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Updated: Feb 19, 2026

An R-Based Landscape Validation of a Competing Risk Model
Published on: September 16, 2022
Converting categorical risk estimates into continuous effects in environmental health systematic reviews and
Lisa Bauleo1, Isabella Bottini2, Manuela De Sario2
1Department of Environment and Health, Italian National Institute of Health, Rome (Italy); lisa.bauleo@iss.it.
Background:
in environmental epidemiology, critical appraisal of evidence across studies and quantitative synthesis is crucial to inform public health, but it is challenged by the heterogeneity in exposure assessment methods. Even when assessing the same exposure, different studies frequently report risk estimates using varying categorical exposure intervals, making it difficult to compare and synthetize findings quantitatively. Advanced meta-analytical methodologies capable of harmonizing different exposure categorizations and effect estimates are crucial for generating flexible, policy-relevant, and locally applicable evidence that can be used in Health Impact Assessments of the disease burden related to environmental exposures and of the potential impact of mitigation measures.
Objectives:
to present a transparent and reproducible approach for harmonizing diverse categorical risk estimates (based on differently defined categories) into a per-unit continuous effect estimate, thereby including them in meta-analyses. The method is exemplified through a practical application.
Methods:
the method involves three steps: 1. estimating the midpoint of each exposure category and calculating category-specific per-unit continuous beta coefficients from categorical effect estimates; 2. deriving a study-specific continuous effect estimate as a weighted average of these beta coefficients; 3. calculating the uncertainty (i.e., confidence intervals) of the resulting estimate. This approach assumes linearity of risk within categories and independence of category-specific estimates. The method was illustrated through a practical application to the dataset reported by Mataloni et al. (2016), with the aim of deriving a continuous hazard risk associated with a 1 ng/m³ increase in H2S exposure. Method robustness was assessed by comparing results with the true continuous effect and with those deriving from previously published pooling methods that overcome some limitations, including the absence of risk modelling across categories and covariance estimation. The effect of different definitions of central category exposures was also examined.
Results:
the proposed method was applied in cases where the same exposure (e.g., H2S) was examined across studies for a given health outcome, but varying exposure intervals. A sample calculation is provided, along with an R script and corresponding Excel formulas. The method appears to provide an unbiased estimation of the 'true' continuous effect and obtained results comparable with other more complex methods both in terms of point and interval estimates pooled across categories and was robust to different central category exposures definitions.
Conclusions:
the proposed method provides a practical and replicable approach for converting categorical risk estimates into continuous effect estimates, enabling the harmonization of heterogeneous exposure categories across studies. This allows comparability and enables to carry out meta-analyses even in settings with a limited evidence base, where the addition of a single study can meaningfully contribute to the pooled estimate. The method helps overcome a frequent source of heterogeneity in environmental epidemiology, enhancing the robustness, precision, and interpretability of meta-analytical results. Applying methods such as the one here presented to systematic reviews and meta-analyses in the field of environmental epidemiology - where commonly potential effects of exposures are highly uncertain, as in the case of municipal solid waste disposal sites - more valid and robust estimates of the effects of specific environmental exposures can be obtained, therefore providing a stronger evidence base to inform public health decision-making.
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