On null hypotheses in survival analysis

TL;DR

This paper introduces a flexible framework for testing a variety of null hypotheses in survival analysis by leveraging differential equations, enabling more relevant and interpretable tests beyond traditional hazard comparisons.

Contribution

The authors propose a generic method to define test statistics for diverse survival hypotheses using differential equations, enhancing flexibility and interpretability in survival analysis.

Findings

Simulations show good performance of the proposed tests across scenarios.

Application to colon cancer data demonstrates practical utility.

The method allows testing hypotheses beyond hazards, improving interpretability.

Abstract

The conventional nonparametric tests in survival analysis, such as the log-rank test, assess the null hypothesis that the hazards are equal at all times. However, hazards are hard to interpret causally, and other null hypotheses are more relevant in many scenarios with survival outcomes. To allow for a wider range of null hypotheses, we present a generic approach to define test statistics. This approach utilizes the fact that a wide range of common parameters in survival analysis can be expressed as solutions of differential equations. Thereby we can test hypotheses based on survival parameters that solve differential equations driven by cumulative hazards, and it is easy to implement the tests on a computer. We present simulations, suggesting that our tests perform well for several hypotheses in a range of scenarios. Finally, we use our tests to evaluate the effect of adjuvant chemotherapies in patients with colon cancer, using data from a randomised controlled trial.