stat-survival-analysis

Skill: Survival Analysis

Use When

• User wants to analyze time-to-event data (overall survival, disease-free survival, time to relapse)
• User wants to compare survival curves between two or more groups (e.g., high vs. low expression, treated vs. untreated)
• User wants to identify predictors of survival using multivariable Cox regression
• Use cases: clinical trial outcomes, patient survival, cancer prognosis

Inputs

• Required:
  • Data table (CSV or TSV) with: time-to-event column (numeric), event indicator column (1 = event occurred, 0 = censored)
  • Time column name
  • Event column name
• Optional:
  • Group column name for Kaplan-Meier comparison and log-rank test (if omitted: single KM curve)
  • Covariate column names for Cox regression (if provided: runs multivariable Cox model)
  • Time unit label (default: days)
  • Output directory (default: ./survival_output)

Workflow

1. Read data; validate that time column is non-negative numeric and event column is binary (0/1).
2. Compute Kaplan-Meier survival estimate for each group (or overall if no group column).
3. Report median survival time and 95% confidence interval (Greenwood formula) per group.
4. If multiple groups: run log-rank test (Mantel-Cox); report chi-square statistic and p-value.
5. Generate Kaplan-Meier plot with confidence intervals, censoring tick marks, and at-risk table.
6. If covariate columns provided: a. Fit Cox proportional hazards model. b. Test proportional hazards assumption (Schoenfeld residuals). c. Report for each covariate: hazard ratio, 95% CI, z-statistic, p-value. d. Generate forest plot of hazard ratios.
7. Write results and plots (PDF) to output directory.
8. Save the executable analysis script (analysis_code.py or analysis_code.R) and software version manifest (session_info.txt) used to produce results.

Output Contract

• KM table (TSV): time, survival_probability, ci_lower, ci_upper, n_at_risk, n_events, group
• Median survival table (TSV): group, median_survival, ci_lower, ci_upper
• Log-rank test result (TSV): chi_square, df, p_value (if multiple groups)
• Cox regression table (TSV): covariate, hazard_ratio, ci_lower, ci_upper, z_statistic, p_value (if covariates provided)
• Kaplan-Meier plot with at-risk table (PDF)
• Forest plot (PDF, Cox only)
• Reproducibility artifacts: analysis_code.py or analysis_code.R, plus session_info.txt

Limits

• Requires accurate censoring information; informative censoring (censored because of outcome-related reasons) biases results.
• Cox model assumes proportional hazards — verify with Schoenfeld residuals test (p > 0.05 for each covariate).
• Log-rank test has low power when hazard ratio changes over time (crossing survival curves).
• Common failure: event column containing values other than 0/1 (e.g., 2 for competing events) — binarize or use competing risks models.