Régression logistique : introduction

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1 Chapitre 16 Introduction à la statistique avec R Régression logistique : introduction

2 Une variable à expliquer binaire Expliquer un risque suicidaire élevé en prison par La durée de la peine L existence de mesures disciplinaire Des antécédents d abus dans l enfance

3 Les limites de la régression linéaire Haut risque de suicide = a + b duree + c discip + d abus + bruit

4 Les limites de la régression linéaire Haut risque de suicide = a + b duree + c discip + d abus + bruit La distribution du «bruit» est normale, donc «a + b duree + c discip + d abus + bruit» varie entre plus et moins l infini, or la variable «haut risque de suicide» est binaire

5 Les limites de la régression linéaire prob HR suicide oui Log prob HR suicide oui 1 ( ) a b duree c discip d abus

6 Les limites de la régression linéaire prob HR suicide oui Log prob HR suicide oui 1 ( ) a b duree c discip d abus Varie entre + et - l infini

7 Une seule variable explicative Log prob haut risque de suicide 1 prob haut risque de suicide = a + b abus

8 Une seule variable explicative Log prob haut risque de suicide 1 prob haut risque de suicide = a + b abus > mod1 <- glm(suicide.hr~abus, data=smp.l, family="binomial") > summary(mod1) Call: glm(formula = suicide.hr ~ abus, family = "binomial", data = smp.l) Deviance Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error z value Pr(> z ) (Intercept) < 2e-16 *** abus e-05 *** --- Signif. codes: 0 *** ** 0.01 * (Dispersion parameter for binomial family taken to be 1) Null deviance: on 752 degrees of freedom Residual deviance: on 751 degrees of freedom (46 observations deleted due to missingness) AIC: Number of Fisher Scoring iterations: 4

9 Une seule variable explicative Log prob haut risque de suicide 1 prob haut risque de suicide = a + b abus > mod1 <- glm(suicide.hr~abus, data=smp.l, family="binomial") > summary(mod1) Call: glm(formula = suicide.hr ~ abus, family = "binomial", data = smp.l) Deviance Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error z value Pr(> z ) (Intercept) < 2e-16 *** abus e-05 *** --- Signif. codes: 0 *** ** 0.01 * (Dispersion parameter for binomial family taken to be 1) Null deviance: on 752 degrees of freedom Residual deviance: on 751 degrees of freedom (46 observations deleted due to missingness) AIC: Number of Fisher Scoring iterations: 4

10 Une seule variable explicative Log prob haut risque de suicide 1 prob haut risque de suicide = a + b abus > mod1 <- glm(suicide.hr~abus, data=smp.l, family="binomial") > summary(mod1) Call: glm(formula = suicide.hr ~ abus, family = "binomial", data = smp.l) Deviance Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error z value Pr(> z ) (Intercept) < 2e-16 *** abus e-05 *** --- Signif. codes: 0 *** ** 0.01 * (Dispersion parameter for binomial family taken to be 1) Null deviance: on 752 degrees of freedom Residual deviance: on 751 degrees of freedom (46 observations deleted due to missingness) AIC: Number of Fisher Scoring iterations: 4

11 Une seule variable explicative Log prob haut risque de suicide 1 prob haut risque de suicide = a + b abus > mod1 <- glm(suicide.hr~abus, data=smp.l, family="binomial") > summary(mod1) Call: glm(formula = suicide.hr ~ abus, family = "binomial", data = smp.l) Deviance Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error z value Pr(> z ) (Intercept) < 2e-16 *** abus e-05 *** --- Signif. codes: 0 *** ** 0.01 * (Dispersion parameter for binomial family taken to be 1) Null deviance: on 752 degrees of freedom Residual deviance: on 751 degrees of freedom (46 observations deleted due to missingness) AIC: Number of Fisher Scoring iterations: 4

12 Une seule variable explicative Log prob haut risque de suicide 1 prob haut risque de suicide = a + b abus > mod1 <- glm(suicide.hr~abus, data=smp.l, family="binomial") > summary(mod1) Call: glm(formula = suicide.hr ~ abus, family = "binomial", data = smp.l) Deviance Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error z value Pr(> z ) (Intercept) < 2e-16 *** abus e-05 *** --- Signif. codes: 0 *** ** 0.01 * (Dispersion parameter for binomial family taken to be 1) Null deviance: on 752 degrees of freedom Residual deviance: on 751 degrees of freedom (46 observations deleted due to missingness) AIC: Number of Fisher Scoring iterations: 4 > exp(0.7688) [1]

13 Une seule variable explicative > exp(0.7688) [1] > library(epi) > twoby2(1-smp.l$suicide.hr, 1-smp.l$abus) 2 by 2 table analysis: Outcome : 0 Comparing : 0 vs P(0) 95% conf. interval % conf. interval Relative Risk: Sample Odds Ratio: Conditional MLE Odds Ratio: Probability difference: Exact P-value: 1e-04 Asymptotic P-value: 1e

14 Conclusion mod1 <- glm(suicide.hr~abus, data=smp.l, family="binomial") summary(mod1) exp(0,7688) library(epi) twoby2(1-smp.l$suicide.hr, 1-smp.l$abus)

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