# Two-sample survival tests based on control arm summary statistics

## TL;DR

This paper introduces a new survival test that accounts for uncertainty in historical survival data when comparing patient outcomes.

## Contribution

A novel survival test is proposed that handles sampling error in reference survival curves without needing full historical data.

## Key findings

- The new test maintains correct type I error rates by accounting for variability in the reference curve.
- Sample size formulas and simulation studies demonstrate the test's validity and performance.
- The test is suitable for scenarios where historical individual patient data is unavailable.

## Abstract

The one-sample log-rank test is the preferred method for analysing the outcome of single-arm survival trials. It compares the survival distribution of patients with a prefixed reference survival curve that usually represents the expected outcome under standard of care. However, classical one-sample log-rank tests assume that the reference curve is known, ignoring that it is frequently estimated from historical data and therefore susceptible to sampling error. Neglecting the variability of the reference curve can lead to an inflated type I error rate, as shown in a previous paper. Here, we propose a new survival test that allows to account for the sampling error of the reference curve without knowledge of the full underlying historical survival time data. Our new test allows to perform a valid historical comparison of patient survival times when only a historical survival curve rather than the full historic data is available. It thus applies in settings where the two-sample log-rank test is not applicable as method of choice due to non-availability of historic individual patient survival time data. We develop sample size calculation formulas, give an example application and study the performance of the new test in a simulation study.