This vignette documents the data format used in PLNmodel by PLN and its variants. It also shows how to create an object in the proper format for further analyses from (i) tabular data, (ii) biom-class objects and (iii) phyloseq-class objects.
We illustrate the format using trichoptera data set, a full description of which can be found in the corresponding vignette.
The trichoptera data set is a list made of two data frames: Abundance (hereafter referred to as the counts) and Covariate (hereafter the covariates).
## List of 2
## $ Abundance:'data.frame': 49 obs. of 17 variables:
## $ Covariate:'data.frame': 49 obs. of 7 variables:The covariates include, among others, the wind, pressure and humidity.
## [1] "Temperature" "Wind" "Pressure" "Humidity"
## [5] "Cloudiness" "Precipitation" "Group"In the PLN framework, we model the counts from the covariates, let’s say wind and pressure, using a Poisson Log-Normal model. Most models in R use the so-called formula interface and it would thus be naturel to write something like
Unfortunately and unlike many generalized linear models, the response in PLN is intrinsically multivariate: it has 17 dimensions in our example. The left hand side (LHS) must encode a multivariate response across multiple samples, using a 2D-array (e.g. a matrix or a data frame).
We must therefore prepare a data structure where Abundance refers to a count matrix whereas Wind and Pressure refer to vectors before feeding it to PLN. That’s the purpose of prepare_data.
trichoptera2 <- prepare_data(counts = trichoptera$Abundance,
covariates = trichoptera$Covariate)
str(trichoptera2)## 'data.frame': 49 obs. of 9 variables:
## $ Abundance : num [1:49, 1:17] 0 0 0 0 0 0 0 0 0 0 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : chr "1" "2" "3" "4" ...
## .. ..$ : chr "Che" "Hyc" "Hym" "Hys" ...
## $ Temperature : num 18.7 19.8 22 23 22.5 23.9 15 17.2 15.4 14.1 ...
## $ Wind : num -2.3 -2.7 -0.7 2.3 2.3 -2 -4.7 -1 -2.7 -3.7 ...
## $ Pressure : num 998 1000 997 991 990 ...
## $ Humidity : num 60 63 73 71 62 64 93 84 88 75 ...
## $ Cloudiness : num 19 0 6 81 50 50 100 19 69 6 ...
## $ Precipitation: num 0 0 0 0 0 0 1.6 0 1.6 0 ...
## $ Group : Factor w/ 12 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ Offset : num 29 13 38 192 79 18 8 34 12 4 ...If you look carefully, you can notice a few difference between trichoptera and trichoptera2:
list whereas the second is a data.frame1;Abundance is a matrix-column of trichoptera2 that you can extract using the usual functions [ and [[ to retrieve the count matrix;trichoptera2 has an additional Offset column (more on that later).It is common practice when modeling count data to introduce an offset term to control for different sampling efforts, exposures, baselines, etc. The proper way to compute sample-specific offsets in still debated and may vary depending on the field. There are nevertheless a few popular methods:
Each of these offset be computed from a counts matrix using the compute_offset function and changing its offset argument:
## same as compute_offset(trichoptera$Abundance, offset = "TSS")
compute_offset(trichoptera$Abundance) ## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
## 29 13 38 192 79 18 8 34 12 4 4 3 49 33 600 172
## 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
## 58 51 56 127 35 13 17 3 27 40 44 8 9 1599 2980 88
## 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
## 135 327 66 90 63 15 14 20 70 53 95 43 62 149 16 31
## 49
## 86In this particular example, the counts are too sparse and sophisticated offset methods all fail (numeric output hidden)
## Warning in offset_function(counts, ...): Some samples only have 1 positive
## values. Can't compute quantiles and fall back to TSS normalization## Warning in offset_function(counts, ...): Because of high sparsity, some samples
## have null or infinite offset.We can mitigate this problem for the RLE offset by adding pseudocounts to the counts although doing so has its own drawbacks.
## 1 2 3 4 5 6 7 8
## 0.9186270 0.8349121 0.8570257 0.9186270 0.9186270 0.8349121 0.8192245 0.8570257
## 9 10 11 12 13 14 15 16
## 0.7322797 0.7322797 0.6321923 0.6321923 0.9240361 0.9186270 1.3788037 0.9240361
## 17 18 19 20 21 22 23 24
## 0.9186270 0.9240361 0.9240361 1.7140514 0.8908577 0.8570257 0.8349121 0.6321923
## 25 26 27 28 29 30 31 32
## 0.9240361 0.9240361 0.9186270 0.8570257 0.8349121 2.7721084 3.2934218 0.9584503
## 33 34 35 36 37 38 39 40
## 1.0406547 0.9584503 0.9584503 0.9186270 0.9584503 0.8908577 0.8349121 0.7322797
## 41 42 43 44 45 46 47 48
## 0.9240361 0.9240361 0.9584503 0.9584503 1.2643846 1.7140514 0.8233555 0.8908577
## 49
## 0.9186270prepare_dataWe’ll already learned that prepare_data can join counts and covariates into a single data.frame. It can also compute offset through compute_offset and does so by default with offset = "TSS", hence the Offset column in trichoptera2. You can change the offset method and provide additional arguments that will passed on to compute_offset.
## 'data.frame': 49 obs. of 9 variables:
## $ Abundance : num [1:49, 1:17] 0 0 0 0 0 0 0 0 0 0 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : chr "1" "2" "3" "4" ...
## .. ..$ : chr "Che" "Hyc" "Hym" "Hys" ...
## $ Temperature : num 18.7 19.8 22 23 22.5 23.9 15 17.2 15.4 14.1 ...
## $ Wind : num -2.3 -2.7 -0.7 2.3 2.3 -2 -4.7 -1 -2.7 -3.7 ...
## $ Pressure : num 998 1000 997 991 990 ...
## $ Humidity : num 60 63 73 71 62 64 93 84 88 75 ...
## $ Cloudiness : num 19 0 6 81 50 50 100 19 69 6 ...
## $ Precipitation: num 0 0 0 0 0 0 1.6 0 1.6 0 ...
## $ Group : Factor w/ 12 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ Offset : num 0.919 0.835 0.857 0.919 0.919 ...Different communities use different standard for the count data where samples are either or columns of the counts matrix. prepare_data uses heuristics to guess the direction of the counts matrix (or fail informatively doing so) and automatically transpose it if needed.
Finally, prepare_data enforces sample-consistency between the counts and the covariates and automatically trims away: - samples for which only covariates or only counts are available; - samples with no positive counts
For example, if we remove the first sample from the counts and the last one from the covariates, we end up with 49 - 2 = 47 samples left, as expected.
nrow(prepare_data(trichoptera$Abundance[-1, ], ## remove first sample
trichoptera$Covariate[-49,] ## remove last sample
))## [1] 47prepare_data_from_[phyloseq|biom]Community composition data are quite popular in microbial ecology and usually stored in flat files using the biom format and/or imported in R as phyloseq-class objects (McMurdie 2013) using the Bioconductor phyloseq package.
We show here how to import data from a biom file (or biom-class object) and form a phyloseq-class object.
Reading from a biom file requires the bioconductor package biomformat. This package is not a standard dependency of PLNmodels and needs to be installed separately.
You can easily prepare your data from a biom file using the following steps:
biomformat::read_biom()biomformat::biom_data()biomformat::sample_metadata() (or build your own)prepare_dataas illustrated below:
## If biomformat is not installed, uncomment the following lines
# if (!requireNamespace("BiocManager", quietly = TRUE)) {
# install.packages("BiocManager")
# }
# BiocManager::install("biomformat")
library(biomformat)
biomfile <- system.file("extdata", "rich_dense_otu_table.biom", package = "biomformat")
biom <- biomformat::read_biom(biomfile)
## extract counts
counts <- as(biomformat::biom_data(biom), "matrix")
## extract covariates (or prepare your own)
covariates <- biomformat::sample_metadata(biom)
## prepare data
my_data <- prepare_data(counts = counts, covariates = covariates)
str(my_data)Likewise, preparing data from a phyloseq-class object requires the bioconductor package phyloseq. This package is not a standard dependency of PLNmodels and needs to be installed separately.
You can easily prepare your data from a phyloseq object using the following steps:
phyloseq::otu_table()phyloseq::sample_data() (or build your own)prepare_dataas illustrated below:
## If biomformat is not installed, uncomment the following lines
# if (!requireNamespace("BiocManager", quietly = TRUE)) {
# install.packages("BiocManager")
# }
# BiocManager::install("phyloseq")
library(phyloseq)
data("enterotype")
## extract counts
counts <- as(phyloseq::otu_table(enterotype), "matrix")
## extract covariates (or prepare your own)
covariates <- phyloseq::sample_data(enterotype)
## prepare data
my_data <- prepare_data(counts = counts, covariates = covariates)
str(my_data)We detail here the mathematical background behind the various offsets and the way they are computed. Note \(\mathbf{C} = (c_{ij})\) the counts matrix where \(c_{ij}\) is the count of species \(j\) in sample \(i\). Assume that there are \(J\) species in total. The offset of sample \(i\) is noted \(O_i\) and computed in the following way.
Offsets are simply the total counts of a sample: \[ O_i = \sum_{j=1}^J c_{ij} \]
Positive counts are used to compute sample-specific quantiles \(q_i^l\) and cumulative sums \(s_i^l\) defined as \[
q_i^l = \min \{q \text{ such that } \sum_j 1_{c_{ij} \leq q} \geq l \sum_j 1_{c_{ij} > 0} \} \qquad s_i^l = \sum_{j: c_{ij} \leq q_i^l} c_{ij}
\] The sample-specific quantiles are then used to compute reference quantiles defined as \(q^l = \text{median} \{q^i_l\}\) and median average deviation around the quantile \(q^l\) as \(d^l = \text{median} |q_i^l - q^l|\). The method then searches for the smallest quantile \(l\) for which it detects instability, defined as large relative increase in the \(d^l\). Formally, \(\hat{l}\) is the smallest \(l\) satisfying \(\frac{d^{l+1} - d^l}{d^l} \geq 0.1\). The scaling sample-specific offset are then chosen as: \[
O_i = s_i^{\hat{l}} / \text{median}_i \{ s_i^{\hat{l}} \}
\] Dividing by the median of the \(s_i^{\hat{l}}\) ensures that offsets are centered around \(1\) and compare sizes differences with respect to the reference sample. Note also that the reference quantiles \(q^l\) can be computed using either the median (default, as in the original Paulson et al. (2013) paper) or the mean, by specifying reference = mean, as implemented in metagenomeseq.
A reference sample \((q_j)_j\) is first built by computing the geometric means of each species count: \[
q_j = \exp \left( \frac{1}{n} \sum_{i} \log(c_{ij})\right)
\] Each sample is then compared to the reference sample to compute one ratio per species and the final offset \(O_i\) is the median of those ratios: \[
O_i = \text{median}_j \frac{c_{ij}}{q_j}
\] The method fails when no species is shared across all sample (as all \(q_j\) are then \(0\)) or when a sample shares less than 50% of species with the reference (in which case the median of the ratios may be null or infinite). The problem can be alleviated by adding pseudocounts to the \(c_{ij}\) with pseudocounts = 1.
This method is similar to RLE but does create a reference sample. Instead, each sample is compared to each other to compute a median ratio (similar to RLE) \[ r_{ii'} = {\text{median}}_{j: c_{ij}.c_{i'j} > 0} \frac{c_{ij}}{c_{i'j}} \] The offset is then taken as the median of all the \(r_{ii'}\): \[ O_i = \text{median}_{i' != i} r_{ii'} \] The method fails when there is only one sample in the data set or when a sample shares no species with any other.
Anders, Simon, and Wolfgang Huber. 2010. “Differential Expression Analysis for Sequence Count Data.” Genome Biology 11 (10): R106. https://doi.org/10.1186/gb-2010-11-10-r106.
Chen, Li, James Reeve, Lujun Zhang, Shengbing Huang, Xuefeng Wang, and Jun Chen. 2018. “GMPR: A Robust Normalization Method for Zero-Inflated Count Data with Application to Microbiome Sequencing Data.” PeerJ 6 (April): e4600. https://doi.org/10.7717/peerj.4600.
McMurdie, Paul J. AND Holmes. 2013. “Phyloseq: An R Package for Reproducible Interactive Analysis and Graphics of Microbiome Census Data.” PLoS ONE 8 (4). Public Library of Science: e61217. https://doi.org/10.1371/journal.pone.0061217.
Paulson, Joseph N, O. Colin Stine, Héctor Corrada Bravo, and Mihai Pop. 2013. “Differential Abundance Analysis for Microbial Marker-Gene Surveys.” Nat Methods 10 (September): 1200–1202. https://doi.org/10.1038/nmeth.2658.
although a data.frame is technically a list↩