Bayesian updating: increasing sample size during the course of a study

Bayesian sequential designs in studies with multilevel data

In many studies in the social and behavioral sciences, the data have a multilevel structure, with subjects nested within clusters. In the design phase of such a study, the number of clusters to achieve a desired power level has to be calculated. This requires a priori estimates of the effect size and intraclass correlation coefficient. If these estimates are incorrect, the study may be under- or overpowered. This may be overcome by using a group-sequential design, where interim tests are done at various points in time of the study. Based on interim test results, a decision is made to either include additional clusters or to reject the null hypothesis and conclude the study. This contribution introduces Bayesian sequential designs as an alternative to group-sequential designs. This approach compares various hypotheses based on the support in the data for each of them. If neither hypothesis receives a sufficient degree of support, additional clusters are included in the study and the Bayes factor is recalculated. This procedure continues until one of the hypotheses receives sufficient support. This paper explains how the Bayes factor is used as a measure of support for a hypothesis and how a Bayesian sequential design is conducted. A simulation study in the setting of a two-group comparison was conducted to study the effects of the minimum and maximum number of clusters per group and the desired degree of support. It is concluded that Bayesian sequential designs are a flexible alternative to the group sequential design.

Beyond empathy: Cognitive capabilities increase or curb altruism in middle childhood

Altruistic behavior, which intentionally benefits a recipient without expectation of a reward or at a cost to the actor, is observed throughout the lifespan from everyday interactions to emergency situations. Empathy has long been considered a major driver of altruistic action, but the social information processing model supports the idea that other cognitive processes may also play a role in altruistic intention and behavior. Our aim was to investigate how visual analysis, attention, inhibitory control, and theory of mind capabilities uniquely contribute to predicting altruistic intention and behavior in a sample of 67 French children (35 girls and 32 boys; Mage = 9.92 ± 0.99 years) from Paris and neighboring suburbs. Using a Bayesian analysis framework, we showed that in younger grade levels visual analysis and selective attention are strong predictors of altruistic intention and that inhibitory control strongly predicts altruistic behavior in a dictator game. Processes underlying theory of mind, however, negatively predict altruistic behavior in the youngest grade. In higher grade levels, we found that stronger attention and inhibitory control predicts lower altruistic intention and behavior. Empathy was not found to predict altruistic intention or behavior. These results suggest that different cognitive capabilities are involved in altruistic intention and behavior and that their contribution changes throughout middle childhood as social constraints deepen and altruism calls on more complex reasoning.

Interpreting frequentist hypothesis tests: insights from Bayesian inference

Randomized controlled trials are one of the best ways of quantifying the effectiveness of medical interventions. Therefore, when the authors of a randomized superiority trial report that differences in the primary outcome between the intervention group and the control group are "significant" (i.e., P ≤ 0.05), we might assume that the intervention has an effect on the outcome. Similarly, when differences between the groups are "not significant," we might assume that the intervention does not have an effect on the outcome. Nevertheless, both assumptions are frequently incorrect.In this article, we explore the relationship that exists between real treatment effects and declarations of statistical significance based on P values and confidence intervals. We explain why, in some circumstances, the chance an intervention is ineffective when P ≤ 0.05 exceeds 25% and the chance an intervention is effective when P > 0.05 exceeds 50%.Over the last decade, there has been increasing interest in Bayesian methods as an alternative to frequentist hypothesis testing. We provide a robust but nontechnical introduction to Bayesian inference and explain why a Bayesian posterior distribution overcomes many of the problems associated with frequentist hypothesis testing.Notwithstanding the current interest in Bayesian methods, frequentist hypothesis testing remains the default method for statistical inference in medical research. Therefore, we propose an interim solution to the "significance problem" based on simplified Bayesian metrics (e.g., Bayes factor, false positive risk) that can be reported along with traditional P values and confidence intervals. We calculate these metrics for four well-known multicentre trials. We provide links to online calculators so readers can easily estimate these metrics for published trials. In this way, we hope decisions on incorporating the results of randomized trials into clinical practice can be enhanced, minimizing the chance that useful treatments are discarded or that ineffective treatments are adopted.

A Bayesian Reanalysis of a Trial of Psilocybin versus Escitalopram for Depression

Objectives

To perform a Bayesian reanalysis of a recent trial of psilocybin (COMP360) versus escitalopram for Major Depressive Disorder (MDD) in order to provide a more informative interpretation of the indeterminate outcome of a previous frequentist analysis.

Design

Reanalysis of a two-arm double-blind placebo controlled trial.

Participants

Fifty-nine patients with MDD.

Interventions

Two doses of psilocybin 25mg and daily oral placebo versus daily escitalopram and 2 doses of psilocybin 1mg, with psychological support for both groups.

Outcome measures

Quick Inventory of Depressive Symptomatology-Self-Report (QIDS SR-16), and three other depression scales as secondary outcomes: HAMD-17, MADRS, and BDI-1A.

Results

Using Bayes factors and 'skeptical priors' which bias estimates towards zero, for the hypothesis that psilocybin is superior by any margin, we found indeterminate evidence for QIDS SR-16, strong evidence for BDI-1A and MADRS, and extremely strong evidence for HAMD-17. For the stronger hypothesis that psilocybin is superior by a 'clinically meaningful amount' (using literature defined values of the minimally clinically important difference), we found moderate evidence against it for QIDS SR-16, indeterminate evidence for BDI-1A and MADRS, and moderate evidence supporting it for HAMD-17. Furthermore, across the board we found extremely strong evidence for psilocybin's non-inferiority versus escitalopram. These findings were robust to prior sensitivity analysis.

Conclusions

This Bayesian reanalysis supports the following inferences: 1) that psilocybin did indeed outperform escitalopram in this trial, but not to an extent that was clinically meaningful--and 2) that psilocybin is almost certainly non-inferior to escitalopram. The present results provide a more precise and nuanced interpretation to previously reported results from this trial, and support the need for further research into the relative efficacy of psilocybin therapy for depression with respect to current leading treatments.

Trial registration number

NCT03429075.

Running-style modulation: Effects of stance-time and flight-time instructions on duty factor and cadence

BACKGROUND

The duty factor (reflecting the ratio of stance to flight time) is an important variable related to running performance, economy, and injury risk. According to the dual-axis model, the duty factor and the cadence are sufficient to describe an individual's running style at a certain speed. To test this model, one should be able to modulate both variables independently. While acoustic pacing is an established method for cadence modulation, no such method is available for duty-factor modulation.

RESEARCH QUESTIONS

Can people modulate their duty factor based on verbal instructions to change either their stance or flight time without changing their cadence? And, if so, which instruction is most effective?

METHODS

Twelve participants ran on an instrumented treadmill and completed four training blocks starting with a baseline trial and ending with a performance trial in which they followed verbal instructions to both increase and decrease their stance and flight time. Acoustic pacing at their preferred cadence was present during the first part of each trial. We calculated the duty factor and cadence for paced and non-paced parts of each trial, assessed the effectiveness of the instructions aimed at changing the duty factor, and examined the effects of instructions and acoustic pacing on cadence using Bayesian statistics.

RESULTS

The duty factor changed in intended directions with verbal instructions to increase and decrease the stance and flight time (18.04 ≤ BF₁₀ ≤ 4954.42), without differences between the instructions or during and after acoustic pacing. The instructions and acoustic pacing did not result in a consistent change in cadence (0.40 ≤ BF₁₀ ≤ 2.59).

SIGNIFICANCE

Runners can change their duty factor through verbal instructions pertaining to stance or flight time, without clear concomitant effects on cadence. Running styles can thus be altered with verbal instructions to change stance or flight time for duty-factor modulation, optionally combined with acoustic pacing to prescribe cadence.