##### CITE BETH TIPTON'S PAPER IN THE DOCUMENTATION #####
#' Calculate `generalizability index` to describe how similar or different trial is from population
#'
#' @param dat1B vector of probabilities of trial participation among individuals in the trial
#' @param dat2B vector of probabilities of trial participation among individuals in the population
#' @return the generalizability index, a value between 0 and 1, where scores greater than 1 indicate greater similarity (see Tipton paper for description)
#' @export
gen_index <- function(dat1B,dat2B) {
#kernel density
kg = function(x,data){
# Bandwidth
n = length(data)
hb = (4*sqrt(var(data))^5/(3*n))^(1/5)
# Kernel density
k = r = length(x)
for(i in 1:k)
r[i] = mean(dnorm((x[i]-data)/hb))/hb
return(r)
}
##B index calculation
return( as.numeric(integrate(function(x) sqrt(kg(x,dat1B)*kg(x,dat2B)),-Inf,Inf)$value))
}
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