Inter-subject

Inter-subject statistics. These statistics are gathered per scaling in the Panda dataframe df_rescale

Mean intra-subject SD

Intra-subject SD averaged across subjects.

\(\mu_s \{ \sigma_t \{ CSA_{rX} \} \}\)

    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['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['sample_size'] = sample_size(df_rescale, config_param)
    print(df_rescale)

Mean intra-subject COV

Intra-subject COV averaged across subjects.

\(\mu_s \{ COV_t \{ CSA_{rX} \} \}\)

    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['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['sample_size'] = sample_size(df_rescale, config_param)
    print(df_rescale)

Inter-subject SD

SD of intra-subject CSA across subjects.

\(\sigma_s \{ \mu_t \{ CSA_{rX} \} \}\)

    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['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['sample_size'] = sample_size(df_rescale, config_param)
    print(df_rescale)

Mean rescale estimated (RE)

rescale_estimated averaged across subjects.

\(\mu_s \left \{ \mu_t \left\{ \frac{CSA_{rX}}{CSA_{r1}} \right\}\right\}\)

    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['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['sample_size'] = sample_size(df_rescale, config_param)
    print(df_rescale)

SD of rescale estimated

SD of rescale_estimated across subjects.

\(\sigma_s \left\{\mu_t \left\{ \frac{CSA_{rX}}{CSA_{r1}} \right\}\right\}\)

    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['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['sample_size'] = sample_size(df_rescale, config_param)
    print(df_rescale)

Mean error

error on the intra-subject CSA estimation averaged across subjects.

\(\mu_s \{ \mu_t \{ CSA_{rX} \} - \mu_t \{ CSA_{r1} \cdot (rX)^2 \} \}\)

    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['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['sample_size'] = sample_size(df_rescale, config_param)
    print(df_rescale)

SD of error

SD of error on intra-subject CSA estimation across subjects.

\(\sigma_s \{ \mu_t \{ CSA_{rX} \} - \mu_t \{ CSA_{r1} \cdot (rX)^2 \} \}\)

    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['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['sample_size'] = sample_size(df_rescale, config_param)
    print(df_rescale)