Bio Machine Learning Survival Analysis

Version Compatibility

Reference examples tested with: matplotlib 3.8+, pandas 2.2+

Before using code patterns, verify installed versions match. If versions differ:

• Python: pip show <package> then help(module.function) to check signatures

If code throws ImportError, AttributeError, or TypeError, introspect the installed package and adapt the example to match the actual API rather than retrying.

Survival Prediction with lifelines

"Analyze patient survival data" → Estimate survival curves (Kaplan-Meier), compare groups (log-rank test), and model time-to-event outcomes with Cox proportional hazards regression.

• Python: lifelines.KaplanMeierFitter(), lifelines.CoxPHFitter()

Kaplan-Meier Curves

Goal: Estimate and visualize the survival probability function from time-to-event data.

Approach: Fit a nonparametric Kaplan-Meier estimator to censored survival data and plot the step function.

from lifelines import KaplanMeierFitter
import matplotlib.pyplot as plt

kmf = KaplanMeierFitter()

# T: time to event or censoring
# E: event indicator (1=event occurred, 0=censored)
kmf.fit(T, event_observed=E)

# Plot survival curve
kmf.plot_survival_function()
plt.xlabel('Time (months)')
plt.ylabel('Survival probability')
plt.savefig('km_curve.png', dpi=150)

Compare Groups with Log-Rank Test

Goal: Test whether survival distributions differ significantly between risk groups.

Approach: Fit separate Kaplan-Meier curves per group, overlay them, and apply a log-rank test for statistical comparison.

from lifelines import KaplanMeierFitter
from lifelines.statistics import logrank_test
import matplotlib.pyplot as plt

fig, ax = plt.subplots(figsize=(8, 6))

for group, color in zip(['high', 'low'], ['red', 'blue']):
    mask = df['risk_group'] == group
    kmf = KaplanMeierFitter()
    kmf.fit(df.loc[mask, 'time'], event_observed=df.loc[mask, 'event'], label=group)
    kmf.plot_survival_function(ax=ax, color=color)

# Log-rank test
high = df[df['risk_group'] == 'high']
low = df[df['risk_group'] == 'low']
results = logrank_test(high['time'], low['time'], event_observed_A=high['event'], event_observed_B=low['event'])
print(f'Log-rank p-value: {results.p_value:.4e}')

ax.set_xlabel('Time (months)')
ax.set_ylabel('Survival probability')
ax.set_title(f'Log-rank p = {results.p_value:.4e}')
plt.savefig('km_comparison.png', dpi=150)

Cox Proportional Hazards Regression

Goal: Model the effect of covariates on survival time using a semi-parametric hazard model.

Approach: Fit a Cox PH model to extract hazard ratios, confidence intervals, and a concordance index for predictive accuracy.

from lifelines import CoxPHFitter

# Prepare data: must have 'time' and 'event' columns
# Include covariates as additional columns
cph = CoxPHFitter()
cph.fit(df, duration_col='time', event_col='event')

# Summary with hazard ratios
cph.print_summary()

# Get hazard ratios as DataFrame
hr = cph.summary[['exp(coef)', 'exp(coef) lower 95%', 'exp(coef) upper 95%', 'p']]
print(hr)

# Concordance index (c-index): 0.5=random, 1.0=perfect
print(f'C-index: {cph.concordance_index_:.3f}')

Multivariate Cox Model

Goal: Assess the independent prognostic value of clinical and molecular features in a single model.

Approach: Combine clinical covariates and gene expression values into a regularized Cox model to identify independently prognostic variables.

from lifelines import CoxPHFitter
import pandas as pd

# Combine clinical and omics features
cox_df = pd.DataFrame({
    'time': meta['survival_months'],
    'event': meta['vital_status'],
    'age': meta['age'],
    'stage': meta['stage_numeric'],
    'GENE1': expr.loc['GENE1'],
    'GENE2': expr.loc['GENE2']
})

cph = CoxPHFitter(penalizer=0.1)  # L2 regularization for stability
cph.fit(cox_df, duration_col='time', event_col='event')
cph.print_summary()

Predict Risk Scores

Goal: Stratify patients into risk groups based on a fitted Cox model.

Approach: Compute partial hazard scores from model coefficients and split at the median to define high/low risk groups for downstream KM visualization.

# Partial hazard (risk score)
risk_scores = cph.predict_partial_hazard(cox_df)

# Median risk split for KM plot
df['risk_group'] = (risk_scores > risk_scores.median()).map({True: 'high', False: 'low'})

Check Proportional Hazards Assumption

Goal: Verify that the proportional hazards assumption holds for all covariates.

Approach: Run the built-in Schoenfeld residual tests and inspect diagnostic plots for time-varying effects.

# Test PH assumption
cph.check_assumptions(df, p_value_threshold=0.05, show_plots=True)

Survival at Specific Time

Goal: Extract survival probability estimates at clinically meaningful time points.

Approach: Query the fitted Kaplan-Meier survival function at specific durations and report the median survival time.

# Survival probability at specific times
survival_probs = kmf.survival_function_at_times([12, 24, 60])
print(survival_probs)

# Median survival
print(f'Median survival: {kmf.median_survival_time_:.1f}')

Feature Selection for Survival

Goal: Screen thousands of genes to identify those significantly associated with patient survival.

Approach: Fit univariate Cox models for each gene, extract hazard ratios and p-values, and rank candidates for multivariate modeling.

from lifelines import CoxPHFitter
import pandas as pd

# Univariate screening
results = []
for gene in expr.index[:1000]:
    cox_df = pd.DataFrame({
        'time': meta['survival_months'],
        'event': meta['vital_status'],
        'gene': expr.loc[gene]
    })
    cph = CoxPHFitter()
    cph.fit(cox_df, duration_col='time', event_col='event')
    results.append({
        'gene': gene,
        'hr': cph.hazard_ratios_['gene'],
        'p': cph.summary.loc['gene', 'p']
    })

results_df = pd.DataFrame(results)
sig_genes = results_df[results_df['p'] < 0.05].sort_values('p')

Related Skills

• clinical-databases/variant-prioritization - Clinical variant interpretation
• differential-expression/de-results - Find DE genes for survival model
• machine-learning/biomarker-discovery - Select predictive features