import matplotlib.pyplot as plt
import seaborn as sns
import pandas as pd
import numpy as np
from lifelines import KaplanMeierFitter
from lifelines.statistics import logrank_test生存曲线（Python）
Kaplan–Meier 估计从右删失的随访数据中读出随时间变化的生存概率，log-rank 检验比较两臂。生存曲线是临床研究的核心图形——肿瘤、移植、器械研究皆然——审稿人期望删失刻度、置信带与明确的检验方法。lifelines 提供估计器、置信带与检验。
示例
环境配置
- 系统要求：跨平台（Linux/MacOS/Windows）
- 编程语言：Python
- 依赖包：
matplotlib、seaborn、pandas、numpy、lifelines
数据准备
我们模拟每臂 60 名患者（Control、Treatment）的指数生存——中位 12 对 24 个月——管理删失在 10 到 72 个月之间均匀分布，随访足够长以使两臂中位生存均可估计。
np.random.seed(141)
n = 60
def simulate_arm(median):
true_time = np.random.exponential(median / np.log(2), n)
censor = np.random.uniform(10, 72, n)
return pd.DataFrame({
'Months': np.minimum(true_time, censor),
'Event': (true_time <= censor).astype(int),
})
surv = pd.concat([
simulate_arm(12).assign(Arm='Control'),
simulate_arm(24).assign(Arm='Treatment'),
], ignore_index=True)
lr = logrank_test(
surv.loc[surv.Arm == 'Control', 'Months'],
surv.loc[surv.Arm == 'Treatment', 'Months'],
event_observed_A=surv.loc[surv.Arm == 'Control', 'Event'],
event_observed_B=surv.loc[surv.Arm == 'Treatment', 'Event'])
arm_styles = {'Control': ('#457b9d', 'o'), 'Treatment': ('#e63946', 's')}可视化
带置信带的 Kaplan–Meier 曲线
plot_survival_function 绘制阶梯曲线、置信区间与删失刻度；每臂样本量应写入图注或图例。
fig, ax = plt.subplots(figsize=(6, 4.4))
kmf = KaplanMeierFitter()
for arm, (color, marker) in arm_styles.items():
sub = surv[surv.Arm == arm]
kmf.fit(sub.Months, sub.Event, label=f'{arm} (n={len(sub)})')
kmf.plot_survival_function(ax=ax, ci_show=True, ci_alpha=0.12,
color=color, marker=marker,
show_censors=True, censor_styles=dict(ms=5, alpha=0.7))
ax.axhline(0.5, color='0.6', linewidth=0.8, linestyle=':')
ax.set_ylim(0, 1.02)
ax.set_xlabel('Months since treatment')
ax.set_ylabel('Survival probability')
ax.legend(frameon=False, loc='lower left')
ax.spines[['top', 'right']].set_visible(False)
plt.tight_layout()
plt.show()
标注 Log-Rank 检验与中位生存
log-rank p 值与各臂中位生存是读者最关心的两个数字；放在图内，并把中位点标在 0.5 参考线上。
fig, ax = plt.subplots(figsize=(6, 4.4))
medians = {}
for arm, (color, marker) in arm_styles.items():
sub = surv[surv.Arm == arm]
kmf.fit(sub.Months, sub.Event, label=f'{arm} (n={len(sub)})')
kmf.plot_survival_function(ax=ax, ci_show=True, ci_alpha=0.12,
color=color, marker=marker,
show_censors=True, censor_styles=dict(ms=5, alpha=0.7))
medians[arm] = kmf.median_survival_time_
ax.plot([kmf.median_survival_time_], [0.5], marker=marker, color=color,
markersize=7, clip_on=False)
SUP = str.maketrans('0123456789', '⁰¹²³⁴⁵⁶⁷⁸⁹')
mantissa, exponent = f'{lr.p_value:.1e}'.split('e-')
ax.text(0.98, 0.96, f'Log-rank p = {mantissa} × 10⁻{exponent.translate(SUP)}',
transform=ax.transAxes, ha='right', va='top', fontsize=10)
ax.text(0.98, 0.88,
'Median: ' + ', '.join(f'{k} {v:.0f} mo' for k, v in medians.items()),
transform=ax.transAxes, ha='right', va='top', fontsize=9, color='0.3')
ax.axhline(0.5, color='0.6', linewidth=0.8, linestyle=':')
ax.set_ylim(0, 1.02)
ax.set_xlabel('Months since treatment')
ax.set_ylabel('Survival probability')
ax.legend(frameon=False, loc='lower left')
ax.spines[['top', 'right']].set_visible(False)
plt.tight_layout()
plt.show()
参考文献
- Kaplan, E. L., & Meier, P. (1958). Nonparametric Estimation from Incomplete Observations. Journal of the American Statistical Association, 53(282), 457-481.
- Davidson-Pilon, C. (2019). lifelines: survival analysis in Python. Journal of Open Source Software, 4(40), 1317.