IntervalDRMA

Reproducibility materials for Contrast-Level Aggregate-Data Dose--Response Meta-Analysis for Heterogeneous Exposure Intervals.

This repository is intentionally limited to the code, data, machine-readable results, and generated figures needed to reproduce and validate the analyses. Manuscript and journal-submission files are maintained separately.

The method represents every exposure support as an interval with nonnegative width. Positive-width intervals are represented by conditional means under a working exposure distribution. Exact exposure values are zero-width intervals; their representative means are evaluated directly at the reported values. The conditional mean is the unique constant minimizing mean squared error for the exposure within a support, and it is coherent when supports are split or combined using their exposure probabilities. The model is a support-based extension of conventional point-dose DRMA that contains conventional contrast-design DRMA as an exact special case: when every support width is zero, the support mapping is the identity under the same basis, covariance, and random-effects specification. Midpoint analysis is the second nested special case: it is recovered exactly when exposure is Uniform within each bounded interval.

Repository contents

• data/analytic_contrasts.xlsx: the public, analysis-ready example dataset containing the 33 contrast-level observations used in the methodological illustration, with a data dictionary.
• data/radon_lung_cancer_contrasts.xlsx: a source-linked dataset of 56 adjusted residential-radon--lung-cancer OR contrasts from 16 studies, together with historical and current country-specific distribution inputs.
• code/run_analysis.py: primary eight-study AFO working analysis, OR-only and explicit-support restrictions, midpoint and open-tail comparisons, 30 distribution/correlation sensitivity analyses (including a registry-source sensitivity), decorrelated-residual diagnostics, and a support-mapping fragility analysis, with a studentized parametric-bootstrap interval for the primary fit.
• code/radon_example_analysis.py: independent analysis using outcome-independent country-specific Lognormal residential-radon distributions, including CR2, one-contrast-per-study, distribution-source, correlation, and open-tail point-score sensitivities.
• code/interval_drma_core.py: unit-equivariant core GLS/profile-REML estimator with an exact heterogeneity boundary and adaptive optimization.
• code/interval_drma.py: one-call second-stage fitting interface for analysis-ready support means and adjusted log ORs.
• code/mixed_support_simulation.py: mixed-support simulation study, including study-count experiments at K = 10, 20, and 30.
• code/make_score_assumption_figure.py: direct visual benchmark of the distribution-based mappings and conventional assigned-score analyses.
• code/make_distance_density_figure.py: vector and high-resolution versions of the regional Gamma working-distribution figure.
• code/make_support_to_design_figure.py: vector support-to-design framework diagram.
• code/make_support_fragility_figure.py: local support-mapping fragility diagnostic.
• code/support_uncertainty.py: numerical delta-method and parametric-bootstrap utilities for propagating first-stage support-distribution uncertainty.
• code/test_intervaldrma.py: 20 deterministic checks of unit rescaling, exact and extreme-tail supports, boundary heterogeneity, ordering, the zero-width rule, and primary point estimates, including agreement with a separately constructed conventional DRMA fit when all supports are points, and exact agreement with midpoint DRMA under Uniform interval exposure.
• code/reproduce_all.py: one-command reproduction of tests, analyses, simulations, figures, and a machine-readable environment manifest.
• results/: machine-readable analysis, simulation, and environment results, plus reproducibly generated figures in results/figures/.

Reproduce

Python 3.13.9 was used for the archived results. From the repository root:

python -m pip install -r code/requirements.txt
python code/reproduce_all.py

The equivalent individual commands are:

python code/test_intervaldrma.py
python code/run_analysis.py --output results/analysis_results.json
python code/radon_example_analysis.py --output results/radon_example_results.json
python code/mixed_support_simulation.py --replicates 5000 --output results/mixed_support_simulation_results.json
python code/make_score_assumption_figure.py
python code/make_distance_density_figure.py
python code/make_support_to_design_figure.py
python code/make_support_fragility_figure.py --results results/analysis_results.json --output results/figures/Support_mapping_fragility.pdf

The full simulation uses fixed random-number seeds and may take several minutes. It reports bias, root mean squared error (RMSE), confidence-interval coverage, and type-I error under dedicated null-effect settings and resampled empirical study-block configurations. The analysis outputs also provide a study-count Student-t sensitivity interval for random-effects slopes and a studentized parametric-bootstrap interval when few independent study blocks are available. These are labeled sensitivity intervals: the bootstrap's repeated-sampling coverage has not been validated for the present small-study design. The core estimator standardizes design values internally, evaluates the exact tau = 0 boundary, expands its dimensionless upper bracket adaptively, and reports convergence and boundary diagnostics before transforming results back to the requested exposure units. The application standard errors are conditional on the fitted support distribution. The fitting scripts requested numerical Hessians, but the observation-level distance files and Hessian matrices were not retained in the reproducibility bundle, so a defensible first-stage covariance cannot be reconstructed from the stored point estimates. The code includes the general unconditional covariance and bootstrap procedures for use when a first-stage covariance is retained. The profiled REML criterion in the machine-readable outputs is an optimization diagnostic within a fixed design mapping and must not be compared across mappings that change the fixed-effect design vector. Both empirical-analysis result files also report leave-one-study-out refits for influence assessment.

Data provenance

The workbook contains the subset of reported association estimates selected from a co-author-curated living systematic-review dataset for the illustrative analysis. The workbook retains the extracted values and recorded support bounds. The code applies the source-based exact-distance interpretation to the five Schultz comparisons. The Type field is retained because it identifies the support-mapping rule used by the analysis: 1 denotes an explicit comparison/reference pair and 2 denotes a binary-buffer proxy.

The primary AFO working analysis contains all 33 mapped contrasts from eight studies: 29 reported ORs and four Simões animal-count hazard ratios treated as approximate ORs on the log-OR analysis scale. An OR-only restriction removes the four hazard-ratio proxies. A strict explicit-support OR restriction retains 15 reported ORs from four studies, including five exact-distance Schultz spline contrasts, and removes the binary-buffer and animal-count proxy mappings. The independent radon dataset contains 56 reported adjusted OR contrasts.

The first-stage regional site layers are not interchangeable. North Carolina and Wisconsin use permitted-facility sources. The Pennsylvania fit used a public agricultural-producer directory, and the Netherlands fit used livestock-keyword-filtered agricultural businesses in Eijsden-Margraten; these two are geospatial proxies rather than verified AFO permit registries. The analysis therefore includes a source-quality sensitivity that replaces their Gamma parameters with the pooled North Carolina/Wisconsin permitted-facility working distribution.

The independent radon workbook reproduces the time-weighted exposure supports, adjusted ORs, and confidence limits in Table 2 of Pavia et al. (2003): https://doi.org/10.1590/S0042-96862003001000008. Country-specific Lognormal parameters are taken from UNSCEAR 2000, the WHO 2009 handbook, and UNSCEAR 2024. The estimator uses no exposure-category frequencies, event counts, or denominators. The cumulative-exposure-only Letourneau study is excluded because its scale is incompatible with the common time-weighted Bq/m^3 metric.

Citation and archiving

Repository URL: https://github.com/ChongWangStat/IntervalDRMA

Versioned Zenodo archive: https://doi.org/10.5281/zenodo.21984414

License

The MIT License applies to the software. The data files contain factual numerical information extracted from the cited publications and independently organized and processed by the authors. No source-article text, figures, or table images are reproduced.