# This is semi-generic code for doing a power analysis of a logistic regression with 4
# levels in a factor
# when there's some pilot values already available and defined
#modelled heavily the simulation example explained in:
#http://meeting.spsp.org/2016/sites/default/files/Lane%2C%20Hennes%2C%20West%20SPSP%20Power%20Workshop%202016.pdf

library('batman')
library('reshape')

l2p <- function(b) {
 odds <- exp(b) 
 prob <- odds/(1+odds)
 return(prob)
}


makeData <- function(n) { #make a random dataset of size n
 #4 group IDs 
 tDF <- data.frame(
     Group0=rbinom(n=n, size=1, prob=l2p(pilot.b0)),        #ASK: what about se in pilot data?
     Group1=rbinom(n=n, size=1, prob=l2p(pilot.b0 + pilot.b1)), # shouldn't my probs 
     Group2=rbinom(n=n, size=1, prob=l2p(pilot.b0 + pilot.b2)), # include se?
     Group3=rbinom(n=n, size=1, prob=l2p(pilot.b0 + pilot.b3)))
 sDF <- melt(tDF, id.vars = 0) #AKA the index is the unique id, as far as that goes
 colnames(sDF) <- c('source', 'nd')
 
 return(sDF) 
}

powerCheck <- function(n, nSims) { #run a power calculation on the dataset given
  #set up some empty arrays b/c R
  signif0 <- rep(NA, nSims)
  signif1 <- rep(NA, nSims)
  signif2 <- rep(NA, nSims)
  signif3 <- rep(NA, nSims)
  signifM <- rep(NA, nSims)
  for (s in 1:nSims) {           # repeatedly we will....
    simData <- makeData(n)       # make some data
    m1.sim <- glm(nd ~ source,   # give the anticipated regression a try
                  family=binomial(link="logit"), data=simData)
    p0 <- coef(summary(m1.sim))[1,4]
    p1 <- coef(summary(m1.sim))[2,4]
    p2 <- coef(summary(m1.sim))[3,4]
    p3 <- coef(summary(m1.sim))[4,4]
    signif0[s] <- p0 <=.05
    signif1[s] <- p1 <=.05
    signif2[s] <- p2 <=.05
    signif3[s] <- p3 <=.05
    signifM[s] <- p0 <=.05 & p1 <=.05 & p2 <=.05 & p3 <=.05
  }  
  power <- c(mean(signif0), mean(signif1), mean(signif2), mean(signif3), mean(signifM))
  return(power)
}