[R-meta] Non-positive definite covariance matrix for rma.mv

Mon Jul 1 14:17:53 CEST 2024

Hi,

I surely do not fully comprehend the problem. But what I do not understand is why fully consistent treatment effects should lead to a non-positive definite covariance matrix. In network meta-analysis, we always estimate fully consistent treatment effects for all pairwise comparisons, and the full covariance matrix will always be positive definite. This has nothing to do with the (by the way, unnecessary) choice of a baseline treatment. Or am I misunderstanding anything?

Best,
Gerta

UNIVERSITÄTSKLINIKUM FREIBURG
Institute for Medical Biometry and Statistics

Dr. Gerta Rücker
Guest Scientist

Stefan-Meier-Straße 26 · 79104 Freiburg
gerta.ruecker using uniklinik-freiburg.de

https://www.uniklinik-freiburg.de/imbi-en/employees.html?imbiuser=ruecker

-----Ursprüngliche Nachricht-----
Von: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org> Im Auftrag von Andreas Voldstad via R-sig-meta-analysis
Gesendet: Montag, 1. Juli 2024 00:23
An: James Pustejovsky <jepusto using gmail.com>; R Special Interest Group for Meta-Analysis <r-sig-meta-analysis using r-project.org>
Cc: Andreas Voldstad <andreas.voldstad using kellogg.ox.ac.uk>
Betreff: Re: [R-meta] Non-positive definite covariance matrix for rma.mv

Hi James, thank you for responding. Indeed, I am fitting a model across all the contrasts, and metafor did yell at me for the NPD V matrix. Is this a case where it might be appropriate to use the nearpd = T argument in vcalc?

Best wishes,
Andreas

Sent from Outlook for iOS<https://aka.ms/o0ukef>
________________________________
From: James Pustejovsky <jepusto using gmail.com>
Sent: Sunday, June 30, 2024 5:13:32 PM
To: R Special Interest Group for Meta-Analysis <r-sig-meta-analysis using r-project.org>
Cc: Andreas Voldstad <andreas.voldstad using kellogg.ox.ac.uk>
Subject: Re: [R-meta] Non-positive definite covariance matrix for rma.mv

Hi Andreas,

I think the NPD issue arises from having treatment contrasts that are perfectly collinear. Consider that if you know the contrasts Tx1 vs Passive, Tx2 vs Passive, and Tx1 vs Active, then you can infer the Tx2 vs Active contrast:
(Tx2 vs Passive) - (Tx1 vs Passive) + (Tx1 vs Active) = (Tx2 - Tx1)  + (Tx1 vs Active) = (Tx2 vs Active)

As far as I can see, the only way to avoid this is to calculate all effect size contrasts relative to a common comparison condition.

Depending on the meta-analytic model in which you use this covariance matrix, the NPD issue might or might not be important—it really depends on the structure of the model. For example, if you are going to run separate models with the active control contrasts and passive control contrasts, then the fact that the whole covariance matrix is NPD is NBD—not a big deal. But if you’re fitting some sort of multilevel meta-analysis model across all the contrasts, then metafor will yell at you if you use an NBD matrix in the V argument.

James

> On Jun 30, 2024, at 8:37 AM, Andreas Voldstad via R-sig-meta-analysis <r-sig-meta-analysis using r-project.org> wrote:
>
> Dear everyone,
>
> I have one study in my meta-analysis with a covariance matrix that is non-positive definite.
>
> I am wondering what consequences this might have for my meta-analysis with rma.mv, and whether you have any suggestions of how to deal with the issue.
>
> The study had four arms and effect sizes are additionally correlated over time and within dyads.
>
> The correlations over time and dyad members used for creating the covariance matrix was based on the corresponding correlations between participants' scores, estimated from the study dataset.
>
> Because of the four arms, some effect sizes have no overlap, leading to blocks of zeros in the covariance matrix.
>
> The covariance matrix is reproduced below:
>
> study_escalc <- data.frame(  StudyID = c("StudyA", "StudyA", "StudyA", "StudyA", "StudyA", "StudyA", "StudyA", "StudyA", "StudyA", "StudyA", "StudyA", "StudyA", "StudyA", "StudyA", "StudyA", "StudyA"),  Role = c("Husband", "Husband", "Wife", "Wife", "Husband", "Husband", "Wife", "Wife", "Husband", "Husband", "Wife", "Wife", "Husband", "Husband", "Wife", "Wife"),  Timenum = c(2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3),  Tx = c("Tx1", "Tx1", "Tx1", "Tx1", "Tx2", "Tx2", "Tx2", "Tx2", "Tx1", "Tx1", "Tx1", "Tx1", "Tx2", "Tx2", "Tx2", "Tx2"),  Control = c("Passive", "Passive", "Passive", "Passive", "Passive", "Passive", "Passive", "Passive", "Active", "Active", "Active", "Active", "Active", "Active", "Active", "Active"),  Contrast = c("Tx1 vs Passive", "Tx1 vs Passive", "Tx1 vs Passive", "Tx1 vs Passive", "Tx2 vs Passive", "Tx2 vs Passive", "Tx2 vs Passive", "Tx2 vs Passive", "Tx1 vs Active", "Tx1 vs Active", "Tx1 vs Active", "Tx1 vs Active", "Tx2 vs Active", "Tx2 vs Active", "Tx2 vs Active", "Tx2 vs Active"),  delta = c(0.467304, 0.429311, 0.145277, 0.248136, 0.684523, 0.537425, 0.380137, 0.335112, 0.432723, 0.480095, 0.145031, 0.252715, 0.628890, 0.572478, 0.373187, 0.338829),  v = c(0.053375, 0.053154, 0.051417, 0.051710, 0.056543, 0.056865, 0.052208, 0.052756, 0.053863, 0.053454, 0.050774, 0.053052, 0.056766, 0.057132, 0.051522, 0.054108),  N_tx = c(38, 39, 39, 38, 36, 35, 39, 37, 38, 39, 39, 38, 36, 35, 39, 37),  N_Control = c(39, 38, 39, 40, 39, 38, 39, 40, 38, 38, 40, 38, 38, 38, 40, 38),  Category = c("Husband_2", "Husband_3", "Wife_2", "Wife_3", "Husband_2", "Husband_3", "Wife_2", "Wife_3", "Husband_2", "Husband_3", "Wife_2", "Wife_3", "Husband_2", "Husband_3", "Wife_2", "Wife_3"),  Effect = c("Tx1 vs Passive_Husband_2", "Tx1 vs Passive_Husband_3", "Tx1 vs Passive_Wife_2", "Tx1 vs Passive_Wife_3", "Tx2 vs Passive_Husband_2", "Tx2 vs Passive_Husband_3", "Tx2 vs Passive_Wife_2", "Tx2 vs Passive_Wife_3", "Tx1 vs Active_Husband_2", "Tx1 vs Active_Husband_3", "Tx1 vs Active_Wife_2", "Tx1 vs Active_Wife_3", "Tx2 vs Active_Husband_2", "Tx2 vs Active_Husband_3", "Tx2 vs Active_Wife_2", "Tx2 vs Active_Wife_3"))
>
> study_cormat <- matrix(c(  1.000000, 0.781447, 0.689538, 0.639455,  0.781447, 1.000000, 0.565192, 0.653545,  0.689538, 0.565192, 1.000000, 0.820650,  0.639455, 0.653545, 0.820650, 1.000000),  nrow=4, byrow=TRUE, dimnames = list(    c("Husband_2", "Husband_3", "Wife_2", "Wife_3"),    c("Husband_2", "Husband_3", "Wife_2", "Wife_3")))
>
> Study_Vmat <-   vcalc(vi = v,        cluster = StudyID,        obs = Category,                 grp1 = Tx,         grp2 = Control,                 w1 = N_tx,        w2 = N_Control,                rho = study_cormat,        data = study_escalc)
>
> # Warning message: The var-cov matrix appears to be not positive definite in cluster StudyA. cov2cor(Study_Vmat)
>
>
>
> Warm wishes,
>
> Andreas Voldstad (he/him)
> PhD student in Psychiatry
> University of Oxford
> Please don’t feel obliged to read or respond to my email outside your own working hours.
>
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