Binary factor

Of the output table, the estimate columns start with the prefix c_ indicate composition, or with v_ indicate variability (when formula_variability is set).

sccomp_result = 
  sce_obj |>
  sccomp_estimate( 
    formula_composition = ~ type, 
    .sample =  sample, 
    .cell_group = cell_group, 
    cores = 1 
  ) |> 
  sccomp_remove_outliers(cores = 1) |> # Optional
  sccomp_test()

sccomp_result = 
  counts_obj |>
  sccomp_estimate( 
    formula_composition = ~ type, 
    .sample = sample,
    .cell_group = cell_group,
    .count = count, 
    cores = 1, verbose = FALSE
  ) |> 
  sccomp_remove_outliers(cores = 1, verbose = FALSE) |> # Optional
  sccomp_test()

sccomp_result

Summary plots

A plot of group proportions, faceted by groups. The blue boxplots represent the posterior predictive check. If the model is descriptively adequate for the data, the blue boxplots should roughly overlay the black boxplots, which represent the observed data. The outliers are coloured in red. A boxplot will be returned for every (discrete) covariate present in formula_composition. The colour coding represents the significant associations for composition and/or variability.

sccomp_result |> 
  sccomp_boxplot(factor = "type")

A plot of estimates of differential composition (c_) on the x-axis and differential variability (v_) on the y-axis. The error bars represent 95% credible intervals. The dashed lines represent the minimal effect that the hypothesis test is based on. An effect is labelled as significant if it exceeds the minimal effect according to the 95% credible interval. Facets represent the covariates in the model.

sccomp_result |> 
  plot_1D_intervals()

We can plot the relationship between abundance and variability. As we can see below, they are positively correlated. sccomp models this relationship to obtain a shrinkage effect on the estimates of both the abundance and the variability. This shrinkage is adaptive as it is modelled jointly, thanks to Bayesian inference.

sccomp_result |> 
  plot_2D_intervals()

You can produce the series of plots calling the plot method.

sccomp_result |> plot() 

Model proportions directly (e.g. from deconvolution)

Note: If counts are available, we strongly discourage the use of proportions, as an important source of uncertainty (i.e., for rare groups/cell types) is not modeled.

The use of proportions is better suited for modelling deconvolution results (e.g., of bulk RNA data), in which case counts are not available.

Proportions should be greater than 0. Assuming that zeros derive from a precision threshold (e.g., deconvolution), zeros are converted to the smallest non-zero value.

Continuous factor

sccomp is able to fit erbitrary complex models. In this example we have a continuous and binary covariate.

res =
    seurat_obj |>
    sccomp_estimate(
      formula_composition = ~ type + continuous_covariate, 
      .sample = sample, .cell_group = cell_group,
      cores = 1, verbose=FALSE
    )

res

Random Effect Modeling

sccomp supports multilevel modeling by allowing the inclusion of random effects in the compositional and variability formulas. This is particularly useful when your data has hierarchical or grouped structures, such as measurements nested within subjects, batches, or experimental units. By incorporating random effects, sccomp can account for variability at different levels of your data, improving model fit and inference accuracy.

seurat_obj[[]] |> as_tibble()

## Loading required package: SeuratObject

## Loading required package: sp

## 'SeuratObject' was built under R 4.4.0 but the current version is
## 4.4.1; it is recomended that you reinstall 'SeuratObject' as the ABI
## for R may have changed

## 'SeuratObject' was built with package 'Matrix' 1.7.0 but the current
## version is 1.7.1; it is recomended that you reinstall 'SeuratObject' as
## the ABI for 'Matrix' may have changed

## 
## Attaching package: 'SeuratObject'

## The following objects are masked from 'package:base':
## 
##     intersect, t

## # A tibble: 106,297 × 9
##    cell_group nCount_RNA nFeature_RNA group__ group__wrong sample type  group2__
##    <chr>           <dbl>        <int> <chr>   <chr>        <chr>  <chr> <chr>   
##  1 CD4 naive           0            0 GROUP1  1            SI-GA… canc… GROUP21 
##  2 Mono clas…          0            0 GROUP1  1            SI-GA… canc… GROUP21 
##  3 CD4 cm S1…          0            0 GROUP1  1            SI-GA… canc… GROUP21 
##  4 B immature          0            0 GROUP1  1            SI-GA… canc… GROUP21 
##  5 CD8 naive           0            0 GROUP1  1            SI-GA… canc… GROUP21 
##  6 CD4 naive           0            0 GROUP1  1            SI-GA… canc… GROUP21 
##  7 Mono clas…          0            0 GROUP1  1            SI-GA… canc… GROUP21 
##  8 CD4 cm S1…          0            0 GROUP1  1            SI-GA… canc… GROUP21 
##  9 CD4 cm hi…          0            0 GROUP1  1            SI-GA… canc… GROUP21 
## 10 B immature          0            0 GROUP1  1            SI-GA… canc… GROUP21 
## # ℹ 106,287 more rows
## # ℹ 1 more variable: continuous_covariate <dbl>

res = 
  seurat_obj |>
  sccomp_estimate( 
    formula_composition = ~ type + (1 | group__), 
    .sample = sample,
    .cell_group = cell_group,
    bimodal_mean_variability_association = TRUE,
    cores = 1, verbose = FALSE
  ) 

res

res = 
  seurat_obj |>
  sccomp_estimate(
      formula_composition = ~ type + (type | group__),
      .sample = sample,
      .cell_group = cell_group,
      bimodal_mean_variability_association = TRUE,
      cores = 1, verbose = FALSE
    )

res

res = 
  seurat_obj |>
  sccomp_estimate(
      formula_composition = ~ type + (type | group__) + (1 | group2__),
      .sample = sample,
      .cell_group = cell_group,
      bimodal_mean_variability_association = TRUE,
      cores = 1, verbose = FALSE
    )

res

An aid to result interpretation and communication

The estimated effects are expressed in the unconstrained space of the parameters, similar to differential expression analysis that expresses changes in terms of log fold change. However, for differences in proportion, logit fold change must be used, which is harder to interpret and understand.

Therefore, we provide a more intuitive proportional fold change that can be more easily understood. However, these cannot be used to infer significance (use sccomp_test() instead), and a lot of care must be taken given the nonlinearity of these measures (a 1-fold increase from 0.0001 to 0.0002 carries a different weight than a 1-fold increase from 0.4 to 0.8).

From your estimates, you can specify which effects you are interested in (this can be a subset of the full model if you wish to exclude unwanted effects), and the two points you would like to compare.

In the case of a categorical variable, the starting and ending points are categories.

sccomp_result |> 
   sccomp_proportional_fold_change(
     formula_composition = ~  type,
     from =  "healthy", 
     to = "cancer"
    ) |> 
  select(cell_group, statement)

Contrasts

seurat_obj |>
  sccomp_estimate( 
    formula_composition = ~ 0 + type, 
    .sample = sample,
    .cell_group = cell_group, 
    cores = 1, verbose = FALSE
  ) |> 
  sccomp_test( contrasts =  c("typecancer - typehealthy", "typehealthy - typecancer"))

Categorical factor (e.g. Bayesian ANOVA)

This is achieved through model comparison with loo. In the following example, the model with association with factors better fits the data compared to the baseline model with no factor association. For comparisons check_outliers must be set to FALSE as the leave-one-out must work with the same amount of data, while outlier elimination does not guarantee it.

If elpd_diff is away from zero of > 5 se_diff difference of 5, we are confident that a model is better than the other reference. In this case, -79.9 / 11.5 = -6.9, therefore we can conclude that model one, the one with factor association, is better than model two.

library(loo)

# Fit first model
model_with_factor_association = 
  seurat_obj |>
  sccomp_estimate( 
    formula_composition = ~ type, 
    .sample =  sample, 
    .cell_group = cell_group, 
    inference_method = "hmc",
    enable_loo = TRUE
  )

# Fit second model
model_without_association = 
  seurat_obj |>
  sccomp_estimate( 
    formula_composition = ~ 1, 
    .sample =  sample, 
    .cell_group = cell_group, 
    inference_method = "hmc",
    enable_loo = TRUE
  )

# Compare models
loo_compare(
   attr(model_with_factor_association, "fit")$loo(),
   attr(model_without_association, "fit")$loo()
)

Differential variability, binary factor

We can model the cell-group variability also dependent on the type, and so test differences in variability

res = 
  seurat_obj |>
  sccomp_estimate( 
    formula_composition = ~ type, 
    formula_variability = ~ type,
    .sample = sample,
    .cell_group = cell_group,
    cores = 1, verbose = FALSE
  )

res

Plot 1D significance plot

plots = res |> sccomp_test() |> plot()

plots$credible_intervals_1D

Plot 2D significance plot Data points are cell groups. Error bars are the 95% credible interval. The dashed lines represent the default threshold fold change for which the probabilities (c_pH0, v_pH0) are calculated. pH0 of 0 represent the rejection of the null hypothesis that no effect is observed.

This plot is provided only if differential variability has been tested. The differential variability estimates are reliable only if the linear association between mean and variability for (intercept) (left-hand side facet) is satisfied. A scatterplot (besides the Intercept) is provided for each category of interest. For each category of interest, the composition and variability effects should be generally uncorrelated.

plots$credible_intervals_2D

For single-cell RNA sequencing

We recommend setting bimodal_mean_variability_association = TRUE. The bimodality of the mean-variability association can be confirmed from the plots$credible_intervals_2D (see below).

For CyTOF and microbiome data

We recommend setting bimodal_mean_variability_association = FALSE (Default).

Visualisation of the MCMC chains from the posterior distribution

It is possible to directly evaluate the posterior distribution. In this example, we plot the Monte Carlo chain for the slope parameter of the first cell type. We can see that it has converged and is negative with probability 1.

library(cmdstanr)
library(posterior)
library(bayesplot)

# Assuming res contains the fit object from cmdstanr
fit <- res |> attr("fit")

# Extract draws for 'beta[2,1]'
draws <- as_draws_array(fit$draws("beta[2,1]"))

# Create a traceplot for 'beta[2,1]'
mcmc_trace(draws, pars = "beta[2,1]")

sessionInfo()

## R version 4.4.1 (2024-06-14)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 24.04.1 LTS
## 
## Matrix products: default
## BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3 
## LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so;  LAPACK version 3.12.0
## 
## locale:
##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=en_US.UTF-8        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       
## 
## time zone: Etc/UTC
## tzcode source: system (glibc)
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] SeuratObject_5.0.2 sp_2.1-4           tidyr_1.3.1        forcats_1.0.0     
## [5] ggplot2_3.5.1      sccomp_1.11.0      dplyr_1.1.4        prettydoc_0.4.1   
## 
## loaded via a namespace (and not attached):
##  [1] tidyselect_1.2.1            farver_2.1.2               
##  [3] fastmap_1.2.0               SingleCellExperiment_1.28.0
##  [5] dotCall64_1.2               digest_0.6.37              
##  [7] lifecycle_1.0.4             processx_3.8.4             
##  [9] magrittr_2.0.3              compiler_4.4.1             
## [11] rlang_1.1.4                 sass_0.4.9                 
## [13] tools_4.4.1                 utf8_1.2.4                 
## [15] yaml_2.3.10                 knitr_1.48                 
## [17] S4Arrays_1.6.0              DelayedArray_0.33.1        
## [19] abind_1.4-8                 withr_3.0.2                
## [21] purrr_1.0.2                 BiocGenerics_0.53.0        
## [23] sys_3.4.3                   grid_4.4.1                 
## [25] stats4_4.4.1                fansi_1.0.6                
## [27] colorspace_2.1-1            future_1.34.0              
## [29] progressr_0.15.0            globals_0.16.3             
## [31] scales_1.3.0                SummarizedExperiment_1.36.0
## [33] cli_3.6.3                   rmarkdown_2.28             
## [35] crayon_1.5.3                generics_0.1.3             
## [37] future.apply_1.11.3         httr_1.4.7                 
## [39] tzdb_0.4.0                  cachem_1.1.0               
## [41] stringr_1.5.1               zlibbioc_1.52.0            
## [43] parallel_4.4.1              XVector_0.46.0             
## [45] matrixStats_1.4.1           vctrs_0.6.5                
## [47] Matrix_1.7-1                jsonlite_1.8.9             
## [49] callr_3.7.6                 IRanges_2.41.0             
## [51] hms_1.1.3                   patchwork_1.3.0            
## [53] S4Vectors_0.44.0            ggrepel_0.9.6              
## [55] listenv_0.9.1               maketools_1.3.1            
## [57] jquerylib_0.1.4             spam_2.11-0                
## [59] parallelly_1.38.0           glue_1.8.0                 
## [61] codetools_0.2-20            ps_1.8.1                   
## [63] stringi_1.8.4               gtable_0.3.6               
## [65] GenomeInfoDb_1.43.0         GenomicRanges_1.59.0       
## [67] UCSC.utils_1.2.0            munsell_0.5.1              
## [69] instantiate_0.2.3           tibble_3.2.1               
## [71] pillar_1.9.0                htmltools_0.5.8.1          
## [73] GenomeInfoDbData_1.2.13     R6_2.5.1                   
## [75] evaluate_1.0.1              lattice_0.22-6             
## [77] Biobase_2.67.0              readr_2.1.5                
## [79] bslib_0.8.0                 Rcpp_1.0.13                
## [81] SparseArray_1.6.0           xfun_0.48                  
## [83] MatrixGenerics_1.19.0       fs_1.6.5                   
## [85] buildtools_1.0.0            pkgconfig_2.0.3