Meta-regression using restricted cubic splines (with rma() from the metafor package and rcs())

Question

I would like to compile data from several published studies. I am trying to conduct a meta-regression using restricted cubic splines to analyse and plot the association between two variables (x and y), which is not linear.

Here's a simplified version of the code I used to fit the restricted cubic splines in the meta-regression:

library(metafor)

spl <- rma(y, y_se, mods = ~ rcs(x, c(1,2,3,4,5)), data=data, method="DL", random = ~ 1 | id)

However, the estimates of the regression between the knots are very high (+1111) and low (-1826), when I expected much less variation (-2 to 2).

    Model Results:

                          estimate
intrcpt                    89.7615
rcs(x, c(1,2,3,4,5))x        14.0133
rcs(x, c(1,2,3,4,5))x '     -112.4379
rcs(x, c(1,2,3,4,5))x ''    1111.1094
rcs(x, c(1,2,3,4,5))x '''  -1826.6025

And when I plot these, it gives me also a very odd plot:

with(predict(spl, dose), plot(dose, pred, type = "l"))

Do you have an idea why? Is this because rcs() cannot be used with rma()? If this is the problem, what is the alternative to include a restricted cubic spline model within rma()?

Thanks in advance for your help!

Answer 1

Here is an example to illustrate the use of a restricted cubic spline with metafor.

library(metafor)
library(rms)

### load data
dat <- get(data(dat.raudenbush1985, package="metafor"))

### plot data
with(dat, plot(weeks, yi, pch=19, xlab="Weeks", ylab="Standardized Mean Difference"))
xs <- seq(0,25,by=1)

### linear model
res <- rma(yi ~ weeks, vi, data=dat)
lines(xs, predict(res, newmods=xs)$pred, lwd=2)

### model with restricted cubic spline
knots <- c(1,2,5,10)
res <- rma(yi~rcs(weeks,knots), vi, data=dat)
lines(xs, predict(res, newmods=rcspline.eval(xs, knots, inclx=TRUE))$pred, col="red", lwd=2)