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##' @export
logit <- function(p) log(p/(1-p))
##' @export
expit <- function(z) 1/(1+exp(-z))
##' @export
tigol <- expit
##' Calculate prevalence, sensitivity, specificity, and positive and
##' negative predictive values
##'
##' @title Calculate diagnostic tests for 2x2 table
##' @aliases diagtest odds riskcomp OR Ratio Diff
##' @param table Table or (matrix/data.frame with two columns)
##' @param positive Switch reference
##' @param exact If TRUE exact binomial proportions CI/test will be used
##' @param p0 Optional null hypothesis (test prevalenc, sensitivity, ...)
##' @param confint Type of confidence limits
##' @param ... Additional arguments to lower level functions
##' @author Klaus Holst
##' @details Table should be in the format with outcome in columns and
##' test in rows. Data.frame should be with test in the first
##' column and outcome in the second column.
##' @examples
##' M <- as.table(matrix(c(42,12,
##' 35,28),ncol=2,byrow=TRUE,
##' dimnames=list(rater=c("no","yes"),gold=c("no","yes"))))
##' diagtest(M,exact=TRUE)
##' @export
diagtest <- function(table,positive=2,exact=FALSE,p0=NA,confint=c("logit","arcsin","pseudoscore","exact"),...) {
if (!inherits(table,c("table","data.frame","matrix","multinomial")))
stop("Expecting a table or data.frame.")
if (is.table(table)) {
lev <- dimnames(table)[[2]]
}
if (inherits(table,"multinomial")) {
lev <- dimnames(table$P)[[2]]
}
if (!is.table(table) & (is.matrix(table) || is.data.frame(table))) {
if (is.factor(table[,2])) {
lev <- levels(table[,2])
} else
lev <- unique(table[,2])
}
if (is.character(positive)) {
positive <- match(positive,lev)
}
if (!(positive%in%c(1,2))) stop("Expecting and index of 1 or 2.")
negative <- positive%%2+1L
if (!is.null(confint) && confint[1]=="exact") exact <- TRUE
if (exact) {
if (!is.table(table) && (is.matrix(table) || is.data.frame(table))) {
table <- base::table(table[,c(1,2),drop=FALSE])
##names(dimnames(table)) <- colnames(table)[1:2]
}
if (!is.table(table) || nrow(table)!=2 || ncol(table)!=2) stop("2x2 table expected")
n <- sum(table)
nc <- colSums(table)
nr <- rowSums(table)
test <- TRUE
if (is.na(p0)) {
test <- FALSE
p0 <- 0.5
}
## Prevalence
p1 <- with(stats::binom.test(nc[positive],n,p=p0),c(estimate,conf.int,p.value))
## Test marginal
p2 <- with(stats::binom.test(nr[positive],n,p=p0),c(estimate,conf.int,p.value))
## Sensitivity/Specificity
sens <- with(stats::binom.test(table[positive,positive],nc[positive],p=p0),c(estimate,conf.int,p.value))
spec <- with(stats::binom.test(table[negative,negative],nc[negative],p=p0),c(estimate,conf.int,p.value))
## PPV,NPV
ppv <- with(stats::binom.test(table[positive,positive],nr[positive],p=p0),c(estimate,conf.int,p.value))
npv <- with(stats::binom.test(table[negative,negative],nr[negative],p=p0),c(estimate,conf.int,p.value))
## Accuracy
acc <- with(stats::binom.test(table[positive,positive]+table[negative,negative],n,p=p0),c(estimate,conf.int,p.value))
## Symmetry (McNemar):
## number of discordant pairs under null: b~bin(b+c,0.5)
sym <- with(stats::binom.test(table[positive,negative],table[positive,negative]+table[negative,positive],p=0.5),c(estimate,conf.int,p.value))
coefmat <- rbind(Prevalence=p1,
Test=p2,
Sensitivity=sens,
Specificity=spec,
PositivePredictiveValue=ppv,
NegativePredictiveValue=npv,
Accuracy=acc,
Homogeneity=sym)
if (!test) coefmat[seq(nrow(coefmat)-1),4] <- NA
coefmat <- cbind(coefmat[,1,drop=FALSE],NA,coefmat[,-1,drop=FALSE])
colnames(coefmat) <- c("Estimate","Std.Err","2.5%","97.5%","P-value")
res <- list(table=table, prop.table=table/sum(table),
coefmat=coefmat)
} else {
if (inherits(table,"table"))
M <- multinomial(table)
else {
if (inherits(table,"multinomial")) {
M <- table
table <- round(M$P*nrow(M$data))
} else {
M <- multinomial(table[,1:2],...)
table <- base::table(table)
}
}
calc_diag <- function(p,...) {
P <- matrix(p[1:4],2)
p1 <- sum(P[,positive])
p2 <- sum(P[positive,])
res <- c(Prevalence=p1, ##(p[1]+p[2]),
Test=p2, ##(p[1]+p[3]),
Sensitivity=P[positive,positive]/p1, ## p[1]/(p[1]+p[2]), # Prob test + | given (true) disease (True positive rate)
Specificity=P[negative,negative]/(1-p1), ## p[4]/(1-p[1]-p[2]), # Prob test - | given no disease (True negative rate)
PositivePredictiveValue=P[positive,positive]/p2, ## p[1]/(p[1]+p[3]), # Prob disease | test +
NegativePredictiveValue=P[negative,negative]/(1-p2), ## p[4]/(1-p[1]-p[3]), # Prob disease free | test -
Accuracy=(P[1,1]+P[2,2])/sum(P),
Homogeneity=P[negative,positive]-P[positive,negative]
)
if (!is.null(confint)) {
if (tolower(confint[1])=="logit") {
res[seq(length(res)-1)] <- logit(res[seq(length(res)-1)])
} else if (tolower(confint[1])=="arcsin") {
res[seq(length(res)-1)] <- asin(sqrt(res[seq(length(res)-1)]))
}
}
return(res)
}
names(dimnames(table)) <- paste0(c("Test:","Outcome:"),names(dimnames(table)))
prfun <- function(x,...) {
printCoefmat(x$coefmat[,c(-2)],na.print="",...)
print(cli::rule())
cat("\n")
cat("Prevalence: Prob( outcome+ )\n")
cat("Test: Prob( test+ )\n")
cat("Sensitivity (True positive rate): Prob( test+ | outcome+ )\n")
cat("Specificity (True negative rate): Prob( test- | outcome- )\n")
cat("Positive predictive value (Precision): Prob( outcome+ | test+ )\n")
cat("Negative predictive value: Prob( outcome- | test- )\n")
cat("Accuracy: Prob( correct classification )\n")
cat("Homogeneity/Symmetry: Prob( outcome+ ) - Prob( test+ )\n")
}
btransform <- NULL
if (!is.null(confint)) {
if (tolower(confint[1])=="logit") {
btransform <- function(x) {
rbind(expit(x[seq(nrow(x)-1),,drop=FALSE]),
x[nrow(x),,drop=FALSE])
}
} else if (tolower(confint[1])=="pseudoscore") {
## TODO, agresti-ryu, biometrika 2010
} else if (tolower(confint[1])=="arcsin") {
btransform <- function(x) {
rbind(sin(x[seq(nrow(x)-1),,drop=FALSE])^2,
x[nrow(x),,drop=FALSE])
}
}
}
res <- estimate(M,calc_diag,print=prfun,null=c(rep(p0,7),0),back.transform=btransform,...)
}
CI <- confint[1]
if (exact) CI <- "exact"
if (is.null(CI)) CI <- "wald"
res <- structure(c(res,
list(table=table, prop.table=table/sum(table),
confint=CI,
positive=positive,
negative=negative,
levels=dimnames(table)
)),
class=c("diagtest","estimate"))
res$call <- match.call()
rownames(res$coefmat) <- gsub("\\[|\\]","",rownames(res$coefmat))
names(res$coef) <- rownames(res$coefmat)
return(res)
}
##' @export
print.diagtest <- function(x,...) {
cat("Call: ")
print(x$call)
cat("Confidence limits: ", x$confint, "\n", sep="")
print(cli::rule())
printmany(x$table, x$prop.table,nspace=2, ...)
cat("\nPositive outcome: '",
x$levels[[2]][x$positive], "'\n",
sep = ""
)
## cat("\tNegative outcome: '", x$levels[[2]][x$positive%%2+1],"'\n",sep="")
print(cli::rule())
printCoefmat(x$coefmat[, c(-2)], na.print="", ...)
print(cli::rule())
cat("\n")
cat("Prevalence: Prob( outcome+ )\n")
cat("Test: Prob( test+ )\n")
cat("Sensitivity (True positive rate): Prob( test+ | outcome+ )\n")
cat("Specificity (True negative rate): Prob( test- | outcome- )\n")
cat("Positive predictive value (Precision): Prob( outcome+ | test+ )\n")
cat("Negative predictive value: Prob( outcome- | test- )\n")
cat("Accuracy: Prob( correct classification )\n")
if (x$confint == "exact") {
cat("Homogeneity/Symmetry: Prob( outcome+, test- | discordant ), H0: p=0.5 \n")
} else {
cat("Homogeneity/Symmetry: H0: Prob( outcome+ ) - Prob( test+ ), H0: p=0\n")
}
cat("\n")
}
##' @export
summary.diagtest <- function(object, ...) {
object[c("IC", "print", "id", "compare")] <- NULL
return(object)
}
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