I have been using the metafor package for some meta-analyses and would like to adjust for a single continuous covariate (mean age) using meta-regression. However, I require some clarification regarding the outputs and what they mean. Below I have shared the output for the base case analysis as well as the meta-regression (same studies in both, with the only difference being the addition of covariates for the meta-regression).
Base case output
Random-Effects Model (k = 36; tau^2 estimator: DL) logLik deviance AIC BIC AICc -18.8613 60.5927 41.7226 44.8896 42.0862 tau^2 (estimated amount of total heterogeneity): 0.0633 (SE = 0.0327) tau (square root of estimated tau^2 value): 0.2515 I^2 (total heterogeneity / total variability): 51.46% H^2 (total variability / sampling variability): 2.06 Test for Heterogeneity: Q(df = 35) = 72.1031, p-val = 0.0002 Model Results: estimate se zval pval ci.lb ci.ub 0.1266 0.0633 2.0014 0.0453 0.0026 0.2506 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Meta-regression (output)
Mixed-Effects Model (k = 36; tau^2 estimator: DL) logLik deviance AIC BIC AICc -18.7696 60.4092 43.5391 48.2897 44.2891 tau^2 (estimated amount of residual heterogeneity): 0.0677 (SE = 0.0346) tau (square root of estimated tau^2 value): 0.2601 I^2 (residual heterogeneity / unaccounted variability): 52.84% H^2 (unaccounted variability / sampling variability): 2.12 R^2 (amount of heterogeneity accounted for): 0.00% Test for Residual Heterogeneity: QE(df = 34) = 72.1024, p-val = 0.0001 Test of Moderators (coefficient(s) 2): QM(df = 1) = 0.2456, p-val = 0.6202 Model Results: estimate se zval pval ci.lb ci.ub intrcpt -0.3741 1.0140 -0.3690 0.7122 -2.3616 1.6133 mods 0.0085 0.0172 0.4955 0.6202 -0.0252 0.0423 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
My questions are:
Why are we observing an R-squared of 0% in the meta-regression (is it simply because the covariate is not significant or do you suspect something is not correct)?
How can we interpret the outputs of the meta-regression? With back-transformation of the logHRs we suspect something like below, but would like to make sure that I am interpreting the ‘intrcpt’ and ‘mods’ values correctly.
I have assumed mods represents the pooled HR taking into account the adjustment for age.
I have assumed intrcpt represents the covariate effect (beta) – i.e. the amount that the logHR changes for a one unit increase in age. Also, I have back-transformed this output, which I am not sure is appropriate, or if I should present as is.