Interim analyses

Interim Analyses - The Planned Peek

• Planned analysis of data in an ongoing RCT before the study's conclusion.
• Primary goal: To determine if the trial should be stopped early for:
  • Overwhelming efficacy
  • Futility (unlikely to show benefit)
  • Unexpected harm
• ⚠️ Problem: Each "peek" at the data increases the overall Type I error rate (false positive) if not adjusted.
• Solution: Use a pre-specified statistical "stopping rule" with alpha-spending functions to maintain the overall study-wide $α$ (usually < 0.05).

⭐ The O'Brien-Fleming boundary is a common, conservative method that requires a very low p-value for early stopping, preserving statistical power for the final analysis.

Stopping Boundaries - Guarding the Alpha

Repeatedly analyzing data during a trial inflates the overall Type I error rate (family-wise error rate), increasing the chance of a false-positive result. Stopping boundaries are pre-specified rules to control this risk.

• Formal Methods to Adjust Significance:
  • O'Brien-Fleming (OBF):
    • Very conservative early in the trial; requires an extremely low p-value to stop.
    • The significance boundary becomes less stringent as more data is collected.
    • Preserves statistical power and the final analysis uses an alpha level very close to the nominal 0.05.
    • 📌 O'Brien-Fleming = Oh Boy, Far to go! (Hard to stop early).
  • Pocock:
    • Uses the same, constant significance level (e.g., p < 0.015) at each interim analysis.
    • "Spends" alpha equally at each look, making it easier to stop early compared to OBF.

⭐ The O'Brien-Fleming method is most common for clinical trials because its early conservatism prevents premature termination based on transient effects, preserving overall trial power and integrity.

Trial Adjustments - The Ripple Effect

• Interim analyses risk ↑ Type I error (false positives) from repeated data "peeking." The total trial alpha (e.g., 0.05) must be "spent" across looks.
• Alpha-spending functions adjust significance boundaries:
  • O'Brien-Fleming: Very conservative early on; preserves power.
  • Pocock: Constant p-value boundary for each look.
  • Haybittle-Peto Rule: Use a strict interim $p < \textbf{0.001}$ and the original final $p < \textbf{0.05}$.
• Other changes (e.g., sample size re-estimation) can be made but risk introducing bias.

⭐ Each data "peek" is another roll of the dice, increasing the cumulative chance of a false-positive (Type I error) if the significance threshold isn't adjusted.

High‑Yield Points - ⚡ Biggest Takeaways

• Interim analyses are performed during an RCT to monitor for efficacy, futility, or harm.
• Requires an independent Data and Safety Monitoring Board (DSMB) to review unblinded data.
• Uses pre-specified stopping boundaries to guide decisions on trial continuation or termination.
• Multiple analyses increase the risk of Type I error (false positives).
• Statistical adjustments, like alpha-spending functions, are used to maintain the overall p-value < 0.05.
• Early stopping for benefit is a major ethical consideration.