pclrc

Probabilistic context likelihood of relatedness^[1] to study the correlation network differences^[2]. This package is developed using Python 3.10.

Note

The package can be extremely slow for relatively large number of samples or variables.

Requirements

The following packages are required:

cython 3.X
numpy
matplotlib
tqdm

All can be easily installed using pip or conda.

Installation

To install, download the package from the Releases. Uncompress the file and move them to the working directory. Open command line tool like Command Prompt (in Windows) or Terminal (in macOS) and set current directory to the working directory using cd command. In Windows, run

Python -m setup install

or in macOS, run

Python3 -m setup install

The package will be installed.

Run

To run the package, in Python IDLE or other environment like JupyterLab,

from PCLRC import PCLRC

• Create PCLRC object with specified arguments:

  pclrc = PCLRC(num_sampling: int = int(1e5), frac_sampling: float = 0.75, q: float = 0.3, corr_prob: float = 0.9, bootstrap: bool = False, num_perms: int = int(1e4), num_cores: Optional[int] = None)

  • Arguments:
    • num_sampling: The number of subsampling procedures. Defaults to 100000.
    • frac_sampling: Fraction of samples selected in each subsampling procedure to calculate Pearson Correlation Coefficients (PCCs). Defaults to 0.75.
    • q: The top q * 100% PCCs are considered as valid associations using the data subsampled, which will be set to 1 in binary adjacent matrix, otherwise will be set to 0. Defaults to 0.3.
      • If q is set to 0., a hard threshold defined in Ref [3] is used.
    • corr_prob: Correlation probability threshold for justifying significant associations, so that corresponding PCCs will be used to calculating differences in connectivity.
    • bootstrap: Whether to use bootstrap sampling during subsampling procedures. This is used because some dataset may have very small number of samples. Defaults to False.
    • num_perms: Number of permutations used in permutation tests. Defaults to 10000.
    • num_cores: Whether running the permutation tests in parallel and number of cores used for the parallelization. Defaults to None which means no parallelization is used.

• Run PCLRC with data matrix x and sample labels in groups:

  pclrc.network_diffs(x: np.ndarray, groups: np.ndarray)

  • Arguments:
    • x: Data matrix with size n rows by p columns, where n is the number of samples, and p is number of variables.
    • groups: Group names in 1-D array with number of n elements.

  [!NOTE]
  Only two groups are allowed for running the analysis, i.e., len(set(groups))=2.

• Other than the method network_diffs, a method is implemented to obtain the correlation probability matrix:

  pclrc.corr_probs(x: np.ndarray, prog_bar: bool = True)

  • Arguments:
    • x: Data matrix with size n rows by p columns, where n is the number of samples, and p is number of variables.
    • prog_bar: Whether to show progress bar for calculation.

Analyze the results

After running pclrc.network_diffs,

• to obtain the correlation probability: pclrc.pearson_corr_probs(label: Optional[Any] = None)

  • Arguments:
    • label: Group name in groups input when running pclrc.network_diffs, if set it to None, correlation probability for both groups will be output, with first prob. matrix corresponding to group groups[0], second to group groups[1].

• to obtain differences in connectivity: pclrc.diff_connectivity

• to obtain the significant differences in connectivity: pclrc.sig_diff_connectivity(fdr: float=0.05)

  • Arguments:
    • fdr: The false discovery rate (FDR) to select significant differences in connectivity, which is the adjust p value threshold after BH correction.

• to obtain permutated probabilities for all variables: pclrc.perm_probs

• to obtain the labels/group names: pclrc.data_labels

Demonstration

To demonstrate how to run the package, a jupyter notebook was provided in the package, which can also be obtained at pclrc.demo.ipynb. The dataset was downloaded from Metabolomics Workbench, study ST003751, in negative mode. The figures shown in the references, e.g., connections between variables, differences in connectivity, were also provided in the demonstration.

References

[1] Saccenti E, et al. J. Proteome Res. 2015, 14, 2, 1101–1111.
[2] Vignoli A, et al. J. Proteome Res. 2020, 19, 949−961.
[3] Suarez-Diez M, et al. J. Proteome Res. 2015, 14, 12, 5119–5130.