Using Bayes factors for testing hypotheses about intervention effectiveness in addictions research

Abstract

Background and aims: It has been proposed that more use should be made of Bayes factors in hypothesis testing in addiction research. Bayes factors are the ratios of the likelihood of a specified hypothesis (e.g. an intervention effect within a given range) to another hypothesis (e.g. no effect). They are particularly important for differentiating lack of strong evidence for an effect and evidence for lack of an effect. This paper reviewed randomized trials reported in Addiction between January and June 2013 to assess how far Bayes factors might improve the interpretation of the data.

Methods: Seventy-five effect sizes and their standard errors were extracted from 12 trials. Seventy-three per cent (n = 55) of these were non-significant (i.e. P > 0.05). For each non-significant finding a Bayes factor was calculated using a population effect derived from previous research. In sensitivity analyses, a further two Bayes factors were calculated assuming clinically meaningful and plausible ranges around this population effect.

Results: Twenty per cent (n = 11) of the non-significant Bayes factors were < ⅓ and 3.6% (n = 2) were > 3. The other 76.4% (n = 42) of Bayes factors were between ⅓ and 3. Of these, 26 were in the direction of there being an effect (Bayes factor > 1 and < 3); 12 tended to favour the hypothesis of no effect (Bayes factor < 1 and > ⅓); and for four there was no evidence either way (Bayes factor = 1). In sensitivity analyses, 13.3% of Bayes Factors were < ⅓ (n = 20), 62.7% (n = 94) were between ⅓ and 3 and 24.0% (n = 36) were > 3, showing good concordance with the main results.

Conclusions: Use of Bayes factors when analysing data from randomized trials of interventions in addiction research can provide important information that would lead to more precise conclusions than are obtained typically using currently prevailing methods.

Keywords: Addiction; Bayes factors; Bayesian; RCT; hypothesis testing; non-significant.