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A partial fraction is a component of a rational expression represented as the sum of simpler fractions. When a rational function is expressed as a ratio of two polynomials, it can often be decomposed into a sum of fractions whose denominators are simpler polynomials, typically linear or irreducible quadratic factors. This process is called partial fraction decomposition, and it is used to simplify complex expressions for integration, solving equations, or analysis.Partial fraction decomposition...
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Sequences are fundamental mathematical objects consisting of ordered lists of numbers that follow a specific rule or pattern. Sequences are critical in various mathematical concepts, including calculus, series, and number theory. They can model real-world phenomena such as population growth, financial investments, and physical processes like the diminishing height of a bouncing ball.Each number in a sequence is referred to as a term. Typically, the terms are denoted as a1, a2, a3,…, where...
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Revisiting sequential attributable fractions.

John Ferguson1, Maurice O'Connell1, Martin O'Donnell1

  • 1HRB Clinical Research Facility, NUI Galway, Galway, Ireland.

Archives of Public Health = Archives Belges De Sante Publique
|July 25, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces causal definitions for sequential and average attributable fractions, improving disease risk partitioning. The novel causal inference methods accurately estimate disease burden from multiple risk factors.

Keywords:
Attributable fractionBayesian networkCausal DAGCausal inferenceDo-operator

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Area of Science:

  • Epidemiology
  • Causal Inference
  • Biostatistics

Background:

  • Sequential and average attributable fractions partition disease risk among exposures.
  • These causal concepts were not traditionally estimated within a causal inference framework.
  • Existing methods do not fully account for complex causal pathways.

Purpose of the Study:

  • To propose causal definitions of sequential and average attributable fractions using the potential outcomes framework.
  • To develop a method for estimating these fractions that accounts for direct and indirect effects of risk factors.
  • To enable consistent estimation under general causal structures.

Main Methods:

  • Utilized the potential outcomes framework for causal definitions.
  • Employed causal Bayesian networks to model exposure-disease interrelationships.
  • Applied Pearl's do-operator and simulation for estimating sequential attributable fractions.

Main Results:

  • Demonstrated application to the INTERSTROKE study data.
  • Quantified disease burden attributable to major stroke risk factors.
  • Compared novel estimations with traditional single logistic model approaches.

Conclusions:

  • Proposed methods allow consistent estimation of attributable fractions under general causal structures.
  • The new approach improves upon traditional regression models by accounting for complex causal pathways.
  • Enables more accurate partitioning of disease risk among multiple exposures.