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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
A2.4 Calcul de taille d’échantillon pour les essais randomisés (RCTs)
Learning Outcomes
By the end of this section, students will be able to:
- Explain the key concept of power and what impacts it
- Estimate the power of a given study
- Estimate the sample size needed to test hypotheses in different study designs
You can download a copy of the slides here: A2.4: Sample Size Calculations for RCTs
Video A2.4 Sample Size Calculation for RCTs (11 minutes)
A2.4 PRACTICAL: R
Sample size calculation for testing a hypothesis (Clinical trials or clinical interventional studies)
Here is an example:
In a parallel RCT, 25% of the subjects on the standard therapy had a successful outcome. It is only of clinical relevance if a 40% absolute improvement is observed in the new therapy. How many subjects are required in order to detect this difference with 80% power at the 5% level of significance?
In this case we need to assess a difference in proportions again, this time with an effect size that has a 0.40 difference between the groups:
> power6<-pwr.2p.test(h=ES.h(p1=0.25, p2=0.65), power=0.8, sig.level=0.05)
> power6
Difference of proportion power calculation for binomial distribution (arcsine transformation)
h = 0.8282914
n = 22.88076
sig.level = 0.05
power = 0.8
alternative = two.sided
NOTE: same sample sizes
23 subjects per group and 46 subjects are required in total.
Question A2.4: In the same parallel trial as described in the example above, we still observe that 25% of the subjects on the standard therapy had a successful outcome, but this time it is only of clinical relevance if a 40% relative improvement is observed in the new therapy. How many subjects are required in order to detect this difference with 80% power at the 5% level of significance?
Answer
First you need to work out what a 40% relative increase on 25% is: 0.25*1.40=35% of subjects would need to have a successful outcome for there to be clinical relevance.
> power7<-pwr.2p.test(h=ES.h(p1=0.25, p2=0.35), power=0.8, sig.level=0.05)
> power7
Difference of proportion power calculation for binomial distribution (arcsine transformation)
h = 0.2189061
n = 327.5826
sig.level = 0.05
power = 0.8
alternative = two.sided
NOTE: same sample sizes
We need many more patients than in the example above due to the small effect size that we now wish to detect.
A2.4 PRACTICAL: Stata
Sample size calculation for testing a hypothesis (Clinical trials or clinical interventional studies)
Here is an example:
In a parallel RCT, 25% of the subjects on the standard therapy had a successful outcome. It is only of clinical relevance if a 40% absolute improvement is observed in the new therapy. How many subjects are required in order to detect this difference with 80% power at the 5% level of significance?
power twoproportions 0.25 0.65, alpha(0.05) power(0.80)
*– Estimated sample sizes:
N = 48
N per group = 24
24 subjects per group and 48 subjects are required in total.
Question A2.4: In the same parallel trial as described in the example above, we still observe that 25% of the subjects on the standard therapy had a successful outcome, but this time it is only of clinical relevance if a 40% relative improvement is observed in the new therapy. How many subjects are required in order to detect this difference with 80% power at the 5% level of significance?
Answer
First you need to work out what a 40% relative increase on 25% is: 0.25*1.40=35% of subjects would need to have a successful outcome for there to be clinical relevance.
power twoproportions 0.25 0.35, alpha(0.05) power(0.80)
Estimated sample sizes for a two-sample proportions test
Pearson’s chi-squared test
Ho: p2 = p1 versus Ha: p2 != p1
Study parameters:
alpha = 0.0500
power = 0.8000
delta = 0.1000 (difference)
p1 = 0.2500
p2 = 0.3500
Estimated sample sizes:
N = 658
N per group = 329
We need many more patients than in the example above due to the small effect size that we now wish to detect.
A2.4 PRACTICAL: SPSS
Sample size calculation for testing a hypothesis (Clinical trials or clinical interventional studies)
In a parallel RCT, 25% of the subjects on the standard therapy had a successful outcome. It is only of clinical relevance if a 40% absolute improvement is observed in the new therapy. How many subjects are required in order to detect this difference with 80% power at the 5% level of significance? Use the same test as in the previous practical (Independent Samples Binomial Test) but adapt the input values for this scenario.
In the same parallel trial as described in the example above, we still observe that 25% of the subjects on the standard therapy had a successful outcome, but this time it is only of clinical relevance if a 40% relative improvement is observed in the new therapy. How many subjects are required in order to detect this difference with 80% power at the 5% level of significance?
Answer
In the first part we calculate that 24 subjects per group and 48 subjects are required in total when we are looking for 40% absolute difference.
In the second part, we first need to work out what a 40% relative increase on 25% is (0.25*1.40=35%). Therefore 35% of subjects would need to have a successful outcome for there to be clinical relevance.
When we conduct the test we calculate that we need 329 subjects per group and 658 overall.
We need many more patients than in the example above due to the small effect size that we now wish to detect.
