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PreprintCC BY 4.0arXiv

Bounding the Risk Difference Bias Given Incomplete Parameters for Externally Adjusting Uncontrolled Confounding

  • Onyebuchi A. Arah
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Abstract

Bias due to uncontrolled confounding can be analyzed using several external adjustment formulas. Like other bias expressions, the risk difference bias formula involving an uncontrolled polytomous confounder requires only three externally obtainable parameters: confounder prevalences among the exposed and unexposed and the confounder-outcome risk difference. This paper presents two-parameter bounds on the risk difference bias expression when only one of the three required bias parameters is unavailable. Each bound is sharp over the full range of the unknown parameter. Some numerical examples with graphs are provided.

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Cite

BibTeXRIS
BibTeX
@misc{arah2026bounding,
  title = {{Bounding the Risk Difference Bias Given Incomplete Parameters for Externally Adjusting Uncontrolled Confounding}},
  author = {Onyebuchi A. Arah},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.24999},
  eprint = {2609.24999},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24999},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Bounding the Risk Difference Bias Given Incomplete Parameters for Externally Adjusting Uncontrolled Confounding
AU  - Onyebuchi A. Arah
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.24999
UR  - https://arxiv.org/abs/2609.24999
AB  - Bias due to uncontrolled confounding can be analyzed using several external adjustment formulas. Like other bias expressions, the risk difference bias formula involving an uncontrolled polytomous confounder requires only three externally obtainable parameters: confounder prevalences among the exposed and unexposed and the confounder-outcome risk difference. This paper presents two-parameter bounds on the risk difference bias expression when only one of the three required bias parameters is unavailable. Each bound is sharp over the full range of the unknown parameter. Some numerical examples with graphs are provided.
ER  -