Design-Indexed Heterogeneity in Meta-Analysis: A Constrained Location-Scale Specification
Abstract
An analyst should not assume that a design score improves a meta-analysis simply because it is labeled as robustness. This paper treats declining heterogeneity along a prespecified, outcome-separated design score as a falsifiable directional hypothesis. In an 18-study illustration, the constrained model lands at γ= 0 and becomes numerically identical to conventional random effects, while the unrestricted scale fit points in the opposite direction. Simulations that deliberately violate the restriction show the same graceful fallback under wrong-direction and U-shaped heterogeneity; a stepwise decreasing variance function retains an efficiency gain despite functional-form misspecification. DR-Meta formalizes the hypothesis as τ2(DR) = τ02 exp(−γDR), γ≥ 0, within an established location-scale framework. Exact nesting, conditional weight monotonicity, a fixed-effect upper bound, pseudo-true targets under mean misspecification, and score-rescaling behavior are derived with full proofs. Efficiency gains are negligible around an empirically anchored γ near 1 and become material only under stronger gradients; the largest RMSE reduction, about 9.6 percent, occurs in a deliberately extreme condition. Plug-in intervals under-cover relative to random effects, and modified Knapp-Hartung adjustment improves coverage only modestly. Widening the γ optimization bound changes γ estimates much more than pooled-estimate RMSE. The practical contribution is therefore diagnostic rather than automatic efficiency: a nested directional restriction can be supported, contradicted, or collapse transparently to random effects, provided constrained, unrestricted, location, and sensitivity analyses are reported together.
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BibTeX
@misc{hait2026designindexed,
title = {{Design-Indexed Heterogeneity in Meta-Analysis: A Constrained Location-Scale Specification}},
author = {Subir Hait},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29637},
eprint = {2609.29637},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29637},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Design-Indexed Heterogeneity in Meta-Analysis: A Constrained Location-Scale Specification
AU - Subir Hait
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.29637
UR - https://arxiv.org/abs/2609.29637
AB - An analyst should not assume that a design score improves a meta-analysis simply because it is labeled as robustness. This paper treats declining heterogeneity along a prespecified, outcome-separated design score as a falsifiable directional hypothesis. In an 18-study illustration, the constrained model lands at γ= 0 and becomes numerically identical to conventional random effects, while the unrestricted scale fit points in the opposite direction. Simulations that deliberately violate the restriction show the same graceful fallback under wrong-direction and U-shaped heterogeneity; a stepwise decreasing variance function retains an efficiency gain despite functional-form misspecification. DR-Meta formalizes the hypothesis as τ^2(DR) = τ_0^2 exp(−γDR), γ≥ 0, within an established location-scale framework. Exact nesting, conditional weight monotonicity, a fixed-effect upper bound, pseudo-true targets under mean misspecification, and score-rescaling behavior are derived with full proofs. Efficiency gains are negligible around an empirically anchored γ near 1 and become material only under stronger gradients; the largest RMSE reduction, about 9.6 percent, occurs in a deliberately extreme condition. Plug-in intervals under-cover relative to random effects, and modified Knapp-Hartung adjustment improves coverage only modestly. Widening the γ optimization bound changes γ estimates much more than pooled-estimate RMSE. The practical contribution is therefore diagnostic rather than automatic efficiency: a nested directional restriction can be supported, contradicted, or collapse transparently to random effects, provided constrained, unrestricted, location, and sensitivity analyses are reported together.
ER -