Fig. 2: Small-study effects and meta-regressions.

In all plots, Hedges’ g is the effect size and indicates the standardised mean difference between the naltrexone and placebo conditions in ratings of social connectedness (A–E), positive mood, and negative mood (F, G). Negative effect sizes indicate lower social connectedness/positive mood/negative mood after administration of naltrexone compared to placebo. A Funnel plot. The vertical dotted line indicates the average effect size of g = −0.20 obtained with multilevel random-effects meta-analysis. White shading indicates the 95% confidence interval (CI) around this average effect size at various levels of precision (i.e., standard error). B Egger’s test. Meta-regression assessing the relationship between effect size and precision. The medium grey band is the 95% confidence band around the solid black regression line. C Contour-enhanced funnel plot. The vertical dotted line indicates an effect size of g = 0 (i.e., no difference in social connectedness between the naltrexone and placebo conditions). White, dark grey and medium grey shading indicates the 90%, 95%, and 99% CI (respectively) around this null-effect at various levels of precision. D Trim-and-fill funnel plot. Because the trim-and-fill method has not been generalised to multilevel random-effects meta-analysis, this method was applied to aggregated study effect sizes. Effect sizes within studies were aggregated in R using the aggregate function from the metafor package [50]. The vertical dotted line indicates the adjusted average effect size of g = −0.20 obtained with the trim-and-fill method. White shading indicates the 95% CI around this adjusted average effect size at various levels of precision. Circles indicate aggregated observed effect sizes. E–G Meta-regressions assessing predictors of the effect of naltrexone (vs placebo) on social connectedness. These predictors include (E) study quality as assessed with the Jadad Scale (possible range = 0–5) [53]; (F) the effect of naltrexone (vs placebo) on positive mood; (G) the effect of naltrexone (vs placebo) on negative mood; and (H) the likely type of relationships (new, unspecified or established) considered by participants when rating their feelings of social connectedness. The medium grey band represents the 95% confidence interval around the solid black regression line. Individual effect sizes are scaled according to their relative weight in each model, with larger circles indicating greater relative weight.