A Kaplan-Meier survival plot visualizes the probability of survival (or event-free time) over a time period using a step function. It is the standard method for estimating survival functions from time-to-event data, handling censored observations where the event has not yet occurred. The plot shows how survival probability decreases over time, with optional confidence intervals and comparison between groups.
""" anyplot.ai
survival-kaplan-meier: Kaplan-Meier Survival Plot
Library: bokeh 3.9.0 | Python 3.13.13
Quality: 90/100 | Updated: 2026-05-11
"""
import os
import time
from pathlib import Path
import numpy as np
from bokeh.io import output_file, save
from bokeh.models import ColumnDataSource, Span
from bokeh.plotting import figure
from selenium import webdriver
from selenium.webdriver.chrome.options import Options
# Theme tokens
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
TREATMENT_COLOR = "#009E73" # Okabe-Ito position 1 (brand green)
CONTROL_COLOR = "#C475FD" # Okabe-Ito position 2 (vermillion)
# Data - Simulated clinical trial with two treatment groups
np.random.seed(42)
# Treatment group (new drug) - better survival
n_treatment = 80
treatment_times = np.random.exponential(scale=24, size=n_treatment)
treatment_times = np.clip(treatment_times, 0.5, 36)
treatment_censored = np.random.binomial(1, 0.35, n_treatment)
treatment_events = 1 - treatment_censored
# Control group (standard care) - worse survival
n_control = 80
control_times = np.random.exponential(scale=16, size=n_control)
control_times = np.clip(control_times, 0.5, 36)
control_censored = np.random.binomial(1, 0.3, n_control)
control_events = 1 - control_censored
# Calculate Kaplan-Meier estimator
def compute_km(times, events):
"""Compute Kaplan-Meier survival curve with 95% confidence intervals."""
order = np.argsort(times)
times = times[order]
events = events[order]
unique_event_times = np.unique(times[events == 1])
survival = [1.0]
time_points = [0.0]
var_sum = 0
ci_lower = [1.0]
ci_upper = [1.0]
censored_times = []
censored_survival = []
for t in unique_event_times:
at_risk = np.sum(times >= t)
d = np.sum((times == t) & (events == 1))
if at_risk > 0:
s_prob = 1 - d / at_risk
survival.append(survival[-1] * s_prob)
time_points.append(t)
if at_risk > d:
var_sum += d / (at_risk * (at_risk - d))
se = np.sqrt(var_sum) if var_sum > 0 else 0
log_s = np.log(survival[-1]) if survival[-1] > 0 else -np.inf
ci_factor = 1.96 * se / abs(log_s) if log_s != 0 else 0
ci_lower.append(survival[-1] ** np.exp(ci_factor))
ci_upper.append(survival[-1] ** np.exp(-ci_factor))
# Find censored observation positions
for t, e in zip(times, events, strict=True):
if e == 0:
idx = np.searchsorted(time_points[1:], t, side="right")
if idx < len(survival):
censored_times.append(t)
censored_survival.append(survival[idx])
return (
np.array(time_points),
np.array(survival),
np.array(ci_lower),
np.array(ci_upper),
np.array(censored_times),
np.array(censored_survival),
)
t_time, t_surv, t_ci_low, t_ci_up, t_cens_t, t_cens_s = compute_km(treatment_times, treatment_events)
c_time, c_surv, c_ci_low, c_ci_up, c_cens_t, c_cens_s = compute_km(control_times, control_events)
# Convert to step functions
def to_steps(x, y):
"""Convert point data to step function."""
x_step = np.repeat(x, 2)[1:]
y_step = np.repeat(y, 2)[:-1]
return x_step, y_step
t_x_step, t_y_step = to_steps(t_time, t_surv)
c_x_step, c_y_step = to_steps(c_time, c_surv)
t_ci_low_x, t_ci_low_y = to_steps(t_time, t_ci_low)
t_ci_up_x, t_ci_up_y = to_steps(t_time, t_ci_up)
c_ci_low_x, c_ci_low_y = to_steps(c_time, c_ci_low)
c_ci_up_x, c_ci_up_y = to_steps(c_time, c_ci_up)
# Create figure
p = figure(
width=4800,
height=2700,
title="survival-kaplan-meier · bokeh · anyplot.ai",
x_axis_label="Time (months)",
y_axis_label="Survival Probability",
x_range=(0, 38),
y_range=(0, 1.05),
)
# Plot confidence interval bands
treatment_ci = ColumnDataSource(
data={"x": np.concatenate([t_ci_low_x, t_ci_up_x[::-1]]), "y": np.concatenate([t_ci_low_y, t_ci_up_y[::-1]])}
)
control_ci = ColumnDataSource(
data={"x": np.concatenate([c_ci_low_x, c_ci_up_x[::-1]]), "y": np.concatenate([c_ci_low_y, c_ci_up_y[::-1]])}
)
p.patch(x="x", y="y", source=treatment_ci, fill_color=TREATMENT_COLOR, fill_alpha=0.15, line_alpha=0)
p.patch(x="x", y="y", source=control_ci, fill_color=CONTROL_COLOR, fill_alpha=0.15, line_alpha=0)
# Plot survival curves
p.line(x=t_x_step, y=t_y_step, line_color=TREATMENT_COLOR, line_width=4, legend_label="Treatment (n=80)")
p.line(x=c_x_step, y=c_y_step, line_color=CONTROL_COLOR, line_width=4, legend_label="Control (n=80)")
# Plot censored observations as tick marks
if len(t_cens_t) > 0:
p.scatter(x=t_cens_t, y=t_cens_s, marker="dash", size=28, angle=1.5708, line_color=TREATMENT_COLOR, line_width=4)
if len(c_cens_t) > 0:
p.scatter(x=c_cens_t, y=c_cens_s, marker="dash", size=28, angle=1.5708, line_color=CONTROL_COLOR, line_width=4)
# Add median survival reference line
median_line = Span(location=0.5, dimension="width", line_color=INK_SOFT, line_width=3, line_dash="dashed")
p.add_layout(median_line)
# Style
p.background_fill_color = PAGE_BG
p.border_fill_color = PAGE_BG
p.outline_line_color = INK_SOFT
p.title.text_color = INK
p.title.text_font_size = "28pt"
p.xaxis.axis_label_text_color = INK
p.xaxis.axis_label_text_font_size = "22pt"
p.xaxis.major_label_text_color = INK_SOFT
p.xaxis.major_label_text_font_size = "18pt"
p.xaxis.axis_line_color = INK_SOFT
p.xaxis.major_tick_line_color = INK_SOFT
p.yaxis.axis_label_text_color = INK
p.yaxis.axis_label_text_font_size = "22pt"
p.yaxis.major_label_text_color = INK_SOFT
p.yaxis.major_label_text_font_size = "18pt"
p.yaxis.axis_line_color = INK_SOFT
p.yaxis.major_tick_line_color = INK_SOFT
p.xgrid.grid_line_color = INK
p.ygrid.grid_line_color = INK
p.xgrid.grid_line_alpha = 0.10
p.ygrid.grid_line_alpha = 0.10
p.legend.location = "bottom_left"
p.legend.label_text_color = INK_SOFT
p.legend.label_text_font_size = "20pt"
p.legend.background_fill_color = ELEVATED_BG
p.legend.border_line_color = INK_SOFT
# Save
output_file(f"plot-{THEME}.html")
save(p)
# Screenshot with headless Chrome
W, H = 4800, 2700
opts = Options()
for arg in (
"--headless=new",
"--no-sandbox",
"--disable-dev-shm-usage",
"--disable-gpu",
f"--window-size={W},{H}",
"--hide-scrollbars",
):
opts.add_argument(arg)
driver = webdriver.Chrome(options=opts)
driver.set_window_size(W, H)
driver.get(f"file://{Path(f'plot-{THEME}.html').resolve()}")
time.sleep(3)
driver.save_screenshot(f"plot-{THEME}.png")
driver.quit()
Part of Kaplan-Meier Survival Plot on anyplot.ai.