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

[Michael Dewey]

Dear Corentin

I have not investigated this in detail but there are two packages on 
CRAN you might want to look at.

https://cran.r-project.org/package=multinma

claims to be able to integrate IPD and aggregate data in one analysis

https://cran.r-project.org/package=metagam

which claims to be able to get the other researchers to run the analysis 
and share it with you when they are not allowed to share the data.

As I say I have not looked at any of them in detail so this may be wide 
of the mark but worth a brief look.

Michael

On 08/08/2020 09:14, GOSLING Corentin wrote:
> Dear Pr Viechtbauer,
> 
> Thank you very much for your answer!
> 
> 1) Sorry for the family argument, I suppressed it when I copy/paste the
> code.
> 2) I was not aware of this solution in the glm function. I have compared it
> with the initial solution using emmeans and it gives similar results. Since
> your solution is definitively more elegant, we are going to use it.
> 3) Great, it is very reassuring to have your confirmation! We had the
> feeling that this was feasible but we were afraid to miss the reason
> preventing us from applying our approach to a patient-level moderator.
> 
> Thank you so much for your help!
> Best
> Corentin J Gosling
> 
> 
> Le ven. 7 août 2020 à 20:34, Viechtbauer, Wolfgang (SP) <
> wolfgang.viechtbauer using maastrichtuniversity.nl> a écrit :
> 
>> 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
>>
> 
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-- 
Michael
http://www.dewey.myzen.co.uk/home.html