# cpam

## About

This tutorial demonstrates the R package `cpam` for the analysis of time series omics data. It serves as a basic introduction to the package. There are also two detailed case studies using real world data:

- Arabidopsis Case Study
- Human embryo Case Study

These case studies and several simulation studies are presented in the accompanying manuscript by Yates et al. (2024). See also, the package website.

## Data

The data for the following examples have been simulated based on empirical RNA-seq data. These data are gene-level counts from a case-only design with 6 time points and 5 replicates per time point. Code to reproduce the data is available in this repository.

## Installation

You can install `cpam` using:

    install.packages("cpam")

# Getting started

## Load packages

    library(cpam)
    library(dplyr)
    library(tidyr)
    library(stringr)
    library(ggplot2)

## Experimental design

An example experimental design is included in the `cpam` package. Since it is case-only design, there are no experimental conditions beyond time.

    # load example data
    load(system.file("extdata", "exp_design_example.rda", package = "cpam"))
    exp_design_example

## Count matrix

The example count data for are provided as a matrix. Let’s take a look at the first few rows.

    # load example data
    load(system.file("extdata", "count_matrix_example.rda", package = "cpam"))
    as.data.frame(count_matrix_example) %>% head

## Fitting `cpam`

To fit the models, we first prepare the `cpam` object, then compute p-values, estimate changepoints, and select the shape for each gene. In this simple example, simulated data are gene-level, that is we do not have isoform-level counts. As such, we leave ````the transcript-to-gene mapping (`t2g`) and we set`gene_level = T`.

      cpo <- prepare_cpam(exp_design = exp_design_example,
                          count_matrix = count_matrix_example,
                          model_type = "case-only",
                          t2g = NULL,
                          gene_level = T,
                          num_cores = 1) # just for the example
      cpo <- compute_p_values(cpo) # 6 seconds
      cpo <- estimate_changepoint(cpo) # 4 seconds
      cpo <- select_shape(cpo) # 5 seconds

We can look at a summary of the fitted cpam object

    cpo

If you run the code on your own computer, you can launch the Shiny app to visualise the results interactively using `visualise(cpo)`.

## Result tables

The results of the analysis are summarised using the `results` function.

    results(cpo)

The generated results can be filtered by specifying minimum counts, minimum log-fold changes, and maximum \(p\)-values. For example, to return only the transcripts with a log-fold change greater than 1, at least 10 counts, and a \(p\)-value less than 0.01, we can run

    results(cpo, min_count = 10, min_lfc = 1, p_threshold = 0.01)

## Plotting genes and transcripts

A single gene can be plotted using the `plot_cpam` function. Here we plot the gene g063

    plot_cpam(cpo, gene_id = "g063")

The subtitle shows `(1,cv)` indicating a changepoint at first time point (i.e., the gene responds immediately) and a convex (`'cv'`) shaped trend.

Let’s look for a gene that has a more complex trend. Unconstrained shapes in `cpam` are denoted by `'tp'`.1 We can filter the results for genes with unconstrained shapes and plot one of them.

    results(cpo) %>%
      filter(shape == "tp")

We plot the first gene in the list.

    plot_cpam(cpo, gene_id = "g210")

This selection of `'tp'` suggests that the trend for this gene does not conform to one of the simpler shape types that `cpam` uses. We can exclude `'tp'` as an option and force `cpam` to choose among the simpler forms by setting `shape_type = "shape2"` in the `plot_cpam` function (`"shape1"`, the default, allows the `'tp'`). This choice can be useful for analysis such as clustering. For example:

    plot_cpam(cpo, gene_id = "g210",shape_type = "shape2")

Here a monotonic increasing concave shape (‘micv’) is chosen, and we can see this trend deviates from the data substantially more that the unconstrained shape. See the manuscript for more details on the shape types available in `cpam`.

Next we look for a gene with a changepoint by filtering for genes with changepoints at the third time point.

    results(cpo) %>%
      filter(cp == 3)

Again, we plot the first gene in the list.

    plot_cpam(cpo, gene_id = "g013")

## Clusters

The results function can be used to generate clusters according to selected filters. The `plot_cluster` function can then be used to visualise the clusters. With such a small simulated data set, we don’t have many genes in each cluster, but we can try a few different clustering options to get an idea of how the function works.

    res <- results(cpo)
    plot_cluster(cpo, res, changepoints = 1, shapes = c("cv"))

There are 19 genes with a concave shape and a changepoint at the first time point.

More than one shape or changepoint can be provided. For example:

    plot_cluster(cpo, res, changepoints = 2, shapes = c("dlin","mdcx"))

There are just four genes with decreasing linear or monotonic decreasing convex shapes which have a changepoint at the second time point.

Clustering can be further refined based on, for example, the rate at which the above transcripts attain their maximum values. We illustrate advanced refinements such as this case study.

## Many more options

This is just a simple example to get you started. The package has many more features and options. Check out the two case studies to see how `cpam` can be used to analyse real-world data:

- Arabidopsis Case Study
- Human Embryo Case Study

# Session Info

Click to expand

    sessionInfo()
    #> R version 4.4.3 (2025-02-28)
    #> Platform: x86_64-pc-linux-gnu
    #> Running under: Pop!_OS 22.04 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-r0.3.20.so;  LAPACK version 3.10.0
    #>
    #> locale:
    #>  [1] LC_CTYPE=en_AU.UTF-8       LC_NUMERIC=C               LC_TIME=en_AU.UTF-8        LC_COLLATE=C
    #>  [5] LC_MONETARY=en_AU.UTF-8    LC_MESSAGES=en_AU.UTF-8    LC_PAPER=en_AU.UTF-8       LC_NAME=C
    #>  [9] LC_ADDRESS=C               LC_TELEPHONE=C             LC_MEASUREMENT=en_AU.UTF-8 LC_IDENTIFICATION=C
    #>
    #> time zone: Australia/Hobart
    #> tzcode source: system (glibc)
    #>
    #> attached base packages:
    #> [1] stats     graphics  grDevices utils     datasets  methods   base
    #>
    #> other attached packages:
    #> [1] ggplot2_3.5.1 stringr_1.5.1 tidyr_1.3.1   dplyr_1.1.4   cpam_0.1.3
    #>
    #> loaded via a namespace (and not attached):
    #>  [1] sass_0.4.9         generics_0.1.3     stringi_1.8.4      lattice_0.22-6     digest_0.6.37      magrittr_2.0.3
    #>  [7] RColorBrewer_1.1-3 evaluate_1.0.3     grid_4.4.3         fastmap_1.2.0      jsonlite_1.8.9     Matrix_1.7-2
    #> [13] limma_3.61.8       mgcv_1.9-1         purrr_1.0.4        scales_1.3.0       codetools_0.2-20   jquerylib_0.1.4
    #> [19] cli_3.6.4          rlang_1.1.5        pbmcapply_1.5.1    munsell_0.5.1      splines_4.4.3      scam_1.2-18
    #> [25] withr_3.0.2        cachem_1.1.0       yaml_2.3.10        tools_4.4.3        parallel_4.4.3     colorspace_2.1-1
    #> [31] locfit_1.5-9.10    vctrs_0.6.5        R6_2.6.1           matrixStats_1.5.0  lifecycle_1.0.4    edgeR_4.3.7
    #> [37] pkgconfig_2.0.3    pillar_1.10.1      bslib_0.9.0        gtable_0.3.6       glue_1.8.0         Rcpp_1.0.14
    #> [43] statmod_1.5.0      xfun_0.51          tibble_3.2.1       tidyselect_1.2.1   rstudioapi_0.17.0  knitr_1.49
    #> [49] farver_2.1.2       htmltools_0.5.8.1  nlme_3.1-167       labeling_0.4.3     rmarkdown_2.27     compiler_4.4.3
    #> [55] mvnfast_0.2.8

1 `tp` stands for thinplate which is the type of spline used for the ‘unconstrained’ curves as defined in the `mgcv` package. The curves are still penalised to be smooth, but the shape type is not fixed.

# References

Yates, Luke A., Jazmine L. Humphreys, Michael A. Charleston, and Steven M. Smith. 2024. “Shape-Constrained, Changepoint Additive Models for Time Series Omics Data with Cpam.” BioRxiv, December. https://doi.org/10.1101/2024.12.22.630003.