A Likelihood-based Alternative to Null Hypothesis Significance Testing

TL;DR

This paper introduces a likelihood-based method for interpreting research results, providing a more logical alternative to traditional P-value significance testing, and demonstrates its application on high-profile clinical trials.

Contribution

It proposes a novel likelihood ratio approach to assess clinical significance, replacing null hypothesis significance testing with a more intuitive metric called the S-value.

Findings

The likelihood ratio test yields a clear measure of clinical significance.

Application to high-profile trials illustrates the method's practical utility.

The approach offers advantages over traditional P-value based methods.

Abstract

The logical and practical difficulties associated with research interpretation using P values and null hypothesis significance testing have been extensively documented. This paper describes an alternative, likelihood-based approach to P-value interpretation. The P-value and sample size of a research study are used to derive a likelihood function with a single parameter, the estimated population effect size, and the method of maximum likelihood estimation is used to calculate the most likely effect size. Comparison of the likelihood of the most likely effect size and the likelihood of the minimum clinically significant effect size using the likelihood ratio test yields the clinical significance support level (or S-value), a logical and easily understood metric of research evidence. This clinical significance likelihood approach has distinct advantages over null hypothesis significance testing. As motivating examples we demonstrate the calculation and interpretation of S-values applied to two recent widely publicised trials, WOMAN from the Lancet and RELIEF from the New England Journal of Medicine.