Time-to-event analysis

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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).

Kaplan-Meier curve: Atezolizumab vs. Durvalumab

⭐ 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.

Kaplan-Meier curve: Progression-free survival

  • 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.

Kaplan-Meier curves: survival free from primary endpoint

Assumptions & Censoring - The Fine Print

Kaplan-Meier curve showing right-censoring by class

  • 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.

Practice Questions: Time-to-event analysis

Test your understanding with these related questions

A researcher is trying to determine whether a newly discovered substance X can be useful in promoting wound healing after surgery. She conducts this study by enrolling the next 100 patients that will be undergoing this surgery and separating them into 2 groups. She decides which patient will be in which group by using a random number generator. Subsequently, she prepares 1 set of syringes with the novel substance X and 1 set of syringes with a saline control. Both of these sets of syringes are unlabeled and the substances inside cannot be distinguished. She gives the surgeon performing the surgery 1 of the syringes and does not inform him nor the patient which syringe was used. After the study is complete, she analyzes all the data that was collected and performs statistical analysis. This study most likely provides which level of evidence for use of substance X?

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Flashcards: Time-to-event analysis

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_____ studies are useful for calculating relative risk (RR)

TAP TO REVEAL ANSWER

_____ studies are useful for calculating relative risk (RR)

Cohort

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