Solved – Metafor package in R: meta regression and scatter plot

meta-analysismeta-regressionr

I am doing a meta-regression with metafor package in R. The mixed-effect model for proportion is used to assess the linearity between study performed year and medication prevalence. Here below is my script in R:

model_A <- rma.glmm(xi=A, ni=Sample, measure="PLO", mods=~year)
print(model_A)

And results I got from R are:

Mixed-Effects Model (k = 32; tau^2 estimator: ML)

tau^2 (estimated amount of residual heterogeneity):     1.6349
tau (square root of estimated tau^2 value):             1.2786
I^2 (residual heterogeneity / unaccounted variability): 99.40%
H^2 (unaccounted variability / sampling variability):   168.00

Tests for Residual Heterogeneity: 
Wld(df = 30) = 2221.4535, p-val < .0001
LRT(df = 30) = 3187.7073, p-val < .0001

Test of Moderators (coefficient(s) 2): 
QM(df = 1) = 22.7322, p-val < .0001

Model Results:

          estimate        se     zval    pval      ci.lb      ci.ub
intrcpt  -554.8145  116.4605  -4.7640  <.0001  -783.0728  -326.5561  ***
year        0.2767    0.0580   4.7678  <.0001     0.1630     0.3905  ***

---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Followed by this model, I would also like to perform a scatterplot in R. So my script is:

wi <- 0.5/sqrt(dat$vi)
preds <- predict(model_A, transf = transf.ilogit, addx=TRUE)
plot(year, transf.ilogit(dat$yi), cex=wi)
lines(year, preds$pred)

The plot I got is:
enter image description here

Apparently, it doesn't seem right!. So my questions are:

  1. Did I use the right model with rma.glmm?

  2. How could I weight individual study (cex=wi?)? How to calculate standard error for individual study?

  3. How could I fit a right estimated line in scatterplot?

Many thanks.

Updates:

Followed by Wolfgang's suggestions, I managed to rescale the bubble and get predicted line fitted (the model remains the same):

enter image description here

Obviously, the line wasn't straight! Should I change model into polynomial regression? Or is that normal with this graph?

I tried polynomial model like:

model1<-rma.glmm(xi=A, ni=Sample, measure="PLO", mods=~year+I(year^2))

The error came with "Error in print(model1) :
error in evaluating the argument 'x' in selecting a method for function 'print': Error: object 'model1' not found"

And I tried another model:

model2: model2<-rma.glmm(xi=A, ni=Sample, measure="PLO", mods=~year+year^2)

I got exactly the same result as original model, which has only the year as covariate fitted. I am not sure where the problem is….

Many thanks!

Min

Best Answer

  1. Assuming you are trying to model the relationship between year and the log odds of the outcome of interest using a logistic mixed-effects model, then yes, you used the right model.

  2. You may want to rescale wi a bit. Such as:

    wi <- 0.5 + 3.0 * (wi - min(wi))/(max(wi) - min(wi))

  3. Something like this should do:

    years <- 1998:2014
preds <- predict(model_A, transf = transf.ilogit, newmods = years)
plot(year, transf.ilogit(dat$yi), cex=wi)
lines(years, preds$pred)
lines(years, preds$ci.lb, lty="dashed")
lines(years, preds$ci.ub, lty="dashed")

See also here for a related example:

http://www.metafor-project.org/doku.php/plots:meta_analytic_scatterplot

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