Introduction to Bayesian statistics: a practical framework for clinical pharmacists.

OBJECTIVES

Most pharmaceutical investigations have relied on p values to infer conclusions from their study findings. Central to this paradigm is the concept of null hypothesis significance testing. This approach is however fraught with overuse and misinterpretations. Several alternatives have already been proposed, yet uptake remains low. In this study, we aimed to discuss the pitfalls of p value-based testing and to provide readers with the basics to apply Bayesian statistics.

METHODS

Jeffreys's Amazing Statistical Package (JASP) was used to evaluate the effect of a clinical pharmacy (CP) intervention (opposed to usual care) on the number of emergency department (ED) visits without hospital admission. Basic Bayesian terminology was explained and compared with classical p value-based testing. In the study example, a Cauchy prior distribution was used to determine the effect size with a scale parameter r=0.707 at location=0 and Bayes factors (BF) were subsequently estimated. A robustness analysis was then performed to visualise the impact of different r values on the BF value.

RESULTS

A BF of 4.082 was determined, indicating that the observed data were about four times more likely to occur under the alternative hypothesis that the CP intervention was effective. The median effect size of the CP intervention on ED visits was found to be 0.337 with a 95% credible interval of 0.074 to 0.635. A robustness check was performed and all BF values were in favour of the CP intervention.

CONCLUSION

Bayesian inference can be an important addition to the statistical armamentarium of pharmacists, who should become more acquainted with the basic terminology and rationale of such testing. To prove our point, Jeffreys' approach was applied to a CP study example, using an easy-to-use software program JASP.