Time-to-event analysis

Time-to-Event Analysis - The Waiting Game

• Analyzes time until an event (e.g., death, disease remission). Key feature is handling censored data-when the event is not observed (e.g., patient lost to follow-up, study ends).
• Kaplan-Meier Curve:
  • Stepwise curve showing survival probability over time.
  • Drops = events; horizontal lines = no events.
  • Compares curves with the Log-rank test (p < 0.05 is significant).
• Cox Proportional Hazards Model:
  • Determines effects of variables on survival.
  • Calculates Hazard Ratio (HR):
    • HR > 1: ↑ risk of event.
    • HR < 1: ↓ risk of event (protective).

⭐ The Cox model's core assumption is proportional hazards: the hazard ratio between groups must remain constant throughout the study period.

Kaplan-Meier Curves - Survival Steppers

• A graphical method of displaying survival data over time. The y-axis shows the estimated probability of survival, and the x-axis shows time.
• The curve is a series of horizontal steps. Each downward step represents an event (e.g., death).
• Censored data are subjects lost to follow-up or for whom the study ends. They are indicated by small tick marks on the curve and are crucial for the analysis.

• Allows for the comparison of survival between different groups (e.g., treatment vs. placebo).

⭐ The log-rank test is the statistical test used to compare Kaplan-Meier curves. A p-value < 0.05 indicates a significant difference in survival between the groups.

Hazard Ratio & Cox Model - The Risk Race

• Hazard Ratio (HR): The primary measure in survival analysis. It represents the instantaneous risk of an event (e.g., death) in the intervention group relative to the control group at any given time.
  • HR = 1: No difference in hazard.
  • HR > 1: Increased hazard in the intervention group.
  • HR < 1: Decreased hazard (protective effect) in the intervention group.
• Cox Proportional Hazards Model: A regression method to investigate the effect of several variables on the time to an event.
  • Calculates an adjusted HR for each predictor, controlling for others.
  • Key assumption: The hazards are proportional, meaning the ratio of hazards between groups is constant over time.

⭐ On a Kaplan-Meier plot, if the survival curves for two groups cross, the proportional hazards assumption is violated, and a standard Cox model is inappropriate.

Assumptions & Censoring - The Fine Print

• Proportional Hazards Assumption: The effect of a predictor on hazard is constant over time. The Hazard Ratio (HR) remains stable throughout the study period.
• Censoring: Subjects are observed for a limited time; their event time is incomplete.
  • Right-Censoring: Most common type. The event has not occurred by the study's end, or the subject is lost to follow-up.
  • Key Principle: Censoring must be non-informative; the reason for censoring is unrelated to the event risk.

⭐ Non-Informative Censoring: A patient lost to follow-up after moving is non-informative. A patient dropping out due to severe side effects of the drug being studied is informative and biases results.

High‑Yield Points - ⚡ Biggest Takeaways

• Time-to-event (survival) analysis is a key method for cohort studies.
• It tracks time until an event (e.g., death, disease) occurs, accounting for censored data (e.g., loss to follow-up).
• Kaplan-Meier curves visually represent survival probability; steeper drops mean worse outcomes.
• Use the log-rank test to compare survival curves between different groups.
• The Hazard Ratio (HR) represents the instantaneous event risk; HR > 1 indicates increased risk.