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Reference curve sampling variability in one-sample log-rank tests.

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Summary
This summary is machine-generated.

The one-sample log-rank test inflates Type I error rates in clinical trials by ignoring reference survival curve sampling error. This study derives the test statistic's actual distribution, accounting for this variability.

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Area of Science:

  • Biostatistics
  • Clinical Trial Design
  • Survival Analysis

Background:

  • The one-sample log-rank test is standard for single-arm Phase II trials with time-to-event outcomes.
  • It compares patient survival against a reference curve, often from historical data.
  • Crucially, it assumes the reference curve is known, disregarding its inherent sampling error.

Purpose of the Study:

  • To investigate the Type I error rate inflation caused by ignoring reference curve sampling variability.
  • To derive the true distribution of the one-sample log-rank test statistic when this variability is considered.
  • To provide a method for estimating the underestimation factor of the test statistic's variance.

Main Methods:

  • Analytical derivations of the one-sample log-rank test statistic's distribution.
  • Monte Carlo simulations to assess Type I error rate inflation.
  • Development of a consistent estimator for the variance underestimation factor.
  • Case study utilizing real-world data for practical demonstration.

Main Results:

  • Ignoring the sampling variability of reference survival curves leads to inflated Type I error rates.
  • The actual distribution of the one-sample log-rank test statistic was derived, accounting for reference curve uncertainty.
  • A method was established to quantify the extent to which the test statistic's variance is underestimated.

Conclusions:

  • The assumption of a known reference curve in the one-sample log-rank test is problematic.
  • Accounting for reference curve sampling error is essential for accurate Type I error control in clinical trials.
  • The findings provide a practical approach to estimate and manage error inflation during trial planning.