From 9be518a0d95b9e2af42c8f4b5eb439e6d69e6eaa Mon Sep 17 00:00:00 2001
From: CamDavidsonPilon <cam.davidson.pilon@gmail.com>
Date: Wed, 17 Jun 2020 11:12:56 -0400
Subject: [PATCH] adding survival calibration example

---
 examples/survival_calibration.py | 76 ++++++++++++++++++++++++++++++++
 1 file changed, 76 insertions(+)
 create mode 100644 examples/survival_calibration.py

diff --git a/examples/survival_calibration.py b/examples/survival_calibration.py
new file mode 100644
index 000000000..90500eba8
--- /dev/null
+++ b/examples/survival_calibration.py
@@ -0,0 +1,76 @@
+# -*- coding: utf-8 -*-
+"""
+Smoothed calibration curves for time-to-event models
+
+https://onlinelibrary.wiley.com/doi/full/10.1002/sim.8570
+
+"""
+
+
+def ccl(p):
+    return np.log(-np.log(1 - p))
+
+
+from lifelines.datasets import load_regression_dataset
+
+df = load_regression_dataset()
+T = "T"
+E = "E"
+
+T_0 = 15
+
+
+# fit original model and make survival predictions
+cph = CoxPHFitter(baseline_estimation_method="spline", n_baseline_knots=4).fit(df, T, E)
+predictions_at_T_0 = 1 - cph.predict_survival_function(df, times=[T_0]).T.squeeze()
+cll_predictions_at_T_0 = ccl(predictions_at_T_0)
+
+# create new dataset with the predictions
+prediction_df = pd.DataFrame({"ccl_at_%d" % T_0: cll_predictions_at_T_0, "constant": 1, "week": df[T], "arrest": df[E]})
+
+# fit new dataset to flexible spline model
+# this new model connects prediction probabilities and actual survival. It should be very flexible, almost to the point of overfitting. It's goal is just to smooth out the data!
+
+regressors = {
+    "beta_": ["ccl_at_%d" % T_0],
+    "gamma0_": ["constant"],
+    "gamma1_": ["constant"],
+    "gamma2_": ["constant"],
+    "gamma3_": ["constant"],
+}
+# this model is from examples/royson_crowther_clements_splines.py
+crc = CRCSplineFitter(4).fit(prediction_df, "week", "arrest", regressors=regressors)
+
+# predict new model at values 0 to 1, but remember to ccl it!
+x = np.linspace(np.clip(predictions_at_T_0.min() - 0.05, 0, 1), np.clip(predictions_at_T_0.max() + 0.05, 0, 1), 100)
+y = 1 - crc.predict_survival_function(pd.DataFrame({"ccl_at_%d" % T_0: ccl(x), "constant": 1}), times=[T_0]).T.squeeze()
+
+
+# plot our results
+fig, ax = plt.subplots()
+ax.set_title("Smoothed calibration curve of predicted vs observed probabilities")
+plt.ylim(x[0], x[-1])
+plt.xlim(x[0], x[-1])
+
+
+color = "tab:red"
+ax.plot(x, y, label="smoothed calibration curve", color=color)
+ax.set_xlabel("Predicted probability of \nt=%d mortality" % T_0)
+ax.set_ylabel("Observed probability of \nt=%d mortality" % T_0, color=color)
+ax.tick_params(axis="y", labelcolor=color)
+
+# plot x=y line
+ax.plot(x, x, c="k", ls="--")
+
+
+# plot histogram of our original predictions
+color = "tab:blue"
+twin_ax = ax.twinx()
+twin_ax.set_ylabel("histogram of \npredicted probabilities", color=color)  # we already handled the x-label with ax1
+twin_ax.tick_params(axis="y", labelcolor=color)
+
+
+twin_ax.hist(predictions_at_T_0, alpha=0.3, bins="sqrt", color=color)
+
+ax.legend()
+plt.tight_layout()