diff --git a/NEWS.md b/NEWS.md
index d89c08c..c4a2910 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -1,3 +1,15 @@
+# hdnom 6.2.0
+
+## Improvements
+
+- Updated selected code examples to use `rule = "lambda.min"` where glmnet 5.0
+  could otherwise select a null Cox model with `rule = "lambda.1se"` (#24).
+- Added a `cox.ties` argument to glmnet-based Cox model fitting helpers,
+  including `fit_lasso()`, and forwarded it to the underlying `cv.glmnet()`
+  and `glmnet()` calls. The default remains `"breslow"` to lock in current
+  behavior and silence the glmnet tie-handling migration warning, while
+  `"efron"` is available for users who want to opt in (#25).
+
 # hdnom 6.1.0
 
 ## Breaking changes
diff --git a/R/1_1_model.R b/R/1_1_model.R
index 5200d29..2b90cac 100644
--- a/R/1_1_model.R
+++ b/R/1_1_model.R
@@ -10,6 +10,8 @@
 #' \code{"lambda.1se"}. See \code{\link[glmnet]{cv.glmnet}}
 #' for details.
 #' @param seed A random seed for cross-validation fold division.
+#' @param cox.ties Cox tie-handling method passed to
+#' \code{\link[glmnet]{cv.glmnet}} and \code{\link[glmnet]{glmnet}}.
 #'
 #' @export fit_lasso
 #'
@@ -32,13 +34,19 @@
 fit_lasso <- function(
   x, y, nfolds = 5L,
   rule = c("lambda.min", "lambda.1se"),
-  seed = 1001
+  seed = 1001,
+  cox.ties = c("breslow", "efron")
 ) {
   call <- match.call()
   rule <- match.arg(rule)
+  cox.ties <- match.arg(cox.ties)
 
   set.seed(seed)
-  lasso_cv <- cv.glmnet(x, y, family = "cox", nfolds = nfolds, alpha = 1)
+  lasso_cv <- cv.glmnet(
+    x, y,
+    family = "cox", nfolds = nfolds,
+    alpha = 1, cox.ties = cox.ties
+  )
 
   if (rule == "lambda.min") {
     lambda_opt <- lasso_cv$lambda.min
@@ -49,7 +57,8 @@ fit_lasso <- function(
   lasso_full <- glmnet(
     x, y,
     family = "cox",
-    lambda = lambda_opt, alpha = 1
+    lambda = lambda_opt, alpha = 1,
+    cox.ties = cox.ties
   )
 
   if (lasso_full$df < 0.5) {
@@ -66,6 +75,7 @@ fit_lasso <- function(
     "lambda" = lambda_opt,
     "type" = "lasso",
     "seed" = seed,
+    "cox.ties" = cox.ties,
     "call" = call
   )
 
@@ -86,6 +96,8 @@ fit_lasso <- function(
 #' for details.
 #' @param seed Two random seeds for cross-validation fold division
 #' in two estimation steps.
+#' @param cox.ties Cox tie-handling method passed to
+#' \code{\link[glmnet]{cv.glmnet}} and \code{\link[glmnet]{glmnet}}.
 #'
 #' @export fit_alasso
 #'
@@ -108,14 +120,20 @@ fit_lasso <- function(
 fit_alasso <- function(
   x, y, nfolds = 5L,
   rule = c("lambda.min", "lambda.1se"),
-  seed = c(1001, 1002)
+  seed = c(1001, 1002),
+  cox.ties = c("breslow", "efron")
 ) {
   call <- match.call()
   rule <- match.arg(rule)
+  cox.ties <- match.arg(cox.ties)
 
   # Tune lambda for the both two stages of adaptive lasso estimation
   set.seed(seed[1L])
-  lasso_cv <- cv.glmnet(x, y, family = "cox", nfolds = nfolds, alpha = 0)
+  lasso_cv <- cv.glmnet(
+    x, y,
+    family = "cox", nfolds = nfolds,
+    alpha = 0, cox.ties = cox.ties
+  )
 
   if (rule == "lambda.min") {
     lambda_opt_init <- lasso_cv$lambda.min
@@ -126,7 +144,8 @@ fit_alasso <- function(
   lasso_full <- glmnet(
     x, y,
     family = "cox",
-    lambda = lambda_opt_init, alpha = 0
+    lambda = lambda_opt_init, alpha = 0,
+    cox.ties = cox.ties
   )
 
   bhat <- as.matrix(lasso_full$beta)
@@ -139,7 +158,8 @@ fit_alasso <- function(
   alasso_cv <- cv.glmnet(
     x, y,
     family = "cox", nfolds = nfolds, alpha = 1,
-    penalty.factor = adpen
+    penalty.factor = adpen,
+    cox.ties = cox.ties
   )
 
   if (rule == "lambda.min") {
@@ -151,7 +171,8 @@ fit_alasso <- function(
   alasso_full <- glmnet(
     x, y,
     family = "cox", lambda = lambda_opt,
-    alpha = 1, penalty.factor = adpen
+    alpha = 1, penalty.factor = adpen,
+    cox.ties = cox.ties
   )
 
   if (alasso_full$df < 0.5) {
@@ -175,6 +196,7 @@ fit_alasso <- function(
     "pen_factor" = adpen_vec,
     "type" = "alasso",
     "seed" = seed,
+    "cox.ties" = cox.ties,
     "call" = call
   )
 
@@ -199,6 +221,8 @@ fit_alasso <- function(
 #' default is \code{FALSE}. To enable parallel tuning, load the
 #' \code{doParallel} package and run \code{registerDoParallel()}
 #' with the number of CPU cores before calling this function.
+#' @param cox.ties Cox tie-handling method passed to
+#' \code{\link[glmnet]{cv.glmnet}} and \code{\link[glmnet]{glmnet}}.
 #'
 #' @export fit_enet
 #'
@@ -230,16 +254,19 @@ fit_alasso <- function(
 fit_enet <- function(
   x, y, nfolds = 5L, alphas = seq(0.05, 0.95, 0.05),
   rule = c("lambda.min", "lambda.1se"),
-  seed = 1001, parallel = FALSE
+  seed = 1001, parallel = FALSE,
+  cox.ties = c("breslow", "efron")
 ) {
   call <- match.call()
   rule <- match.arg(rule)
+  cox.ties <- match.arg(cox.ties)
 
   enet_cv <- glmnet_tune_alpha(
     x, y,
     family = "cox",
     nfolds = nfolds, alphas = alphas,
-    seed = seed, parallel = parallel
+    seed = seed, parallel = parallel,
+    cox.ties = cox.ties
   )
 
   alpha_opt <- enet_cv$best.alpha
@@ -254,7 +281,8 @@ fit_enet <- function(
     x, y,
     family = "cox",
     lambda = lambda_opt,
-    alpha = alpha_opt
+    alpha = alpha_opt,
+    cox.ties = cox.ties
   )
 
   if (enet_full$df < 0.5) {
@@ -272,6 +300,7 @@ fit_enet <- function(
     "lambda" = lambda_opt,
     "type" = "enet",
     "seed" = seed,
+    "cox.ties" = cox.ties,
     "call" = call
   )
 
@@ -297,6 +326,8 @@ fit_enet <- function(
 #' default is \code{FALSE}. To enable parallel tuning, load the
 #' \code{doParallel} package and run \code{registerDoParallel()}
 #' with the number of CPU cores before calling this function.
+#' @param cox.ties Cox tie-handling method passed to
+#' \code{\link[glmnet]{cv.glmnet}} and \code{\link[glmnet]{glmnet}}.
 #'
 #' @importFrom glmnet glmnet
 #'
@@ -331,17 +362,20 @@ fit_aenet <- function(
   x, y, nfolds = 5L, alphas = seq(0.05, 0.95, 0.05),
   rule = c("lambda.min", "lambda.1se"),
   seed = c(1001, 1002),
-  parallel = FALSE
+  parallel = FALSE,
+  cox.ties = c("breslow", "efron")
 ) {
   call <- match.call()
   rule <- match.arg(rule)
+  cox.ties <- match.arg(cox.ties)
 
   # Tune alpha for the both two stages of adaptive enet estimation
   enet_cv <- glmnet_tune_alpha(
     x, y,
     family = "cox",
     nfolds = nfolds, alphas = alphas,
-    seed = seed[1L], parallel = parallel
+    seed = seed[1L], parallel = parallel,
+    cox.ties = cox.ties
   )
 
   alpha_opt_init <- enet_cv$best.alpha
@@ -356,7 +390,8 @@ fit_aenet <- function(
     x, y,
     family = "cox",
     lambda = lambda_opt_init,
-    alpha = alpha_opt_init
+    alpha = alpha_opt_init,
+    cox.ties = cox.ties
   )
 
   bhat <- as.matrix(enet_full$beta)
@@ -372,7 +407,8 @@ fit_aenet <- function(
     penalty.factor = adpen,
     alphas = alphas,
     seed = seed[2L],
-    parallel = parallel
+    parallel = parallel,
+    cox.ties = cox.ties
   )
 
   alpha_opt <- aenet_cv$best.alpha
@@ -389,7 +425,8 @@ fit_aenet <- function(
     exclude = which(bhat == 0),
     lambda = lambda_opt,
     alpha = alpha_opt,
-    penalty.factor = adpen
+    penalty.factor = adpen,
+    cox.ties = cox.ties
   )
 
   if (aenet_full$df < 0.5) {
@@ -415,6 +452,7 @@ fit_aenet <- function(
     "pen_factor" = adpen_vec,
     "type" = "aenet",
     "seed" = seed,
+    "cox.ties" = cox.ties,
     "call" = call
   )
 
diff --git a/R/3_1_validate.R b/R/3_1_validate.R
index 44adc80..a76b06e 100644
--- a/R/3_1_validate.R
+++ b/R/3_1_validate.R
@@ -22,6 +22,7 @@
 #' model fits on the resampled data. From the fitted Cox model.
 #' @param pen.factor Penalty factors to apply to each coefficient.
 #' From the fitted \emph{adaptive lasso} or \emph{adaptive elastic-net} model.
+#' @param cox.ties Cox tie-handling method for glmnet model refits.
 #' @param gamma Value of the model parameter gamma for
 #' MCP/SCAD/Mnet/Snet models.
 #' @param lambda1 Value of the penalty parameter lambda1 for fused lasso model.
@@ -168,11 +169,13 @@ validate <- function(
   method = c("bootstrap", "cv", "repeated.cv"),
   boot.times = NULL, nfolds = NULL, rep.times = NULL,
   tauc.type = c("CD", "SZ", "UNO"), tauc.time,
+  cox.ties = c("breslow", "efron"),
   seed = 1001, trace = TRUE
 ) {
   model.type <- match.arg(model.type)
   method <- match.arg(method)
   tauc.type <- match.arg(tauc.type)
+  cox.ties <- match.arg(cox.ties)
 
   set.seed(seed)
 
@@ -205,7 +208,8 @@ validate <- function(
           glmnet_validate_tauc(
             x_tr = x_tr, x_te = x_te, y_tr = y_tr, y_te = y_te,
             alpha = alpha, lambda = lambda, pen.factor = pen.factor,
-            tauc.type = tauc.type, tauc.time = tauc.time
+            tauc.type = tauc.type, tauc.time = tauc.time,
+            cox.ties = cox.ties
           )
       }
 
@@ -258,7 +262,8 @@ validate <- function(
           glmnet_validate_tauc(
             x_tr = x_tr, x_te = x_te, y_tr = y_tr, y_te = y_te,
             alpha = alpha, lambda = lambda, pen.factor = pen.factor,
-            tauc.type = tauc.type, tauc.time = tauc.time
+            tauc.type = tauc.type, tauc.time = tauc.time,
+            cox.ties = cox.ties
           )
       }
 
@@ -317,7 +322,8 @@ validate <- function(
             glmnet_validate_tauc(
               x_tr = x_tr, x_te = x_te, y_tr = y_tr, y_te = y_te,
               alpha = alpha, lambda = lambda, pen.factor = pen.factor,
-              tauc.type = tauc.type, tauc.time = tauc.time
+              tauc.type = tauc.type, tauc.time = tauc.time,
+              cox.ties = cox.ties
             )
         }
 
@@ -356,6 +362,7 @@ validate <- function(
         attr(tauc, "alpha") <- alpha
         attr(tauc, "lambda") <- lambda
         attr(tauc, "pen.factor") <- pen.factor
+        attr(tauc, "cox.ties") <- cox.ties
         attr(tauc, "boot.times") <- boot.times
         attr(tauc, "tauc.type") <- tauc.type
         attr(tauc, "tauc.time") <- tauc.time
@@ -401,6 +408,7 @@ validate <- function(
         attr(tauc, "alpha") <- alpha
         attr(tauc, "lambda") <- lambda
         attr(tauc, "pen.factor") <- pen.factor
+        attr(tauc, "cox.ties") <- cox.ties
         attr(tauc, "nfolds") <- nfolds
         attr(tauc, "tauc.type") <- tauc.type
         attr(tauc, "tauc.time") <- tauc.time
@@ -446,6 +454,7 @@ validate <- function(
         attr(tauc, "alpha") <- alpha
         attr(tauc, "lambda") <- lambda
         attr(tauc, "pen.factor") <- pen.factor
+        attr(tauc, "cox.ties") <- cox.ties
         attr(tauc, "nfolds") <- nfolds
         attr(tauc, "rep.times") <- rep.times
         attr(tauc, "tauc.type") <- tauc.type
diff --git a/R/3_2_validate_utils.R b/R/3_2_validate_utils.R
index 1cdb640..3374b55 100644
--- a/R/3_2_validate_utils.R
+++ b/R/3_2_validate_utils.R
@@ -9,18 +9,21 @@
 glmnet_validate_tauc <- function(
   x_tr, x_te, y_tr, y_te,
   alpha, lambda, pen.factor,
-  tauc.type, tauc.time
+  tauc.type, tauc.time,
+  cox.ties
 ) {
   if (is.null(pen.factor)) {
     samp_fit <- glmnet(
       x = x_tr, y = y_tr, family = "cox",
-      alpha = alpha, lambda = lambda
+      alpha = alpha, lambda = lambda,
+      cox.ties = cox.ties
     )
   } else {
     samp_fit <- glmnet(
       x = x_tr, y = y_tr, family = "cox",
       alpha = alpha, lambda = lambda,
-      penalty.factor = pen.factor
+      penalty.factor = pen.factor,
+      cox.ties = cox.ties
     )
   }
 
diff --git a/R/4_1_calibrate.R b/R/4_1_calibrate.R
index 294f109..6703420 100644
--- a/R/4_1_calibrate.R
+++ b/R/4_1_calibrate.R
@@ -22,6 +22,7 @@
 #' model fits on the resampled data. From the Cox model you have built.
 #' @param pen.factor Penalty factors to apply to each coefficient.
 #' From the built \emph{adaptive lasso} or \emph{adaptive elastic-net} model.
+#' @param cox.ties Cox tie-handling method for glmnet model refits.
 #' @param gamma Value of the model parameter gamma for
 #' MCP/SCAD/Mnet/Snet models.
 #' @param lambda1 Value of the penalty parameter lambda1 for fused lasso model.
@@ -145,10 +146,12 @@ calibrate <- function(
   method = c("fitting", "bootstrap", "cv", "repeated.cv"),
   boot.times = NULL, nfolds = NULL, rep.times = NULL,
   pred.at, ngroup = 5,
+  cox.ties = c("breslow", "efron"),
   seed = 1001, trace = TRUE
 ) {
   model.type <- match.arg(model.type)
   method <- match.arg(method)
+  cox.ties <- match.arg(cox.ties)
   if (length(pred.at) != 1L) stop("pred.at should only contain 1 time point")
 
   set.seed(seed)
@@ -164,7 +167,8 @@ calibrate <- function(
       pred_list <- glmnet_calibrate_surv_prob_pred(
         x_tr = x, x_te = x, y_tr = Surv(time, event),
         alpha = alpha, lambda = lambda, pen.factor = pen.factor,
-        pred.at = pred.at
+        pred.at = pred.at,
+        cox.ties = cox.ties
       )
     }
 
@@ -225,7 +229,8 @@ calibrate <- function(
         pred_list_list[[i]] <- glmnet_calibrate_surv_prob_pred(
           x_tr = x_tr, x_te = x_te, y_tr = y_tr,
           alpha = alpha, lambda = lambda, pen.factor = pen.factor,
-          pred.at = pred.at
+          pred.at = pred.at,
+          cox.ties = cox.ties
         )
       }
 
@@ -295,7 +300,8 @@ calibrate <- function(
         pred_list_list[[i]] <- glmnet_calibrate_surv_prob_pred(
           x_tr = x_tr, x_te = x_te, y_tr = y_tr,
           alpha = alpha, lambda = lambda, pen.factor = pen.factor,
-          pred.at = pred.at
+          pred.at = pred.at,
+          cox.ties = cox.ties
         )
       }
 
@@ -374,7 +380,8 @@ calibrate <- function(
           pred_list_list[[j]][[i]] <- glmnet_calibrate_surv_prob_pred(
             x_tr = x_tr, x_te = x_te, y_tr = y_tr,
             alpha = alpha, lambda = lambda, pen.factor = pen.factor,
-            pred.at = pred.at
+            pred.at = pred.at,
+            cox.ties = cox.ties
           )
         }
 
@@ -445,6 +452,7 @@ calibrate <- function(
         attr(prob, "alpha") <- alpha
         attr(prob, "lambda") <- lambda
         attr(prob, "pen.factor") <- pen.factor
+        attr(prob, "cox.ties") <- cox.ties
       }
 
       if (model.type %in% c("mcp", "mnet", "scad", "snet")) {
@@ -475,6 +483,7 @@ calibrate <- function(
         attr(prob, "alpha") <- alpha
         attr(prob, "lambda") <- lambda
         attr(prob, "pen.factor") <- pen.factor
+        attr(prob, "cox.ties") <- cox.ties
         attr(prob, "boot.times") <- boot.times
       }
 
@@ -508,6 +517,7 @@ calibrate <- function(
         attr(prob, "alpha") <- alpha
         attr(prob, "lambda") <- lambda
         attr(prob, "pen.factor") <- pen.factor
+        attr(prob, "cox.ties") <- cox.ties
         attr(prob, "nfolds") <- nfolds
       }
 
@@ -541,6 +551,7 @@ calibrate <- function(
         attr(prob, "alpha") <- alpha
         attr(prob, "lambda") <- lambda
         attr(prob, "pen.factor") <- pen.factor
+        attr(prob, "cox.ties") <- cox.ties
         attr(prob, "nfolds") <- nfolds
         attr(prob, "rep.times") <- rep.times
       }
diff --git a/R/4_2_calibrate_utils.R b/R/4_2_calibrate_utils.R
index c8847a9..fff00a2 100644
--- a/R/4_2_calibrate_utils.R
+++ b/R/4_2_calibrate_utils.R
@@ -9,18 +9,21 @@
 glmnet_calibrate_surv_prob_pred <- function(
   x_tr, x_te, y_tr,
   alpha, lambda, pen.factor,
-  pred.at
+  pred.at,
+  cox.ties
 ) {
   if (is.null(pen.factor)) {
     object <- glmnet(
       x = x_tr, y = y_tr, family = "cox",
-      alpha = alpha, lambda = lambda
+      alpha = alpha, lambda = lambda,
+      cox.ties = cox.ties
     )
   } else {
     object <- glmnet(
       x = x_tr, y = y_tr, family = "cox",
       alpha = alpha, lambda = lambda,
-      penalty.factor = pen.factor
+      penalty.factor = pen.factor,
+      cox.ties = cox.ties
     )
   }
 
diff --git a/R/5_1_compare_by_validate.R b/R/5_1_compare_by_validate.R
index 3022dba..5e81c45 100644
--- a/R/5_1_compare_by_validate.R
+++ b/R/5_1_compare_by_validate.R
@@ -26,6 +26,7 @@
 #' the time-dependent AUC.
 #' @param rule Model selection criterion for glmnet models,
 #' `"lambda.min"` or `"lambda.1se"`. Defaults to `"lambda.min"`.
+#' @param cox.ties Cox tie-handling method for glmnet model fits and refits.
 #' @param seed A random seed for cross-validation fold division.
 #' @param trace Logical. Output the validation progress or not.
 #' Default is \code{TRUE}.
@@ -76,11 +77,13 @@ compare_by_validate <- function(
   boot.times = NULL, nfolds = NULL, rep.times = NULL,
   tauc.type = c("CD", "SZ", "UNO"), tauc.time,
   rule = c("lambda.min", "lambda.1se"),
+  cox.ties = c("breslow", "efron"),
   seed = 1001, trace = TRUE
 ) {
   method <- match.arg(method)
   tauc.type <- match.arg(tauc.type)
   rule <- match.arg(rule)
+  cox.ties <- match.arg(cox.ties)
 
   if (!all(model.type %in% c(
     "lasso", "alasso", "flasso", "enet", "aenet",
@@ -124,7 +127,8 @@ compare_by_validate <- function(
         cvfit <- fit_lasso(
           x, Surv(time, event),
           nfolds = 5L,
-          rule = rule, seed = seed
+          rule = rule, seed = seed,
+          cox.ties = cox.ties
         )
 
         tauclist[[i]] <- hdnom::validate(
@@ -133,6 +137,7 @@ compare_by_validate <- function(
           alpha = 1, lambda = cvfit$"lambda",
           method = method, boot.times = boot.times, nfolds = nfolds, rep.times = rep.times,
           tauc.type = tauc.type, tauc.time = tauc.time,
+          cox.ties = cox.ties,
           seed = seed, trace = trace
         )
       },
@@ -140,7 +145,8 @@ compare_by_validate <- function(
         cvfit <- fit_alasso(
           x, Surv(time, event),
           nfolds = 5L,
-          rule = rule, seed = rep(seed, 2)
+          rule = rule, seed = rep(seed, 2),
+          cox.ties = cox.ties
         )
 
         tauclist[[i]] <- hdnom::validate(
@@ -149,6 +155,7 @@ compare_by_validate <- function(
           alpha = 1, lambda = cvfit$"lambda", pen.factor = cvfit$"pen_factor",
           method = method, boot.times = boot.times, nfolds = nfolds, rep.times = rep.times,
           tauc.type = tauc.type, tauc.time = tauc.time,
+          cox.ties = cox.ties,
           seed = seed, trace = trace
         )
       },
@@ -170,7 +177,8 @@ compare_by_validate <- function(
           x, Surv(time, event),
           nfolds = 5L,
           alphas = c(0.1, 0.25, 0.5, 0.75, 0.9), # to reduce computation time
-          rule = rule, seed = seed
+          rule = rule, seed = seed,
+          cox.ties = cox.ties
         )
 
         tauclist[[i]] <- hdnom::validate(
@@ -179,6 +187,7 @@ compare_by_validate <- function(
           alpha = cvfit$"alpha", lambda = cvfit$"lambda",
           method = method, boot.times = boot.times, nfolds = nfolds, rep.times = rep.times,
           tauc.type = tauc.type, tauc.time = tauc.time,
+          cox.ties = cox.ties,
           seed = seed, trace = trace
         )
       },
@@ -187,7 +196,8 @@ compare_by_validate <- function(
           x, Surv(time, event),
           nfolds = 5L,
           alphas = c(0.1, 0.25, 0.5, 0.75, 0.9), # to reduce computation time
-          rule = rule, seed = rep(seed, 2)
+          rule = rule, seed = rep(seed, 2),
+          cox.ties = cox.ties
         )
 
         tauclist[[i]] <- hdnom::validate(
@@ -196,6 +206,7 @@ compare_by_validate <- function(
           alpha = cvfit$"alpha", lambda = cvfit$"lambda", pen.factor = cvfit$"pen_factor",
           method = method, boot.times = boot.times, nfolds = nfolds, rep.times = rep.times,
           tauc.type = tauc.type, tauc.time = tauc.time,
+          cox.ties = cox.ties,
           seed = seed, trace = trace
         )
       },
diff --git a/R/5_3_compare_by_calibrate.R b/R/5_3_compare_by_calibrate.R
index dac07e2..fc36995 100644
--- a/R/5_3_compare_by_calibrate.R
+++ b/R/5_3_compare_by_calibrate.R
@@ -22,6 +22,7 @@
 #' @param ngroup Number of groups to be formed for calibration.
 #' @param rule Model selection criterion for glmnet models,
 #' `"lambda.min"` or `"lambda.1se"`. Defaults to `"lambda.min"`.
+#' @param cox.ties Cox tie-handling method for glmnet model fits and refits.
 #' @param seed A random seed for cross-validation fold division.
 #' @param trace Logical. Output the calibration progress or not.
 #' Default is \code{TRUE}.
@@ -55,10 +56,12 @@ compare_by_calibrate <- function(
   boot.times = NULL, nfolds = NULL, rep.times = NULL,
   pred.at, ngroup = 5,
   rule = c("lambda.min", "lambda.1se"),
+  cox.ties = c("breslow", "efron"),
   seed = 1001, trace = TRUE
 ) {
   method <- match.arg(method)
   rule <- match.arg(rule)
+  cox.ties <- match.arg(cox.ties)
 
   if (length(pred.at) != 1L) stop("pred.at should only contain 1 time point")
 
@@ -110,7 +113,8 @@ compare_by_calibrate <- function(
         cvfit <- fit_lasso(
           x, Surv(time, event),
           nfolds = 5L,
-          rule = rule, seed = seed
+          rule = rule, seed = seed,
+          cox.ties = cox.ties
         )
 
         problist[[i]] <- hdnom::calibrate(
@@ -119,6 +123,7 @@ compare_by_calibrate <- function(
           alpha = 1, lambda = cvfit$"lambda",
           method = method, boot.times = boot.times, nfolds = nfolds, rep.times = rep.times,
           pred.at = pred.at, ngroup = ngroup,
+          cox.ties = cox.ties,
           seed = seed, trace = trace
         )
       },
@@ -126,7 +131,8 @@ compare_by_calibrate <- function(
         cvfit <- fit_alasso(
           x, Surv(time, event),
           nfolds = 5L,
-          rule = rule, seed = rep(seed, 2)
+          rule = rule, seed = rep(seed, 2),
+          cox.ties = cox.ties
         )
 
         problist[[i]] <- hdnom::calibrate(
@@ -135,6 +141,7 @@ compare_by_calibrate <- function(
           alpha = 1, lambda = cvfit$"lambda", pen.factor = cvfit$"pen_factor",
           method = method, boot.times = boot.times, nfolds = nfolds, rep.times = rep.times,
           pred.at = pred.at, ngroup = ngroup,
+          cox.ties = cox.ties,
           seed = seed, trace = trace
         )
       },
@@ -156,7 +163,8 @@ compare_by_calibrate <- function(
           x, Surv(time, event),
           nfolds = 5L,
           alphas = c(0.1, 0.25, 0.5, 0.75, 0.9), # to reduce computation time
-          rule = rule, seed = seed
+          rule = rule, seed = seed,
+          cox.ties = cox.ties
         )
 
         problist[[i]] <- hdnom::calibrate(
@@ -165,6 +173,7 @@ compare_by_calibrate <- function(
           alpha = cvfit$"alpha", lambda = cvfit$"lambda",
           method = method, boot.times = boot.times, nfolds = nfolds, rep.times = rep.times,
           pred.at = pred.at, ngroup = ngroup,
+          cox.ties = cox.ties,
           seed = seed, trace = trace
         )
       },
@@ -173,7 +182,8 @@ compare_by_calibrate <- function(
           x, Surv(time, event),
           nfolds = 5L,
           alphas = c(0.1, 0.25, 0.5, 0.75, 0.9), # to reduce computation time
-          rule = rule, seed = rep(seed, 2)
+          rule = rule, seed = rep(seed, 2),
+          cox.ties = cox.ties
         )
 
         problist[[i]] <- hdnom::calibrate(
@@ -182,6 +192,7 @@ compare_by_calibrate <- function(
           alpha = cvfit$"alpha", lambda = cvfit$"lambda", pen.factor = cvfit$"pen_factor",
           method = method, boot.times = boot.times, nfolds = nfolds, rep.times = rep.times,
           pred.at = pred.at, ngroup = ngroup,
+          cox.ties = cox.ties,
           seed = seed, trace = trace
         )
       },
diff --git a/man/calibrate.Rd b/man/calibrate.Rd
index a240b9a..616a6e3 100644
--- a/man/calibrate.Rd
+++ b/man/calibrate.Rd
@@ -22,6 +22,7 @@ calibrate(
   rep.times = NULL,
   pred.at,
   ngroup = 5,
+  cox.ties = c("breslow", "efron"),
   seed = 1001,
   trace = TRUE
 )
@@ -76,6 +77,8 @@ repeated cross-validation.}
 
 \item{ngroup}{Number of groups to be formed for calibration.}
 
+\item{cox.ties}{Cox tie-handling method for glmnet model refits.}
+
 \item{seed}{A random seed for resampling.}
 
 \item{trace}{Logical. Output the calibration progress or not.
diff --git a/man/compare_by_calibrate.Rd b/man/compare_by_calibrate.Rd
index 4bde584..3ac2b35 100644
--- a/man/compare_by_calibrate.Rd
+++ b/man/compare_by_calibrate.Rd
@@ -17,6 +17,7 @@ compare_by_calibrate(
   pred.at,
   ngroup = 5,
   rule = c("lambda.min", "lambda.1se"),
+  cox.ties = c("breslow", "efron"),
   seed = 1001,
   trace = TRUE
 )
@@ -53,6 +54,8 @@ repeated cross-validation.}
 \item{rule}{Model selection criterion for glmnet models,
 `"lambda.min"` or `"lambda.1se"`. Defaults to `"lambda.min"`.}
 
+\item{cox.ties}{Cox tie-handling method for glmnet model fits and refits.}
+
 \item{seed}{A random seed for cross-validation fold division.}
 
 \item{trace}{Logical. Output the calibration progress or not.
diff --git a/man/compare_by_validate.Rd b/man/compare_by_validate.Rd
index 3b60752..35e3908 100644
--- a/man/compare_by_validate.Rd
+++ b/man/compare_by_validate.Rd
@@ -17,6 +17,7 @@ compare_by_validate(
   tauc.type = c("CD", "SZ", "UNO"),
   tauc.time,
   rule = c("lambda.min", "lambda.1se"),
+  cox.ties = c("breslow", "efron"),
   seed = 1001,
   trace = TRUE
 )
@@ -57,6 +58,8 @@ the time-dependent AUC.}
 \item{rule}{Model selection criterion for glmnet models,
 `"lambda.min"` or `"lambda.1se"`. Defaults to `"lambda.min"`.}
 
+\item{cox.ties}{Cox tie-handling method for glmnet model fits and refits.}
+
 \item{seed}{A random seed for cross-validation fold division.}
 
 \item{trace}{Logical. Output the validation progress or not.
diff --git a/man/fit_aenet.Rd b/man/fit_aenet.Rd
index 6a78a85..a8b24eb 100644
--- a/man/fit_aenet.Rd
+++ b/man/fit_aenet.Rd
@@ -11,7 +11,8 @@ fit_aenet(
   alphas = seq(0.05, 0.95, 0.05),
   rule = c("lambda.min", "lambda.1se"),
   seed = c(1001, 1002),
-  parallel = FALSE
+  parallel = FALSE,
+  cox.ties = c("breslow", "efron")
 )
 }
 \arguments{
@@ -34,6 +35,9 @@ in two estimation steps.}
 default is \code{FALSE}. To enable parallel tuning, load the
 \code{doParallel} package and run \code{registerDoParallel()}
 with the number of CPU cores before calling this function.}
+
+\item{cox.ties}{Cox tie-handling method passed to
+\code{\link[glmnet]{cv.glmnet}} and \code{\link[glmnet]{glmnet}}.}
 }
 \description{
 Automatic model selection for high-dimensional Cox models
diff --git a/man/fit_alasso.Rd b/man/fit_alasso.Rd
index 49a421b..a3f4484 100644
--- a/man/fit_alasso.Rd
+++ b/man/fit_alasso.Rd
@@ -9,7 +9,8 @@ fit_alasso(
   y,
   nfolds = 5L,
   rule = c("lambda.min", "lambda.1se"),
-  seed = c(1001, 1002)
+  seed = c(1001, 1002),
+  cox.ties = c("breslow", "efron")
 )
 }
 \arguments{
@@ -25,6 +26,9 @@ for details.}
 
 \item{seed}{Two random seeds for cross-validation fold division
 in two estimation steps.}
+
+\item{cox.ties}{Cox tie-handling method passed to
+\code{\link[glmnet]{cv.glmnet}} and \code{\link[glmnet]{glmnet}}.}
 }
 \description{
 Automatic model selection for high-dimensional Cox models
diff --git a/man/fit_enet.Rd b/man/fit_enet.Rd
index b438d30..5487e8b 100644
--- a/man/fit_enet.Rd
+++ b/man/fit_enet.Rd
@@ -11,7 +11,8 @@ fit_enet(
   alphas = seq(0.05, 0.95, 0.05),
   rule = c("lambda.min", "lambda.1se"),
   seed = 1001,
-  parallel = FALSE
+  parallel = FALSE,
+  cox.ties = c("breslow", "efron")
 )
 }
 \arguments{
@@ -33,6 +34,9 @@ for details.}
 default is \code{FALSE}. To enable parallel tuning, load the
 \code{doParallel} package and run \code{registerDoParallel()}
 with the number of CPU cores before calling this function.}
+
+\item{cox.ties}{Cox tie-handling method passed to
+\code{\link[glmnet]{cv.glmnet}} and \code{\link[glmnet]{glmnet}}.}
 }
 \description{
 Automatic model selection for high-dimensional Cox models
diff --git a/man/fit_lasso.Rd b/man/fit_lasso.Rd
index 7772207..f31632a 100644
--- a/man/fit_lasso.Rd
+++ b/man/fit_lasso.Rd
@@ -4,7 +4,14 @@
 \alias{fit_lasso}
 \title{Model selection for high-dimensional Cox models with lasso penalty}
 \usage{
-fit_lasso(x, y, nfolds = 5L, rule = c("lambda.min", "lambda.1se"), seed = 1001)
+fit_lasso(
+  x,
+  y,
+  nfolds = 5L,
+  rule = c("lambda.min", "lambda.1se"),
+  seed = 1001,
+  cox.ties = c("breslow", "efron")
+)
 }
 \arguments{
 \item{x}{Data matrix.}
@@ -18,6 +25,9 @@ fit_lasso(x, y, nfolds = 5L, rule = c("lambda.min", "lambda.1se"), seed = 1001)
 for details.}
 
 \item{seed}{A random seed for cross-validation fold division.}
+
+\item{cox.ties}{Cox tie-handling method passed to
+\code{\link[glmnet]{cv.glmnet}} and \code{\link[glmnet]{glmnet}}.}
 }
 \description{
 Automatic model selection for high-dimensional Cox models
diff --git a/man/glmnet_calibrate_surv_prob_pred.Rd b/man/glmnet_calibrate_surv_prob_pred.Rd
index 39be1f2..4c838e7 100644
--- a/man/glmnet_calibrate_surv_prob_pred.Rd
+++ b/man/glmnet_calibrate_surv_prob_pred.Rd
@@ -11,7 +11,8 @@ glmnet_calibrate_surv_prob_pred(
   alpha,
   lambda,
   pen.factor,
-  pred.at
+  pred.at,
+  cox.ties
 )
 }
 \value{
diff --git a/man/glmnet_validate_tauc.Rd b/man/glmnet_validate_tauc.Rd
index c374947..cd451e9 100644
--- a/man/glmnet_validate_tauc.Rd
+++ b/man/glmnet_validate_tauc.Rd
@@ -13,7 +13,8 @@ glmnet_validate_tauc(
   lambda,
   pen.factor,
   tauc.type,
-  tauc.time
+  tauc.time,
+  cox.ties
 )
 }
 \value{
diff --git a/man/validate.Rd b/man/validate.Rd
index 0dc7c81..7ec9b24 100644
--- a/man/validate.Rd
+++ b/man/validate.Rd
@@ -22,6 +22,7 @@ validate(
   rep.times = NULL,
   tauc.type = c("CD", "SZ", "UNO"),
   tauc.time,
+  cox.ties = c("breslow", "efron"),
   seed = 1001,
   trace = TRUE
 )
@@ -79,6 +80,8 @@ Including \code{"CD"} proposed by Chambless and Diao (2006).,
 \item{tauc.time}{Numeric vector. Time points at which to evaluate
 the time-dependent AUC.}
 
+\item{cox.ties}{Cox tie-handling method for glmnet model refits.}
+
 \item{seed}{A random seed for resampling.}
 
 \item{trace}{Logical. Output the validation progress or not.