[R-meta] Moderation analysis in IPD meta-analysis

[Viechtbauer, Wolfgang (SP)]

Dear Corentin,

Overall, your approach seems sound. But a few notes:

1) study1<-glm(DV~IV, data=datastudy1) is not logistic regression. You need:

study1 <- glm(DV ~ IV, data=datastudy1, family=binomial)

2) I've only played around with emmeans a little bit, so can't comment on that part. But I don't think you even need it. You can just fit the model in such a way that you directly get the three log odds ratios for the three levels of IV. In fact, the estimates of the three log odds ratios are independent, so one could even just fit three simple logistic regression models that will give you the same results. An example:

dat <- data.frame(DV = c(1,0,0,1,0,1,1,1,0,1,1,1),
                  IV = c(1,3,2,3,5,3,7,7,4,9,6,3),
                  VM = rep(c("a","b","c"),each=4))

# parameterize logistic regression model so we get the three log odds ratios directly
res <- glm(DV ~ VM + IV:VM - 1, data=dat, family=binomial)
summary(res)

# the covariance between the three estimates is 0
round(vcov(res), 5)

# show that the simple logistic regression model for a subset gives the same results
res.a <- glm(DV ~ IV, data=dat, family=binomial, subset=VM=="a")
summary(res.a)

So actually the V matrix corresponding to the three log odds ratios is diagonal. But you still would want to account for potential dependency in the underlying true log odds ratios, so the model

model <- rma.mv(yi, V, mods = ~ VM-1, random=~VM|study, struct="UN", data=dat)

is still appropriate (with V being diagonal, so you can also just pass a vector with the sampling variances to rma.mv).

3) The statement that 2-stage approaches cannot be used to analyze patient-level moderators isn't quite true. If one actually analyzes the patient-level moderator in stage 1 (as you describe), then the 2-stage approach definitely allows you to examine such a patient-level moderator.

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org]
>On Behalf Of GOSLING Corentin
>Sent: Friday, 07 August, 2020 20:03
>To: r-sig-meta-analysis using r-project.org
>Subject: [R-meta] Moderation analysis in IPD meta-analysis
>
>Dear Metafor’s users,
>
>This is the first time that I post on this mailing list.
>
>Our team is currently planning an individual patient data meta-analysis of
>prospective cohorts.
>
>We adopt an IPD approach because no prospective study has yet reported this
>association while many should have the data to assess it (i.e., they have
>access to the targeted variables but did not report the association).
>Unfortunately, we anticipate that most of the included studies will not
>have an ethics committee that gives the right to share their data with us.
>
>To overcome this, we plan to ask the authors of the included studies to
>perform the analyses on their own data and to share only the results of the
>analyses with us. Our dependent variable is binary (DV: yes/no) and our
>independent variable is an ordered variable (IV: a scale variable in 12
>points [from 1 to 12]) treated as a continuous variable.
>
>We ask authors to perform a logistic regression. Based on their results
>(log odds ratio and associated variance), we adopt a classic two-stage
>approach. I show the R code for a particular study to highlight our
>approach.
>
>#R code for study 1
>
>study1<-glm(DV~IV, data=datastudy1)
>
>yi1<- summary(study1)$coefficients[2,1] #extract the log odds ratio
>
>vi1<- summary(study1)$coefficients[2,2]^2 #extract the squared standard
>error
>
># then, we repeat the same process for each included study
>
># Once all the effect sizes and their variance are collected, we can store
>them within a dataset and run a standard two stage meta-analysis
>
>dat<-data.frame(
>yi=c(yi1, yi2, yi3…),
>vi=c(vi1, vi2, vi3…),
>study=c(1, 2, 3…))
>
>model<-rma(yi,vi, dat)
>
>This is the code for our primary analysis. In an exploratory analysis, we
>would like to perform a moderation analysis with a patient-level moderator.
>We understand how to perform a moderation analysis for a study-level
>moderator but we are not sure on how to implement it with a patient-level
>moderator. The aim of this moderation analysis will be to obtain the
>estimated average effects for each level of a moderator. I describe here
>the approach we have envisaged:
>
># example of R code for study 1
>
>#let VM denote a participant-level moderator with 3 categories (a,b,c)
>
>study1<-glm(DV~IV*VM, data=datastudy1)
>
>EM1<-emmeans::emtrends(study1, ~VM, var=" IV")
>
>yi1<- as.data.frame(EM1$emtrends)[,2] #extract log odds ratio for each
>level of the VM for study 1 (contains 3 values)
>
>V1<-vcov(EM1) # extract the variance/covariance matrix for study 1 (a 3x3
>matrix)
>
># then, we can build a dataset which will look like this...
>
>dat<-data.frame(
>yi=c(yi1, yi2, yi3…),
>VM=c(a,b,c,a,b,c,a,b,c…),
>study=c(1,1,1, 2,2,2, 3,3,3…))
>
># ...and a variance-covariance matrix using the bldiag function
>
>V<-bldiag(list(V1,V2,V3…))
>
># Last, we plan to perform a multivariate model in which we leave out the
>model intercept and in which we use an unstructured variance structure (if
>the model converges).
>
>model<-rma.mv(yi, V, mods = ~ VM-1, random=~VM|study, struct="UN", data=dat)
>
>We were wondering if you could give us some feedback on the correctness of
>our approach. We have read in several textbooks that two-stage
>meta-analyses are not designed to assess patient-level moderator but, given
>that asking for raw data would probably decrease the likelihood of getting
>return from authors of primary studies, we would prefer staying at a
>two-stage approach.
>
>Thank you very much for your help and for this amazing mailing list!
>
>Corentin J Gosling
>Charlotte Pinabiaux
>Serge Caparos
>Richard Delorme
>Samuele Cortese