From 7ee4b0f461ecb0f8f5b337402c0d93fc091751ad Mon Sep 17 00:00:00 2001
From: Daniel Sabanes Bove <DBove@ITS.JNJ.com>
Date: Fri, 12 Jun 2026 13:57:11 +0000
Subject: [PATCH 01/13] start dev

---
 R/prop_diff_test.R | 12 +++++++++---
 1 file changed, 9 insertions(+), 3 deletions(-)

diff --git a/R/prop_diff_test.R b/R/prop_diff_test.R
index 1c5f4be587..b9b9385d9b 100644
--- a/R/prop_diff_test.R
+++ b/R/prop_diff_test.R
@@ -9,7 +9,7 @@
 #' supplied via the `strata` element of the `variables` argument.
 #'
 #' @inheritParams argument_convention
-#' @param method (`string`)\cr one of `chisq`, `cmh`, `cmh_wh`, `fisher`, or `schouten`;
+#' @param method (`string`)\cr one of `chisq`, `cmh`, `cmh_sato`, `cmh_wh`, `fisher`, or `schouten`;
 #'   specifies the test used to calculate the p-value.
 #' @param .stats (`character`)\cr statistics to select for the table.
 #'
@@ -53,7 +53,7 @@ s_test_proportion_diff <- function(df,
                                    .ref_group,
                                    .in_ref_col,
                                    variables = list(strata = NULL),
-                                   method = c("chisq", "schouten", "fisher", "cmh", "cmh_wh"),
+                                   method = c("chisq", "schouten", "fisher", "cmh", "cmh_sato", "cmh_wh"),
                                    alternative = c("two.sided", "less", "greater"),
                                    ...) {
   method <- match.arg(method)
@@ -82,6 +82,7 @@ s_test_proportion_diff <- function(df,
 
     tbl <- switch(method,
       cmh = table(grp, rsp, strata),
+      cmh_sato = table(grp, rsp, strata),
       cmh_wh = table(grp, rsp, strata),
       table(grp, rsp)
     )
@@ -91,6 +92,7 @@ s_test_proportion_diff <- function(df,
       cmh = prop_cmh(tbl, alternative = alternative),
       fisher = prop_fisher(tbl, alternative = alternative),
       schouten = prop_schouten(tbl, alternative = alternative),
+      cmh_sato = prop_cmh(tbl, alternative = alternative, diff_se = "sato"),
       cmh_wh = prop_cmh(tbl, alternative = alternative, transform = "wilson_hilferty")
     )
   }
@@ -118,6 +120,7 @@ d_test_proportion_diff <- function(method, alternative = c("two.sided", "less",
     "schouten" = "Chi-Squared Test with Schouten Correction",
     "chisq" = "Chi-Squared Test",
     "cmh" = "Cochran-Mantel-Haenszel Test",
+    "cmh_sato" = "Cochran-Mantel-Haenszel Test with Sato Variance Estimator",
     "cmh_wh" = "Cochran-Mantel-Haenszel Test with Wilson-Hilferty Transformation",
     "fisher" = "Fisher's Exact Test",
     stop(paste(method, "does not have a description"))
@@ -235,7 +238,7 @@ a_test_proportion_diff <- function(df,
 test_proportion_diff <- function(lyt,
                                  vars,
                                  variables = list(strata = NULL),
-                                 method = c("chisq", "schouten", "fisher", "cmh", "cmh_wh"),
+                                 method = c("chisq", "schouten", "fisher", "cmh", "cmh_sato", "cmh_wh"),
                                  alternative = c("two.sided", "less", "greater"),
                                  var_labels = vars,
                                  na_str = default_na_str(),
@@ -321,17 +324,20 @@ prop_chisq <- function(tbl, alternative = c("two.sided", "less", "greater")) {
 #'
 #' @param ary (`array`, 3 dimensions)\cr array with two groups in rows, the binary response
 #'   (`TRUE`/`FALSE`) in columns, and the strata in the third dimension.
+#' @param diff_se (`string`)\cr either `standard` or `sato`; specifies whether to use the Sato variance estimator to calculate the chi-squared statistic.
 #' @param transform (`string`)\cr either `none` or `wilson_hilferty`; specifies whether to apply
 #'   the Wilson-Hilferty transformation of the chi-squared statistic.
 #'
 #' @keywords internal
 prop_cmh <- function(ary,
                      alternative = c("two.sided", "less", "greater"),
+                     diff_se = c("standard", "sato"),
                      transform = c("none", "wilson_hilferty")) {
   checkmate::assert_array(ary)
   checkmate::assert_integer(c(ncol(ary), nrow(ary)), lower = 2, upper = 2)
   checkmate::assert_integer(length(dim(ary)), lower = 3, upper = 3)
   alternative <- match.arg(alternative)
+  diff_se <- match.arg(diff_se)
   transform <- match.arg(transform)
 
   strata_sizes <- apply(ary, MARGIN = 3, sum)

From 695615e8f2e65094abe2c232d721d3765c58013a Mon Sep 17 00:00:00 2001
From: Daniel Sabanes Bove <daniel@rconis.com>
Date: Mon, 15 Jun 2026 11:49:19 +0800
Subject: [PATCH 02/13] make sato test work

---
 R/prop_diff.R                                 | 154 ++++++++++++------
 R/prop_diff_test.R                            |  39 +++--
 tests/testthat/_snaps/test_proportion_diff.md |  29 +++-
 tests/testthat/test-test_proportion_diff.R    |  99 ++++++++++-
 4 files changed, 253 insertions(+), 68 deletions(-)

diff --git a/R/prop_diff.R b/R/prop_diff.R
index 1e10395134..ba4aa187f1 100644
--- a/R/prop_diff.R
+++ b/R/prop_diff.R
@@ -596,6 +596,81 @@ prop_diff_nc <- function(rsp,
   )
 }
 
+#' @describeIn h_prop_diff Helper function to calculate the CMH weighted 
+#' difference in proportions.
+#' 
+#' @param tbl (`array`)\cr 3-dimensional array with dimensions corresponding to 
+#'   group, response, and strata. The second dimension (response) should have names 
+#'   "TRUE" and "FALSE".
+#' 
+#' @keywords internal
+h_diff_cmh <- function(tbl) {
+  checkmate::assert_array(tbl)
+  checkmate::assert_integer(c(ncol(tbl), nrow(tbl)), lower = 2, upper = 2)
+  checkmate::assert_integer(length(dim(tbl)), lower = 3, upper = 3)
+  checkmate::assert_true(identical(dimnames(tbl)[[2]], c("TRUE", "FALSE")))
+
+  n1 <- colSums(tbl[1, 1:2, ])
+  n2 <- colSums(tbl[2, 1:2, ])
+  x1 <- tbl[1, 1, ]
+  p1 <- x1 / n1
+  x2 <- tbl[2, 1, ]
+  p2 <- x2 / n2
+  # CMH weights
+  use_stratum <- (n1 > 0) & (n2 > 0)
+  n1 <- n1[use_stratum]
+  n2 <- n2[use_stratum]
+  p1 <- p1[use_stratum]
+  p2 <- p2[use_stratum]
+  wt <- (n1 * n2 / (n1 + n2))
+  wt_normalized <- wt / sum(wt)
+  est1 <- sum(wt_normalized * p1)
+  est2 <- sum(wt_normalized * p2)
+  diff_est <- est2 - est1
+
+  list(
+    x1 = x1,
+    n1 = n1,
+    p1 = p1,
+    x2 = x2,
+    n2 = n2,
+    p2 = p2,
+    wt = wt,
+    wt_normalized = wt_normalized,
+    est1 = est1,
+    est2 = est2,
+    diff_est = diff_est
+  )
+}
+
+#' @describeIn h_prop_diff Helper function to calculate the standard error for the 
+#'   CMH weighted difference in proportions.
+#' 
+#' @param cmh_results (`list`)\cr output of [h_diff_cmh()].
+#' 
+#' @keywords internal
+h_diff_cmh_se <- function(cmh_results, diff_se = c("standard", "sato")) {
+  checkmate::assert_list(cmh_results, types = "numeric", any.missing = FALSE, names = "unique")
+  diff_se <- match.arg(diff_se)
+  l <- cmh_results # For easier readability of the formulas below.
+  if (diff_se == "standard") {
+    terms1 <- l$p1 * (1 - l$p1) / l$n1
+    terms2 <- l$p2 * (1 - l$p2) / l$n2
+    sqrt(sum((terms1 + terms2) * l$wt_normalized^2))
+  } else {
+    # Sato variance estimator.
+    p_terms_num <- l$n2^2 * l$x1 - 
+      l$n1^2 * l$x2 + 
+      l$n1 * l$n2 * (l$n1 - l$n2) / 2
+    p_terms <- p_terms_num / (l$n1 + l$n2)^2
+    q_terms_num <- l$x1 * (l$n2 - l$x2) + l$x2 * (l$n1 - l$x1)
+    q_terms <- q_terms_num / (2 * (l$n1 + l$n2))
+    num <- l$diff_est * sum(p_terms) + sum(q_terms)
+    denom <- sum(l$wt)^2
+    sqrt(num / denom)
+  }
+}
+
 #' @describeIn h_prop_diff Calculates the weighted difference. This is defined as the difference in
 #'   response rates between the experimental treatment group and the control treatment group, adjusted
 #'   for stratification factors by applying Cochran-Mantel-Haenszel (CMH) weights. For the CMH chi-squared
@@ -645,66 +720,43 @@ prop_diff_cmh <- function(rsp,
     warning("Less than 5 observations in some strata.")
   }
 
-  # first dimension: FALSE, TRUE
-  # 2nd dimension: CONTROL, TX
+  # first dimension: CONTROL, TX
+  # 2nd dimension: TRUE, FALSE
   # 3rd dimension: levels of strata
-  # rsp as factor rsp to handle edge case of no FALSE (or TRUE) rsp records
+  # Note: rsp needs to be a factor to handle edge case of 
+  #       no FALSE (or TRUE) rsp records.
   t_tbl <- table(
-    factor(rsp, levels = c("FALSE", "TRUE")),
     grp,
+    factor(rsp, levels = c("TRUE", "FALSE")),
     strata
   )
-  n1 <- colSums(t_tbl[1:2, 1, ])
-  n2 <- colSums(t_tbl[1:2, 2, ])
-  x1 <- t_tbl[2, 1, ]
-  p1 <- x1 / n1
-  x2 <- t_tbl[2, 2, ]
-  p2 <- x2 / n2
-  # CMH weights
-  use_stratum <- (n1 > 0) & (n2 > 0)
-  n1 <- n1[use_stratum]
-  n2 <- n2[use_stratum]
-  p1 <- p1[use_stratum]
-  p2 <- p2[use_stratum]
-  wt <- (n1 * n2 / (n1 + n2))
-  wt_normalized <- wt / sum(wt)
-  est1 <- sum(wt_normalized * p1)
-  est2 <- sum(wt_normalized * p2)
-  estimate <- c(est1, est2)
+  cmh <- h_diff_cmh(t_tbl)
+
+  estimate <- c(cmh$est1, cmh$est2)
   names(estimate) <- levels(grp)
-  se1 <- sqrt(sum(wt_normalized^2 * p1 * (1 - p1) / n1))
-  se2 <- sqrt(sum(wt_normalized^2 * p2 * (1 - p2) / n2))
+  se1 <- sqrt(sum(cmh$wt_normalized^2 * cmh$p1 * (1 - cmh$p1) / cmh$n1))
+  se2 <- sqrt(sum(cmh$wt_normalized^2 * cmh$p2 * (1 - cmh$p2) / cmh$n2))
   z <- stats::qnorm((1 + conf_level) / 2)
   err1 <- z * se1
   err2 <- z * se2
-  ci1 <- c((est1 - err1), (est1 + err1))
-  ci2 <- c((est2 - err2), (est2 + err2))
+  ci1 <- c((cmh$est1 - err1), (cmh$est1 + err1))
+  ci2 <- c((cmh$est2 - err2), (cmh$est2 + err2))
   estimate_ci <- list(ci1, ci2)
   names(estimate_ci) <- levels(grp)
-  diff_est <- est2 - est1
 
   if (diff_se %in% c("standard", "sato")) {
-    se_diff <- if (diff_se == "standard") {
-      sqrt(sum(((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)) * wt_normalized^2))
-    } else {
-      # Sato variance estimator.
-      p_terms <- (n2^2 * x1 - n1^2 * x2 + n1 * n2 * (n1 - n2) / 2) / (n1 + n2)^2
-      q_terms <- (x1 * (n2 - x2) + x2 * (n1 - x1)) / (2 * (n1 + n2))
-      num <- diff_est * sum(p_terms) + sum(q_terms)
-      denom <- sum(wt)^2
-      sqrt(num / denom)
-    }
-    diff_ci <- c(diff_est - z * se_diff, diff_est + z * se_diff)
+    se_diff <- h_diff_cmh_se(cmh, diff_se = diff_se)
+    diff_ci <- c(cmh$diff_est - z * se_diff, cmh$diff_est + z * se_diff)
   } else {
     # Miettinen and Nurminen method is used.
     z_stat_fun <- function(delta) {
       var_est <- h_miettinen_nurminen_var_est(
-        n1 = n1, n2 = n2,
-        x1 = x1, x2 = x2,
+        n1 = cmh$n1, n2 = cmh$n2,
+        x1 = cmh$x1, x2 = cmh$x2,
         diff_par = delta
       )$var_est
-      num <- sum(wt * (p2 - p1 - delta))
-      denom <- sqrt(sum(wt^2 * var_est))
+      num <- sum(cmh$wt * (cmh$p2 - cmh$p1 - delta))
+      denom <- sqrt(sum(cmh$wt^2 * var_est))
       num / denom
     }
     # Find upper and lower confidence limits by root finding such that
@@ -712,27 +764,27 @@ prop_diff_cmh <- function(rsp,
     root_lower <- function(delta) z_stat_fun(delta) - z
     root_upper <- function(delta) z_stat_fun(delta) + z
     diff_ci <- c(
-      stats::uniroot(root_lower, interval = c(-0.99, diff_est))$root,
-      stats::uniroot(root_upper, interval = c(diff_est, 0.99))$root
+      stats::uniroot(root_lower, interval = c(-0.99, cmh$diff_est))$root,
+      stats::uniroot(root_upper, interval = c(cmh$diff_est, 0.99))$root
     )
     # Calculate the standard error separately.
     var_est <- h_miettinen_nurminen_var_est(
-      n1 = n1, n2 = n2,
-      x1 = x1, x2 = x2,
-      diff_par = diff_est
+      n1 = cmh$n1, n2 = cmh$n2,
+      x1 = cmh$x1, x2 = cmh$x2,
+      diff_par = cmh$diff_est
     )$var_est
-    se_diff <- sqrt(sum(wt_normalized^2 * var_est))
+    se_diff <- sqrt(sum(cmh$wt_normalized^2 * var_est))
   }
 
   list(
     prop = estimate,
     prop_ci = estimate_ci,
-    diff = diff_est,
+    diff = cmh$diff_est,
     diff_ci = diff_ci,
     se_diff = se_diff,
-    weights = wt_normalized,
-    n1 = n1,
-    n2 = n2
+    weights = cmh$wt_normalized,
+    n1 = cmh$n1,
+    n2 = cmh$n2
   )
 }
 
diff --git a/R/prop_diff_test.R b/R/prop_diff_test.R
index b9b9385d9b..ed75fb6705 100644
--- a/R/prop_diff_test.R
+++ b/R/prop_diff_test.R
@@ -346,22 +346,35 @@ prop_cmh <- function(ary,
     ary <- ary[, , strata_sizes > 1]
   }
 
-  cmh_res <- stats::mantelhaen.test(ary, correct = FALSE, alternative = alternative)
-
-  if (transform == "none") {
-    cmh_res$p.value
+  z_stat <- if (diff_se == "standard") {
+    mh_res <- stats::mantelhaen.test(ary, correct = FALSE, alternative = alternative)
+    checkmate::assert_true(mh_res$parameter == 1)
+    sqrt(unname(mh_res$statistic)) * ifelse(unname(mh_res$estimate) < 1, 1, -1)
   } else {
-    chisq_stat <- unname(cmh_res$statistic)
-    df <- unname(cmh_res$parameter)
-    num <- (chisq_stat / df)^(1 / 3) - (1 - 2 / (9 * df))
-    denom <- sqrt(2 / (9 * df))
-    wh_stat <- num / denom
+    # Use the Sato variance estimator.
+    cmh <- h_diff_cmh(ary)
+    cmh_se <- h_diff_cmh_se(cmh, diff_se = "sato")
+    cmh$diff_est / cmh_se
+  }
 
-    if (alternative == "two.sided") {
-      2 * stats::pnorm(-abs(wh_stat))
-    } else {
-      stats::pnorm(wh_stat, lower.tail = (alternative == "greater"))
+  if (transform == "wilson_hilferty") {
+    if (diff_se == "sato") {
+      warning(
+        "Wilson-Hilferty transformation was not designed ", 
+        "for use with the Sato variance estimator"
+      )
     }
+    chisq_stat <- z_stat^2
+    df <- 1  # Because we only compare two groups.
+    num <- (1 - 2 / (9 * df)) - (chisq_stat / df)^(1 / 3)
+    denom <- sqrt(2 / (9 * df))
+    z_stat <- num / denom * sign(z_stat) # Preserve the direction of effect.
+  }
+
+  if (alternative == "two.sided") {
+    2 * stats::pnorm(-abs(z_stat))
+  } else {
+    stats::pnorm(z_stat, lower.tail = (alternative == "greater"))
   }
 }
 
diff --git a/tests/testthat/_snaps/test_proportion_diff.md b/tests/testthat/_snaps/test_proportion_diff.md
index 9d740d69cd..176cd3ebf1 100644
--- a/tests/testthat/_snaps/test_proportion_diff.md
+++ b/tests/testthat/_snaps/test_proportion_diff.md
@@ -19,7 +19,7 @@
     Output
       [1] 0.02826514
 
-# prop_cmh returns right result
+# prop_cmh returns right result for odds ratio < 1
 
     Code
       res
@@ -30,15 +30,36 @@
 
     Code
       res_less
+    Output
+      [1] 0.3238582
+
+---
+
+    Code
+      res_greater
     Output
       [1] 0.6761418
 
+# prop_cmh returns right result for odds ratio > 1
+
+    Code
+      res
+    Output
+      [1] 0.3833285
+
+---
+
+    Code
+      res_less
+    Output
+      [1] 0.8083357
+
 ---
 
     Code
       res_greater
     Output
-      [1] 0.3238582
+      [1] 0.1916643
 
 # prop_cmh also works when there are strata with just one observation
 
@@ -124,6 +145,10 @@
     Output
       [1] 0.3477347
 
+# prop_cmh with Sato variance estimator and Wilson-Hilferty transformation works
+
+    0.383328522648178
+
 # s_test_proportion_diff and d_test_proportion_diff return right result
 
     Code
diff --git a/tests/testthat/test-test_proportion_diff.R b/tests/testthat/test-test_proportion_diff.R
index 1da73e89f8..73b4ffa4c9 100644
--- a/tests/testthat/test-test_proportion_diff.R
+++ b/tests/testthat/test-test_proportion_diff.R
@@ -20,24 +20,58 @@ testthat::test_that("prop_chisq returns right result", {
   testthat::expect_snapshot(res_greater)
 })
 
-testthat::test_that("prop_cmh returns right result", {
+testthat::test_that("prop_cmh returns right result for odds ratio < 1", {
   set.seed(1, kind = "Mersenne-Twister")
-  rsp <- sample(c(TRUE, FALSE), 100, TRUE)
+  rsp <- factor(sample(c(TRUE, FALSE), 100, TRUE), levels = c("TRUE", "FALSE"))
   grp <- factor(rep(c("A", "B"), each = 50))
   strata <- factor(rep(c("V", "W", "X", "Y", "Z"), each = 20))
   tbl <- table(grp, rsp, strata)
+  checkmate::assert_true(stats::mantelhaen.test(tbl, correct = FALSE)$estimate < 1)
 
   result <- prop_cmh(tbl)
   res <- testthat::expect_silent(result)
   testthat::expect_snapshot(res)
+  expected <- stats::mantelhaen.test(tbl, correct = FALSE)$p.value
+  testthat::expect_equal(result, expected, tolerance = 1e-3)
 
   result_less <- prop_cmh(tbl, alternative = "less")
   res_less <- testthat::expect_silent(result_less)
   testthat::expect_snapshot(res_less)
+  expected_less <- stats::mantelhaen.test(tbl, correct = FALSE, alternative = "less")$p.value
+  testthat::expect_equal(result_less, expected_less, tolerance = 1e-3)
 
   result_greater <- prop_cmh(tbl, alternative = "greater")
   res_greater <- testthat::expect_silent(result_greater)
   testthat::expect_snapshot(res_greater)
+  expected_greater <- stats::mantelhaen.test(tbl, correct = FALSE, alternative = "greater")$p.value
+  testthat::expect_equal(result_greater, expected_greater, tolerance = 1e-3)
+})
+
+testthat::test_that("prop_cmh returns right result for odds ratio > 1", {
+  set.seed(847, kind = "Mersenne-Twister")
+  rsp <- factor(sample(c(TRUE, FALSE), 100, TRUE), levels = c("TRUE", "FALSE"))
+  grp <- factor(rep(c("A", "B"), each = 50))
+  strata <- factor(rep(c("V", "W", "X", "Y", "Z"), each = 20))
+  tbl <- table(grp, rsp, strata)
+  checkmate::assert_true(stats::mantelhaen.test(tbl, correct = FALSE)$estimate > 1)
+
+  result <- prop_cmh(tbl)
+  res <- testthat::expect_silent(result)
+  testthat::expect_snapshot(res)
+  expected <- stats::mantelhaen.test(tbl, correct = FALSE)$p.value
+  testthat::expect_equal(result, expected, tolerance = 1e-3)
+
+  result_less <- prop_cmh(tbl, alternative = "less")
+  res_less <- testthat::expect_silent(result_less)
+  testthat::expect_snapshot(res_less)
+  expected_less <- stats::mantelhaen.test(tbl, correct = FALSE, alternative = "less")$p.value
+  testthat::expect_equal(result_less, expected_less, tolerance = 1e-3)
+
+  result_greater <- prop_cmh(tbl, alternative = "greater")
+  res_greater <- testthat::expect_silent(result_greater)
+  testthat::expect_snapshot(res_greater)
+  expected_greater <- stats::mantelhaen.test(tbl, correct = FALSE, alternative = "greater")$p.value
+  testthat::expect_equal(result_greater, expected_greater, tolerance = 1e-3)
 })
 
 testthat::test_that("prop_cmh also works when there are strata with just one observation", {
@@ -161,6 +195,67 @@ testthat::test_that("prop_cmh with Wilson-Hilferty transformation works", {
   expect_equal(result_greater, result_cmh_greater, tolerance = 1e-1)
 })
 
+testthat::test_that("prop_cmh with Sato variance estimator works", {
+  tbl1 <- structure(
+    c(
+      2L, 5L, 14L, 11L,
+      3L, 4L, 8L, 6L,
+      2L, 7L, 17L, 13L,
+      4L, 5L, 13L, 12L
+    ),
+    .Dim = c(2L, 2L, 4L),
+    .Dimnames = list(
+      grp = c("B", "A"),
+      rsp = c("TRUE", "FALSE"),
+      strata = c("S1", "S2", "S3", "S4")
+    ),
+    class = "table"
+  )
+  result1 <- prop_cmh(tbl1, diff_se = "sato")
+  testthat::expect_equal(result1, 0.035, tolerance = 1e-3)
+
+  tbl2 <- structure(
+    c(
+      2L, 7L, 14L, 8L,
+      3L, 3L, 8L, 7L,
+      2L, 10L, 17L, 10L,
+      4L, 5L, 13L, 12L
+    ),
+    .Dim = c(2L, 2L, 4L),
+    .Dimnames = list(
+      grp = c("B", "A"),
+      rsp = c("TRUE", "FALSE"),
+      strata = c("S1", "S2", "S3", "S4")
+    ),
+    class = "table"
+  )
+  result2 <- prop_cmh(tbl2, diff_se = "sato")
+  testthat::expect_equal(result2, 0.004, tolerance = 1e-2)
+})
+
+testthat::test_that("prop_cmh with Sato variance estimator and Wilson-Hilferty transformation works", {
+  tbl <- structure(
+    c(
+      2L, 5L, 14L, 11L,
+      3L, 4L, 8L, 6L,
+      2L, 7L, 17L, 13L,
+      4L, 5L, 13L, 12L
+    ),
+    .Dim = c(2L, 2L, 4L),
+    .Dimnames = list(
+      grp = c("B", "A"),
+      rsp = c("TRUE", "FALSE"),
+      strata = c("S1", "S2", "S3", "S4")
+    ),
+    class = "table"
+  )
+  testthat::expect_warning(
+    result <- prop_cmh(tbl, diff_se = "sato", transform = "wilson_hilferty"),
+    "not designed for use with the Sato variance estimator"
+  )
+  testthat::expect_snapshot_value(res, style = "deparse", tolerance = 1e-3)
+})
+
 testthat::test_that("s_test_proportion_diff and d_test_proportion_diff return right result", {
   set.seed(1984, kind = "Mersenne-Twister")
   dta <- data.frame(

From 9c87b991cd98aa73a3bc1c4107edeab22322b5ce Mon Sep 17 00:00:00 2001
From: Daniel Sabanes Bove <daniel@rconis.com>
Date: Mon, 15 Jun 2026 11:53:34 +0800
Subject: [PATCH 03/13] add NEWS entry

---
 NEWS.md | 10 ++++++----
 1 file changed, 6 insertions(+), 4 deletions(-)

diff --git a/NEWS.md b/NEWS.md
index f4fa10b877..cc12a22411 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -1,19 +1,21 @@
 # tern 0.9.10.9012
 
-### Miscellaneous
-* Updated `roxygen2` to 8.0.0 and added `@exportS3Method` tags for S3 methods in `decorate_grob.R` and `utils_grid.R`.
-* Converted  `s_surv_time()`to exported functions.
-
 ### Enhancements
 * Added `alternative` argument to `s_coxph_pairwise()` to allow one-sided hypothesis testing. 
 * Added `lr_stat_df` to the parameters return list of `s_coxph_pairwise()`.
 * Added `uncond_exact_diff` method to `estimate_proportion_diff()` for the unconditional exact confidence interval for the difference in proportions by inverting one-sided tail tests over a nuisance parameter.
+* Added `cmh_sato` as option for `test_proportion_diff()` to enable CMH test with Sato variance estimator.
 * Added `range_with_cens_info` statistic to `s_surv_time()`.
 * Added `lsmean_se`, `lsmean_ci`, and `lsmean_diffci` statistics to `s_ancova()`.
 * Added `s_ancova()` to exported functions.
 
 ### Bug Fixes
 * Fixed bug in `prop_diff_cmh()` which previously failed when strata combinations had 0 observations.
+* Fixed bug in `prop_cmh()` where previously the Wilson-Hilferty transformation did not always preserve the direction of the effect for one-sided tests.
+
+### Miscellaneous
+* Updated `roxygen2` to 8.0.0 and added `@exportS3Method` tags for S3 methods in `decorate_grob.R` and `utils_grid.R`.
+* Converted  `s_surv_time()`to exported functions.
 
 # tern 0.9.10
 

From c7c1ab12fb24b49875dbf3ef1732e88cb562b43d Mon Sep 17 00:00:00 2001
From: Daniel Sabanes Bove <daniel@rconis.com>
Date: Mon, 15 Jun 2026 11:57:02 +0800
Subject: [PATCH 04/13] add edge case test

---
 tests/testthat/_snaps/test_proportion_diff.md | 10 +++++++++
 tests/testthat/test-test_proportion_diff.R    | 22 +++++++++++++++++++
 2 files changed, 32 insertions(+)

diff --git a/tests/testthat/_snaps/test_proportion_diff.md b/tests/testthat/_snaps/test_proportion_diff.md
index 176cd3ebf1..c6ff2a9bce 100644
--- a/tests/testthat/_snaps/test_proportion_diff.md
+++ b/tests/testthat/_snaps/test_proportion_diff.md
@@ -263,3 +263,13 @@
       Variable Label                                                                         
           p-value (Cochran-Mantel-Haenszel Test with Wilson-Hilferty Transformation)       NA
 
+# test_proportion_diff edge case: all responder by CMH with Sato variance estimator
+
+    Code
+      res
+    Output
+                                                                                B     A   
+      ————————————————————————————————————————————————————————————————————————————————————
+      Variable Label                                                                      
+          p-value (Cochran-Mantel-Haenszel Test with Sato Variance Estimator)       1.0000
+
diff --git a/tests/testthat/test-test_proportion_diff.R b/tests/testthat/test-test_proportion_diff.R
index 73b4ffa4c9..d239e16012 100644
--- a/tests/testthat/test-test_proportion_diff.R
+++ b/tests/testthat/test-test_proportion_diff.R
@@ -448,3 +448,25 @@ testthat::test_that("test_proportion_diff edge case: all responder by CMH with W
   res <- testthat::expect_silent(result)
   testthat::expect_snapshot(res)
 })
+
+testthat::test_that("test_proportion_diff edge case: all responder by CMH with Sato variance estimator", {
+  dta <- data.frame(
+    rsp = rep(TRUE, each = 100),
+    grp = factor(rep(c("A", "B"), each = 50)),
+    strata = factor(rep(c("V", "W", "X", "Y", "Z"), each = 20))
+  )
+
+  result <- basic_table() %>%
+    split_cols_by(var = "grp", ref_group = "B", split_fun = ref_group_position("first")) %>%
+    test_proportion_diff(
+      vars = "rsp",
+      var_labels = "Variable Label",
+      show_labels = "visible",
+      method = "cmh_sato",
+      variables = list(strata = "strata")
+    ) %>%
+    build_table(df = dta)
+
+  res <- testthat::expect_silent(result)
+  testthat::expect_snapshot(res)
+})

From cb20233d3d1bcb978829b41b6ef1dc2a69ef537a Mon Sep 17 00:00:00 2001
From: Daniel Sabanes Bove <daniel@rconis.com>
Date: Mon, 15 Jun 2026 11:58:47 +0800
Subject: [PATCH 05/13] run styler

---
 R/coxph.R                              |  3 +--
 R/h_step.R                             |  6 ++----
 R/prop_diff.R                          | 22 +++++++++++-----------
 R/prop_diff_test.R                     |  4 ++--
 R/utils_default_stats_formats_labels.R |  6 ++++--
 tests/testthat/test-survival_time.R    |  4 ++--
 6 files changed, 22 insertions(+), 23 deletions(-)

diff --git a/R/coxph.R b/R/coxph.R
index 5427f7eb8b..7f7cb6b495 100644
--- a/R/coxph.R
+++ b/R/coxph.R
@@ -195,8 +195,7 @@ try_car_anova <- function(mod,
         invokeRestart("muffleWarning")
       }
     ),
-    finally = {
-    }
+    finally = {}
   )
 
   return(y)
diff --git a/R/h_step.R b/R/h_step.R
index e2ea4ae1d8..6ba8a314d7 100644
--- a/R/h_step.R
+++ b/R/h_step.R
@@ -171,8 +171,7 @@ h_step_survival_est <- function(formula,
         invokeRestart("muffleWarning")
       }
     ),
-    finally = {
-    }
+    finally = {}
   )
   if (!is.null(coxph_warnings)) {
     warning(paste(
@@ -285,8 +284,7 @@ h_step_rsp_est <- function(formula,
         invokeRestart("muffleWarning")
       }
     ),
-    finally = {
-    }
+    finally = {}
   )
   if (!is.null(fit_warnings)) {
     warning(paste(
diff --git a/R/prop_diff.R b/R/prop_diff.R
index ba4aa187f1..f403c6bdc1 100644
--- a/R/prop_diff.R
+++ b/R/prop_diff.R
@@ -596,13 +596,13 @@ prop_diff_nc <- function(rsp,
   )
 }
 
-#' @describeIn h_prop_diff Helper function to calculate the CMH weighted 
+#' @describeIn h_prop_diff Helper function to calculate the CMH weighted
 #' difference in proportions.
-#' 
-#' @param tbl (`array`)\cr 3-dimensional array with dimensions corresponding to 
-#'   group, response, and strata. The second dimension (response) should have names 
+#'
+#' @param tbl (`array`)\cr 3-dimensional array with dimensions corresponding to
+#'   group, response, and strata. The second dimension (response) should have names
 #'   "TRUE" and "FALSE".
-#' 
+#'
 #' @keywords internal
 h_diff_cmh <- function(tbl) {
   checkmate::assert_array(tbl)
@@ -643,11 +643,11 @@ h_diff_cmh <- function(tbl) {
   )
 }
 
-#' @describeIn h_prop_diff Helper function to calculate the standard error for the 
+#' @describeIn h_prop_diff Helper function to calculate the standard error for the
 #'   CMH weighted difference in proportions.
-#' 
+#'
 #' @param cmh_results (`list`)\cr output of [h_diff_cmh()].
-#' 
+#'
 #' @keywords internal
 h_diff_cmh_se <- function(cmh_results, diff_se = c("standard", "sato")) {
   checkmate::assert_list(cmh_results, types = "numeric", any.missing = FALSE, names = "unique")
@@ -659,8 +659,8 @@ h_diff_cmh_se <- function(cmh_results, diff_se = c("standard", "sato")) {
     sqrt(sum((terms1 + terms2) * l$wt_normalized^2))
   } else {
     # Sato variance estimator.
-    p_terms_num <- l$n2^2 * l$x1 - 
-      l$n1^2 * l$x2 + 
+    p_terms_num <- l$n2^2 * l$x1 -
+      l$n1^2 * l$x2 +
       l$n1 * l$n2 * (l$n1 - l$n2) / 2
     p_terms <- p_terms_num / (l$n1 + l$n2)^2
     q_terms_num <- l$x1 * (l$n2 - l$x2) + l$x2 * (l$n1 - l$x1)
@@ -723,7 +723,7 @@ prop_diff_cmh <- function(rsp,
   # first dimension: CONTROL, TX
   # 2nd dimension: TRUE, FALSE
   # 3rd dimension: levels of strata
-  # Note: rsp needs to be a factor to handle edge case of 
+  # Note: rsp needs to be a factor to handle edge case of
   #       no FALSE (or TRUE) rsp records.
   t_tbl <- table(
     grp,
diff --git a/R/prop_diff_test.R b/R/prop_diff_test.R
index ed75fb6705..04096ee02a 100644
--- a/R/prop_diff_test.R
+++ b/R/prop_diff_test.R
@@ -360,12 +360,12 @@ prop_cmh <- function(ary,
   if (transform == "wilson_hilferty") {
     if (diff_se == "sato") {
       warning(
-        "Wilson-Hilferty transformation was not designed ", 
+        "Wilson-Hilferty transformation was not designed ",
         "for use with the Sato variance estimator"
       )
     }
     chisq_stat <- z_stat^2
-    df <- 1  # Because we only compare two groups.
+    df <- 1 # Because we only compare two groups.
     num <- (1 - 2 / (9 * df)) - (chisq_stat / df)^(1 / 3)
     denom <- sqrt(2 / (9 * df))
     z_stat <- num / denom * sign(z_stat) # Preserve the direction of effect.
diff --git a/R/utils_default_stats_formats_labels.R b/R/utils_default_stats_formats_labels.R
index cbd0f885bc..c998ea4176 100644
--- a/R/utils_default_stats_formats_labels.R
+++ b/R/utils_default_stats_formats_labels.R
@@ -580,8 +580,10 @@ tern_default_stats <- list(
   estimate_odds_ratio = c("or_ci", "n_tot"),
   estimate_proportion = c("n_prop", "prop_ci"),
   estimate_proportion_diff = c("diff", "diff_ci"),
-  summarize_ancova = c("n", "lsmean", "lsmean_se", "lsmean_ci",
-                       "lsmean_diff", "lsmean_diff_ci", "lsmean_diff_with_ci", "pval"),
+  summarize_ancova = c(
+    "n", "lsmean", "lsmean_se", "lsmean_ci",
+    "lsmean_diff", "lsmean_diff_ci", "lsmean_diff_with_ci", "pval"
+  ),
   summarize_coxreg = c("n", "hr", "ci", "pval", "pval_inter"),
   summarize_glm_count = c("n", "rate", "rate_ci", "rate_ratio", "rate_ratio_ci", "pval"),
   summarize_num_patients = c("unique", "nonunique", "unique_count"),
diff --git a/tests/testthat/test-survival_time.R b/tests/testthat/test-survival_time.R
index ebaf7b5717..8da67ac970 100644
--- a/tests/testthat/test-survival_time.R
+++ b/tests/testthat/test-survival_time.R
@@ -223,8 +223,8 @@ testthat::test_that("s_surv_time range_with_cens_info flags upper censored (0, 1
   )
   result <- s_surv_time(anl, .var = "AVAL", is_event = "is_event")
   rwci <- result$range_with_cens_info
-  testthat::expect_equal(as.numeric(rwci[3]), 0)  # lower not censored
-  testthat::expect_equal(as.numeric(rwci[4]), 1)  # upper censored
+  testthat::expect_equal(as.numeric(rwci[3]), 0) # lower not censored
+  testthat::expect_equal(as.numeric(rwci[4]), 1) # upper censored
 })
 
 testthat::test_that("s_surv_time range_with_cens_info flags lower censored (1, 0)", {

From 898552b464cf444d8881be6eba393609fb64ec65 Mon Sep 17 00:00:00 2001
From: github-actions <41898282+github-actions[bot]@users.noreply.github.com>
Date: Mon, 15 Jun 2026 04:02:59 +0000
Subject: [PATCH 06/13] [skip roxygen] [skip vbump] Roxygen Man Pages Auto
 Update

---
 man/d_test_proportion_diff.Rd         |  2 +-
 man/extreme_format.Rd                 |  1 +
 man/format_auto.Rd                    |  1 +
 man/format_count_fraction.Rd          |  1 +
 man/format_count_fraction_fixed_dp.Rd |  1 +
 man/format_count_fraction_lt10.Rd     |  1 +
 man/format_extreme_values.Rd          |  1 +
 man/format_extreme_values_ci.Rd       |  1 +
 man/format_fraction.Rd                |  1 +
 man/format_fraction_fixed_dp.Rd       |  1 +
 man/format_fraction_threshold.Rd      |  1 +
 man/format_range_cens.Rd              | 24 ++++++++++++------------
 man/format_sigfig.Rd                  |  1 +
 man/format_xx.Rd                      |  1 +
 man/formatting_functions.Rd           |  1 +
 man/h_prop_diff.Rd                    | 21 ++++++++++++++++++++-
 man/h_prop_diff_test.Rd               |  3 +++
 man/prop_diff_test.Rd                 |  6 +++---
 18 files changed, 52 insertions(+), 17 deletions(-)

diff --git a/man/d_test_proportion_diff.Rd b/man/d_test_proportion_diff.Rd
index eacf3efd93..5dd4f3ec59 100644
--- a/man/d_test_proportion_diff.Rd
+++ b/man/d_test_proportion_diff.Rd
@@ -7,7 +7,7 @@
 d_test_proportion_diff(method, alternative = c("two.sided", "less", "greater"))
 }
 \arguments{
-\item{method}{(\code{string})\cr one of \code{chisq}, \code{cmh}, \code{cmh_wh}, \code{fisher}, or \code{schouten};
+\item{method}{(\code{string})\cr one of \code{chisq}, \code{cmh}, \code{cmh_sato}, \code{cmh_wh}, \code{fisher}, or \code{schouten};
 specifies the test used to calculate the p-value.}
 
 \item{alternative}{(\code{string})\cr whether \code{two.sided}, or one-sided \code{less} or \code{greater} p-value
diff --git a/man/extreme_format.Rd b/man/extreme_format.Rd
index 5b20fc0b1a..0a036cb0f1 100644
--- a/man/extreme_format.Rd
+++ b/man/extreme_format.Rd
@@ -64,6 +64,7 @@ Other formatting functions:
 \code{\link[=format_fraction]{format_fraction()}},
 \code{\link[=format_fraction_fixed_dp]{format_fraction_fixed_dp()}},
 \code{\link[=format_fraction_threshold]{format_fraction_threshold()}},
+\code{\link[=format_range_cens]{format_range_cens()}},
 \code{\link[=format_sigfig]{format_sigfig()}},
 \code{\link[=format_xx]{format_xx()}},
 \code{\link{formatting_functions}}
diff --git a/man/format_auto.Rd b/man/format_auto.Rd
index 70ed8f3e7a..849369549e 100644
--- a/man/format_auto.Rd
+++ b/man/format_auto.Rd
@@ -53,6 +53,7 @@ Other formatting functions:
 \code{\link[=format_fraction]{format_fraction()}},
 \code{\link[=format_fraction_fixed_dp]{format_fraction_fixed_dp()}},
 \code{\link[=format_fraction_threshold]{format_fraction_threshold()}},
+\code{\link[=format_range_cens]{format_range_cens()}},
 \code{\link[=format_sigfig]{format_sigfig()}},
 \code{\link[=format_xx]{format_xx()}},
 \code{\link{formatting_functions}}
diff --git a/man/format_count_fraction.Rd b/man/format_count_fraction.Rd
index 57285437e2..bca0febb17 100644
--- a/man/format_count_fraction.Rd
+++ b/man/format_count_fraction.Rd
@@ -35,6 +35,7 @@ Other formatting functions:
 \code{\link[=format_fraction]{format_fraction()}},
 \code{\link[=format_fraction_fixed_dp]{format_fraction_fixed_dp()}},
 \code{\link[=format_fraction_threshold]{format_fraction_threshold()}},
+\code{\link[=format_range_cens]{format_range_cens()}},
 \code{\link[=format_sigfig]{format_sigfig()}},
 \code{\link[=format_xx]{format_xx()}},
 \code{\link{formatting_functions}}
diff --git a/man/format_count_fraction_fixed_dp.Rd b/man/format_count_fraction_fixed_dp.Rd
index 2cb787bb40..5c2662de8f 100644
--- a/man/format_count_fraction_fixed_dp.Rd
+++ b/man/format_count_fraction_fixed_dp.Rd
@@ -36,6 +36,7 @@ Other formatting functions:
 \code{\link[=format_fraction]{format_fraction()}},
 \code{\link[=format_fraction_fixed_dp]{format_fraction_fixed_dp()}},
 \code{\link[=format_fraction_threshold]{format_fraction_threshold()}},
+\code{\link[=format_range_cens]{format_range_cens()}},
 \code{\link[=format_sigfig]{format_sigfig()}},
 \code{\link[=format_xx]{format_xx()}},
 \code{\link{formatting_functions}}
diff --git a/man/format_count_fraction_lt10.Rd b/man/format_count_fraction_lt10.Rd
index 2e496677d9..3f481893d2 100644
--- a/man/format_count_fraction_lt10.Rd
+++ b/man/format_count_fraction_lt10.Rd
@@ -36,6 +36,7 @@ Other formatting functions:
 \code{\link[=format_fraction]{format_fraction()}},
 \code{\link[=format_fraction_fixed_dp]{format_fraction_fixed_dp()}},
 \code{\link[=format_fraction_threshold]{format_fraction_threshold()}},
+\code{\link[=format_range_cens]{format_range_cens()}},
 \code{\link[=format_sigfig]{format_sigfig()}},
 \code{\link[=format_xx]{format_xx()}},
 \code{\link{formatting_functions}}
diff --git a/man/format_extreme_values.Rd b/man/format_extreme_values.Rd
index 8690f386d6..f04829db64 100644
--- a/man/format_extreme_values.Rd
+++ b/man/format_extreme_values.Rd
@@ -36,6 +36,7 @@ Other formatting functions:
 \code{\link[=format_fraction]{format_fraction()}},
 \code{\link[=format_fraction_fixed_dp]{format_fraction_fixed_dp()}},
 \code{\link[=format_fraction_threshold]{format_fraction_threshold()}},
+\code{\link[=format_range_cens]{format_range_cens()}},
 \code{\link[=format_sigfig]{format_sigfig()}},
 \code{\link[=format_xx]{format_xx()}},
 \code{\link{formatting_functions}}
diff --git a/man/format_extreme_values_ci.Rd b/man/format_extreme_values_ci.Rd
index 6d09b79eee..4a53e33f26 100644
--- a/man/format_extreme_values_ci.Rd
+++ b/man/format_extreme_values_ci.Rd
@@ -36,6 +36,7 @@ Other formatting functions:
 \code{\link[=format_fraction]{format_fraction()}},
 \code{\link[=format_fraction_fixed_dp]{format_fraction_fixed_dp()}},
 \code{\link[=format_fraction_threshold]{format_fraction_threshold()}},
+\code{\link[=format_range_cens]{format_range_cens()}},
 \code{\link[=format_sigfig]{format_sigfig()}},
 \code{\link[=format_xx]{format_xx()}},
 \code{\link{formatting_functions}}
diff --git a/man/format_fraction.Rd b/man/format_fraction.Rd
index 051461a628..970967bc09 100644
--- a/man/format_fraction.Rd
+++ b/man/format_fraction.Rd
@@ -35,6 +35,7 @@ Other formatting functions:
 \code{\link[=format_extreme_values_ci]{format_extreme_values_ci()}},
 \code{\link[=format_fraction_fixed_dp]{format_fraction_fixed_dp()}},
 \code{\link[=format_fraction_threshold]{format_fraction_threshold()}},
+\code{\link[=format_range_cens]{format_range_cens()}},
 \code{\link[=format_sigfig]{format_sigfig()}},
 \code{\link[=format_xx]{format_xx()}},
 \code{\link{formatting_functions}}
diff --git a/man/format_fraction_fixed_dp.Rd b/man/format_fraction_fixed_dp.Rd
index 2c5c5eebef..7134efe7e8 100644
--- a/man/format_fraction_fixed_dp.Rd
+++ b/man/format_fraction_fixed_dp.Rd
@@ -37,6 +37,7 @@ Other formatting functions:
 \code{\link[=format_extreme_values_ci]{format_extreme_values_ci()}},
 \code{\link[=format_fraction]{format_fraction()}},
 \code{\link[=format_fraction_threshold]{format_fraction_threshold()}},
+\code{\link[=format_range_cens]{format_range_cens()}},
 \code{\link[=format_sigfig]{format_sigfig()}},
 \code{\link[=format_xx]{format_xx()}},
 \code{\link{formatting_functions}}
diff --git a/man/format_fraction_threshold.Rd b/man/format_fraction_threshold.Rd
index 6d839f2ffe..f97a23e807 100644
--- a/man/format_fraction_threshold.Rd
+++ b/man/format_fraction_threshold.Rd
@@ -39,6 +39,7 @@ Other formatting functions:
 \code{\link[=format_extreme_values_ci]{format_extreme_values_ci()}},
 \code{\link[=format_fraction]{format_fraction()}},
 \code{\link[=format_fraction_fixed_dp]{format_fraction_fixed_dp()}},
+\code{\link[=format_range_cens]{format_range_cens()}},
 \code{\link[=format_sigfig]{format_sigfig()}},
 \code{\link[=format_xx]{format_xx()}},
 \code{\link{formatting_functions}}
diff --git a/man/format_range_cens.Rd b/man/format_range_cens.Rd
index d5e4c15d3d..9ac1c224b7 100644
--- a/man/format_range_cens.Rd
+++ b/man/format_range_cens.Rd
@@ -28,19 +28,19 @@ fmt(c(1.23, 9.87, 0, 0))
 
 }
 \seealso{
-Other formatting functions: 
+Other formatting functions:
 \code{\link{extreme_format}},
-\code{\link{format_auto}()},
-\code{\link{format_count_fraction}()},
-\code{\link{format_count_fraction_fixed_dp}()},
-\code{\link{format_count_fraction_lt10}()},
-\code{\link{format_extreme_values}()},
-\code{\link{format_extreme_values_ci}()},
-\code{\link{format_fraction}()},
-\code{\link{format_fraction_fixed_dp}()},
-\code{\link{format_fraction_threshold}()},
-\code{\link{format_sigfig}()},
-\code{\link{format_xx}()},
+\code{\link[=format_auto]{format_auto()}},
+\code{\link[=format_count_fraction]{format_count_fraction()}},
+\code{\link[=format_count_fraction_fixed_dp]{format_count_fraction_fixed_dp()}},
+\code{\link[=format_count_fraction_lt10]{format_count_fraction_lt10()}},
+\code{\link[=format_extreme_values]{format_extreme_values()}},
+\code{\link[=format_extreme_values_ci]{format_extreme_values_ci()}},
+\code{\link[=format_fraction]{format_fraction()}},
+\code{\link[=format_fraction_fixed_dp]{format_fraction_fixed_dp()}},
+\code{\link[=format_fraction_threshold]{format_fraction_threshold()}},
+\code{\link[=format_sigfig]{format_sigfig()}},
+\code{\link[=format_xx]{format_xx()}},
 \code{\link{formatting_functions}}
 }
 \concept{formatting functions}
diff --git a/man/format_sigfig.Rd b/man/format_sigfig.Rd
index 3ea1ef6975..429ac42c29 100644
--- a/man/format_sigfig.Rd
+++ b/man/format_sigfig.Rd
@@ -46,6 +46,7 @@ Other formatting functions:
 \code{\link[=format_fraction]{format_fraction()}},
 \code{\link[=format_fraction_fixed_dp]{format_fraction_fixed_dp()}},
 \code{\link[=format_fraction_threshold]{format_fraction_threshold()}},
+\code{\link[=format_range_cens]{format_range_cens()}},
 \code{\link[=format_xx]{format_xx()}},
 \code{\link{formatting_functions}}
 }
diff --git a/man/format_xx.Rd b/man/format_xx.Rd
index b44eb9faed..08f114d449 100644
--- a/man/format_xx.Rd
+++ b/man/format_xx.Rd
@@ -41,6 +41,7 @@ Other formatting functions:
 \code{\link[=format_fraction]{format_fraction()}},
 \code{\link[=format_fraction_fixed_dp]{format_fraction_fixed_dp()}},
 \code{\link[=format_fraction_threshold]{format_fraction_threshold()}},
+\code{\link[=format_range_cens]{format_range_cens()}},
 \code{\link[=format_sigfig]{format_sigfig()}},
 \code{\link{formatting_functions}}
 }
diff --git a/man/formatting_functions.Rd b/man/formatting_functions.Rd
index afc526007c..99f7bed810 100644
--- a/man/formatting_functions.Rd
+++ b/man/formatting_functions.Rd
@@ -22,6 +22,7 @@ Other formatting functions:
 \code{\link[=format_fraction]{format_fraction()}},
 \code{\link[=format_fraction_fixed_dp]{format_fraction_fixed_dp()}},
 \code{\link[=format_fraction_threshold]{format_fraction_threshold()}},
+\code{\link[=format_range_cens]{format_range_cens()}},
 \code{\link[=format_sigfig]{format_sigfig()}},
 \code{\link[=format_xx]{format_xx()}}
 }
diff --git a/man/h_prop_diff.Rd b/man/h_prop_diff.Rd
index a162de655a..343ee80f90 100644
--- a/man/h_prop_diff.Rd
+++ b/man/h_prop_diff.Rd
@@ -5,6 +5,8 @@
 \alias{prop_diff_wald}
 \alias{prop_diff_ha}
 \alias{prop_diff_nc}
+\alias{h_diff_cmh}
+\alias{h_diff_cmh_se}
 \alias{prop_diff_cmh}
 \alias{prop_diff_strat_nc}
 \alias{prop_diff_uncond_exact}
@@ -16,6 +18,10 @@ prop_diff_ha(rsp, grp, conf_level)
 
 prop_diff_nc(rsp, grp, conf_level, correct = FALSE)
 
+h_diff_cmh(tbl)
+
+h_diff_cmh_se(cmh_results, diff_se = c("standard", "sato"))
+
 prop_diff_cmh(
   rsp,
   grp,
@@ -46,12 +52,18 @@ prop_diff_uncond_exact(rsp, grp, conf_level = 0.95)
 \item{correct}{(\code{flag})\cr whether to include the continuity correction. For further
 information, see \code{\link[stats:prop.test]{stats::prop.test()}}.}
 
-\item{strata}{(\code{factor})\cr variable with one level per stratum and same length as \code{rsp}.}
+\item{tbl}{(\code{array})\cr 3-dimensional array with dimensions corresponding to
+group, response, and strata. The second dimension (response) should have names
+"TRUE" and "FALSE".}
+
+\item{cmh_results}{(\code{list})\cr output of \code{\link[=h_diff_cmh]{h_diff_cmh()}}.}
 
 \item{diff_se}{(\code{string})\cr method to estimate the standard error for the difference, either
 \code{standard}, \code{sato} \insertCite{Sato1989}{tern} or
 \code{miettinen_nurminen} \insertCite{MiettinenNurminen1985}{tern}.}
 
+\item{strata}{(\code{factor})\cr variable with one level per stratum and same length as \code{rsp}.}
+
 \item{weights_method}{(\code{string})\cr weights method. Can be either \code{"cmh"} or \code{"heuristic"}
 and directs the way weights are estimated.}
 }
@@ -74,6 +86,12 @@ interval.
 \item \code{prop_diff_nc()}: Newcombe confidence interval. It is based on
 the Wilson score confidence interval for a single binomial proportion \insertCite{Newcombe1998}{tern}.
 
+\item \code{h_diff_cmh()}: Helper function to calculate the CMH weighted
+difference in proportions.
+
+\item \code{h_diff_cmh_se()}: Helper function to calculate the standard error for the
+CMH weighted difference in proportions.
+
 \item \code{prop_diff_cmh()}: Calculates the weighted difference. This is defined as the difference in
 response rates between the experimental treatment group and the control treatment group, adjusted
 for stratification factors by applying Cochran-Mantel-Haenszel (CMH) weights. For the CMH chi-squared
@@ -184,3 +202,4 @@ prop_diff_uncond_exact(rsp = rsp, grp = grp, conf_level = 0.95)
 \seealso{
 \code{\link[=prop_diff]{prop_diff()}} for implementation of these helper functions.
 }
+\keyword{internal}
diff --git a/man/h_prop_diff_test.Rd b/man/h_prop_diff_test.Rd
index 6515ab33f5..66f3fea04a 100644
--- a/man/h_prop_diff_test.Rd
+++ b/man/h_prop_diff_test.Rd
@@ -13,6 +13,7 @@ prop_chisq(tbl, alternative = c("two.sided", "less", "greater"))
 prop_cmh(
   ary,
   alternative = c("two.sided", "less", "greater"),
+  diff_se = c("standard", "sato"),
   transform = c("none", "wilson_hilferty")
 )
 
@@ -29,6 +30,8 @@ should be displayed.}
 \item{ary}{(\code{array}, 3 dimensions)\cr array with two groups in rows, the binary response
 (\code{TRUE}/\code{FALSE}) in columns, and the strata in the third dimension.}
 
+\item{diff_se}{(\code{string})\cr either \code{standard} or \code{sato}; specifies whether to use the Sato variance estimator to calculate the chi-squared statistic.}
+
 \item{transform}{(\code{string})\cr either \code{none} or \code{wilson_hilferty}; specifies whether to apply
 the Wilson-Hilferty transformation of the chi-squared statistic.}
 }
diff --git a/man/prop_diff_test.Rd b/man/prop_diff_test.Rd
index 20f43b1ada..84d22fef6e 100644
--- a/man/prop_diff_test.Rd
+++ b/man/prop_diff_test.Rd
@@ -11,7 +11,7 @@ test_proportion_diff(
   lyt,
   vars,
   variables = list(strata = NULL),
-  method = c("chisq", "schouten", "fisher", "cmh", "cmh_wh"),
+  method = c("chisq", "schouten", "fisher", "cmh", "cmh_sato", "cmh_wh"),
   alternative = c("two.sided", "less", "greater"),
   var_labels = vars,
   na_str = default_na_str(),
@@ -34,7 +34,7 @@ s_test_proportion_diff(
   .ref_group,
   .in_ref_col,
   variables = list(strata = NULL),
-  method = c("chisq", "schouten", "fisher", "cmh", "cmh_wh"),
+  method = c("chisq", "schouten", "fisher", "cmh", "cmh_sato", "cmh_wh"),
   alternative = c("two.sided", "less", "greater"),
   ...
 )
@@ -56,7 +56,7 @@ a_test_proportion_diff(
 
 \item{variables}{(named \code{list} of \code{string})\cr list of additional analysis variables.}
 
-\item{method}{(\code{string})\cr one of \code{chisq}, \code{cmh}, \code{cmh_wh}, \code{fisher}, or \code{schouten};
+\item{method}{(\code{string})\cr one of \code{chisq}, \code{cmh}, \code{cmh_sato}, \code{cmh_wh}, \code{fisher}, or \code{schouten};
 specifies the test used to calculate the p-value.}
 
 \item{alternative}{(\code{string})\cr whether \code{two.sided}, or one-sided \code{less} or \code{greater} p-value

From 57b55fef9364398b88b25251d54be2240887a572 Mon Sep 17 00:00:00 2001
From: Daniel Sabanes Bove <daniel@rconis.com>
Date: Mon, 15 Jun 2026 12:03:33 +0800
Subject: [PATCH 07/13] trigger checks


From 2f29c05109a0092a4fdcf03634506c154c8e2896 Mon Sep 17 00:00:00 2001
From: Daniel Sabanes Bove <daniel@rconis.com>
Date: Mon, 15 Jun 2026 13:18:49 +0800
Subject: [PATCH 08/13] fix typo

---
 tests/testthat/_snaps/test_proportion_diff.md | 2 +-
 tests/testthat/test-test_proportion_diff.R    | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/tests/testthat/_snaps/test_proportion_diff.md b/tests/testthat/_snaps/test_proportion_diff.md
index c6ff2a9bce..9b3cf7690b 100644
--- a/tests/testthat/_snaps/test_proportion_diff.md
+++ b/tests/testthat/_snaps/test_proportion_diff.md
@@ -147,7 +147,7 @@
 
 # prop_cmh with Sato variance estimator and Wilson-Hilferty transformation works
 
-    0.383328522648178
+    0.0660308573944943
 
 # s_test_proportion_diff and d_test_proportion_diff return right result
 
diff --git a/tests/testthat/test-test_proportion_diff.R b/tests/testthat/test-test_proportion_diff.R
index d239e16012..2dba4aa670 100644
--- a/tests/testthat/test-test_proportion_diff.R
+++ b/tests/testthat/test-test_proportion_diff.R
@@ -253,7 +253,7 @@ testthat::test_that("prop_cmh with Sato variance estimator and Wilson-Hilferty t
     result <- prop_cmh(tbl, diff_se = "sato", transform = "wilson_hilferty"),
     "not designed for use with the Sato variance estimator"
   )
-  testthat::expect_snapshot_value(res, style = "deparse", tolerance = 1e-3)
+  testthat::expect_snapshot_value(result, style = "deparse", tolerance = 1e-3)
 })
 
 testthat::test_that("s_test_proportion_diff and d_test_proportion_diff return right result", {

From 4ebed4cba12b4ec609d22cba3e97e5e5a85f8aa4 Mon Sep 17 00:00:00 2001
From: Daniel Sabanes Bove <daniel@rconis.com>
Date: Mon, 15 Jun 2026 13:44:06 +0800
Subject: [PATCH 09/13] fix linter issues

---
 .lintr                  |  1 -
 R/coxph.R               | 17 ++++++++---------
 R/prop_diff_test.R      |  3 ++-
 man/h_prop_diff_test.Rd |  3 ++-
 4 files changed, 12 insertions(+), 12 deletions(-)

diff --git a/.lintr b/.lintr
index b0b8c224d3..e6e3e9d487 100644
--- a/.lintr
+++ b/.lintr
@@ -1,6 +1,5 @@
 linters: linters_with_defaults(
   line_length_linter = line_length_linter(120),
-  cyclocomp_linter = NULL,
   object_usage_linter = NULL,
   object_length_linter = NULL,
   pipe_consistency_linter = NULL
diff --git a/R/coxph.R b/R/coxph.R
index 7f7cb6b495..e971353b49 100644
--- a/R/coxph.R
+++ b/R/coxph.R
@@ -25,8 +25,7 @@ univariate <- function(x) {
 # Get the right-hand-term of a formula
 rht <- function(x) {
   checkmate::assert_formula(x)
-  y <- as.character(rev(x)[[1]])
-  return(y)
+  as.character(rev(x)[[1]])
 }
 
 #' Hazard ratio estimation in interactions
@@ -109,7 +108,7 @@ estimate_coef <- function(variable, given,
   design_mat <- apply(
     X = design_mat, MARGIN = 1, FUN = function(x) {
       mmat[names(mmat) %in% x[-which(names(x) == "given")]] <- 1
-      return(mmat)
+      mmat
     }
   )
   colnames(design_mat) <- interaction_names
@@ -124,7 +123,7 @@ estimate_coef <- function(variable, given,
     y <- vcov[vcov_el, vcov_el]
     y <- sum(y)
     y <- sqrt(y)
-    return(y)
+    y
   })
 
   q_norm <- stats::qnorm((1 + conf_level) / 2)
@@ -135,7 +134,7 @@ estimate_coef <- function(variable, given,
     x["lcl"] <- exp(x["coef"] - q_norm * x["se(coef)"])
     x["ucl"] <- exp(x["coef"] + q_norm * x["se(coef)"])
 
-    return(x)
+    x
   })
 
   y <- t(y)
@@ -147,7 +146,7 @@ estimate_coef <- function(variable, given,
     " hazard ratio given the level of ", given, " compared to ",
     variable, " level ", lvl_var[1], "."
   )
-  return(y)
+  y
 }
 
 #' `tryCatch` around `car::Anova`
@@ -198,7 +197,7 @@ try_car_anova <- function(mod,
     finally = {}
   )
 
-  return(y)
+  y
 }
 
 #' Fit a Cox regression model and ANOVA
@@ -240,7 +239,7 @@ fit_n_aov <- function(formula,
   y <- list(mod = mod, msum = msum, aov = aov)
   attr(y, "message") <- warn_attr
 
-  return(y)
+  y
 }
 
 # argument_checks
@@ -265,7 +264,7 @@ name_covariate_names <- function(covariates) {
   no_names <- is.null(names(covariates))
   if (any(miss_names)) names(covariates)[miss_names] <- vapply(covariates[miss_names], FUN = rht, FUN.VALUE = "name")
   if (no_names) names(covariates) <- vapply(covariates, FUN = rht, FUN.VALUE = "name")
-  return(covariates)
+  covariates
 }
 
 check_increments <- function(increments, covariates) {
diff --git a/R/prop_diff_test.R b/R/prop_diff_test.R
index 04096ee02a..5ab95e4533 100644
--- a/R/prop_diff_test.R
+++ b/R/prop_diff_test.R
@@ -324,7 +324,8 @@ prop_chisq <- function(tbl, alternative = c("two.sided", "less", "greater")) {
 #'
 #' @param ary (`array`, 3 dimensions)\cr array with two groups in rows, the binary response
 #'   (`TRUE`/`FALSE`) in columns, and the strata in the third dimension.
-#' @param diff_se (`string`)\cr either `standard` or `sato`; specifies whether to use the Sato variance estimator to calculate the chi-squared statistic.
+#' @param diff_se (`string`)\cr either `standard` or `sato`; specifies whether to use the Sato 
+#'   variance estimator to calculate the chi-squared statistic.
 #' @param transform (`string`)\cr either `none` or `wilson_hilferty`; specifies whether to apply
 #'   the Wilson-Hilferty transformation of the chi-squared statistic.
 #'
diff --git a/man/h_prop_diff_test.Rd b/man/h_prop_diff_test.Rd
index 66f3fea04a..eed793efa6 100644
--- a/man/h_prop_diff_test.Rd
+++ b/man/h_prop_diff_test.Rd
@@ -30,7 +30,8 @@ should be displayed.}
 \item{ary}{(\code{array}, 3 dimensions)\cr array with two groups in rows, the binary response
 (\code{TRUE}/\code{FALSE}) in columns, and the strata in the third dimension.}
 
-\item{diff_se}{(\code{string})\cr either \code{standard} or \code{sato}; specifies whether to use the Sato variance estimator to calculate the chi-squared statistic.}
+\item{diff_se}{(\code{string})\cr either \code{standard} or \code{sato}; specifies whether to use the Sato
+variance estimator to calculate the chi-squared statistic.}
 
 \item{transform}{(\code{string})\cr either \code{none} or \code{wilson_hilferty}; specifies whether to apply
 the Wilson-Hilferty transformation of the chi-squared statistic.}

From 1b0aa895dbb50d9e4c0ee3c6f7c50da551d99c15 Mon Sep 17 00:00:00 2001
From: github-actions <41898282+github-actions[bot]@users.noreply.github.com>
Date: Mon, 15 Jun 2026 05:46:59 +0000
Subject: [PATCH 10/13] [skip style] [skip vbump] Restyle files

---
 R/prop_diff_test.R | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/R/prop_diff_test.R b/R/prop_diff_test.R
index 5ab95e4533..c145b404f3 100644
--- a/R/prop_diff_test.R
+++ b/R/prop_diff_test.R
@@ -324,7 +324,7 @@ prop_chisq <- function(tbl, alternative = c("two.sided", "less", "greater")) {
 #'
 #' @param ary (`array`, 3 dimensions)\cr array with two groups in rows, the binary response
 #'   (`TRUE`/`FALSE`) in columns, and the strata in the third dimension.
-#' @param diff_se (`string`)\cr either `standard` or `sato`; specifies whether to use the Sato 
+#' @param diff_se (`string`)\cr either `standard` or `sato`; specifies whether to use the Sato
 #'   variance estimator to calculate the chi-squared statistic.
 #' @param transform (`string`)\cr either `none` or `wilson_hilferty`; specifies whether to apply
 #'   the Wilson-Hilferty transformation of the chi-squared statistic.

From a6b91eece45a624d02201628bb0b7eaf37a1909a Mon Sep 17 00:00:00 2001
From: Daniel Sabanes Bove <daniel@rconis.com>
Date: Mon, 15 Jun 2026 13:47:31 +0800
Subject: [PATCH 11/13] trigger checks


From efe34aa1a4ee45b0fbd0cfbdb763333c9facc345 Mon Sep 17 00:00:00 2001
From: Daniel Sabanes Bove <daniel@rconis.com>
Date: Tue, 16 Jun 2026 10:26:11 +0800
Subject: [PATCH 12/13] polish news as suggested and add comment for sign
 derivation

---
 NEWS.md            | 6 +++---
 R/prop_diff_test.R | 5 ++++-
 2 files changed, 7 insertions(+), 4 deletions(-)

diff --git a/NEWS.md b/NEWS.md
index cc12a22411..ed5ebe6fcf 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -4,18 +4,18 @@
 * Added `alternative` argument to `s_coxph_pairwise()` to allow one-sided hypothesis testing. 
 * Added `lr_stat_df` to the parameters return list of `s_coxph_pairwise()`.
 * Added `uncond_exact_diff` method to `estimate_proportion_diff()` for the unconditional exact confidence interval for the difference in proportions by inverting one-sided tail tests over a nuisance parameter.
-* Added `cmh_sato` as option for `test_proportion_diff()` to enable CMH test with Sato variance estimator.
+* Added `cmh_sato` method to `test_proportion_diff()` for CMH testing with the Sato variance estimator. (#1482)
 * Added `range_with_cens_info` statistic to `s_surv_time()`.
 * Added `lsmean_se`, `lsmean_ci`, and `lsmean_diffci` statistics to `s_ancova()`.
 * Added `s_ancova()` to exported functions.
 
 ### Bug Fixes
 * Fixed bug in `prop_diff_cmh()` which previously failed when strata combinations had 0 observations.
-* Fixed bug in `prop_cmh()` where previously the Wilson-Hilferty transformation did not always preserve the direction of the effect for one-sided tests.
+* Fixed one-sided p-values in `prop_cmh()` with Wilson-Hilferty transformation — the sign of the effect was lost, producing incorrect p-values for `alternative = "less"` and `alternative = "greater"`.
 
 ### Miscellaneous
 * Updated `roxygen2` to 8.0.0 and added `@exportS3Method` tags for S3 methods in `decorate_grob.R` and `utils_grid.R`.
-* Converted  `s_surv_time()`to exported functions.
+* Converted `s_surv_time()` to exported functions.
 
 # tern 0.9.10
 
diff --git a/R/prop_diff_test.R b/R/prop_diff_test.R
index c145b404f3..0f9589cd75 100644
--- a/R/prop_diff_test.R
+++ b/R/prop_diff_test.R
@@ -350,7 +350,10 @@ prop_cmh <- function(ary,
   z_stat <- if (diff_se == "standard") {
     mh_res <- stats::mantelhaen.test(ary, correct = FALSE, alternative = alternative)
     checkmate::assert_true(mh_res$parameter == 1)
-    sqrt(unname(mh_res$statistic)) * ifelse(unname(mh_res$estimate) < 1, 1, -1)
+    # Note: The odds ratio (OR) estimate from `mantelhaen.test` and the proportion difference
+    # always agree in direction, therefore we can use the OR estimate to determine the sign here.
+    stat_sign <- ifelse(mh_res$estimate < 1, 1, -1)
+    sqrt(unname(mh_res$statistic)) * stat_sign
   } else {
     # Use the Sato variance estimator.
     cmh <- h_diff_cmh(ary)

From 66371ece8056422b6e2fa27122958bbc78043271 Mon Sep 17 00:00:00 2001
From: Daniel Sabanes Bove <daniel@rconis.com>
Date: Tue, 16 Jun 2026 11:21:06 +0800
Subject: [PATCH 13/13] fix with unname

---
 R/prop_diff_test.R | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/R/prop_diff_test.R b/R/prop_diff_test.R
index 0f9589cd75..968176c74e 100644
--- a/R/prop_diff_test.R
+++ b/R/prop_diff_test.R
@@ -352,7 +352,7 @@ prop_cmh <- function(ary,
     checkmate::assert_true(mh_res$parameter == 1)
     # Note: The odds ratio (OR) estimate from `mantelhaen.test` and the proportion difference
     # always agree in direction, therefore we can use the OR estimate to determine the sign here.
-    stat_sign <- ifelse(mh_res$estimate < 1, 1, -1)
+    stat_sign <- ifelse(unname(mh_res$estimate) < 1, 1, -1)
     sqrt(unname(mh_res$statistic)) * stat_sign
   } else {
     # Use the Sato variance estimator.