# interpretation of meta-regression in meta-analysis for number of participants explanatory variable

I have a meta-analysis with continuous variables, the melhroz study which I defined in the following dataframe

library(meta)
library(metafor)
author  <- c('Hesse','Hesse','Hsieh', 'Kuther','Liao','Wu')
year    <- c(2005, 2014, 2011,2010,2011,2012)
mean.e  <- c(22.45,25.2,0.13,6.89,0.25,3.26)
sd.e    <- c(15.14,11,0.19,9.995,0.17,7.16)
total.e <- c(22,25,12,11,10,14)
mean.c  <- c(17.27,16,0.06,8.49,0.03,-2.88)
sd.c    <- c(13.95,15.7,0.32,11.33,0.28,9.56)
total.c <-c(22,25,6,10,10,28)

melhroz.data <- data.frame(author, year, mean.e, sd.e, total.e, mean.c, sd.c, total.c)
# str(melhroz.data)
# melhroz.data


I defined two groups: studies with less than 14 participants and studies with more than 14 participants in the experimental group and run a meta-regression model

melhroz.data\$nro_experimental <- c(">=14", ">=14", "<14", "<14", "<14", ">=14")

meta1 <- metacont(total.e, mean.e, sd.e,
total.c, mean.c, sd.c,
data=melhroz.data, sm="SMD", comb.fixed=gs("comb.fixed"))

mr1 <- metareg(meta1, nro_experimental)
mr1


With the following results

Test for Residual Heterogeneity:
QE(df = 4) = 3.4174, p-val = 0.4905

Test of Moderators (coefficient(s) 2):
QM(df = 1) = 0.5462, p-val = 0.4599

Model Results:

estimate      se    zval    pval    ci.lb   ci.ub
intrcpt                 0.3221  0.2711  1.1881  0.2348  -0.2092  0.8534
nro_experimental>=14    0.2398  0.3245  0.7391  0.4599  -0.3962  0.8758


So I have no statistical significant results but what does it mean the 0.2398 estimate value? It means that if I had obtained significant pvalue the effect size would have increased in 23.98% for the studies with >= 14 participants?

• I would check the manual of the software if I were in this situation. Dec 11 '18 at 15:28

Since you are using standardised mean differences the estimate is on that scale. So it states that the larger studies had SMD which were on average 0.2398 greater than the smaller studies. Your interpretation is more like what you would get if you had a different sort of measure on a log scale and had then converted them back to the original scale like odds ratio, risk ratio and so on.

As you might expect with few studies your estimates have very wide confidence intervals.

By categorising study size you are assuming that all studies with fewer than 14 participants share the same underlying value of SMD which is different from all the other studies. A less restrictive and arguably more plausible model is to fit study size as a continuous moderator variable.

• Thanks a lot! I should call mr1 <- metareg(meta1, total.e ) ?
– Ana
Dec 11 '18 at 16:53
• Looks plausible, I do not use meta though I use metafor. Dec 11 '18 at 16:57
• I've run it and looks good, if I understand it right, instead of defining only two groups (larger and shorter than 14) I'm using all values total.e <- c(22,25,12,11,10,14)
– Ana
Dec 11 '18 at 17:06
• Yes, that's correct. The coefficient now tells you you extra added for each unit increase in total.e (ie each participant). Dec 11 '18 at 17:25