diff --git a/lifelines/statistics.py b/lifelines/statistics.py
index 324b41b70..e1af4cc81 100644
--- a/lifelines/statistics.py
+++ b/lifelines/statistics.py
@@ -858,8 +858,8 @@ def _chisq_test_p_value(U, degrees_freedom) -> float:
 class TimeTransformers:
 
     TIME_TRANSFOMERS = {
-        # using cumsum is kinda hacky (but smart), should be np.argsort but I run into problems later.
-        "rank": lambda t, c, w: np.cumsum(c),
+        # Rank observed event times, averaging ties independently of row or stratum order.
+        "rank": lambda t, c, w: pd.Series(t).where(np.asarray(c, dtype=bool)).rank(method="average"),
         "identity": lambda t, c, w: t,
         "log": lambda t, c, w: np.log(t),
         "km": lambda t, c, w: (1 - KaplanMeierFitter().fit(t, c, weights=w).survival_function_.loc[t, "KM_estimate"]),
diff --git a/lifelines/tests/test_rank_time_invariance.py b/lifelines/tests/test_rank_time_invariance.py
new file mode 100644
index 000000000..1a0428758
--- /dev/null
+++ b/lifelines/tests/test_rank_time_invariance.py
@@ -0,0 +1,51 @@
+import numpy as np
+import pandas as pd
+import pytest
+
+from lifelines import CoxPHFitter
+from lifelines.datasets import load_lung
+from lifelines.statistics import TimeTransformers, proportional_hazard_test
+
+
+@pytest.mark.parametrize("as_series", [False, True])
+def test_rank_transform_uses_event_times_and_averages_ties(as_series):
+    times = np.array([4.0, 1.0, 2.0, 2.0, 3.0])
+    events = np.array([1, 1, 1, 1, 0], dtype=bool)
+    if as_series:
+        times = pd.Series(times, index=["e", "a", "c", "b", "d"])
+    result = TimeTransformers().get("rank")(times, events, np.ones(5))
+    np.testing.assert_allclose(np.asarray(result)[events], [4.0, 1.0, 2.5, 2.5])
+
+
+def test_rank_transform_preserves_ordered_untied_event_ranks():
+    times = pd.Series([1.0, 2.0, 3.0, 4.0, 5.0])
+    events = pd.Series([True, False, True, False, True])
+    result = TimeTransformers().get("rank")(times, events, np.ones(5))
+    np.testing.assert_array_equal(result[events], [1.0, 2.0, 3.0])
+
+
+def test_ph_rank_is_invariant_to_order_within_ties():
+    x = np.linspace(-2.0, 2.0, 400)
+    frame = pd.DataFrame({"T": np.repeat([1.0, 2.0, 3.0, 4.0, 5.0], len(x)), "E": 1, "x": np.tile(x, 5)})
+    results = []
+    for data in [frame, frame.sample(frac=1, random_state=19)]:
+        model = CoxPHFitter().fit(data, "T", "E")
+        assert model.params_["x"] == pytest.approx(0, abs=1e-12)
+        result = proportional_hazard_test(model, data)
+        results.append(result.summary.loc["x", "p"])
+    np.testing.assert_allclose(results, [1.0, 1.0], atol=1e-12)
+
+
+def test_ph_rank_is_invariant_to_stratum_labels():
+    frame = load_lung()[["time", "status", "age", "sex", "ph.ecog"]].dropna()
+    results = []
+    coefficients = []
+    for reverse in [False, True]:
+        data = frame.copy()
+        levels = data.pop("ph.ecog")
+        data["stratum"] = (3 - levels if reverse else levels).astype(str)
+        model = CoxPHFitter().fit(data, "time", "status", strata="stratum", formula="age + sex")
+        coefficients.append(model.params_.values)
+        results.append(proportional_hazard_test(model, data).summary["p"].values)
+    np.testing.assert_allclose(coefficients[0], coefficients[1], atol=1e-12)
+    np.testing.assert_allclose(results[0], results[1], atol=1e-12)