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#' Odds Ratios, Risk Ratios and Cohen's *h* for 2-by-2 Contingency Tables
#'
#' Report with any [`stats::chisq.test()`] or [`stats::fisher.test()`].
#' \cr\cr
#' Note that these are computed with each **column** representing the different
#' groups, and the *first* column representing the treatment group and the
#' *second* column baseline (or control). Effects are given as `treatment /
#' control`. If you wish you use rows as groups you must pass a transposed
#' table, or switch the `x` and `y` arguments.
#'
#'
#' @inheritParams oddsratio_to_d
#' @inheritParams phi
#' @param alternative a character string specifying the alternative hypothesis;
#' Controls the type of CI returned: `"two.sided"` (two-sided CI; default),
#' `"greater"` (one-sided CI) or `"less"` (one-sided CI). Partial matching is
#' allowed (e.g., `"g"`, `"l"`, `"two"`...). See *One-Sided CIs* in
#' [effectsize_CIs].
#' @param ... Ignored
#'
#' @details
#'
#' # Confidence (Compatibility) Intervals (CIs)
#' For Odds ratios, Risk ratios and Cohen's *h*, confidence intervals are
#' estimated using the standard normal parametric method (see Katz et al., 1978;
#' Szumilas, 2010).
#'
#' @inheritSection effectsize_CIs CIs and Significance Tests
#'
#' @return A data frame with the effect size (`Odds_ratio`, `Risk_ratio`
#' (possibly with the prefix `log_`), `Cohens_h`) and its CIs (`CI_low` and
#' `CI_high`).
#'
#' @family effect sizes for contingency table
#'
#'
#' @references
#' - Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd Ed.). New York: Routledge.
#' - Katz, D. J. S. M., Baptista, J., Azen, S. P., & Pike, M. C. (1978). Obtaining confidence intervals for the risk ratio in cohort studies. Biometrics, 469-474.
#' - Szumilas, M. (2010). Explaining odds ratios. Journal of the Canadian academy of child and adolescent psychiatry, 19(3), 227.
#'
#' @examples
#' data("RCT_table")
#' RCT_table # note groups are COLUMNS
#'
#' oddsratio(RCT_table)
#' oddsratio(RCT_table, alternative = "greater")
#'
#' riskratio(RCT_table)
#'
#' cohens_h(RCT_table)
#'
#' @export
#' @importFrom stats chisq.test qnorm
oddsratio <- function(x, y = NULL, ci = 0.95, alternative = "two.sided", log = FALSE, ...) {
alternative <- .match.alt(alternative)
if (.is_htest_of_type(x, "(Pearson's Chi-squared|Fisher's Exact)", "Chi-squared-test or Fisher's Exact test")) {
return(effectsize(x, type = "or", log = log, ci = ci, alternative = alternative))
} else if (.is_BF_of_type(x, "BFcontingencyTable", "Chi-squared")) {
return(effectsize(x, type = "or", log = log, ci = ci))
}
res <- .get_data_xtabs(x, y)
Obs <- res$observed
if (any(c(colSums(Obs), rowSums(Obs)) == 0L)) {
insight::format_error("Cannot have empty rows/columns in the contingency tables.")
}
if (nrow(Obs) != 2 || ncol(Obs) != 2) {
insight::format_error("Odds ratio only available for 2-by-2 contingency tables")
}
OR <- (Obs[1, 1] / Obs[2, 1]) /
(Obs[1, 2] / Obs[2, 2])
res <- data.frame(Odds_ratio = OR)
if (.test_ci(ci)) {
res$CI <- ci
ci.level <- .adjust_ci(ci, alternative)
alpha <- 1 - ci.level
SE_logodds <- sqrt(sum(1 / Obs))
Z_logodds <- stats::qnorm(alpha / 2, lower.tail = FALSE)
confs <- exp(log(OR) + c(-1, 1) * SE_logodds * Z_logodds)
res$CI_low <- confs[1]
res$CI_high <- confs[2]
ci_method <- list(method = "normal")
res <- .limit_ci(res, alternative, 0, Inf)
} else {
ci_method <- alternative <- NULL
}
if (log) {
res[colnames(res) %in% c("Odds_ratio", "CI_low", "CI_high")] <-
log(res[colnames(res) %in% c("Odds_ratio", "CI_low", "CI_high")])
colnames(res)[1] <- "log_Odds_ratio"
}
class(res) <- c("effectsize_table", "see_effectsize_table", class(res))
attr(res, "ci") <- ci
attr(res, "ci_method") <- ci_method
attr(res, "approximate") <- FALSE
attr(res, "alternative") <- alternative
return(res)
}
#' @rdname oddsratio
#' @export
#' @importFrom stats chisq.test qnorm
riskratio <- function(x, y = NULL, ci = 0.95, alternative = "two.sided", log = FALSE, ...) {
alternative <- .match.alt(alternative)
if (.is_htest_of_type(x, "Pearson's Chi-squared", "Chi-squared-test")) {
return(effectsize(x, type = "rr", log = log, ci = ci, alternative = alternative))
} else if (.is_BF_of_type(x, "BFcontingencyTable", "Chi-squared")) {
return(effectsize(x, type = "rr", log = log, ci = ci, ...))
}
res <- .get_data_xtabs(x, y)
Obs <- res$observed
if (any(c(colSums(Obs), rowSums(Obs)) == 0L)) {
insight::format_error("Cannot have empty rows/columns in the contingency tables.")
}
if (nrow(Obs) != 2 || ncol(Obs) != 2) {
insight::format_error("Risk ratio only available for 2-by-2 contingency tables")
}
n1 <- sum(Obs[, 1])
n2 <- sum(Obs[, 2])
p1 <- Obs[1, 1] / n1
p2 <- Obs[1, 2] / n2
RR <- p1 / p2
res <- data.frame(Risk_ratio = RR)
if (.test_ci(ci)) {
res$CI <- ci
ci.level <- .adjust_ci(ci, alternative)
alpha <- 1 - ci.level
SE_logRR <- sqrt(p1 / ((1 - p1) * n1)) + sqrt(p2 / ((1 - p2) * n2))
Z_logRR <- stats::qnorm(alpha / 2, lower.tail = FALSE)
confs <- exp(log(RR) + c(-1, 1) * SE_logRR * Z_logRR)
res$CI_low <- confs[1]
res$CI_high <- confs[2]
ci_method <- list(method = "normal")
res <- .limit_ci(res, alternative, 0, Inf)
} else {
ci_method <- alternative <- NULL
}
if (log) {
res[colnames(res) %in% c("Risk_ratio", "CI_low", "CI_high")] <-
log(res[colnames(res) %in% c("Risk_ratio", "CI_low", "CI_high")])
colnames(res)[1] <- "log_Risk_ratio"
}
class(res) <- c("effectsize_table", "see_effectsize_table", class(res))
attr(res, "ci") <- ci
attr(res, "ci_method") <- ci_method
attr(res, "approximate") <- FALSE
attr(res, "alternative") <- alternative
return(res)
}
#' @rdname oddsratio
#' @export
#' @importFrom stats qnorm
cohens_h <- function(x, y = NULL, ci = 0.95, alternative = "two.sided", ...) {
alternative <- .match.alt(alternative)
if (.is_htest_of_type(x, "Pearson's Chi-squared", "Chi-squared-test")) {
return(effectsize(x, type = "cohens_h", ci = ci, alternative = alternative))
} else if (.is_BF_of_type(x, "BFcontingencyTable", "Chi-squared")) {
return(effectsize(x, type = "cohens_h", ci = ci, ...))
}
res <- .get_data_xtabs(x, y)
Obs <- res$observed
if (any(c(colSums(Obs), rowSums(Obs)) == 0L)) {
insight::format_error("Cannot have empty rows/columns in the contingency tables.")
}
if (nrow(Obs) != 2 || ncol(Obs) != 2) {
insight::format_error("Cohen's h only available for 2-by-2 contingency tables")
}
n1 <- sum(Obs[, 1])
n2 <- sum(Obs[, 2])
p1 <- Obs[1, 1] / n1
p2 <- Obs[1, 2] / n2
H <- 2 * asin(sqrt(p1)) - 2 * asin(sqrt(p2))
out <- data.frame(Cohens_h = H)
if (.test_ci(ci)) {
out$CI <- ci
ci.level <- .adjust_ci(ci, alternative)
alpha <- 1 - ci.level
se_arcsin <- sqrt(0.25 * (1 / n1 + 1 / n2))
Zc <- stats::qnorm(alpha / 2, lower.tail = FALSE)
out$CI_low <- H - Zc * (2 * se_arcsin)
out$CI_high <- H + Zc * (2 * se_arcsin)
ci_method <- list(method = "normal")
out <- .limit_ci(out, alternative, -pi, pi)
} else {
ci_method <- alternative <- NULL
}
class(out) <- c("effectsize_table", "see_effectsize_table", class(out))
attr(out, "ci") <- ci
attr(out, "ci_method") <- ci_method
attr(out, "approximate") <- FALSE
attr(out, "alternative") <- alternative
return(out)
}
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