Oncology Clinical Trials: Difference Between Log-Rank Test and Cox Proportional Hazards (Cox PH) Model

 

Both the Log-Rank Test and the Cox Proportional Hazards (Cox PH) Model are used in survival analysis to compare survival times between groups, but they have key differences in methodology, assumptions, and applications.

1. Log-Rank Test

Purpose:

  • Compares two or more survival curves (e.g., treatment vs. control) to determine if there is a statistically significant difference in survival times.

Methodology:

  • It is a non-parametric test based on comparing the observed vs. expected number of events (e.g., deaths, progression) at each time point.
  • Uses a chi-square test statistic to determine significance.

Key Assumptions:
✅ Proportional hazards assumption is NOT required.
✅ Works well when the hazard ratio (HR) is constant over time.
❌ Cannot adjust for covariates (e.g., age, sex, biomarkers).

Example Interpretation:

  • p < 0.05: There is a significant difference between survival curves.
  • p ≥ 0.05: No significant difference detected.

2. Cox Proportional Hazards (Cox PH) Model

Purpose:

  • Estimates the hazard ratio (HR) and quantifies the effect of multiple covariates (e.g., treatment, age, biomarkers) on survival.

Methodology:

  • It is a semi-parametric model that estimates the hazard function: h(t∣X)=h0(t)exp⁡(β1X1+β2X2+...+βpXp)h(t | X) = h_0(t) \exp(\beta_1 X_1 + \beta_2 X_2 + ... + \beta_p X_p)
  • Unlike the log-rank test, it provides an adjusted hazard ratio for each covariate.

Key Assumptions:
✅ Assumes the proportional hazards (PH) assumption, meaning the relative risk (HR) is constant over time.
✅ Adjusts for multiple covariates (e.g., treatment, age, sex).
❌ If the PH assumption is violated, results can be biased.

Example Interpretation:

  • HR = 0.58 (95% CI: 0.49–0.70, p < 0.001) → The treatment reduces the risk by 42%, and the result is statistically significant.
  • HR > 1 → Covariate increases risk.

Key Differences

FeatureLog-Rank TestCox PH Model
PurposeCompares survival curvesEstimates hazard ratios (HR)
Type of AnalysisNon-parametricSemi-parametric
Hazard Ratio (HR)❌ Not provided✅ Provided
Adjusts for Covariates❌ No✅ Yes
Proportional Hazards Assumption❌ Not required✅ Required
Interpretationp-value for survival curve differenceHR for each covariate
Best Use CaseComparing two survival distributionsExamining effect of multiple risk factors

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