4 Standard KM + Cox

When the diagnostic engine detects no competing risks, recurrent events, or time-varying exposures, the pipeline routes to the standard Kaplan-Meier and Cox regression module. This is the most common analysis path.

4.1 When to Use

This module is appropriate when:

There is a single event type (e.g., death or relapse)
Each subject contributes one observation
Exposure/treatment is fixed at baseline
No significant clustering or left truncation

4.2 Script Pipeline

Script	Purpose
`01_km_curves.R`	Kaplan-Meier survival curves with `survfit`
`02_logrank_tests.R`	Log-rank and stratified log-rank tests
`03_cox_ph.R`	Univariable and multivariable Cox PH models
`04_ph_diagnostics.R`	Proportional hazards assumption testing
`05_model_diagnostics.R`	Residual plots, influential observations
`06_sensitivity.R`	Subgroup analyses and robustness checks

4.3 Kaplan-Meier Curves

The first script generates KM curves using survminer::ggsurvplot:

library(survival)
library(survminer)

fit <- survfit(Surv(time, status) ~ group, data = df)

ggsurvplot(fit,
  pval = TRUE,
  risk.table = TRUE,
  palette = "lancet",
  xlab = "Time (months)",
  ylab = "Survival probability"
)

Colour Palettes

The pipeline uses ggsci::scale_color_lancet() by default for journal-appropriate, colorblind-safe palettes.

4.4 Cox Proportional Hazards

cox_fit <- coxph(Surv(time, status) ~ group + age + stage, data = df)
summary(cox_fit)

Multivariable models are built stepwise, with covariates selected based on clinical relevance and the DAG, not p-value-based selection.

4.5 PH Assumption Checking

Script 04_ph_diagnostics.R tests the proportional hazards assumption using Schoenfeld residuals:

ph_test <- cox.zph(cox_fit)
print(ph_test)
plot(ph_test)

Violated PH Assumption

If the global test is significant (p < 0.05), consider stratification, time-varying coefficients, or restricted mean survival time (RMST) as alternatives.

4.6 Running the Module

make analyze-standard PROJECT=my-study

This executes all six scripts in order, writing results to projects/my-study/03_analysis/.

4.7 Demo: Standard Survival (Scenario 1)

N=500, 2-arm simulated RCT with HR approximately 0.70.

4.7.1 Kaplan-Meier Curves

Figure 4.1: KM survival curves with risk table

4.7.2 Cox Proportional Hazards

Figure 4.2: Forest plot of adjusted hazard ratios

The multivariable Cox model found a significant treatment effect:

Term	HR	95% CI	p-value
Treatment (vs control)	0.786	0.626–0.987	0.038
Age (per year)	1.006	0.996–1.016	0.248
Sex (M vs F)	0.954	0.761–1.198	0.687

Treatment reduced the hazard by approximately 21% (HR = 0.79, 95% CI: 0.63–0.99, p = 0.038).

4.7.3 PH Assumption Check

Figure 4.3: Schoenfeld residuals for treatment arm

The Schoenfeld residual test confirmed the proportional hazards assumption holds for all covariates:

Variable	Chi-sq	df	p-value
Arm	1.367	1	0.242
Age	0.477	1	0.490
Sex	0.107	1	0.744
GLOBAL	1.896	3	0.594

The global test is non-significant (p = 0.594), confirming the PH assumption is reasonable for this dataset.

4.7.4 Sensitivity: Bootstrap

Figure 4.4: Bootstrap distribution of HR