statistical_analysis.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sklearn\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from numpy import std, mean, sqrt\n",
    "from sklearn.model_selection import train_test_split\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import ttest_ind, mannwhitneyu, wilcoxon\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cohen_d(x,y):\n",
    "    nx = len(x)\n",
    "    ny = len(y)\n",
    "    dof = nx + ny - 2\n",
    "    return (mean(x) - mean(y)) / sqrt(((nx-1)*std(x, ddof=1) ** 2 + (ny-1)*std(y, ddof=1) ** 2) / dof)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "top20 = [\"panelb_ca125\", \n",
    "         \"panelb_he4\",\n",
    "         \"panelc_ca125_log\",\n",
    "         \"panelc_ca125\",\n",
    "         \"panelc_he4_log\",\n",
    "         \"panela_ca_125\",\n",
    "         \"panelc_he4\",\n",
    "         \"panelb_ca72_4\",\n",
    "         \"panelc_slpi\",\n",
    "         \"panela_mif\",\n",
    "         \"paneld_ctap\",\n",
    "         \"paneld_b2m\",\n",
    "         \"panelb_ov_110\",\n",
    "         \"panelb_klk6\",\n",
    "         \"panelc_spondin2_log\",\n",
    "         \"panelb_ca15_3\",\n",
    "         \"paneld_hepc\",\n",
    "         \"panele_mmp_3\",\n",
    "         \"paneld_apo\",\n",
    "         \"paneld_tt\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "DATA = pd.read_csv(\"PLCO.csv\")\n",
    "DATA = DATA[top20+[\"is_case\"]]\n",
    "DATA = DATA.dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, Y = DATA.drop([\"is_case\"], axis=1), DATA[\"is_case\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "CASE = DATA[DATA[\"is_case\"]==1][top20]\n",
    "HEALTHY = DATA[DATA[\"is_case\"]==0][top20]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "case_panelb_ca125 = CASE[\"paneld_tt\"]\n",
    "healthy_panelb_ca125 = HEALTHY[\"paneld_tt\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0018347953583825703"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cohen_d(case_panelb_ca125, healthy_panelb_ca125)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def process(feature):\n",
    "    feature = [v**(-0.215) for v in feature]\n",
    "    return feature\n",
    "\n",
    "def scatter_one_feature(feature_name, data):\n",
    "    feature = data[feature_name]\n",
    "    \n",
    "    feature = process(feature)\n",
    "    \n",
    "    plt.figure(figsize=(15, 5))\n",
    "    plt.hist(feature, bins=10)\n",
    "    plt.xlabel(\"Instance Number\", fontsize=18)\n",
    "    plt.ylabel(\"Value\", fontsize=18)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatter_one_feature(\"panelb_ca125\", HEALTHY)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=0.01838528102241966, pvalue=0.985335118512801)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ttest_ind(case_panelb_ca125, healthy_panelb_ca125)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=50279.0, pvalue=0.8308120907080443)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(case_panelb_ca125, healthy_panelb_ca125)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "top5 = [\"panelb_ca125\", \n",
    "         \"panelb_he4\",\n",
    "         \"panelc_ca125_log\",\n",
    "         \"panelc_ca125\",\n",
    "         \"panelc_he4_log\"]\n",
    "\n",
    "bottom5 = [\"panelb_ca15_3\",\n",
    "         \"paneld_hepc\",\n",
    "         \"panele_mmp_3\",\n",
    "         \"paneld_apo\",\n",
    "         \"paneld_tt\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "values = {}\n",
    "for f in top5 + bottom5:\n",
    "    case_measure, healthy_measure = CASE[f], HEALTHY[f]\n",
    "    values[f] = (mannwhitneyu(case_measure, healthy_measure), cohen_d(case_measure, healthy_measure))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'panelb_ca125': (MannwhitneyuResult(statistic=68726.5, pvalue=1.2610698443825584e-09),\n",
       "  1.0136157106480843),\n",
       " 'panelb_he4': (MannwhitneyuResult(statistic=73728.5, pvalue=7.438843451943191e-15),\n",
       "  1.3068992749062682),\n",
       " 'panelc_ca125_log': (MannwhitneyuResult(statistic=70504.0, pvalue=2.373108216835132e-11),\n",
       "  1.3286714095313037),\n",
       " 'panelc_ca125': (MannwhitneyuResult(statistic=70504.0, pvalue=2.373108216835132e-11),\n",
       "  0.8451507661421163),\n",
       " 'panelc_he4_log': (MannwhitneyuResult(statistic=67741.5, pvalue=9.436033123098185e-09),\n",
       "  1.0268968664583873),\n",
       " 'panelb_ca15_3': (MannwhitneyuResult(statistic=61554.5, pvalue=0.00028528707354338195),\n",
       "  0.647712873446164),\n",
       " 'paneld_hepc': (MannwhitneyuResult(statistic=50504.0, pvalue=0.8910404018079618),\n",
       "  0.039712894740100424),\n",
       " 'panele_mmp_3': (MannwhitneyuResult(statistic=47942.0, pvalue=0.3124801800416487),\n",
       "  -0.02847014441330779),\n",
       " 'paneld_apo': (MannwhitneyuResult(statistic=49313.0, pvalue=0.5872400398938962),\n",
       "  -0.012133790049681181),\n",
       " 'paneld_tt': (MannwhitneyuResult(statistic=50279.0, pvalue=0.8308120907080443),\n",
       "  0.0018347953583825703)}"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "p_value_ranks = {}\n",
    "for col in top20:\n",
    "    healthy = HEALTHY[col]\n",
    "    case = CASE[col]\n",
    "    p_value_ranks[col] = mannwhitneyu(healthy, case).pvalue\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "p_value_ranks = [k for k, v in sorted(p_value_ranks.items(), key=lambda x: x[1])]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['panelb_he4',\n",
       " 'panela_ca_125',\n",
       " 'panelc_ca125_log',\n",
       " 'panelc_ca125',\n",
       " 'panelb_ca125',\n",
       " 'panelc_he4_log',\n",
       " 'panelc_he4',\n",
       " 'panelb_ca72_4',\n",
       " 'panelb_klk6',\n",
       " 'panelb_ca15_3',\n",
       " 'panelb_ov_110',\n",
       " 'panela_mif',\n",
       " 'panelc_spondin2_log',\n",
       " 'panelc_slpi',\n",
       " 'panele_mmp_3',\n",
       " 'paneld_b2m',\n",
       " 'paneld_apo',\n",
       " 'paneld_ctap',\n",
       " 'paneld_tt',\n",
       " 'paneld_hepc']"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_value_ranks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "shapley_ranks = top20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "p_ranks_num = []\n",
    "for r in shapley_ranks:\n",
    "    p_ranks_num.append(p_value_ranks.index(r))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[4, 0, 2, 3, 5, 1, 6, 7, 13, 11, 17, 15, 10, 8, 12, 9, 19, 14, 16, 18]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_ranks_num"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.10/site-packages/scipy/stats/_morestats.py:3414: UserWarning: Exact p-value calculation does not work if there are zeros. Switching to normal approximation.\n",
      "  warnings.warn(\"Exact p-value calculation does not work if there are \"\n"
     ]
    }
   ],
   "source": [
    "wilcoxon_val = wilcoxon(p_ranks_num, range(0, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=67.5, pvalue=0.9793042128380569)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon_val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(range(0, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=3.5, pvalue=0.3125)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon([9, 19, 14, 16, 18], range(15, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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