Increasing the Positive Predictive Value in RCTs: Lessons from Bayes’ Rule

In this chapter, we shall use Bayes’ rule to investigate the parameterisation of the positive predictive value (PPV) as a means of reviewing the possible management of this statistic within the context of null hypothesis significance testing (NHST). We shall also see how this rule can be supportive in seeking to circumvent the influence of the base rate fallacy and the fallacy of confusion of the inverse, through giving precedence to the PPV. This will enable us to consider the Bayesian approach to hypothesis testing, together with a few of the challenges which it presents. As we shall see, while reduction of the significance level, α, may seem to be a particularly promising approach to managing the PPV, this approach should not be perceived ipso facto as a remedy for a so-called replication crisis. Furthermore, in our interpretation of the PPV, we need to remain sensitive to the role of the statistical effect size and clinical significance in deciding whether to accept a statistically significant outcome in favour of an intervention as a positive result. While we shall acknowledge the limitations of the Bayesian approach to NHST, the gentle introduction to Bayesian statistics provided here may be of interest to educators seeking a primer for use with undergraduate medical students and students of other health professions within the constraints of a crowded curriculum.