Pratique des Biostatistiques
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 Dernière modification: 18 novembre 2010

Théorème de Bayes

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  • strict warning: Non-static method view::load() should not be called statically in /home/iamin/www/umdb/biostats/sites/default/modules/views/views.module on line 906.
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  • strict warning: Non-static method view::load() should not be called statically in /home/iamin/www/umdb/biostats/sites/default/modules/views/views.module on line 906.

Le théorème de Bayes permet de déterminer les valeurs prédictives d'un test en connaissant la prévalence de la maladie, la sensibilité et la spécificité du test.

La formule générale du théorème de Bayes peut être retrouvée à partir de la loi des probabilités conditionnelles.

Loi des probabilités conditionnelles: TeX Embedding failed!

Or, il est possible de décomposer les membres de la fraction:

  • au numérateur: TeX Embedding failed!
  • au dénominateur: TeX Embedding failed! 

La formule générale du théorème de Bayes est donc:

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Soient les événements A "être malade " et B "être positif au test" et sachant que p(A) est la prévalence de la maladie (notée p), p(B/A) est la sensibilité et p(B*/A*) est la spécificité, alors le théorème de Bayes, appliqué aux tests diagnostiques, devient:

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