[R-meta] Inflated confidence intervals

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Dear Wasim,

It seems like you are trying to obtained the estimated (average) difference between HDL and LDL. Based on the model with only HDL and LDL, this is equal to -0.0394 (with 95% CI: -0.1254 to 0.0466). However, your code to obtain the analogous value from the model with all three outcomes is not correct. It should be:

predict(resMV, newmods = c(1,0))

(intercept=TRUE isn't needed, since this is the default here). Then this will yield: -0.2376 + 0.1982 = -0.0394, which is the exact same value as obtained from the model with only the two outcomes. I cannot tell you what the CI will be based on the output provided, but I suspect you will get something very similar as you obtained from the model with only the two outcomes.

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-project.org] On Behalf Of Wasim Iqbal (UG)
Sent: Sunday, 16 September, 2018 8:37
To: r-sig-meta-analysis at r-project.org
Cc: Gavin Stewart; Chris Seal
Subject: [R-meta] Inflated confidence intervals

I have finally understood and a found a simple solution or reason for inflated confidence intervals and I thought I would post it here so that it may help others.

I am conducting a multivariate meta-analysis for an upcoming publication in the Campbell library (campbellcollaboration.org<https://campbellcollaboration.org>). This will involve the analysis of various biomarkers. I had made a list of a posterior contrasts. However, when I had compiled these interactions in a multivariate meta-analysis some models led to wider confidence intervals. At first, I had assumed this was because my model had collapsed or that the variability between studies was great. After a lot of reading and contemplating, I can conclude that this was infact to do with highly correlated outcomes (or multicollinearity).

My multivariate meta-analysis relies on an assumed pearson correlation between outcomes. If a pearson correlation is highly correlated this will lead to either an upward or downward bias of the confidence intervals. This is because the multivariate meta-analysis model restricts the average correlation between -1.00 and +1.00 to produce a symmetric var-cov matrix (or positive definite) so that the model can be formed. Removing outcomes that appear to be highly correlated leads to narrower confidence intervals.

Here is an example of a model with studies looking at serum total cholesterol, high density lipoprotein and low density lipoprotein:

Multivariate Meta-Analysis Model (k = 105; method: REML)

Variance Components:

outer factor: Study?????? (nlvls = 35)
inner factor: Measurement (nlvls = 3)

??????????? estim??? sqrt? k.lvl? fixed? level
tau^2.1??? 0.0812? 0.2850???? 35???? no? A LDL
tau^2.2??? 0.0076? 0.0874???? 35???? no??? HDL
tau^2.3??? 0.0487? 0.2208???? 35???? no???? TC

?????? rho.ALDL? rho.HDL? rho.TC??? ALDL? HDL? TC
A LDL???????? 1?? 0.4819? 0.8774?????? -?? no? no
HDL????? 0.4819??????? 1? 0.8432????? 35??? -? no
TC?????? 0.8774?? 0.8432?????? 1????? 35?? 35?? -

Test for Residual Heterogeneity:
QE(df = 102) = 207.8936, p-val < .0001

Test of Moderators (coefficient(s) 2:3):
QM(df = 2) = 18.1033, p-val = 0.0001

Model Results:

??????????????? estimate????? se???? zval??? pval??? ci.lb??? ci.ub
intrcpt????????? -0.2376? 0.0648? -3.6655? 0.0002? -0.3647? -0.1106? ***
MeasurementHDL??? 0.1982? 0.0513?? 3.8681? 0.0001?? 0.0978?? 0.2987? ***
MeasurementTC??? -0.0148? 0.0656? -0.2251? 0.8219? -0.1433?? 0.1138

---
Signif. codes:? 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

In the above model which includes 35 studies each contributing all three outcomes. Total serum cholesterol (TC) appears to be highly correlated with low density lipoprotein (LDL) and high density lipoprotein (HDL). Therefore, when we use the predict function this leads to a much wider confidence interval than a bivariate model that includes only LDL and HDL.

Model with all three contrasts/interactions:
?>predict(resMV,newmods = c(1,1),intercept = T)
??? pred???? se?? ci.lb? ci.ub cr.lb cr.ub tau2.level
?-0.0541 0.0588 -0.1695 0.0612??? NA??? NA???????? NA

Model with only HDL and LDL:
?>pred???? se?? ci.lb? ci.ub cr.lb cr.ub tau2.level
?-0.0394 0.0439 -0.1254 0.0466??? NA??? NA???????? NA

Another reason for multicollinarity or wider confidence intervals is if your multivariate meta-analysis does not include enough studies to estimate an accurate "between study outcomes pearson correlation".

Hope this helps anyone that has experienced a similar problem or confusion.

Kind regards
Wasim Iqbal