Omixer: multivariate and reproducible randomization to proactively counter batch effects in omics studies
26 October 2021
Package
Omixer 1.4.0
1 Introduction
Batch effects can have a major impact on the results of omics studies (Leek et al. 2010). Randomization is the first, and arguably most influential, step in handling them. However, its implementation suffers from a few key issues:
- A single,ATTEMPT314 random draw can inadvertently result in high correlation between technical covariates and biological factors. Particularly in studies with large numbers of batches and outcomes of interest, minimizing these correlations is crucial.
- Long, randomized sample lists are unintuitive and translate poorly into any wet lab that is not fully automated. This can result in errors and sample mixups.
- The randomization process is inherently unclear in many publications, rarely described despite the varying efficacy of methods.
- Randomized layouts are not always reproducible, resulting in inconsistent results.
To combat these problems, we developed Omixer - an R package for multivariate randomization and reproducible generation of intuitive sample layouts.
1.1 Dependencies
This document has the following dependencies.
library(Omixer)
library(tibble)
library(forcats)
library(stringr)
library(dplyr)
library(ggplot2)
library(magick)1.2 Workflow
Omixer randomizes input sample lists multiple times (default: 1,000) and then combines these randomized lists with plate layouts, which can be selected from commonly used setups or custom-made. It can handle paired samples, keeping these adjacent but shuffling their order, and allows explicit masking of specific wells if, for example, plates are shared between different studies.
After performing robust tests of correlation between technical covariates and selected randomization factors, a layout is chosen using these criteria:
- No test provided sufficient evidence to suggest correlation between the variables (all p-values over 0.05).
- From the remaining layouts, return one where the absolute sum of correlations is minimized.
The optimal randomized list can then be processed by omixerSheet, returning
intuitive sample layouts for the wet lab.
2 Creating Layouts
In order to establish correlations between technical covariates and biological
factors, Omixer needs to know the plate layout that your samples will be
randomized to. There are several options for automatically creating some
common layouts. Alternatively, a data frame can be input to the layout
option alongside specified techVars. Possibilities are discussed in more
detail below.
2.1 Automated Layouts
Several options can be used to automatically generate common layouts:
wellsspecifies the number of wells on a plate, which can be 96, 48, or 24.plateNumdetermines how many copies of the plate your samples will need.divis optional, and subdivides the plate into batches. This can be used to specify chips within a plate, for example.positionalallows positions withindivto also be treated as batches. This is useful for 450K experiments where positional batch effects have been identified (Jiao et al. 2018).
2.2 Subdivisions
By default, div is set to “none”, but it can be set to “col”, “row”,
“col-block”, or “row-block”.
coltreats each column in the plate as a batchrowtreats each row in the plate as a batchcol-blockwill separate the plate into batches that are 2 columns widerow-blockseparates the plate into 2 row wide batches
So, for wells=48, div="col", each column of a 48-well plate will be
treated as a batch (different colours in the image below).
If you instead specify div="row", the rows will be treated as batches.
Similarly, you can set div="col-block" or div="row-block" for
batches that are 2 columns or rows wide, respectively. The image below shows
how a 48 well plate would be subdivided with the div="col-block" option.
Combining the above will allow you to create a large number of layouts commonly used in omics experiments.
2.3 Masking
If your experiment requires certain wells to be left empty, then these can be
specified with the mask option. By default, no wells are masked, but you can
specify masking, with 1 representing a masked well and 0 signifying that a
sample should be randomized to this position.
Wells are numbered along each row sequentially. In the images above, row A includes wells 1 through 8, row B is wells 9 to 16, and so on until well 48 at F8.
2.4 Custom Layouts
If none of the automated layouts represent your setup you can input your own
plate layout as a data frame. The only requirement is that the number of
unmasked wells is equal to the number of samples in your experiment, and that
you input the names of technical covariate columns to the techVars option.
For example, if we wanted to create a 96-well plate to send for 450K DNA
methylation profiling, we might submit the following layout and techVars.
layout <- tibble(plate=rep(1, 96), well=1:96,
row=factor(rep(1:8, each=12), labels=toupper(letters[1:8])),
column=rep(1:12, 8), chip=as.integer(ceiling(column/2)),
chipPos=ifelse(column %% 2 == 0, as.numeric(row)+8, row))
techVars <- c("chip", "chipPos")
layout
#> # A tibble: 96 × 6
#> plate well row column chip chipPos
#> <dbl> <int> <fct> <int> <int> <dbl>
#> 1 1 1 A 1 1 1
#> 2 1 2 A 2 1 9
#> 3 1 3 A 3 2 1
#> 4 1 4 A 4 2 9
#> 5 1 5 A 5 3 1
#> 6 1 6 A 6 3 9
#> 7 1 7 A 7 4 1
#> 8 1 8 A 8 4 9
#> 9 1 9 A 9 5 1
#> 10 1 10 A 10 5 9
#> # … with 86 more rows3 Simple example
We create toy data, representing 48 samples to be sent off for RNA sequencing. All samples will be on a single 48-well flowcell, with each of the 8-sample rows being pipetting onto a lane, resulting in 6 lanes. This setup can be represented using provided Omixer layouts, as is described below.
First, we build the sample list that will be provided to Omixer, with information on the age, sex, and smoking status of individuals alongside sample isolation dates. We want to optimize distribution of these randomization variables across lanes on the flowcell to minimize batch effects.
sampleList <- tibble(sampleId=str_pad(1:48, 4, pad="0"),
sex=as_factor(sample(c("m", "f"), 48, replace=TRUE)),
age=round(rnorm(48, mean=30, sd=8), 0),
smoke=as_factor(sample(c("yes", "ex", "never"), 48,
replace=TRUE)),
date=sample(seq(as.Date('2008/01/01'), as.Date('2016/01/01'),
by="day"), 48))
sampleList
#> # A tibble: 48 × 5
#> sampleId sex age smoke date
#> <chr> <fct> <dbl> <fct> <date>
#> 1 0001 m 25 ex 2013-02-27
#> 2 0002 m 17 ex 2010-05-25
#> 3 0003 m 37 ex 2015-01-25
#> 4 0004 f 31 never 2014-02-02
#> 5 0005 m 21 ex 2009-07-07
#> 6 0006 f 40 never 2015-11-14
#> 7 0007 f 33 ex 2013-11-01
#> 8 0008 f 28 never 2012-03-26
#> 9 0009 m 37 yes 2015-05-04
#> 10 0010 m 37 never 2011-08-18
#> # … with 38 more rows3.1 Randomization Variables
Using the randVars option, we inform Omixer which columns in our data
represent randomization variables. You can specify any number of variables,
but with increasing numbers it will become more difficult to optimize their
distribution across batches.
randVars <- c("sex", "age", "smoke", "date")3.2 Running Omixer
To perform multivariate randomization use the omixerRand function. For our
example, we have one 96-well flowcell wells=96, plateNum=1 and want to
optimize sample distribution across lanes div="row".
Following randomization, omixerRand will display a visualization of
correlations between randomization and technical variables. If the returning
correlations are higher than you would like, you can increase the iterNum
or decrease the number of randomization variables.
omixerLayout <- omixerRand(sampleList, sampleId="sampleId",
block="block", iterNum=100, wells=48, div="row",
plateNum=1, randVars=randVars)
#> Random seed saved to working directory
Following omixerRand, an optimal randomized sample list is returned. This
can be used as is or processed by omixerSheet to create lab-friendly sample
sheets, which will be shown below.
head(omixerLayout[1:11])
#> sampleId sex age smoke date plate well row column mask chip
#> 1 0009 m 37 yes 2015-05-04 1 1 A 1 0 1
#> 2 0028 f 30 ex 2014-02-25 1 2 B 1 0 2
#> 3 0001 m 25 ex 2013-02-27 1 3 C 1 0 3
#> 4 0042 f 32 yes 2011-08-05 1 4 D 1 0 4
#> 5 0017 f 24 ex 2009-11-02 1 5 E 1 0 5
#> 6 0026 m 29 never 2015-01-13 1 6 F 1 0 63.3 Regenerating Layouts
Since multivariate randomization can take some time with large datasets and
many randomization variables, we provide the omixerSpecific function to
reproduce previously generated layouts. After running omixerRand, the seed
of the optimal layout is saved to the working directory.
After setting the global variable .Random.seed, you can run omixerSpecific
to regenerate the optimal layout.
load("randomSeed.Rdata")
.GlobalEnv$.Random.seed <- randomSeed
omixerLayout <- omixerSpecific(sampleList, sampleId="sampleId",
block="block", wells=96, div="row",
plateNum=1, randVars=randVars)3.4 Sample Sheets
Once the multivariate randomization is complete, the resulting data frame can
be input into omixerSheet to produce lab-friendly sample layouts. These will
be saved in your working directory as a PDF document.
It is possible to colour code these sheets by a specific factor using the
group option, and this is demonstrated in the extended example.
omixerSheet(omixerLayout)
4 Extended example
To demonstrate the full functionality of Omixer, we present an extended example.
Here, our toy data represents 616 samples ready to be sent off for EPIC DNA
methylation profiling. These samples will be randomized to 7 96-well plates
where each of the 8 columns are transferred to a 12-sample EPIC chip. The
last chip on each plate needs to be kept empty for control samples, and we
will communicate this to Omixer using the mask option.
Our samples are taken from 4 different tissues of 77 individuals, and we are
interested in how DNA methylation changes over 2 timepoints. Given our
primary research question, we would like to keep the timepoints adjacent on
the array but randomize their order. We can do this in Omixer with the
block option, as demonstrated below.
4.1 Creating Toy Data
As well as a sample ID, we need to tell Omixer which variables specify
paired sample blocks using a blocking variable, which we name block.
sampleList<- tibble(sampleId=str_pad(1:616, 4, pad="0"),
block=rep(1:308, each=2),
time=rep(0:1, 308),
tissue=as_factor(rep(c("blood", "fat", "muscle", "saliva"),
each=2, 77)),
sex=as_factor(rep(sample(c("male", "female"), 77, replace=TRUE),
each=8)),
age=round(rep(rnorm(77, mean=60, sd=10), each=8), 0),
bmi=round(rep(rnorm(77, mean=25, sd=2), each=8) , 1),
date=rep(sample(seq(as.Date('2015/01/01'), as.Date('2020/01/01'),
by="day"), 77), each=8))
sampleList
#> # A tibble: 616 × 8
#> sampleId block time tissue sex age bmi date
#> <chr> <int> <int> <fct> <fct> <dbl> <dbl> <date>
#> 1 0001 1 0 blood male 61 26.9 2016-02-28
#> 2 0002 1 1 blood male 61 26.9 2016-02-28
#> 3 0003 2 0 fat male 61 26.9 2016-02-28
#> 4 0004 2 1 fat male 61 26.9 2016-02-28
#> 5 0005 3 0 muscle male 61 26.9 2016-02-28
#> 6 0006 3 1 muscle male 61 26.9 2016-02-28
#> 7 0007 4 0 saliva male 61 26.9 2016-02-28
#> 8 0008 4 1 saliva male 61 26.9 2016-02-28
#> 9 0009 5 0 blood female 42 24.9 2018-07-16
#> 10 0010 5 1 blood female 42 24.9 2018-07-16
#> # … with 606 more rows
save(sampleList, file="sampleList.Rdata")4.2 Setting up Variables
We set up our randomization variables to optimize distribution of our biological factors across chips and plates. Randomization variables in our example are tissue, sex, age, body mass index (BMI), and isolation date.
randVars <- c("tissue", "sex", "age", "bmi", "date")Since the last chip on each plate needs to be reserved, we specify a mask so that Omixer knows not to assign samples to these wells.
In the mask, a 0 indicates that a sample will be assigned to that well, and
a 1 indicates that it should be left empty.
mask <- rep(c(rep(0, 88), rep(1, 8)), 7)4.3 Running Omixer
Now we are ready to perform multivariate randomization with the omixerRand
function. We specify 7 96-well plates wells=96, plateNum=7 subdivided into
8-sample EPIC chips div="col".
omixerLayout <- omixerRand(sampleList, sampleId="sampleId",
block="block", iterNum=100, wells=96, div="col", plateNum=7,
randVars=randVars, mask=mask)
#> Random seed saved to working directory
4.4 Simple Randomization
Looking at the above correlations, you may wonder how Omixer compares to simple randomization. Briefly, we will investigate this.
Simple randomization can be replicated using omixerRand with a iterNum=1.
Here, only one randomized layout will be created. If this is not optimal, a
warning will print but the layout will still be returned.
simpleLayout <- omixerRand(sampleList, sampleId="sampleId",
block="block",iterNum=1, wells=96, div="col", plateNum=7,
randVars=randVars, mask=mask)
#> Warning in min(absSum): no non-missing arguments to min; returning Inf
#> Warning in omixerRand(sampleList, sampleId = "sampleId", block = "block", : All
#> randomized layouts contained unwanted correlations.
#> Warning in omixerRand(sampleList, sampleId = "sampleId", block = "block", :
#> Returning best possible layout.
#> Random seed saved to working directory
Here, we see strong evidence of a correlation between:
- Age and chip (τ = -0.082, p = 0.005)
- Age and plate (τ = -0.073, p = 0.011)
- Date and plate (τ = 0.082, p = 0.005)
These patterns threaten the validity of our future inferences, as the effects of biological factors are entangled with technical variations.
In comparison, there is insufficient evidence to suggest correlation between any biological factor and technical covariate in the Omixer produced layout, and the largest correlation coefficient returned is 0.048, which is considerably lower than many seen in the simple randomized layout.
4.5 Regenerating layouts
As in the simple example, any Omixer layouts can be regenerated using the
saved random environment in the omixerSpecific function.
After setting the global variable .Random.seed, you can run omixerSpecific
to regenerate the optimal layout.
load("randomSeed.Rdata")
.GlobalEnv$.Random.seed <- randomSeed
omixerLayout <- omixerSpecific(sampleList, sampleId="sampleId",
block="block", wells=96, div="col", plateNum=7,
randVars=randVars, mask=mask)4.6 Sample Sheets
The bridge between dry and wet labs can be precarious. Technicians are often faced with long, monotonous lists of samples, which they need to pipette accurately to minimize sample mixups. This is especially prevalent in more complicated setups as in this extended example.
The omixerSheet function smooths this transition by creating lab-friendly
PDFs of sample layouts.
You can colour code wells by another variable. In our example, we want to
highlight wells of each tissue, since samples from one tissue are likely to be
stored together group="tissue". The first page of the resulting PDF is shown
below.
omixerSheet(omixerLayout, group="tissue")
5 References
Jiao, Chuan, Chunling Zhang, Rujia Dai, Yan Xia, Kangli Wang, Gina Giase, Chao Chen, and Chunyu Liu. 2018. “Positional effects revealed in Illumina methylation array and the impact on analysis.” Epigenomics 10 (5): 643–59. https://doi.org/10.2217/epi-2017-0105.
Leek, Jeffrey T., Robert B. Scharpf, Héctor Corrada Bravo, David Simcha, Benjamin Langmead, W. Evan Johnson, Donald Geman, Keith Baggerly, and Rafael A. Irizarry. 2010. “Tackling the widespread and critical impact of batch effects in high-throughput data” 11 (10): 733–39. https://doi.org/10.1038/nrg2825.
6 Session Info
sessionInfo()
#> R version 4.1.1 (2021-08-10)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: Ubuntu 20.04.3 LTS
#>
#> Matrix products: default
#> BLAS: /home/biocbuild/bbs-3.14-bioc/R/lib/libRblas.so
#> LAPACK: /home/biocbuild/bbs-3.14-bioc/R/lib/libRlapack.so
#>
#> locale:
#> [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
#> [3] LC_TIME=en_GB LC_COLLATE=C
#> [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
#> [7] LC_PAPER=en_US.UTF-8 LC_NAME=C
#> [9] LC_ADDRESS=C LC_TELEPHONE=C
#> [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
#>
#> attached base packages:
#> [1] stats graphics grDevices utils datasets methods base
#>
#> other attached packages:
#> [1] magick_2.7.3 ggplot2_3.3.5 dplyr_1.0.7 stringr_1.4.0
#> [5] forcats_0.5.1 tibble_3.1.5 Omixer_1.4.0 BiocStyle_2.22.0
#>
#> loaded via a namespace (and not attached):
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