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# ACAT function by Yaowu Liu, with changes
ACATO <- function(p){
if (all(is.na(p))) return(NA)
p <- p[!is.na(p)]
p[p == 1] <- 1 - 1e-16
#### check if there are very small non-zero p values
is.small <- (p < 1e-16)
if (sum(is.small) == 0) {
cct.stat <- sum(tan((0.5 - p) * pi))/length(p)
} else {
cct.stat <- sum((1 / p[is.small]) / pi)
cct.stat <- cct.stat + sum(tan((0.5 - p[!is.small]) * pi))
cct.stat <- cct.stat/length(p)
}
#### check if the test statistic is very large.
if (cct.stat > 1e+15){
pval <- (1 / cct.stat) / pi
} else {
pval <- 1 - pcauchy(cct.stat)
}
pval
}
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