sampleSizeCalculationAUC

sampleSizeCalculationAUC

## AUC expected versus AUC minimal 

## sample size calculatino AUC
## we use formula 7.5 in http://dx.doi.org/10.1016/j.jbi.2014.02.013 
## Variance of AUC, following Appendix A (nonparametric AUC)

minimalAcceptableAUC<-0.7
expectedAUC<-0.8
ratioControlToCases<-2
ZBeta<-0.8416212
Q1H0<-minimalAcceptableAUC/(2-minimalAcceptableAUC)
Q2H0<-(2*minimalAcceptableAUC^2)/(1+minimalAcceptableAUC)

Q1H1<-expectedAUC/(2-expectedAUC)
Q2H1<-2*expectedAUC^2/(1+expectedAUC)
## Formula A2 in Appendix A:
VarAUCH0 <- (Q1H0/ratioControlToCases)+Q2H0 -((minimalAcceptableAUC^2*((1/ratioControlToCases)+1)))
VarAUCH1 <- (Q1H1/ratioControlToCases)+Q2H1 -(expectedAUC^2*((1/ratioControlToCases)+1))
VarAUCH0
VarAUCH1


## Formula 7.5 
cases<- ceiling((((1.96*(VarAUCH0^0.5))+(ZBeta*VarAUCH1^0.5))^2)/((expectedAUC-minimalAcceptableAUC)^2))
controls<-ceiling(cases*ratioControlToCases)
controls
cases
total<-cases+controls
total