Introduction

The objective of this vignette is to compare the coefficient of variation (CV) of the three spike-in bacteria in the Stammler_2016_16S_spikein dataset using relative abundance (TSS) and centered-log-ratio transformation (CLR). However, since CLR is log transformed and TSS is not, a geometric mean normalization (GMN) method will be used instead of CLR.

S. ruber will be used for re-calibrating the abundance data (counts). This is referred to as SCML. The data will also be normalized with TSS (TSS) or GMN (GMN). The CV of the abundance data of the three spike-in bacteria across samples using these two normalization methods will be calculated and compared.

Data

tse <- getBenchmarkData('Stammler_2016_16S_spikein', dryrun = FALSE)[[1]]

Recalibrate with spike-in Salinibacter ruber

spk_bac <- c(
    `S. ruber` = 'AF323500XXXX', 
    `R. radiobacter` = 'AB247615XXXX',
    `A. acidiphilus` = 'AB076660XXXX'
)
counts <- assay(tse, 'counts')
s_ruber <- counts[spk_bac['S. ruber'], ]
size_factor <- s_ruber/mean(s_ruber)
SCML_data <- counts 
for(i in seq(ncol(SCML_data))){
    SCML_data[,i] <- round(SCML_data[,i] / size_factor[i])
}
assay(tse, 'SCML') <- SCML_data

Tranform with TSS (relative abundance) and CLR

tss_fun <- function(x) (x + 1) / sum((x + 1))
# tss_fun <- function(x) log((x + 1) / sum((x + 1)))
# tss_fun <- function(x) (x) / sum((x))
gmn_fun <- function(x) (x + 1) / exp(mean(log((x + 1))))
# gnm_fun <- function(x) (x + 1) / prod((x + 1)^(1 / length(x)))
# gmn_fun <- function(x) log((x + 1) / exp(mean(log((x + 1)))))
assay(tse, "TSS") <- apply(assay(tse, 'counts'), 2,  tss_fun)
assay(tse, "GMN") <- apply(assay(tse, 'counts'), 2, gmn_fun) 

Extract data of sipike-in bacteria

spk_bac_tse <- tse[spk_bac,]
rownames(spk_bac_tse) <- names(spk_bac)
spk_bac_tse
#> class: TreeSummarizedExperiment 
#> dim: 3 17 
#> metadata(0):
#> assays(4): counts SCML TSS GMN
#> rownames(3): S. ruber R. radiobacter A. acidiphilus
#> rowData names(1): taxonomy
#> colnames(17): MID26 MID27 ... MID42 MID43
#> colData names(12): dataset subject_id ... country description
#> reducedDimNames(0):
#> mainExpName: NULL
#> altExpNames(0):
#> rowLinks: NULL
#> rowTree: NULL
#> colLinks: NULL
#> colTree: NULL

Get tidy data

data <- spk_bac_tse |> 
    assays() |> 
    names() |> 
    map({
        ~ tidy.RangedSummarizedExperiment(spk_bac_tse, assay = .x) |> 
            magrittr::set_colnames(c("taxon", "sample", .x))
    }) |> 
    reduce(.f = \(.x, .y) left_join(.x, .y, by = c("taxon", "sample")))
DT::datatable(data, filter = 'top')

Calculate coefficient of variation

Define a formula for calculating coefficient of variation

get_cv <- function(x) {
    cv <- function(x, n) { sd(x[n]) / abs(mean(x[n])) } 
    boot::boot(x, cv, R = 1000) |>
        broom::tidy() |>
        dplyr::rename(cv = statistic)
} 
cv_res <- data %>% 
    group_by(taxon) %>% 
    summarize(across(.cols = counts:last_col(), .fns = get_cv)) %>% 
    pivot_longer(
        cols = 2:last_col(), names_to = 'norm', values_to = 'cv_res' 
    ) %>% 
    unnest(cols = 'cv_res')
   
DT::datatable(cv_res, filter = 'top')     

Table in wider format:

cv_res |> 
    rename(
        Species = taxon, `Normalization method` = norm,
        CV = cv, SE = std.error
    ) |> 
    filter(`Normalization method` %in% c("GMN", "TSS")) |> 
    select(-bias) |> 
    mutate(
        CV = round(CV, 2), SE = round(SE, 2)
    ) |> 
    mutate(
        `Normalization method` = ifelse(
            test = `Normalization method` == "TSS", 
            yes = "Relative abundance",
            no = `Normalization method`
        )
    ) |> 
    DT::datatable(
        extensions = 'Buttons',,
        filter = "top",
        options = list(
        dom = 'Bfrtip',
        buttons = list(
            list(
                extend = 'copy',
                text = 'Copy '
                )
            )
        )
    )

Compare coefficient of variation

cv_res |>  
    filter(norm != 'counts') |> 
    mutate(
        norm = factor(norm, levels = c(
            'counts', 'SCML', 'TSS',  'GMN'
            )
        )
    ) %>%
    mutate(taxon = forcats::fct_relevel(taxon, 'S. ruber')) |> 
    ggplot(aes(reorder(norm, cv), cv)) +
    geom_point(aes(color = norm), size = 2) + 
    geom_errorbar(
        aes(ymin = cv - std.error, ymax = cv + std.error, color = norm),
        width = 0.4, size = 0.5
    ) +
    scale_color_brewer(type = 'qual', palette = 'Set2') +
    facet_wrap(~taxon) + 
    labs(
        y = 'Coefficient of variation across all samples',
        x = 'Data transformation'
    ) + 
    theme_bw() + 
    theme(
        # axis.text.x = element_text(angle = 45, hjust = 1),
        panel.grid.major.x = element_blank(),
        strip.text = element_text(face = 'italic'),
        legend.position = 'none'
    )
#> Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
#>  Please use `linewidth` instead.
#> This warning is displayed once every 8 hours.
#> Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
#> generated.

Conclusion

TSS normalizaion has lower CV values than GMN. This could indicate that it introduces less bias than GMN, which is related to CLR.

Session info

sessioninfo::session_info()
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