csa_rescale_stat.py

from __future__ import division

# !/usr/bin/env python
# -*- coding: utf-8
#########################################################################################
#
# Evaluate the robustness of automated CSA with global rescaled images
#
# example: python csa_rescale_stat.py -i <results>
# ---------------------------------------------------------------------------------------
# Authors: Paul Bautin
#
# About the license: see the file LICENSE
#########################################################################################

# TODO: add plot of STD across transfo

import pandas as pd
import numpy as np
import os
import argparse
import matplotlib.pyplot as plt
from math import ceil
from ruamel.yaml import YAML
from scipy import stats


# Parser
#########################################################################################

def get_parser():
    """parser function"""
    parser = argparse.ArgumentParser(
        description="Compute statistics based on the csv files containing the CSA metrics:",
        formatter_class=argparse.RawTextHelpFormatter,
        prog=os.path.basename(__file__).strip(".py")
    )

    mandatory = parser.add_argument_group("\nMANDATORY ARGUMENTS")
    mandatory.add_argument(
        "-i",
        required=True,
        default='csa_atrophy_results',
        help='Path to folder that contains output csv files (e.g. "csa_atrophy_results/results")',
    )
    mandatory.add_argument(
        '-config',
        required=True,
        help='Path to config file, which contains parameters for the statistics and figures. Example: config_script.yml',
    )
    optional = parser.add_argument_group("\nOPTIONAL ARGUMENTS")
    optional.add_argument(
        '-fig',
        help='Generate figures',
        action='store_true'
    )
    optional.add_argument(
        '-l',
        help='Vertebrae levels on which to compute the statistics. \nExample: -l 2 3 4 5',
        nargs="*",
    )
    optional.add_argument(
        '-o',
        help='Path where figures will be saved. By default, they will be saved in the current directory.',
        default=""
    )
    return parser


# Functions
def concatenate_csv_files(path_results):
    """Fetch and concatenate data from all csv files in results/csa_data to compute statistics with pandas
    :param path_results: path to folder containing csv files for statistics
    """
    files = []
    for file in os.listdir(path_results):
        path = os.path.join(path_results, file)
        if ".csv" in file and "csa" and "sub" in file:
            files.append(path)
    if not files:
        raise FileExistsError("Folder {} does not contain any results csv file.".format(path_results))
    #metrics = pd.concat(
       #[pd.read_csv(f).assign(rescale=os.path.basename(f).split('_')[4].split('.csv')[0]) for f in files])
    print("Concatenate csv files. This will take a few seconds...")
    metrics = pd.concat(pd.read_csv(f) for f in files)
    # output csv file in PATH_RESULTS
    metrics.to_csv(os.path.join(path_results, r'csa_all.csv'))


def yaml_parser(config_file):
    """parse config_script.yml file containing pipeline's parameters"""
    with open(config_file, 'r') as config_var:
        yaml = YAML(typ='safe')
        config_param = yaml.load(config_var)
    return config_param


def plot_perc_err(df, path_output):
    """plot percentage difference between measured rescaling and rescaling
    :param df: dataframe for computing stats across subject: df_rescale
    :param path_output: directory in which plot is saved
    """
    df = df.reset_index().set_index('rescale_area')
    fig, axes = plt.subplots(nrows=2, ncols=1, figsize=(8, 6))
    df.groupby('rescale_area')['mean_perc_error'].mean().plot(kind='bar', ax=axes[0], grid=True)
    axes[0].set_title('mean error function of area rescaling')
    axes[0].set_ylabel('error in %')
    df['std_perc_error'].plot(kind='bar', ax=axes[1], sharex=True, sharey=True, legend=False)
    axes[1].set_title('STD of error in function of area rescaling')
    plt.xlabel('area rescaling in %')
    plt.ylabel('STD in %')
    plt.grid()
    plt.tight_layout()
    output_file = os.path.join(path_output, "fig_err.png")
    plt.savefig(output_file)
    print("--> Created figure: {}".format(output_file))


def boxplot_csa(df, path_output):
    """boxplot CSA for different rescaling values
    :param df: dataframe with csv files data: df_sub
    :param path_output: directory in which plot is saved
    """
    fig2 = plt.figure()
    meanpointprops = dict(marker='x' , markeredgecolor='red' ,
                          markerfacecolor='red')
    # round rescale area
    df['rescale_area'] = round(df['rescale_area'], ndigits=0).astype(int)
    df.boxplot(column=['mean'], by='rescale_area', positions=sorted(set(df['rescale_area'].values)), showmeans=True, meanprops=meanpointprops)
    min_rescale = min(df['rescale_area'].values)
    max_rescale = max(df['rescale_area'].values)
    max_y = df.groupby('rescale').get_group(1).mean()['mean']
    plt.plot([min_rescale, max_rescale], [max_y * (0.93 ** 2) , max_y] , ls="--" , c=".3")
    plt.title('Boxplot of CSA in function of area rescaling')
    plt.suptitle("")
    plt.ylabel('CSA in mm^2')
    plt.xlabel('CSA scaling')
    output_file = os.path.join(path_output, "fig_boxplot_csa.png")
    plt.savefig(output_file)
    print("--> Created figure: {}".format(output_file))


def boxplot_atrophy(df, path_output):
    """boxplot error for different rescaling values
    :param df: dataframe for computing stats per subject: df_sub
    :param path_output: directory in which plot is saved
    """
    fig = plt.figure()
    # convert to percentage
    df['rescale_estimated'] = df['rescale_estimated'] * 100
    # round rescale area
    df['rescale_area'] = round(df['rescale_area'], ndigits=0).astype(int)
    meanpointprops = dict(marker='x' , markeredgecolor='red' ,
                          markerfacecolor='red')
    df.boxplot(column='rescale_estimated', by='rescale_area', positions=sorted(set(df['rescale_area'].values)), showmeans=True, meanline=False, figsize=(10,8), meanprops=meanpointprops)
    min_rescale = min(df['rescale_area'].values)
    max_rescale = max(df['rescale_area'].values)
    plt.plot([min_rescale, max_rescale], [min_rescale, max_rescale], ls="--", c=".3")
    plt.title('Boxplot of measured atrophy in function of CSA scaling')
    plt.suptitle("")
    plt.ylabel('Atrophied CSA in % of the un-rescaled CSA')
    plt.xlabel('CSA scaling')
    plt.axis('scaled')
    output_file = os.path.join(path_output, "fig_boxplot_atrophy.png")
    plt.savefig(output_file)
    print("--> Created figure: {}".format(output_file))


def plot_sample_size(z_conf, z_power, std_arr, mean_csa, path_output):
    """plot minimum number of patients required to detect an atrophy of a given value
    :param z_conf: z score for X % uncertainty. Example: z_conf=1.96
    :param z_power: z score for X % Power. Example: z_power=(0.84, 1.282)
    :param std_arr: STD around mean CSA of control subjects (without rescaling),
    CSA STD for atrophied subjects and control subjects are considered equal
    :param mean_csa: mean value of CSA to compute the atrophy percentage. Example: 80 mm^2
    :param path_output: directory in which plot is saved
    """
    fig_sample, ax = plt.subplots()
    # data for plotting
    n_t1 = []
    n_t2 =[]
    for z_p in z_power:
        # x_axis values ranging from 1.5 to 8.0 mm^2
        atrophy = np.arange(1.5, 8.0, 0.05)
        # numerator of sample size equation T1w
        num_n_t1 = 2 * ((z_conf + z_p) ** 2) * (std_arr[0] ** 2)
        n_t1.append(num_n_t1 / ((0.01*atrophy*mean_csa[0]) ** 2))
        # numerator of sample size equation T2w
        num_n_t2 = 2 * ((z_conf + z_p) ** 2) * (std_arr[1] ** 2)
        n_t2.append(num_n_t2 / ((0.01*atrophy*mean_csa[1]) ** 2))
    # plot
    ax.plot(atrophy / mean_csa[0] * 100, n_t1[0], 'b.', markevery=3, markersize=10, label='t1 80% power')
    ax.plot(atrophy / mean_csa[0] * 100, n_t1[1], 'r.', markevery=3, markersize=10, label='t1 90% power')
    ax.plot(atrophy / mean_csa[1] * 100, n_t2[0], 'c', label='t2 80% power')
    ax.plot(atrophy / mean_csa[1] * 100, n_t2[1], 'm', label='t2 90% power')
    ax.set_ylabel('number of participants per group of study \n(patients or controls) with ratio 1:1')
    ax.set_xlabel('atrophy in %')
    plt.suptitle('minimum number of participants to detect an atrophy with 5% uncertainty', fontsize=16, y=1.05)
    ax.set_title('T1w (1.0 mm iso): SD = {} mm², mean CSA= {} mm² \nT2w (0.8 mm iso): SD = {} mm², mean CSA= {} mm²'.format(
            str(
                round(std_arr[0], 2)), str(mean_csa[0]), str(round(std_arr[1], 2)) , str(mean_csa[1])))
    ax.legend()
    ax.grid()
    output_file = os.path.join(path_output, "fig_min_subj.png")
    plt.savefig(output_file, bbox_inches='tight')
    print("--> Created figure: {}".format(output_file))


def error_function_of_csa(df, path_output):
    """Scatter plot of CSA as a function of Mean error %
    :param df: dataframe for computing stats per subject: df_sub
    :param path_output: directory in which plot is saved
    """
    fig, ax = plt.subplots(figsize=(7, 7))
    df['Normalized CSA in mm²'] = df['mean'].div(df['rescale'])
    # compute linear regression
    z = np.polyfit(x=df.loc[:, 'perc_error'], y=df.loc[:, 'Normalized CSA in mm²'], deg=1)
    p = np.poly1d(z)
    # plot
    df.plot.scatter(x='perc_error', y='Normalized CSA in mm²', c='rescale', colormap='viridis')
    min_err = min(df['perc_error'].values)
    max_err = max(df['perc_error'].values)
    plt.plot([min_err, max_err], [min_err*z[0]+z[1], max_err*z[0]+z[1]], ls="--", c=".3")
    plt.title('Normalized CSA in function of error %,\n linear regression: {}'.format(p))
    plt.xlabel('Mean error %')
    ax.legend(loc='upper right')
    plt.grid()
    output_file = os.path.join(path_output, "fig_err_in_function_of_csa.png")
    plt.savefig(output_file, bbox_inches='tight')
    print("--> Created figure: {}".format(output_file))


def error_function_of_intra_cov(df, path_output):
    """Scatter plot of intra-subject COV in function of error %
    :param df: dataframe for computing stats per subject: df_sub
    :param path_output: directory in which plot is saved
    """
    fig, ax = plt.subplots(figsize=(7, 7))
    # remove rescale=1 because error=0
    df = df[df['rescale'] != 1]
    # compute linear regression
    z = np.polyfit(x=df.loc[:, 'perc_error'], y=df.loc[:, 'cov'], deg=1)
    p = np.poly1d(z)
    # plot
    df.plot.scatter(x='perc_error', y='cov', c='rescale', colormap='viridis')
    min_err = min(df['perc_error'].values)
    max_err = max(df['perc_error'].values)
    plt.plot([min_err, max_err], [min_err*z[0]+z[1], max_err*z[0]+z[1]], ls="--", c=".3")
    plt.xlabel('Mean error %')
    plt.ylabel('COV')
    plt.title('COV in function of % error,\n linear regression: {}'.format(p))
    ax.legend(loc='upper right')
    plt.grid()
    output_file = os.path.join(path_output, "fig_err_in_function_of_cov.png")
    plt.savefig(output_file, bbox_inches='tight')
    print("--> Created figure: {}".format(output_file))


def error_function_of_intra_cov_outlier(df, path_output):
    """Scatter plot of intra-subject COV in function of error % to identify the worst outliers (outside the interval
    [Q1-10IQR, Q3+10IQR] of percentage error)
    :param df: dataframe for computing stats per subject: df_sub
    :param path_output: directory in which plot is saved
    """
    fig, ax = plt.subplots(figsize=(7, 7))
    Q1 = df['perc_error'].quantile(0.25)
    Q3 = df['perc_error'].quantile(0.75)
    # IQR = inter-quartile range.
    IQR = Q3 - Q1
    # identified outliers either high error % or high intra-subject COV
    outliers = set(df[(df['perc_error'] <= Q1 - 10 * IQR) | (df['perc_error'] >= Q3 + 10 * IQR)]['subject'])
    # remove rescale=1 because error=0
    df = df[df['rescale'] != 1]
    ax.scatter(df['perc_error'], df['cov'], color='tab:blue', label='others')
    # scatter outliers
    for outlier in outliers:
        df_t1 = df.groupby(['subject']).get_group(outlier)
        ax.scatter(df_t1['perc_error'], df_t1['cov'], color='tab:red', label=outlier)
        df_t1 = []
    # plot
    ax.set_xlabel('Mean error %')
    ax.set_ylabel('COV')
    plt.title("Intra subject COV as a function of mean absolute error %")
    ax.legend(loc='upper right')
    plt.grid()
    # save image
    output_file = os.path.join(path_output, "fig_err_in_function_of_cov_outlier.png")
    plt.savefig(output_file, bbox_inches='tight')
    print("--> Created figure: {}".format(output_file))


def add_columns_df_sub(df):
    """  Add columns theoretic CSA values (rX^2 * MEAN(area)) and CSA without rescaling to dataframe
    :param df: dataframe for computing stats per subject: df_sub
    :return df: modified dataframe with added theoretic_csa and csa_without_rescale
    """
    # get CSA values without rescale
    df = df.set_index('rescale')
    csa_without_rescale = df.groupby('rescale').get_group(1)
    csa_without_rescale = csa_without_rescale.set_index('subject')
    # iterate across rescaling coefficients
    for rescale, group in df.groupby('rescale'):
        # get group rescale value
        group = group.reset_index().set_index('subject')
        # iterate across dataframe subjects
        for subject in group.index.values:
            # if dataframe subject exist in csa_without_rescale register theoretic csa value in th_csa_cX_cY
            if subject in csa_without_rescale.index.values:
                group.loc[subject, 'theoretic_csa'] = csa_without_rescale.loc[subject, 'mean'] * (rescale ** 2)
        df.loc[rescale, 'theoretic_csa'] = group['theoretic_csa'].values
        df.loc[rescale, 'csa_without_rescale'] = csa_without_rescale['mean'].values
        df.loc[rescale, 'csa_without_rescale'] = csa_without_rescale['mean'].values
    df = df.reset_index()
    return df

def pearson(df, df_rescale):
    """  The associated Pearson’s coefficients and p-value between subject’s CSA and the associated Pearson’s
    coefficients and p-value between COV across Monte Carlo transformations (i.e. intra-subject variability) and mean
    CSA error :param df: dataframe for computing stats per subject: df_sub :param df_rescale: dataframe for computing
    stats per rescale: df_rescale :return df_rescale: modified dataframe with added theoretic_csa and
    csa_without_rescale
    """
    pearson_cov = []
    p_value_cov = []
    pearson_csa = []
    p_value_csa = []
    for rescale_area, group in df.groupby('rescale_area'):
        pearson_cov.append(stats.pearsonr(group['cov'], group['perc_error'])[0])
        p_value_cov.append(stats.pearsonr(group['cov'], group['perc_error'])[1])
        pearson_csa.append(stats.pearsonr(group['mean'], group['perc_error'])[0])
        p_value_csa.append(stats.pearsonr(group['mean'], group['perc_error'])[1])
    df_rescale['pearson_cov'] = pearson_cov
    df_rescale['p_value_cov'] = p_value_cov
    df_rescale['pearson_csa'] = pearson_csa
    df_rescale['p_value_csa'] = p_value_csa
    return df_rescale

def sample_size(df, df_rescale):
    """  Minimum sample size ( number of subjects) necessary to detect an atrophy in a between-subject (based on a
    two-sample bilateral t-test) and minimum sample size necessary to detect an atrophy in a
    within-subject ( repeated-measures in longitudinal study: based on a two-sample bilateral paired t-test).
    ref. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3148614/
    :param df: dataframe for computing stats per subject: df_sub :param df_rescale: dataframe for computing stats per
    subject: df_rescale :return df_rescale: modified dataframe with added sample_size_80 (between subjects at 80%
    power), sample_size_90 (between subjects at 90% power), sample_size_long_80 (within subjects at 80% power) and
    sample_size_long_90 (within subjects at 90% power)
    """
    sample_size_80 = []
    sample_size_90 = []
    sample_size_long_80 = []
    sample_size_long_90 = []
    for rescale_area , group in df.groupby('rescale_area'):
        if rescale_area != 100:
            # sample size between-subject
            CSA_mean_diff = df_rescale.groupby('rescale_area').get_group(rescale_area)['mean_diff'].values[0]
            var = df_rescale.groupby('rescale_area').get_group(100)['std_inter'].values[0] ** 2 + df_rescale.groupby('rescale_area').get_group(rescale_area)['std_inter'].values[0] ** 2
            sample_size_80.append(np.ceil((((1.96 + 0.84) ** 2) * (var)) / (CSA_mean_diff ** 2)))
            sample_size_90.append(np.ceil((((1.96 + 1.28) ** 2) * (var)) / (CSA_mean_diff ** 2)))
            # sample size within-subject
            var_diff = df_rescale.groupby('rescale_area').get_group(rescale_area)['std_diff'].values[0] ** 2
            sample_size_long_80.append(np.ceil((((1.96 + 0.84) ** 2) * (var_diff)) / (CSA_mean_diff ** 2)))
            sample_size_long_90.append(np.ceil((((1.96 + 1.28) ** 2) * (var_diff)) / (CSA_mean_diff ** 2)))
        else:
            sample_size_80.append('inf')
            sample_size_90.append('inf')
            sample_size_long_80.append('inf')
            sample_size_long_90.append('inf')
    df_rescale['sample_size_80'] = sample_size_80
    df_rescale['sample_size_90'] = sample_size_90
    df_rescale['sample_size_long_80'] = sample_size_long_80
    df_rescale['sample_size_long_90'] = sample_size_long_90
    return df_rescale



def main():
    """
    main function, gather stats and call plots
    """
    # get parser elements
    parser = get_parser()
    arguments = parser.parse_args()
    path_results = os.path.abspath(os.path.expanduser(arguments.i))
    vertlevels_input = arguments.l
    path_output = os.path.abspath(arguments.o)

    # aggregate all csv results files
    # concatenate_csv_files(path_results)

    # read data
    data = pd.read_csv(os.path.join(path_results, r'csa_all.csv'), decimal=".")

    # create a dataframe from the csv files
    df_vert = pd.DataFrame(data)
    pd.set_option('display.max_rows', None)

    # identify rows with missing values
    print("Remove rows with missing values...")
    lines_to_drop = df_vert[df_vert['MEAN(area)'] == 'None'].index
    df_vert['subject'] = list(sub.split('data_processed/')[1].split('/anat')[0] for sub in df_vert['Filename'])

    # remove rows with missing values
    df_vert = df_vert.drop(df_vert.index[lines_to_drop])
    df_vert['MEAN(area)'] = pd.to_numeric(df_vert['MEAN(area)'])
    print("  Rows removed: {}".format(lines_to_drop))

    # fetch parameters from config.yaml file
    config_param = yaml_parser(arguments.config)

    # add useful columns to dataframe
    df_vert['basename'] = list(os.path.basename(path).split('.nii.gz')[0] for path in df_vert['Filename'])
    df_vert['rescale'] = list(float(b.split('RPI_r_r')[1].split('_')[0]) for b in df_vert['basename'])
    df_vert['slices'] = list(int(slices.split(':')[1]) - int(slices.split(':')[0]) + 1 for slices in df_vert['Slice (I->S)'])

    # verify if vertlevels of interest were given in input by user
    if vertlevels_input is None:
        vertlevels = list(set(df_vert['VertLevel'].values))
    elif vertlevels_input:
        vertlevels = list(map(int, vertlevels_input))
        if not all(elem in set(list(df_vert['VertLevel'].values)) for elem in vertlevels):
            raise ValueError("\nInput vertebral levels '{}' do not exist in csv files".format(vertlevels))
    # register vertebrae levels of interest (Default: all vertebrae levels in csv files)
    print("Stats are averaged across vertebral levels: {}".format(vertlevels))

    # Create new dataframe with only selected vertebral levels
    df = df_vert[df_vert['VertLevel'].isin(vertlevels)]
    # Drop column VertLevel (no more used)
    df = df.drop('VertLevel', 1)
    # Average values across levels, for each subject
    df = df.groupby(['rescale', 'basename']).mean()
    # Reset index because the groupby assigned rescale and basename as the new indexes. We want to re-generate a
    # number-based index
    df = df.reset_index()
    df['subject'] = list(tf.split('_T')[0] for tf in df['basename'])
    df['transfo'] = list(tf.split('_t')[1].split('_seg')[0] for tf in df['basename'])
    # Sum number of slices across selected vertebrae
    df['num_slices'] = df_vert.groupby(['rescale', 'basename'])['slices'].sum().values
    df = df.drop('basename', 1)

    # Create dataframe for computing stats per subject: df_sub
    print("\n==================== subject_dataframe ==========================\n")
    df_sub = pd.DataFrame()
    # add necessary columns to df_sub dataframe
    df_sub['rescale'] = df.groupby(['rescale', 'subject']).mean().reset_index()['rescale']
    df_sub['rescale_area'] = 100 * (df.groupby(['rescale', 'subject']).mean().reset_index()['rescale'] ** 2)
    df_sub['subject'] = df.groupby(['rescale', 'subject']).mean().reset_index()['subject']
    df_sub['num_tf'] = df.groupby(['rescale', 'subject'])['transfo'].count().values
    df_sub['num_slices'] = df.groupby(['rescale', 'subject'])['num_slices'].mean().values
    # add stats to per subject dataframe
    df_sub['mean'] = df.groupby(['rescale', 'subject']).mean()['MEAN(area)'].values
    df_sub['std'] = df.groupby(['rescale', 'subject']).std()['MEAN(area)'].values
    df_sub['cov'] = df_sub['std'].div(df_sub['mean'])
    df_sub = add_columns_df_sub(df_sub)
    df_sub['rescale_estimated'] = df_sub['mean'].div(df_sub['csa_without_rescale'])
    df_sub['error'] = (df_sub['mean'] - df_sub['theoretic_csa'])
    df_sub['perc_error'] = 100 * (df_sub['mean'] - df_sub['theoretic_csa']).div(df_sub['theoretic_csa'])
    diff = []
    for rescale, group in df.groupby('rescale'):
        for sub, subgroup in group.groupby('subject'):
            diff.append((df.groupby('rescale').get_group(1).groupby('subject').get_group(sub).sample(n=len(subgroup))['MEAN(area)'].values - group.groupby('subject').get_group(sub).sample(n=len(subgroup))['MEAN(area)'].values).mean())
    df_sub['diff'] = diff
    # save dataframe in a csv file
    df_sub.to_csv(os.path.join(path_output, r'csa_sub.csv'))

    # Create dataframe for computing stats across subject: df_rescale
    print("\n==================== rescaling_dataframe ==========================\n")
    df_rescale = pd.DataFrame()
    df_rescale['rescale'] = df_sub.groupby(['rescale']).mean().reset_index()['rescale']
    df_rescale['rescale_area'] = df_sub.groupby('rescale_area').mean().reset_index()['rescale_area']
    df_rescale['mean_slices'] = df_sub.groupby(['rescale']).mean()['num_slices'].values
    df_rescale['std_slices'] = df_sub.groupby(['rescale']).std()['num_slices'].values
    df_rescale['num_sub'] = df_sub.groupby('rescale')['mean'].count().values
    df_rescale['mean_inter'] = df_sub.groupby('rescale').mean()['mean'].values
    df_rescale['std_intra'] = df_sub.groupby('rescale').mean()['std'].values
    df_rescale['cov_intra'] = df_sub.groupby('rescale').mean()['cov'].values
    df_rescale['std_inter'] = df_sub.groupby('rescale').std()['mean'].values
    df_rescale['cov_inter'] = df_sub.groupby('rescale').std()['mean'].div(
        df_sub.groupby('rescale').mean()['mean']).values
    df_rescale['mean_rescale_estimated'] = df_sub.groupby('rescale').mean()['rescale_estimated'].values
    df_rescale['std_rescale_estimated'] = df_sub.groupby('rescale').std()['rescale_estimated'].values
    df_rescale['mean_perc_error'] = df_sub.groupby('rescale').mean()['perc_error'].values
    df_rescale['mean_error'] = df_sub.groupby('rescale').mean()['error'].values
    df_rescale['std_perc_error'] = df_sub.groupby('rescale').std()['perc_error'].values
    df_rescale['mean_diff'] = df_sub.groupby('rescale').mean()['diff'].values
    df_rescale['std_diff'] = df_sub.groupby('rescale').std()['diff'].values
    df_rescale = pearson(df_sub, df_rescale)
    df_rescale = sample_size(df_sub, df_rescale)
    # save dataframe in a csv file
    df_rescale.to_csv(os.path.join(path_output, r'csa_rescale.csv'))
    # plot graph if verbose is present
    if arguments.fig:
        if path_output:
            os.makedirs(path_output, exist_ok=True)

        # plot percentage difference between simulated atrophy and ground truth atrophy
        plot_perc_err(df_rescale, path_output)

        # boxplot CSA across different rescaling values
        boxplot_csa(df_sub, path_output)

        # boxplot of atrophy across different rescaling values
        boxplot_atrophy(df_sub, path_output)

        # plot minimum number of patients required to detect an atrophy of a given value
        # z_score for confidence level,
        z_score_confidence = config_param['fig']['sample_size']['conf']
        # z_score for power level,
        z_score_power = config_param['fig']['sample_size']['power']
        # std = STD of subjects without rescaling CSA values
        # mean_csa =  mean CSA value of subjects without rescaling
        plot_sample_size(z_conf=z_score_confidence , z_power=z_score_power , std_arr=[7.56 , 8.29] ,
                         mean_csa=[69.70 , 76.12] , path_output=path_output)
        # scatter plot of COV in function of error %
        error_function_of_intra_cov(df_sub, path_output=path_output)
        # scatter plot of COV in function of error % to identify outliers
        error_function_of_intra_cov_outlier(df_sub, path_output=path_output)
        # scatter plot of CSA in function of error %
        error_function_of_csa(df_sub, path_output=path_output)

if __name__ == "__main__":
    main()