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Apply Benjamini-Hochberg FDR to group correlation stars #10

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Apply Benjamini-Hochberg FDR to group correlation stars #10

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74 changes: 72 additions & 2 deletions group/Group Correlation Matrix.ipynb
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Expand Up @@ -19,7 +19,77 @@
{
"cell_type": "code",
"id": "panyy1gp0ur",
"source": "import pandas as pd\nimport numpy as np\nfrom scipy import stats\nimport matplotlib.pyplot as plt\nimport seaborn as sns\n\nOUTPUT = '../data/group_results'\n\n# load data\nhrv_df = pd.read_csv(f'{OUTPUT}/HRV_SDNN.csv').set_index('Participant')\npupil_df = pd.read_csv(f'{OUTPUT}/Pupil_Dilation_STD.csv').set_index('Participant')\nduration_df = pd.read_csv(f'{OUTPUT}/Psychometric_Test_Duration_STD.csv').set_index('Participant')\n\n# combine all\ncombined = pd.concat([\n hrv_df.add_suffix('_HRV_SDNN'),\n pupil_df.add_suffix('_Pupil_STD'),\n duration_df.add_suffix('_Duration_STD'),\n], axis=1)\n\ncols = combined.columns\nn = len(cols)\n\n# correlation with p-values\nr_matrix = np.zeros((n, n))\np_matrix = np.zeros((n, n))\n\nfor i in range(n):\n for j in range(n):\n r, p = stats.pearsonr(combined.iloc[:, i], combined.iloc[:, j])\n r_matrix[i, j] = r\n p_matrix[i, j] = p\n\nr_df = pd.DataFrame(r_matrix, index=cols, columns=cols)\np_df = pd.DataFrame(p_matrix, index=cols, columns=cols)\n\n# annotation with significance stars\nannot = np.empty_like(r_matrix, dtype=object)\nfor i in range(n):\n for j in range(n):\n stars = \"***\" if p_df.iloc[i, j] < 0.001 else \"**\" if p_df.iloc[i, j] < 0.01 else \"*\" if p_df.iloc[i, j] < 0.05 else \"\"\n annot[i, j] = f\"{r_df.iloc[i, j]:.2f}{stars}\"\n\n# plot heatmap\nplt.figure(figsize=(14, 11))\nsns.heatmap(r_df, annot=annot, fmt='', cmap='coolwarm', vmin=-1, vmax=1, center=0)\nplt.title('Correlation Matrix with Significance (* p<.05, ** p<.01, *** p<.001)')\nplt.tight_layout()\nplt.show()\nplt.close()",
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"from scipy import stats\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"\n",
"OUTPUT = '../data/group_results'\n",
"\n",
"# load data\n",
"hrv_df = pd.read_csv(f'{OUTPUT}/HRV_SDNN.csv').set_index('Participant')\n",
"pupil_df = pd.read_csv(f'{OUTPUT}/Pupil_Dilation_STD.csv').set_index('Participant')\n",
"duration_df = pd.read_csv(f'{OUTPUT}/Psychometric_Test_Duration_STD.csv').set_index('Participant')\n",
"\n",
"# combine all\n",
"combined = pd.concat([\n",
" hrv_df.add_suffix('_HRV_SDNN'),\n",
" pupil_df.add_suffix('_Pupil_STD'),\n",
" duration_df.add_suffix('_Duration_STD'),\n",
"], axis=1)\n",
"\n",
"cols = combined.columns\n",
"n = len(cols)\n",
"n_obs = len(combined)\n",
"\n",
"# pairwise correlations + raw p-values\n",
"r_matrix = np.zeros((n, n))\n",
"p_matrix = np.ones((n, n))\n",
"for i in range(n):\n",
" for j in range(n):\n",
" r, p = stats.pearsonr(combined.iloc[:, i], combined.iloc[:, j])\n",
" r_matrix[i, j] = r\n",
" p_matrix[i, j] = p\n",
"\n",
"r_df = pd.DataFrame(r_matrix, index=cols, columns=cols)\n",
"\n",
"# Benjamini-Hochberg FDR across the unique off-diagonal pairs only.\n",
"# With n_obs = 10 participants and dozens of pairwise tests, uncorrected\n",
"# stars overstate significance; we control the false-discovery rate instead.\n",
"iu = np.triu_indices(n, k=1)\n",
"raw_p = p_matrix[iu]\n",
"order = np.argsort(raw_p)\n",
"ranks = np.empty_like(order)\n",
"ranks[order] = np.arange(1, len(raw_p) + 1)\n",
"q = raw_p * len(raw_p) / ranks\n",
"# enforce monotonicity of BH q-values\n",
"q_sorted = np.minimum.accumulate(q[order][::-1])[::-1]\n",
"q_adj = np.empty_like(q)\n",
"q_adj[order] = np.clip(q_sorted, 0, 1)\n",
"\n",
"q_matrix = np.ones((n, n))\n",
"q_matrix[iu] = q_adj\n",
"q_matrix[(iu[1], iu[0])] = q_adj\n",
"\n",
"def star(qv):\n",
" return \"***\" if qv < 0.001 else \"**\" if qv < 0.01 else \"*\" if qv < 0.05 else \"\"\n",
"\n",
"annot = np.empty((n, n), dtype=object)\n",
"for i in range(n):\n",
" for j in range(n):\n",
" s = \"\" if i == j else star(q_matrix[i, j])\n",
" annot[i, j] = f\"{r_df.iloc[i, j]:.2f}{s}\"\n",
"\n",
"plt.figure(figsize=(14, 11))\n",
"sns.heatmap(r_df, annot=annot, fmt='', cmap='coolwarm', vmin=-1, vmax=1, center=0)\n",
"plt.title(f'Correlation Matrix (Pearson r, n={n_obs}); '\n",
" f'stars = Benjamini-Hochberg FDR q-value (* q<.05, ** q<.01, *** q<.001)')\n",
"plt.tight_layout()\n",
"plt.show()\n",
"plt.close()\n"
],
"metadata": {},
"execution_count": null,
"outputs": []
Expand All @@ -46,4 +116,4 @@
},
"nbformat": 4,
"nbformat_minor": 5
}
}