[R-meta] Violation in non-independece of errors (head to head studies and mutlilevel meta-analysis)?

Natan Gosmann natan.gosmann at gmail.com
Wed Apr 4 02:25:08 CEST 2018

Dear Wolfgang,

Thank you very much for your response and all comments. Here it goes an
example of what we are doing.

Our full data frame is composed of 1100 rows e 700 columns, but an example
of the data structure could be described like this (basically each study
has one or more trt group, identified by drug, compared to placebo
considering multiple outcomes, identified by measurement scales):

study /trt/drug/ outcome/pcb _m1/pcb _sd1/pcb_m2/drug _m1/drug _sd1/drug_m2
1          1      flx      HAM             25               3               19
            26                3                12
1          2      esc     HAM             25               3               19
            24              2.5              13
2          1      cit       SDS               13               2
             9               12              1.5                3
2          1      cit      HAM             24              2.5              20
            25               2                14
3          1      dul    MADRS          31               6              24
             29                6                17
3          1      dul     HAM             20               5               17
             21             4.5               14
3          2      flx     MADRS          31               6              24
             30              5.5               16
3          2      flx      HAM              20               5              17
             20                4                13

(1) We are calculating Differences in Standardized Mean Change from Pre and
Post Means and initial SD according to the Gleser & Olkin 2009 Study;

# assuming a 0.25 correlation between pre and post means (ri)

meta_pcb <- escalc(measure="SMCR", m1i= pcb_m2, m2i= pcb _m1, sd1i= pcb _sd1,
ni=n_pcb, ri=r1,data=mydata2)

meta_drug<- escalc(measure="SMCR", m1i= drug _m2, m2i= drug _m1,
sd1i=drug_sd1, ni=n_drug, ri=r1,data=mydata2)

meta <- data.frame(yi = meta_drug$yi - meta_pcb$yi, vi = meta_drug$vi +

(2) Considering that we also want to include studies with more than one
treatment group, we constructed a full V matrix as you suggested;

calc.v <- function(x) {

   v <- matrix(1/x$n2i[1] + outer(x$yi, x$yi, "*")/(2*x$Ni[1]),
nrow=nrow(x), ncol=nrow(x))

   diag(v) <- x$vi



V <- bldiag(lapply(split(meta, meta$study), calc.v))

(3) So far we were specifying as random variables: Study ID and Measurement
Scale (outcome) as exemplified;

meta_out1<-rma.mv(yi=yi, V=V, data=meta,

                  random=list(~1|outcome, ~1|study),

                  slab=paste(author, outcome, sep=", "),

                  mods = ~relevel(factor(drug), ref="flx"))

However, we have doubts if our current analysis is being performed
correctly. Considering our current data structure (as exemplified above),
isn’t problematic to construct a full V matrix to compute the covariance
for various effect sizes of different treatment groups of the same study,
since we also have different rows for different outcomes of the same
treatment group? Should we also include trt as a random variable?

Any advice or suggestions on that would be greatly appreciated.



2018-03-31 12:52 GMT-03:00 Viechtbauer Wolfgang (SP) <
wolfgang.viechtbauer at maastrichtuniversity.nl>:

> Convergence problems are difficult to anticipate. But in general, they are
> more likely to appear when fitting complex models and/or when the dataset
> is small. It is also possible that one is trying to fit an
> overparameterized model, that is, a model where certain parameters are not
> identifiable. The issue of identifiability is complex, but some articles
> that deal with this are:
> Kreutz, C., Raue, A., Kaschek, D., & Timmer, J. (2013). Profile likelihood
> in systems biology. The FEBS Journal, 280(11), 2564-2571.
> Lavielle, M., & Aarons, L. (2016). What do we mean by identifiability in
> mixed effects models? Journal of Pharmacokinetics and Pharmacodynamics,
> 43(1), 111-122.
> Raue, A., Kreutz, C., Maiwald, T., Bachmann, J., Schilling, M.,
> Klingmuller, U., & Timmer, J. (2009). Structural and practical
> identifiability analysis of partially observed dynamical models by
> exploiting the profile likelihood. Bioinformatics, 25(15), 1923-1929.
> Raue, A., Kreutz, C., Maiwald, T., Klingmuller, U., & Timmer, J. (2011).
> Addressing parameter identifiability by model-based experimentation. IET
> Systems Biolology, 5(2), 120-130.
> Wang, W. (2013). Identifiability of linear mixed effects models.
> Electronic Journal of Statistics, 7, 244-263.
> One way of assessing parameter identifiability is to examine/plot profile
> likelihoods. This is what the profile() function is for. When fitting
> complex models, I would always recommend to profile all
> variance/correlation components.
> Even if all components are identifiable, it may be difficult to find the
> ML/REML estimates. Complex models require optimization over a large number
> of parameters and this is not a trivial task. rma.mv() uses nlminb() by
> default, but that is not always the best option. One can try many other
> optimizers (using the control arguments 'optimizer' and 'optmethod'). See
> the 'Note' section under help(rma.mv).
> As for power, there are these two articles:
> Hedges, L. V., & Pigott, T. D. (2001). The power of statistical tests in
> meta-analysis. Psychological Methods, 6(3), 203-217.
> Hedges, L. V., & Pigott, T. D. (2004). The power of statistical tests for
> moderators in meta-analysis. Psychological Methods, 9(4), 426-445.
> But they do not deal with complex models (just standard
> random/mixed-effects models). Indeed, for complex models, one would need to
> take a simulation approach.
> Best,
> Wolfgang
> -----Original Message-----
> From: Emily Finne [mailto:emily.finne at uni-bielefeld.de]
> Sent: Wednesday, 28 March, 2018 10:35
> To: Viechtbauer Wolfgang (SP); r-sig-meta-analysis at r-project.org
> Subject: Re: [R-meta] Violation in non-independece of errors (head to head
> studies and mutlilevel meta-analysis)?
> I really wished, everything WOULD be so obvious to me... !
> For this analysis the results turned out to be nearly unchanged when
> including the crossed random effects, although you guessed right that
> convergence problems could emerge. These were related to those parameters
> estimating the covariaces between effects within studies.
> I wonder how one can anticipate such problems in advance or rather
> determine how complex a model can be with given data to have enough power
> to test (fixed) moderator effects of interest and to make sure that
> confidence intervals are reliable.
> Is there something like a formal power analysis for meta-analysis or
> meta-regression? I am aware that this is complex and I think in mixed
> effects models, in general, one would use simulations.
> Any advice on literature  I could read to get prepared for further
> projects?
> Best,
> Emily
> Am 25.03.2018 um 12:16 schrieb Viechtbauer Wolfgang (SP):
> See comments below.
> Best,
> Wolfgang
> -----Original Message-----
> From: Emily Finne [mailto:emily.finne at uni-bielefeld.de]
> Sent: Saturday, 24 March, 2018 21:41
> To: Viechtbauer Wolfgang (SP); r-sig-meta-analysis at r-project.org
> Subject: Re: [R-meta] Violation in non-independece of errors (head to
> head studies and mutlilevel meta-analysis)?
> Dear Wolfgang,
> oh yes, many people were  sick during the last weeks, here too. I hope
> you're feeling better by now.
> Thanks - not 100% but good enough to catch up on work.
> Yes, that is exactly the data structure I have. I completely missed out
> to think of the problem as crossed random effects! Thank you!
> I am quite sure that I constructed the var-cov-matrix V right. I used the
> formulas by Gleser & Olkin and James Pustejovsky. I double-checked the
> resulting matrix. Additionally, I used robust estimation, since most
> correlations between outcomes were only a best guess.
> Great!
> Only to make sure, that I understand correctly the point about the random
> effects: I code two different treatment groups within one study with
> different numbers starting with 1 (for example) and than use the code you
> provided for the crossed random effects. But the numbers given to
> different treatments are arbitrary and don't mean that the group with
> 'treatment = 1' always got the same treatment. It is only to code that
> treatment 1 and 2 within one study are different (say medication A and B
> each compared against a placebo control), not that 1 and 2 always means
> the same thing in different studies (it could also stand for medication B
> and C vs. control in another study). Am I right?
> Correct!
> On the other hand, if treatment 1 always stood for medication A and
> treatment 2 always stood for medication B (across all studies), then it
> would make sense to distiniguish the two and, for example, allow a
> different tau^2 for treatment 1 vs treatment 2. I assumed that for
> 'outcome', this is actually the the case (so, for example, outcome 1 always
> stands for measure X and outcome 2 always stands for measure Y).
> One thing I forgot to mention: At the moment, the 'inner' terms in a '~
> inner | outer' formula under random must be a character/factor variable.
> So, if 'outcome' and 'trt' are numeric, then use:
> random = list(~ factor(outcome) | study, ~ factor(trt) | study),
> struct=c("UN","CS")
> Or you could code 'outcome' and 'trt' as character variables to begin with.
> The treatments we look at in our analysis, in fact, are all different in
> some aspects although pursuing the same goal. We use characteristics of
> the treatments as moderators then and hope to explain differences in
> effect sizes.
> Again, spot on. Using this example, it also illustrates why it would make
> sense to include a fixed effect for 'outcome' (since outcome 1 and 2 are
> uniquely defined), while it would not make sense to include a fixed effect
> for 'trt'. For the latter, as you say, we can use characteristics of the
> treatments as moderators.
> Sorry if this is all obvious to you, but having this written down here is
> useful for future reference. Also, to come back to the Konstantopoulos
> (2011) and Berkey et al. (1998) examples, this also explains why we would
> use:
> rma.mv(yi, vi, random = ~ factor(study) | district, struct="CS", data=dat)
> in the Konstantopoulos example (https://tinyurl.com/ybpzn5ra) (so no
> fixed effect for 'study' and struct="CS" -- which is actually the default,
> but added here for clarity)
> and
> rma.mv(yi, V, mods = ~ outcome - 1, random = ~ outcome | trial,
> struct="UN", data=dat)
> in the Berkey example (https://tinyurl.com/y9yv366v) (so with fixed
> effect for 'outcome' and struct="UN").
> In the first case, the coding of 'study' within 'district' is arbitary. In
> the second case, the coding of 'outcome' within 'trial' is meaningful.
> Again, thank you so much for you detailed help.
> I will try, if the model with the crossed effects converge. Otherwise, I
> would stick to the old model (only  random = ~ outcome | study,
> struct="UN") and discuss this as a limitation.
> Best,
> Emily
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