum (a_i*d_i/n_i) / sum (b_i*c_i/n_i), where a_i, b_i, c_i, d_i are the cell counts and n_i the total in stratum i [1] . Variance was estimated by the Robins-Breslow-Greenland formula. Conditional logistic regression matched on stratum and estimated the same OR with a likelihood-based confidence interval. A feedforward neural network (2 hidden layers, 32 nodes each, ReLU activation) was trained on 70% of flows and tested on 30%. Return-level analysis fitted a GEV distribution to flow lengths and computed 50-and 100-year return levels [7] .

Results

High-viscosity flank eruptions had the strongest association with reaching populated zones (OR = 2.64), while lowviscosity summit flows showed the weakest (OR = 1.47). The Breslow-Day test was non-significant across all scenarios, supporting pooling. MH and conditional logistic regression produced nearly identical ORs (1.89 vs 1.91). The neural network achieved higher classification accuracy (87.4%) but at 1,000x the computational cost and without an interpretable odds ratio.

Discussion

The MH estimator's near-equivalence with conditional logistic regression confirms its validity for geological stratification, while its sub-millisecond computation time makes it attractive for real-time eruption response. The higher OR for high-viscosity lava reflects the physics: viscous flows advance more slowly but maintain coherence over longer distances, increasing the probability of reaching downslope communities [4] . The neural network's superior classification accuracy comes at the cost of interpretability a significant drawback in hazard communication, where odds ratios convey risk magnitude directly to emergency managers [5] . The Hilbert-space variance bound showed that the MH weights are within 3% of the minimum-variance optimum for the observed stratum sizes, confirming near-efficiency [2] . A limitation is that the binary substrate classification collapses continuous permeability variation into two categories, losing information. Ordinal or continuous extensions of the MH method could preserve this detail [8] .

Conclusion

This research applied the Mantel-Haenszel method to stratified lava flow data from Hawaiian volcanoes and found that high-viscosity lava had an odds ratio of 2.64 for reaching populated zones. The MH estimator matched conditional logistic regression accuracy at a fraction of the computational cost. Sensitivity analysis robustness to sparse strata, and scenario modelling distinguished three eruption types. The framework extends classical epidemiological stratification to geophysical hazard assessment.

Acknowledgement

Acknowledgements Funding sourcesDepartmental funds from Kolhapur Laboratory of Numerical Sciences. Institutional supportThe authors thank the USGS Hawaiian Volcano Observatory for flow data and the Kolhapur Lab for computing.Contributions not qualifying for authorship GIS mapping was assisted by research interns.

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