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Information sur le cours
Rencontrez l'équipe enseignante -
Jeu de données du cours 1
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Jeu de données du cours 2
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MODULE A1: INTRODUCTION AUX STATISTIQUES AVEC R ET STATAA1.1 Qu'est-ce que les Statistiques?
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A1.2.1a Introduction à Stata
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A1.2.2b: Introduction à R
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A1.2.2c: Introduction to SPSS
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A1.3: Statistiques Descriptives
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A1.4: Estimations et Intervalles de Confiance
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A1.5: Tests d'Hypothèses
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A1.6: Transformation de Variables
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Fin du Module A11 Quiz
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MODULE A2: CALCULS DE PUISSANCE STATISTIQUE & DE TAILLE D’ÉCHANTILLONA2.1 Concepts Clés
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A2.2 Calculs de puissance pour une différence de moyennes
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A2.3 Calculs de puissance pour une différence de proportions
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A2.4 Calcul de taille d’échantillon pour les essais randomisés (RCTs)
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A2.5 Calculs de taille d’échantillon pour les études transversales (ou sondages)
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A2.6 Calcul de taille d'échantillon pour un devis cas-contrôle
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Fin du Module A21 Quiz
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MODULE B1: RÉGRESSION LINÉAIREB1.1 Corrélation et Nuages de Points (scatterplots)
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B1.2 Différences Entre Moyennes (ANOVA à un facteur)
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B1.3 Régression Linéaire Univariée
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B1.4 Régression Linéaire Multivariée
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B1.5 Sélection de Modèles et Tests F
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B1.6 Diagnostics de Régression
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Fin du Module B11 Quiz
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MODULE B2: COMPARAISONS MULTIPLES & MESURES RÉPÉTÉESB2.1 ANOVA Approfondie— Tests Post-Hoc
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B2.2 Correction pour Comparaisons Multiples
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B2.3 ANOVA à deux facteurs (Two-way ANOVA)
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B2.4 Mesures Répétées et Test T Apparié
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B2.5 ANOVA pour Mesures Répétées
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Fin du Module B21 Quiz
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MODULE B3: MÉTHODES NON-PARAMETRICB3.1 Hypothèses des Tests Paramétriques
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B3.2 Test U de Mann-Whitney
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B3.3 Test de Kruskal-Wallis
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B3.4 Test des rangs signés de Wilcoxon
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B3.5 Test de Friedman
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B3.6 Corrélation des Rangs de Spearman
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Fin du Module B31 Quiz
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MODULE C1: DONNÉES BINAIRES & RÉGRESSION LOGISTIQUEC1.1 Introduction à la prévalence, au Risque, aux Cotes (Odds) et aux Taux
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C1.2 Le Test du Chi Carré & le Test de Tendance
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C1.3 Régression Logistique Univariée
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C1.4 Régression Logistique Multivariée
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Fin du Module C11 Quiz
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MODULE C2: DONNÉES DE SURVIEC2.1 Introduction aux Données de Survie
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C2.2 Fonction de Survie de Kaplan-Meier & Test du Log-Rank
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C2.3 Régression de Cox à Risque Proportionnel
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C2.4 Régression de Poisson
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Fin du Module C21 Quiz
Learning Outcomes
By the end of this section, students will be able to:
- Control the association of an exposure for additional variables in a logistic regression model
You can download a copy of the slides here: Video C1.4
Video C1.4 – Controlling for Confounding in Logistic Regression (6 minutes)
C1.4 PRACTICAL: Stata
Controlling for confounders in a logistic regression
Now use the logistic command to obtain the odds ratio for prior CVD with hypertension, adjusted for HDL-C. Similar to the command in linear regression, we add additional variables after the exposure on the command line. This may be obtained as follows:
logistic prior_cvd hyperten hdlc
Note that the output gives us the odds ratio for ‘hyperten’ adjusted for ‘hdlc’ but it also gives us the odds ratios for ‘hdlc’ adjusted for ‘hyperten’.
You will run and interpret this command in the questions below.
We can control for additional variables as well by adding additional variables to the command line as we did above with ‘hdlc’. Each variable we put in the model will be controlled for all the other variables in the model. That is, if we add BMI group to this logistic regression above, we would interpret the coefficient for hypertension as ‘the association of hypertension with the odds of prior CVD, independent (or adjusted for) of HDL-C and BMI group’. BMI group would likewise be interpreted as the association of BMI group with prior CVD, once adjusted for hypertension and HDL-C.
Question C1.4b: What are the odds of having prior CVD if a participant is hypertensive, once you have adjusted for their levels of HDL-C?
C1.4b Answers
Answer C1.4b:
logistic prior_cvd i.hyperten hdlc
Logistic regression Number of obs = 4,293
LR chi2(2) = 86.59
Prob > chi2 = 0.0000
Log likelihood = -2371.6353 Pseudo R2 = 0.0179
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prior_cvd | Odds ratio Std. err. z P>|z| [95% conf. interval]
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1.hyperten | 1.551415 .1191582 5.72 0.000 1.334598 1.803456
hdlc | .4996367 .0501632 -6.91 0.000 .4103876 .6082952
_cons | .6155069 .070238 -4.25 0.000 .4921515 .7697807
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Note: _cons estimates baseline odds.
Here, the odds ratio for prior CVD is 1.55 times greater for participants that are hypertensive rather than normotensive, once adjusted for HDL-C (95% CI: 1.33-1.80).
C1.4 PRACTICAL: SPSS
Controlling for confounders in a logistic regression
You can control for additional variables by adding more variables to the ‘Covariates’ box within the logistic regression analysis pop up. Here we are going to use this to obtain the odds ratio for prior CVD with hypertension, adjusted for HDL-C.
Each variable we put in the model will be controlled for all the other variables in the model. That is, if we add BMI group to this logistic regression above, we would interpret the coefficient for hypertension as ‘the association of hypertension with the odds of prior CVD, independent (or adjusted for) of HDL-C and BMI group’. BMI group would likewise be interpreted as the association of BMI group with prior CVD, once adjusted for hypertension and HDL-C.
Question C1.4a: What are the odds of having prior CVD if a participant is hypertensive, once you have adjusted for their levels of HDL-C?
Answer
The output table will look like the below.
Here, the odds ratio for prior CVD is 1.55 times greater for participants that are hypertensive rather than normotensive, once adjusted for HDL-C (95% CI: 1.34-1.80).
C1.4 PRACTICAL: R
Controlling for confounders in a logistic regression
Now use the ‘glm() ‘ command to obtain the odds ratio for prior CVD with hypertension, adjusted for HDL-C. This may be obtained as follows:
model <- glm(prior_cvd ~ hypertens + hdlc, family = binomial(link = “logit”), data = df)
Note that the output gives us the odds ratio for ‘hyperten’ adjusted for ‘hdlc’ but it also gives us the odds ratios for ‘hdlc’ adjusted for ‘hyperten’.
You will run and interpret this command in the questions below.
We can control for additional variables as well by adding additional variables to the command line as we did above with ‘hdlc’. Each variable we put in the model will be controlled for all the other variables in the model. That is, if we add BMI group to this logistic regression above, we would interpret the coefficient for hypertension as ‘the association of hypertension with the odds of prior CVD, independent of (or adjusted for) HDL-C and BMI group’. BMI group would likewise be interpreted as the association of BMI group with prior CVD, once adjusted for hypertension and HDL-C.
- Question C1.4b: What are the odds of having prior CVD if a participant is hypertensive, once you have adjusted for their levels of HDL-C?
Answer
Answer C1.4a:
> model8 <- glm(prior_cvd ~ hyperten + hdlc, family = binomial(link = “logit”), data = df)
> summary(model8)
Call:
glm(formula = prior_cvd ~ hyperten + hdlc, family = binomial(link = “logit”), data = df)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.1004 -0.7844 -0.6978 1.2748 2.3248
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.4722 0.1144 -4.127 3.67e-05 ***
hyperten 0.4432 0.0770 5.756 8.59e-09 ***
hdlc -0.7038 0.1007 -6.991 2.73e-12 ***
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 4805.5 on 4265 degrees of freedom
Residual deviance: 4717.3 on 4263 degrees of freedom
AIC: 4723.3
Number of Fisher Scoring iterations: 4
> exp(cbind(coef(model8), confint(model8)))
Waiting for profiling to be done…
2.5 % 97.5 %
(Intercept) 0.6236630 0.4984294 0.7805407
hyperten 1.5577272 1.3388762 1.8107175
hdlc 0.4946928 0.4055012 0.6017479
Here, the odds ratio for prior CVD is 1.56 times higher in those with hypertension compared to those without hypertension, after adjusting for HDL-C (OR: 1.56, 95% CI: 1.34-1.81).
