The Substitute for p-Values

An Electronic Screening and Brief Intervention for Hazardous and Harmful Drinking Among Swedish University Students: Reanalysis of Findings From a Randomized Controlled Trial Using a Bayesian Framework

Background

Due to a resurgent debate on the misuse of P values, the Journal of Medical Internet Research is hosting a standing theme issue inviting the reanalysis of (primarily digital health) trial data using a Bayesian framework. This first paper in this series focuses on an electronic screening and brief intervention (eSBI), targeting harmful and hazardous alcohol consumption, which student health care centers across Sweden have routinely administerd to all students during the past decade. The second Alcohol Email Assessment and Feedback Study Dismantling Effectiveness for University Students (AMADEUS-2) trial aimed to assess the effect of the eSBI on alcohol consumption among students who were harmful and hazardous drinkers. A two-arm randomized controlled trial design was employed, randomizing eligible participants to either a waiting list or direct access to an eSBI. Follow-up assessments were conducted 2 months after randomization. Subsequent analysis of the trial followed the conventional null hypothesis approach, and no statistical significance was found between groups at follow-up with respect to the number of standard drinks consumed weekly. However, in an unspecified sensitivity analysis, it was discovered that removing three potential outliers made the difference between the groups significant.

Objective

The objective of this study is to reperform the primary and sensitivity analysis of the AMADEUS-2 trial using a Bayesian framework and to compare the results with those of the original analysis.

Methods

The same regression models used in the original analysis were employed in this reanalysis (negative binomial regression). Model parameters were given uniform priors. Markov chain Monte Carlo was used for Bayesian inference, and posterior probabilities were calculated for prespecified thresholds of interest.

Results

Null hypothesis tests did not identify a statistically significant difference between the intervention and control groups, potentially due to a few extreme data points. The Bayesian analysis indicated a 93.6% probability that there was a difference in grams of alcohol consumed at follow-up between the intervention and control groups and a 71.5% probability that the incidence rate ratio was <0.96. Posterior probabilities increased when excluding three potential outliers, yet such post hoc analyses were not necessary to show the preference toward offering an eSBI to harmful and hazardous drinkers among university students.

Conclusions

The null hypothesis framework relies on point estimates of parameters. P values can therefore swing heavily, depending on a single or few data points alone, casting doubt on the value of the analysis. Bayesian analysis results in a distribution over parameter values and is therefore less sensitive to outliers and extreme values. Results from analyses of trials of interventions where small-to-modest effect sizes are expected can be more robust in a Bayesian framework, making this a potentially better approach for analyzing digital health research data.

Trial Registration

International Standard Randomized Controlled Trial Number (ISRCTN) 02335307; http://www.isrctn.com/ISRCTN02335307

Electronic Screening for Alcohol Use and Brief Intervention by Email for University Students: Reanalysis of Findings From a Randomized Controlled Trial Using a Bayesian Framework

BACKGROUND

Almost a decade ago, Sweden became the first country to implement a national system enabling student health care centers across all universities to routinely administer (via email) an electronic alcohol screening and brief intervention to their students. The Alcohol email assessment and feedback study dismantling effectiveness for university students (AMADEUS-1) trial aimed to assess the effect of the student health care centers' routine practices by exploiting the lack of any standard timing for the email invitation and by masking trial participation from students. The original analyses adopted the conventional null hypothesis framework, and the results were consistently in the expected direction. However, since for some tests the P values did not pass the conventional .05 threshold, some of the analyses were necessarily inconclusive.

OBJECTIVE

The outcomes of the AMADEUS-1 trial were derived from the first 3 items of the Alcohol Use Disorders Identification Test (AUDIT-C). The aim of this paper was to reanalyze the two primary outcomes of the AMADEUS-1 trial (AUDIT-C scores and prevalence of risky drinking), using the same models used in the original publication but applying a Bayesian inference framework and interpretation.

METHODS

The same regression models used in the original analysis were employed in this reanalysis (linear and logistic regression). Model parameters were given uniform priors. Markov chain Monte Carlo was used for Bayesian inference, and posterior probabilities were calculated for prespecified thresholds of interest.

RESULTS

Where the null hypothesis tests showed inconclusive results, the Bayesian analysis showed that offering an intervention at baseline was preferable compared to offering nothing. At follow-up, the probability of a lower AUDIT-C score among those who had been offered an intervention at baseline was greater than 95%, as was the case when comparing the prevalence of risky drinking.

CONCLUSIONS

The Bayesian analysis allows for a more consistent perspective of the data collected in the trial, since dichotomization of evidence is not looked for at some arbitrary threshold. Results are presented that represent the data collected in the trial rather than trying to make conclusions about the existence of a population effect. Thus, policy makers can think about the value of keeping the national system without having to navigate the treacherous landscape of statistical significance.

TRIAL REGISTRATION

ISRCTN Registry ISRCTN28328154; http://www.isrctn.com/ISRCTN28328154.

A Gentle Introduction to the Comparison Between Null Hypothesis Testing and Bayesian Analysis: Reanalysis of Two Randomized Controlled Trials

The debate on the use and misuse of P values has risen and fallen throughout their almost century-long existence in scientific discovery. Over the past few years, the debate has again received front-page attention, particularly through the public reminder by the American Statistical Association on how P values should be used and interpreted. At the core of the issue lies a fault in the way that scientific evidence is dichotomized and research is subsequently reported, and this fault is exacerbated by researchers giving license to statistical models to do scientific inference. This paper highlights a different approach to handling the evidence collected during a randomized controlled trial, one that does not dichotomize, but rather reports the evidence collected. Through the use of a coin flipping experiment and reanalysis of real-world data, the traditional approach of testing null hypothesis significance is contrasted with a Bayesian approach. This paper is meant to be understood by those who rely on statistical models to draw conclusions from data, but are not statisticians and may therefore not be able to grasp the debate that is primarily led by statisticians.