Medical Journal of The Islamic Republic of Iran (MJIRI)
Iran University of Medical Sciences
Sun, Nov 15, 2026
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Volume 40, Issue 1 (1-2026)
Med J Islam Repub Iran 2026 |
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Rakhshani M H, Zeraati H, Hashemi H, Fotouhi A. Hierarchical Bootstrapping for Quadratic Exponential Models in Genetic Epidemiology: Familial Aggregation Analysis with Small Samples and Unequal Family Sizes. , Med J Islam Repub Iran. 2026; 40 (1) :970-977
URL: http://mjiri.iums.ac.ir/article-1-10258-en.html
URL: http://mjiri.iums.ac.ir/article-1-10258-en.html
Department of Epidemiology and Biostatistics, School of Public Health, Tehran University of Medical Sciences, Tehran, Iran , afotouhi@tums.ac.ir
Abstract: (82 Views)
Background: Familial aggregation analysis evaluates whether disease clustering within families exceeds chance expectations. A key challenge is irreproducibility, which arises when a model cannot be consistently applied to families with different family sizes. Although the quadratic exponential model is widely used for correlated binary outcomes, its performance is affected by irreproducibility and small-sample bias.
Methods: This study compares the marginal approach, designed to address irreproducibility, with a hierarchical bootstrap procedure. Simulations were conducted under exchangeable and non exchangeable dependence structures using the quadratic exponential framework, focusing on samples with unequal family sizes. Performance was evaluated using RMSE and empirical coverage. The two methods were also applied to data from the Tehran Eye Study.
Results: In exchangeable settings, both methods produced reasonable estimates for baseline disease odds; however, the hierarchical bootstrap provided more stable inference. It also performed better in estimating the incremental effect associated with an additional affected relative (γ) in samples of 200 families (coverage: 94.8% vs 92.5%). In non-exchangeable scenarios, the bootstrap approach showed better performance for key parameters, including conditional child–parent odds (95.1% vs 93.5%) and γ (93.9% vs 93%). Results from the Tehran Eye Study were consistent with these findings (93.9% vs 93.6% for γ and 94.7% vs 92.6% for γ M
Conclusion: These findings suggest that hierarchical bootstrapping may provide a useful alternative for inference in familial aggregation studies with heterogeneous family sizes.
Methods: This study compares the marginal approach, designed to address irreproducibility, with a hierarchical bootstrap procedure. Simulations were conducted under exchangeable and non exchangeable dependence structures using the quadratic exponential framework, focusing on samples with unequal family sizes. Performance was evaluated using RMSE and empirical coverage. The two methods were also applied to data from the Tehran Eye Study.
Results: In exchangeable settings, both methods produced reasonable estimates for baseline disease odds; however, the hierarchical bootstrap provided more stable inference. It also performed better in estimating the incremental effect associated with an additional affected relative (γ) in samples of 200 families (coverage: 94.8% vs 92.5%). In non-exchangeable scenarios, the bootstrap approach showed better performance for key parameters, including conditional child–parent odds (95.1% vs 93.5%) and γ (93.9% vs 93%). Results from the Tehran Eye Study were consistent with these findings (93.9% vs 93.6% for γ and 94.7% vs 92.6% for
Conclusion: These findings suggest that hierarchical bootstrapping may provide a useful alternative for inference in familial aggregation studies with heterogeneous family sizes.
Keywords: Familial aggregation, Hierarchical bootstrap, Quadratic exponential model, Irreproducibility, Tehran Eye Study
: Original Research |
Subject:
Biostatistics and Epidemiology
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