How to solve biological problems with math 2012 23 Mars 2012.

Présentation au sujet: "How to solve biological problems with math 2012 23 Mars 2012."— Transcription de la présentation:

1 How to solve biological problems with math 2012 23 Mars 2012

2 Phenotypic variation:

3 What is association? chromosomeSNPstrait variant Genetic variation yields phenotypic variation Population with allele Distributions of trait

4 Quantifying Significance

5 T-test t-value (significance) can be translated into p-value (probability)

6 Association using regression genotypeCoded genotype phenotype

7 Regression analysis X Y response feature(s) intercept coefficients residuals

8 Regression formalism (monotonic) transformation phenotype (response variable) of individual i effect size (regression coefficient) coded genotype (feature) of individual i p(β=0) error (residual) Goal: Find effect size that explains best all (potentially transformed) phenotypes as a linear function of the genotypes and estimate the probability (p-value) for the data being consistent with the null hypothesis (i.e. no effect)

9 Matlab function for Linear regression [x p tmp se] = regress_p(pheno,[ones(length(pheno),1) COV1 COV2 Genotype ]

10 Régression logistique Très utilisée en épidémiologie Variable à expliquer: dichotomique La maladie est caractérisée par un risque Exprimer sous forme de risque ( ou de probabilité) la relation entre une variable Y dichotomique et plusieurs variables X (facteurs de risque) (qualitatives ou quantitatives)

11 Méthode destimation de lassociation entre les facteurs de risque et la maladie (les bétas): méthode du maximum de vraisemblance, Odds ratio (rapport des cotes): force de lassociation entre 1 facteur et la maladie (risque relatif) Régression logistique

12 Le modèle logistique Probability of the outcome measure of the total contribution of all the independent variables used in the model and is known as the logit

13 The application of a logistic regression may be illustrated using a fictitious example of death from heart disease. This simplified model uses only three risk factors (age, sex, and blood cholesterol level) to predict the 10-year risk of death from heart disease. These are the parameters that the data fit: The model can hence be expressed as In this model, increasing age is associated with an increasing risk of death from heart disease (z goes up by 2.0 for every year over the age of 50), female sex is associated with a decreased risk of death from heart disease (z goes down by 1.0 if the patient is female), and increasing cholesterol is associated with an increasing risk of death (z goes up by 1.2 for each 1 mmol/L increase in cholesterol above 5 mmol/L). We wish to use this model to predict a particular subject's risk of death from heart disease: he is 50 years old and his cholesterol level is 7.0 mmol/L. The subject's risk of death is therefore This means that by this model, the subject's risk of dying from heart disease in the next 10 years is 0.07 (or 7%).

14 Odds ratio Rapport des chances, rapport des cotes ou risque relatif rapproché est une Mesure statistique, permettant de mesurer le degré de dépendance entre des variables aléatoires qualitatives. Mesure l'effet d'un facteur. Le rapport des chances qu'un événement arrivant, par exemple une maladie, à un groupe de personnes A arrive également à un autre groupe B. Si la probabilité qu'un évènement arrive dans le groupe A est p et q dans le groupe B, le rapport des chances est : Odds ratio (OR) =

15 Matlab function for logistic regression [p0 x0 se0] = log_reg(Pheno,[COV1 COV2 ],Geno)