[R-meta] Queries re: rma.mv

Fri, May 13, 2022 3:32 AM

Hi Adelina,

In multilevel models, one has to distinguish the between- and the within-study relationship between some predictor and the outcome. I don't have access to your data, but possibly those trends differ in your data. So, it might appear visually that the trend is increasing, but not when analyzed using a multilevel model.

The weight structure is more complex in models with moderators, so it's not just a matter of computing row-sum weights to get the same results. In general, there is an entire weight matrix. On the page that I linked to, I only discuss the special case of an "intercept-only model". James Pustejovsky has a blog entry where he goes further into discussing weights also in models with moderators:

https://www.jepusto.com/weighting-in-multivariate-meta-analysis/

I am not aware of a general way of reducing the weight matrix down to a vector of weights, such that a standard meta-analysis model will give the same results as the more complex multilevel/multivariate model from which the weight matrix is derived. So, since it is not generally possible (as far as I know) to compute 'estimate-specific weights', forest and bubble plots just use the diagonal of the weight matrix as a rough indication of how much weight is assigned to individual points (but you are of course free to specify other point sizes).

Best,
Wolfgang

-----Original Message-----
From: Adelina Artenie [mailto:adelina.artenie at bristol.ac.uk]
Sent: Friday, 13 May, 2022 11:38
To: Viechtbauer, Wolfgang (NP); r-sig-meta-analysis at r-project.org
Subject: Re: Queries re: rma.mv

Hi Wolfgang,

Thank you for your detailed response. It has been very helpful. I am still
pondering one thing though about the weights, if I could have your advice please:

I have re-calculated the weights as you suggested (shown in my code below) and if
I run a bubble plot using regplot and use these weights as the size of the
bubbles, it would appear that, indeed, the correlated data are down-weighted.

The issue is the following (note: my moderator is a measure of time): looking at
the bubble plot, one can tell visually that the trend is clearly increasing over
time. However, the coefficient from rma.mv and the best fit line in regplot show
a decreasing trend. The only way this would occur is if the weights of the
correlated data used in the model are not, in fact, down-weighted but up-weighted
(the correlated data have a decreasing trend over time). In other words, it seems
as if rma.mv is not using the row-sum weights but the weights that are based on
the diagonal of the matrix (or some other weights..).

Relatedly, I also wonder why, if the default weights shown in the forest plot or
the bubble/regplot, are not the ones used by the rma.mv model, why are they the
default weights plotted? This too makes me think that these are the ones used
internally in the model estimation by rma.mv

Apologies for the long e-mail. This package has been incredibly useful so far.
I've just hit a point where I do not fully understand how rma.mv works and how to
make sense of my results.

Many thanks for your help
Adelina

My code:

Inci_trends$prs_yrs_100 = Inci_trends$prs_yrs/100
trend_dat_Inci <- escalc(measure="IRLN", xi=cases, ti=prs_yrs_100,
data=Inci_trends)
summary.escalc(trend_dat_Inci)

multi_level_m_Inci <- rma.mv(yi = yi,
????????????????????????????V = vi,
????????????????????????????slab = author,
??????????????????????????? data = trend_dat_Inci,
??????????????????????????? random = ~ 1 |slab/ID,
????????????????????????????test = "z",
????????????????????????????method = "REML",
??????????????????????????? mods = ~ midpoint )
summary(multi_level_m_Inci)
round(exp(coef(summary(multi_level_m_Inci))[-1,c("estimate", "ci.lb", "ci.ub")]),
2)

w_reg_Inci <- weights(multi_level_m_Inci)
w_m_Inci <- weights(multi_level_m_Inci, type = "matrix")

w_m_Inci_adjw <- rowSums(w_m_Inci) / sum(w_m_Inci) * 100

regplot(multi_level_m_Inci, label = F, transf=exp,
??????? ylab = "Rate",
??????? xlab = "midpoint",
??????? col="grey",
??????? bg="red",
??????? labsize = 0.5,
??????? legend = F,
??????? psize=c(w_m_Inci_adjw)
)

From: Viechtbauer, Wolfgang (SP) <wolfgang.viechtbauer at maastrichtuniversity.nl>
Date: Wednesday, 20 April 2022 at 19:42
To: Adelina Artenie <adelina.artenie at bristol.ac.uk>, r-sig-meta-analysis at r-
project.org <r-sig-meta-analysis at r-project.org>
Subject: RE: Queries re: rma.mv
Dear Adelina,

See below for my responses.

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-project.org] On
Behalf Of Adelina Artenie
Sent: Wednesday, 20 April, 2022 19:15
To: r-sig-meta-analysis at r-project.org
Subject: [R-meta] Queries re: rma.mv

Hello

I am trying to do a meta-regression to explore whether incidence rates are
changing over time. Some of the estimates are correlated so I am using the

rma.mv

function. The moderator is a measure of time.

I have two questions please:

? 1.? I am trying to understand why is it that the correlated estimates are
systematically up-weighted. I would have thought that any correlated data would
be down-weighted or, at the very least, have a similar weight as the

uncorrelated

data. I appreciate that the weight calculation in this case is complex
(https://www.metafor-project.org/doku.php/tips:weights_in_rma.mv_models ). I
wonder if, conceptually, this would be expected? In my mock example, the
correlated estimates have weights of 7-10% whereas the uncorrelated ones have
weights of 4%. I see a similar trend in my own data, and I find the difference

in

the weights to be quite considerable.

I assume you are referring to the weights shown in the forest plot. These are
just based on the diagonal of the weight matrix. As you note, the weighting in
such models is more complex, so looking at these weights doesn't really allow you
to draw such a conclusion. In fact, generally, the effect will be as you expect,
namely that correlated estimates will be downweighted. Consider the
dat.konstantopoulos2011 dataset and let's make all sampling variances equal to
each other to see this more clearly. Also, we will compute the row-sum weights,
since these reflect more directly the weight each estimate is getting in this
model.

dat <- dat.konstantopoulos2011

dat$vi <- median(dat$vi)
res <- rma.mv(yi, vi, random = ~ 1 | district/school, data=dat)
res

wi <- weights(res, type="rowsum")

data.frame(k = c(table(dat$district)),
?????????? weight = tapply(wi, dat$district, mean))

So, as you can see, in clusters with more estimates, each individual estimate
gets less weight.

Things will be more complicated when sampling variances differ and also when
including moderators in the model.

? 2.? Could I confirm with you that my interpretation of the coefficient for the
moderator is correct? In this case, the estimate is 0.0846, which represents the
mean/median log IRR (incidence rate ratio) for a one-unit increase in the
moderator. Therefore, the IRR is 1.088: for each unit increase in time, the
incidence rate increases on average by 8.8% (ignoring the confidence intervals
for now).

Correct.

Many thanks in advance,
Adelina

Adelina Artenie, MSc, PhD
CIHR Postdoctoral Research Fellow
Population Health Sciences
Bristol Medical School
University of Bristol

Code
***

ID <- c(1:18)
author <- c("AA", "AA", "BB", "CC", "DD", "EE", "EE", "EE", "FF", "GG", "HH",
"II", "JJ",
??????????? "KK", "LL", "MM", "NN", "OO")
cases <- c(8:25)
prs_yrs <-
c(200,150,3000,400,500,100,400,300,1200,456,177,296,664,123,123,432,67,3045)
moderator<-c(1:18)

mydata<-data.frame(ID,author,cases,prs_yrs,moderator)
print(mydata)

my_example <- escalc(measure="IRLN", xi=cases, ti=prs_yrs, data=mydata)
my_example
my_meta_reg <- rma.mv(yi = yi,
??????????????????????????? V = vi,
??????????????????????????? slab = author,
??????????????????????????? data = my_example,
??????????????????????????? random = ~ 1 | author/ID,
??????????????????????????? test = "z",
??????????????????????????? method = "REML",
??????????????????????????? mods = ~ moderator)

summary(my_meta_reg)
regplot(my_meta_reg, label = T, transf=exp,
??????? ylab = "Incidence rate",
??????? xlab = "Moderator",
??????? col="black",
??????? plim = c(1,NA),
??????? labsize = 0.5,
??????? legend = F)
forest(my_meta_reg, showweights=TRUE)

[R-meta] Queries re: rma.mv

Thread (3 messages)