I would like to conduct a meta-analysis in the context where I have studies available that measure a continuos variable at multiple time points (0, 1, 2, 3, 4, 5). Time 0 represents the baseline where values are at 100%. Right afterwards there is an intervention and the effect of the intervention is measured over time (114% represents a 14% change relative to baseline). Also I have given two different groups that received different interventions.
Please consider the following dummy data set:
library(ggplot2) library(metafor) library(dplyr) n <- 10 a <- c(rnorm(n,100,0), rnorm(n, 110,2), rnorm(n,130,2), rnorm(n,135,2), rnorm(n,130,2), rnorm(n,125,2)) b <- c(rnorm(n,100,0), rnorm(n,107,2), rnorm(n,122,2), rnorm(n,128,2), rnorm(n,122,2), rnorm(n,125,2)) sd <- rnorm(n,10,1) my_dat <- data.frame(mean=c(a, b), sd=rep(sd,12), time=rep(c(rep(0,n), rep(1,n), rep(2,n), rep(3,n), rep(4,n), rep(5,n)),2), group=c(rep("A", 60), rep("B",60)), n=rep(n,120)) my_dat$study <- 1:10 p <- ggplot(aes(y=mean, x=time, colour=group), data=my_dat) p + geom_jitter() + geom_smooth() + ylab("% relative to baseline") + xlab("time")
I would like to :
1) investigate the main effect of time (as well as post-hoc tests) for each group individually using the metafor package.
2) investigate the main effect of group (as well as post-hoc tests) for each point in time using the metafor package.
3) investigate group-time interactions.
Thus I rearrange the data and calculate hegdes g relative to baseline t0:
t0_dat <- summarise(group_by(my_dat[my_dat$time==0,], study, group), t0_mean=mean(mean), t0_sd=mean(sd)) my_dat <- merge(my_dat, t0_dat, by=c("study", "group"), all.x=T) my_dat <- escalc(m1i=mean, m2i=t0_mean, sd1i=sd, sd2i=t0_sd, n1i=n, n2i=n, measure="SMD", data=my_dat, append=T) p <- ggplot(aes(y=yi, x=time, xmin=yi-vi, xmax=yi+vi, colour=group), data=my_dat) p + geom_point() + geom_smooth() + ylab("hedges g") + xlab("time") + xlim(c(0,5)) + ylim(c(0,5))
Finally I can run the meta-analysis:
m1 <- rma(yi,vi, data=my_dat, mods=~time*group) summary(m1)
This indicates a sig. effect of time, a sig. effect of group but no interaction: Model Results:
estimate se zval pval ci.lb ci.ub intrcpt 1.4500 0.2159 6.7158 <.0001 1.0269 1.8732 *** time 0.3294 0.0667 4.9363 <.0001 0.1986 0.4602 *** groupB -0.6808 0.2994 -2.2738 0.0230 -1.2676 -0.0940 * time:groupB 0.0802 0.0932 0.8609 0.3893 -0.1024 0.2628 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Is this an valid approach? Would it be appropriate to instead of converting to effect size (hedges g) to use the percentage values (as extracted from the papers) and log-transform them as suggested in this question, in this question or in the comments below? Hints to papers that conducted comparable analysis are more then welcome!