#########################################################################
###Função para Deteminar Tamanho de amostra para prevalencia ############
#########################################################################
nsample=function(p,se=1,esp=1,delta=0.05,prob=0.95,deff=1,popsize=NULL){
 alpha=(1-prob)/2
 z=qnorm(alpha,lower.tail =FALSE)
 p1=seq(0,1,0.05)
 n=((z/delta)^2)*((se*p+(1-esp)*(1-p))*(1-se*p-(1-esp)*(1-p)))/((se+esp-1)^2)
 n1=((z/delta)^2)*((se*p1+(1-esp)*(1-p1))*(1-se*p1-(1-esp)*(1-p1)))/((se+esp-1)^2)
 if(deff!=1){
  n=n*deff
  n1=n1*deff
 }
 if(!is.null(popsize)){
  n=n/(1+n/popsize)
  n1=n1/(1+n1/popsize)
 }
 n=round(n)
 n1=round(n1)
 y=max(n1)+0.05*max(n1)
 plot(p1,n1,type="l",xlab="Proporção",ylab="Tamanho de Amostra",ylim=c(0,y))
 resul=list("Proporção"=p,"Intervalo de confiança"=prob,"Delta"=delta,"Tamanho População"=popsize,"Tamanho de Amostra"=round(n))
 resul
}

##############################################################################
##Tamanho de amostra para amostragem simples considerando população infinita##
##############################################################################


nsample(p=0.5,delta=0.035,prob=0.95,deff=1.0)

nsample(p=0.5,delta=0.035,prob=0.95,deff=1.0)


#Considerando sensibilidade e especificidade
nsample(p=0.5,se=0.95,esp=0.98,delta=0.05,prob=0.95)

#Considerando efeito do conglomerado
nsample(p=0.5,delta=0.05,prob=0.95,deff=1.5)

##############################################################################
###Tamanho de amostra para amostragem simples considerando população finita###
##############################################################################

nsample(p=0.5,delta=0.03,prob=0.95,popsize=50000)

#Considerando sensibilidade e especificidade
nsample(p=0.5,se=0.95,esp=0.98,delta=0.05,prob=0.95,popsize=50000)

#Considerando efeito do conglomerado
nsample(p=0.5,delta=0.05,prob=0.95,deff=1.5,popsize=50000)