Chapter 3 Applications
3.1 Application I: Individual-level data
The dataset used here consists of a total of 14 metabolites (N = 14) and two groups (Liyanage et al. 2024). The 12 samples in the two groups had been extracted using the same method in a controlled experiment but run separately in two different instruments: Liquid Chromatography-Mass Spectrometry (LC/MS) and Gas Chromatography-Mass Spectrometry (GC/MS), leading to two separate datasets. Thus, in this example, each separate dataset from each instrument forms a different ‘study’ (\(K = 2\)), which can be integrated using meta-analysis methods. We will use `MetaHD’ for combining summary estimates obtained from these multiple metabolomic studies.
This GC-LC dataset is available in the `MetaHD’ package and can be loaded using the following command.
As explained in Section 3.1 `MetaHDInput’ function can then be used to calculate the treatment effect sizes and their associated variances and within-study covariance matrices as shown below.
## met1 met2 met3 met4 met5 met6
## study1 -0.08509765 0.0693374 0.21205246 0.1555140 -0.07131115 -0.010729262
## study2 -0.19103975 0.1985993 0.05266387 0.3042082 -0.08507508 -0.002200277
## met7 met8 met9 met10 met11 met12
## study1 -0.06351313 0.07239534 -0.02854481 -0.1874413 0.07670815 -0.04170964
## study2 -0.02427915 -0.08497286 -0.10315078 -0.1196099 0.07105905 0.21213759
## met13 met14
## study1 0.3378766 -0.20944830
## study2 0.2136121 -0.03345043## met1 met2 met3 met4 met5
## met1 0.0194438538 0.0005017922 -0.0025219163 -0.002766591 0.004992537
## met2 0.0005017922 0.0161291933 0.0042058671 0.019843118 0.002535913
## met3 -0.0025219163 0.0042058671 0.0078052190 0.007030307 -0.001285968
## met4 -0.0027665912 0.0198431182 0.0070303073 0.074406890 -0.003247293
## met5 0.0049925375 0.0025359133 -0.0012859676 -0.003247293 0.007725915
## met6 0.0036952818 0.0035899796 0.0007582538 0.004244171 0.003155352
## met6 met7 met8 met9 met10
## met1 0.0036952818 0.0036649961 0.0014738763 0.002466527 0.006057970
## met2 0.0035899796 0.0023004763 0.0009291760 0.003908964 0.001622693
## met3 0.0007582538 -0.0002967142 0.0010746462 0.001839553 -0.002939468
## met4 0.0042441714 0.0033677211 0.0053704235 0.004464203 -0.001121570
## met5 0.0031553517 0.0026034856 -0.0006582206 0.002925312 0.005845677
## met6 0.0035383608 0.0025416742 0.0003542152 0.003045991 0.003098343
## met11 met12 met13 met14
## met1 0.003742686 0.0058389366 -0.017656900 0.006189749
## met2 0.006128897 0.0057661483 -0.015584915 0.002615291
## met3 0.002551313 0.0003375944 0.001663327 -0.001850528
## met4 0.005545238 0.0033374745 -0.012707585 0.001019416
## met5 0.004305489 0.0060072612 -0.020351263 0.004988612
## met6 0.003080440 0.0039539767 -0.012411644 0.003099160When both within and between study correlations are set to zero, MetaHD reduces to the usual random effects model analysis of individual metabolites (i.e. univariate meta-analyses). Additionally, when the between-study variances are also set to zero, then MetaHD reduces to a fixed-effects model univariate meta-analysis. We can perform univariate random-effects and univariate fixed-effects meta-analysis in MetaHD as follows:
diag_Slist <- list()
K <- nrow(Y)
for (k in 1:K) {
diag_Slist[[k]] <- diag(diag(Slist[[k]]))
}
# Univariate random-effects meta-analysis
model2 <- MetaHD(Y, diag_Slist, method = "reml", bscov = "diag")
model2$estimate## [1] -0.152812327 0.137090057 0.125448886 0.236485102 -0.079158201
## [6] -0.003400281 -0.041614290 -0.005823006 -0.067093550 -0.145743651
## [11] 0.073429537 0.097636180 0.224770248 -0.115441898## [1] 0.06809548 0.11762486 0.11412429 0.19892382 0.16958255 0.87887530
## [7] 0.28159217 0.94100531 0.29722212 0.01244124 0.16187645 0.43956056
## [13] 0.00950358 0.18855174# Univariate fixed-effects meta-analysis
model3 <- MetaHD(Y, diag_Slist, method = "fixed")
model3$estimate## [1] -0.152812327 0.137090057 0.119263841 0.236485102 -0.079158213
## [6] -0.003400281 -0.041614290 -0.004927685 -0.067093550 -0.145743651
## [11] 0.073429398 0.139309196 0.224769883 -0.102735148## [1] 0.068095484 0.117624861 0.036764299 0.198923825 0.169579632 0.878875296
## [7] 0.281592165 0.914730005 0.297222122 0.012441239 0.161809425 0.011347289
## [13] 0.009502382 0.034970100When missing data are available, we can use MetaHD to handle missing values by setting the argument “impute.na = TRUE”. This replaces the missing effect sizes and variances by zero and a large constant value respectively, so that the missing outcome is allocated a lower weight in the meta-analysis.
3.2 Application II: Summary-level data
In this example, we use a simulated dataset as described by (Liyanage et al. 2024). Here we have prepared separate data frames for effect- sizes and within-study covariance matrices in the ‘simdata.1’ dataset as follows..
Now, we can carry out the meta-analysis using MetaHD as follows.
Y <- simdata.1$Y #as.matrix(unname(Y1[[1]]))
Slist <- simdata.1$Slist
## Multivariate random-effects meta analyis
model_1 <- MetaHD(Y,
Slist,
method = "reml",
bscov = "unstructured")
model_1$estimate # TRUE VALUES ARE: 5, 1, 3, 2, 4, 2, 1, 1, 5, 1, 1, 5, 5, 2, 3, 5, 4, 5, 1, 1, 2, 5, 1, 2, 1, 5, 4, 1, 4, 2