EstMB_MWAS.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import packages\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import seaborn as sns \n",
    "from sklearn.metrics import pairwise_distances\n",
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Read the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# read sp-level abundance table\n",
    "path = '/Users/katerynapantiukh/Documents/1MyDisk/PhD/!MAIN_data/'\n",
    "#path = '/Users/ketpantuh/Documents/1MyDisk/PhD/!MAIN_data/' # home\n",
    "\n",
    "abud = pd.read_csv(str(path)+'bgi_abud_tables/bgi_assembly_v1_SpLevel_RelAbund.csv')\n",
    "# skip first row\n",
    "abud = abud.iloc[1:]\n",
    "abud.set_index('rep_MAG_ID', inplace=True)\n",
    "abud = abud.T\n",
    "abud.reset_index(inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# read the phenotypes\n",
    "import os\n",
    "files = os.listdir(str(path)+'pheno/')\n",
    "# remove hidden files\n",
    "files = [file for file in files if not file.startswith('.')]\n",
    "# remove first 5 characters from each file name\n",
    "files = [file[6:] for file in files]\n",
    "ph_list = [file[:-4] for file in files]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>code</th>\n",
       "      <th>name</th>\n",
       "      <th>type</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>B18</td>\n",
       "      <td>Chronic viral hepatitis</td>\n",
       "      <td>disease</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>B37</td>\n",
       "      <td>Candidiasis</td>\n",
       "      <td>disease</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  code                     name     type\n",
       "0  B18  Chronic viral hepatitis  disease\n",
       "1  B37              Candidiasis  disease"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# drugs description\n",
    "ph_names = pd.read_excel(str(path)+'pheno_description/phenotype_names.xlsx')\n",
    "ph_names.head(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data preparation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial bacteria species count is 2101.\n",
      "Final sp. number after filtering is 1595.\n",
      "24.08% of bacteria species were filtered out.\n",
      "Significance level after Bonferoni correction is 3.134796238244514e-05.\n"
     ]
    }
   ],
   "source": [
    "# filter out sp with prevalence <1%\n",
    "abud = abud.loc[:, abud.astype(bool).sum(axis=0) >= 21]\n",
    "\n",
    "# perform CLR transformation for columns starting from H\n",
    "abud.iloc[:, 1:] = abud.iloc[:, 1:].apply(lambda x: x/x.sum(), axis=1)\n",
    "abud.to_csv('bgi_assembly_v1_SpLevel_RelAbund_CLR_1prev.csv')\n",
    "\n",
    "# write stats\n",
    "fspNumb = len(abud.columns)\n",
    "perc = (len(abud)-fspNumb)/len(abud)*100\n",
    "\n",
    "# Bonferoni corrected significance level\n",
    "alpha = 0.05 / fspNumb\n",
    "\n",
    "print(f\"Initial bacteria species count is {len(abud)}.\")\n",
    "print(f\"Final sp. number after filtering is {fspNumb}.\")\n",
    "print(f\"{str(perc)[0:5]}% of bacteria species were filtered out.\")\n",
    "print(f\"Significance level after Bonferoni correction is {alpha}.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial number of disease phenotype is 66.\n",
      "Number of phenotype with more then 100 cases is 33.\n",
      "50.0% of phenotypes were filtered out.\n"
     ]
    }
   ],
   "source": [
    "des = ph_names[ph_names['type'] == 'disease']['code'].to_list()\n",
    "ph_des_sel = []\n",
    "\n",
    "for ph_name in des:\n",
    "    # read phenotype\n",
    "    ph = pd.read_csv(str(path)+'/pheno/Pheno_'+ph_name+'.csv')\n",
    "    if ph[ph_name].sum() > 100:\n",
    "        # add value to list\n",
    "        ph_des_sel.append(ph_name)\n",
    "\n",
    "perc2 = (len(des)-len(ph_des_sel))/len(des)*100\n",
    "\n",
    "print(f\"Initial number of disease phenotype is {len(des)}.\")\n",
    "print(f\"Number of phenotype with more then 100 cases is {len(ph_des_sel)}.\")\n",
    "print(f\"{str(perc2)[0:5]}% of phenotypes were filtered out.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial number of drugs phenotype is 132.\n",
      "Number of phenotype with more then 100 cases is 1.\n",
      "99.24% of phenotypes were filtered out.\n"
     ]
    }
   ],
   "source": [
    "dr = ph_names[ph_names['type'] != 'disease']['code'].to_list()\n",
    "ph_dr_sel = []\n",
    "\n",
    "for ph_name in dr:\n",
    "    # read phenotype\n",
    "    ph = pd.read_csv(str(path)+'/pheno/Pheno_'+ph_name+'.csv')\n",
    "    if ph[ph_name].sum() > 100:\n",
    "        # add value to list\n",
    "        ph_dr_sel.append(ph_name)\n",
    "\n",
    "perc3 = (len(dr)-len(ph_dr_sel))/len(dr)*100\n",
    "\n",
    "print(f\"Initial number of drugs phenotype is {len(dr)}.\")\n",
    "print(f\"Number of phenotype with more then 100 cases is {len(ph_dr_sel)}.\")\n",
    "print(f\"{str(perc3)[0:5]}% of phenotypes were filtered out.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Start loop correlation analysis through the phenotypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H1531_CALXSV01_sp944390945\n",
      "1.9477281427590836e-05\n",
      "2.2191754904054234e-05\n",
      "-----------------\n",
      "H0862_Phil1_sp004558525\n",
      "8.346134583067753e-06\n",
      "0.0005307679065972345\n",
      "-----------------\n",
      "H0583_Absicoccus_sp000434355\n",
      "2.861282808867806e-05\n",
      "0.0001543716513238516\n",
      "-----------------\n"
     ]
    }
   ],
   "source": [
    "# one phenotype test\n",
    "ph_name = 'D50'\n",
    "# Define your covariates\n",
    "covariates = ['Age_at_MBsample', 'BMI', 'gender']\n",
    "\n",
    "pheno = pd.read_csv(str(path)+'pheno/Pheno_'+str(ph_name)+'.csv')\n",
    "mrg = abud.merge(pheno, left_on='index', right_on='vkood', how='inner')\n",
    "\n",
    "# perform CLR transformation for columns with bacteria species\n",
    "tc = len(mrg.columns)-5\n",
    "\n",
    "# fill NA values with mean\n",
    "mrg['BMI'].fillna(mrg['BMI'].mean(), inplace=True)\n",
    "mrg['gender'].fillna(mrg['gender'].mean(), inplace=True)\n",
    "mrg['Age_at_MBsample'].fillna(mrg['Age_at_MBsample'].mean(), inplace=True)\n",
    "\n",
    "# create a df with results for each phenotype\n",
    "df = pd.DataFrame(columns=['bacteria', 'p-value', 'betta'])\n",
    "\n",
    "n = len(mrg.columns)-5\n",
    "bac = mrg.columns[1:n]\n",
    "len(bac)\n",
    "\n",
    "for b in bac:\n",
    "    # Create a design matrix by adding the covariates to the model\n",
    "    X = mrg[covariates + [ph_name]]\n",
    "    X = sm.add_constant(X)\n",
    "\n",
    "    y = mrg[b]\n",
    "    model = sm.OLS(y, X).fit()\n",
    "    if model.pvalues[ph_name] < alpha:\n",
    "                print(b)\n",
    "                print(model.pvalues[ph_name])  \n",
    "                print(model.params[ph_name])\n",
    "                print('-----------------')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WOW! It is enought samples for phenotype B37. We found 407 cases!\n",
      "...\n",
      "There are no significant correlations\n",
      "---\n",
      "WOW! It is enought samples for phenotype D50. We found 255 cases!\n",
      "...\n",
      "H1531_CALXSV01_sp944390945\n",
      "H0862_Phil1_sp004558525\n",
      "H0583_Absicoccus_sp000434355\n",
      "---\n",
      "WOW! It is enought samples for phenotype E55. We found 102 cases!\n",
      "...\n",
      "H2215_Ventrimonas_sp900540335\n",
      "H0885_Borkfalkia_excrementipullorum\n",
      "H1238_Enterocloster_clostridioformis\n",
      "H0653_Aphodousia_sp900544345\n",
      "H1619_Oscillospiraceae_undG\n",
      "---\n",
      "WOW! It is enought samples for phenotype E78. We found 417 cases!\n",
      "...\n",
      "There are no significant correlations\n",
      "---\n",
      "WOW! It is enought samples for phenotype F32. We found 392 cases!\n",
      "...\n",
      "There are no significant correlations\n",
      "---\n",
      "WOW! It is enought samples for phenotype F33. We found 177 cases!\n",
      "...\n",
      "H1506_Hungatella_effluvii\n",
      "H0478_Desulfovibrio_faecigallinarum\n",
      "H0722_Bacteroides_faecis\n",
      "H2126_Alistipes_undS\n",
      "---\n",
      "WOW! It is enought samples for phenotype F41. We found 287 cases!\n",
      "...\n",
      "H2123_Paraprevotella_sp900548345\n",
      "H0063_Bacteroides_uniformis\n",
      "---\n",
      "WOW! It is enought samples for phenotype G43. We found 133 cases!\n",
      "...\n",
      "H0224_Merdimorpha_sp002314265\n",
      "H0569_Merdimorpha_sp002314265\n",
      "---\n",
      "WOW! It is enought samples for phenotype H25. We found 209 cases!\n",
      "...\n",
      "There are no significant correlations\n",
      "---\n",
      "WOW! It is enought samples for phenotype H40. We found 116 cases!\n",
      "...\n",
      "H0220_Ruminiclostridium_E_sp900539195\n",
      "H2126_Alistipes_undS\n",
      "---\n",
      "WOW! It is enought samples for phenotype I10. We found 457 cases!\n",
      "...\n",
      "H2215_Ventrimonas_sp900540335\n",
      "---\n",
      "WOW! It is enought samples for phenotype I11. We found 377 cases!\n",
      "...\n",
      "There are no significant correlations\n",
      "---\n",
      "WOW! It is enought samples for phenotype I25. We found 115 cases!\n",
      "...\n",
      "H0068_Escherichia_coli\n",
      "H2144_Nanosynbacter_undS\n",
      "H1763_Merdibacter_merdavium\n",
      "H1733_JADFUS01_undS\n",
      "H1485_Copromonas_sp900541255\n",
      "H0594_Succiniclasticum_sp900544275\n",
      "---\n",
      "There are not enought samples for phenotype I48. Only 98 cases found\n",
      "---\n",
      "WOW! It is enought samples for phenotype I49. We found 283 cases!\n",
      "...\n",
      "There are no significant correlations\n",
      "---\n",
      "WOW! It is enought samples for phenotype I50. We found 102 cases!\n",
      "...\n",
      "H0529_Scatousia_sp900554385\n",
      "H1063_Streptococcus_parasanguinis_E\n",
      "H0091_Lachnospira_sp900316325\n",
      "H1293_CAKTXU01_undS\n",
      "H1013_Stercorousia_undS\n",
      "H1181_CAKNOI01_sp930990125\n",
      "H0906_Prevotella_sp022769285\n",
      "H0594_Succiniclasticum_sp900544275\n",
      "---\n",
      "WOW! It is enought samples for phenotype I84. We found 236 cases!\n",
      "...\n",
      "There are no significant correlations\n",
      "---\n",
      "WOW! It is enought samples for phenotype J02. We found 388 cases!\n",
      "...\n",
      "H1780_UMGS1470_sp900552105\n",
      "---\n",
      "WOW! It is enought samples for phenotype J03. We found 159 cases!\n",
      "...\n",
      "There are no significant correlations\n",
      "---\n",
      "WOW! It is enought samples for phenotype J20. We found 396 cases!\n",
      "...\n",
      "There are no significant correlations\n",
      "---\n",
      "WOW! It is enought samples for phenotype J30. We found 398 cases!\n",
      "...\n",
      "H0371_Bacteroides_ovatus\n",
      "H1461_Bacteroides_intestinigallinarum\n",
      "---\n",
      "WOW! It is enought samples for phenotype J31. We found 124 cases!\n",
      "...\n",
      "H1550_Bilophila_undS\n",
      "H1250_SIG427_undS\n",
      "H1875_Leuconostoc_falkenbergense\n",
      "---\n",
      "WOW! It is enought samples for phenotype J35. We found 456 cases!\n",
      "...\n",
      "There are no significant correlations\n",
      "---\n",
      "WOW! It is enought samples for phenotype J45. We found 168 cases!\n",
      "...\n",
      "H0987_Turicibacter_bilis\n",
      "H0882_Coproplasma_sp905207385\n",
      "---\n",
      "WOW! It is enought samples for phenotype K21. We found 400 cases!\n",
      "...\n",
      "There are no significant correlations\n",
      "---\n",
      "WOW! It is enought samples for phenotype K29. We found 306 cases!\n",
      "...\n",
      "There are no significant correlations\n",
      "---\n",
      "WOW! It is enought samples for phenotype K58. We found 129 cases!\n",
      "...\n",
      "There are no significant correlations\n",
      "---\n",
      "WOW! It is enought samples for phenotype K80. We found 127 cases!\n",
      "...\n",
      "H0947_UBA1259_undS\n",
      "H1271_Evtepia_gabavorous\n",
      "H0809_Bilophila_faecipullorum\n",
      "---\n",
      "WOW! It is enought samples for phenotype L70. We found 214 cases!\n",
      "...\n",
      "H0334_Blautia_A_massiliensis\n",
      "---\n",
      "There are not enought samples for phenotype M13. Only 90 cases found\n",
      "---\n",
      "WOW! It is enought samples for phenotype M15. We found 223 cases!\n",
      "...\n",
      "There are no significant correlations\n",
      "---\n",
      "WOW! It is enought samples for phenotype N95. We found 350 cases!\n",
      "...\n",
      "There are no significant correlations\n",
      "---\n",
      "There are not enought samples for phenotype N97. Only 94 cases found\n",
      "---\n"
     ]
    }
   ],
   "source": [
    "# phenotypes with more then 100 cases\n",
    "nMore = []\n",
    "# number of phenotypes with less then 100 cases\n",
    "nLess = []\n",
    "\n",
    "# Define your covariates\n",
    "covariates = ['Age_at_MBsample', 'BMI', 'gender']\n",
    "# create a new df for all correlation table\n",
    "allCor = pd.DataFrame(columns=['pheno','bacteria', 'p-value', 'betta'])\n",
    "# create a new df for aggregated results\n",
    "res = pd.DataFrame(columns=['phenotype', 'ass_found', 'ass_bact','cases','controls'])\n",
    "\n",
    "for ph_name in ph_des_sel:\n",
    "    #reads phenotype data\n",
    "    pheno = pd.read_csv(str(path)+'pheno/Pheno_'+str(ph_name)+'.csv')\n",
    "    mrg = abud.merge(pheno, left_on='index', right_on='vkood', how='inner')\n",
    "\n",
    "    # perform CLR transformation for columns with bacteria species\n",
    "    tc = len(mrg.columns)-5\n",
    "    #mrg.iloc[:, 1:tc] = mrg.iloc[:, 1:tc].apply(lambda x: x/x.sum(), axis=1)\n",
    "\n",
    "    if len(mrg[mrg[ph_name] == 1]) <100:\n",
    "        print(\"There are not enought samples for phenotype {}. Only {} cases found\".format(ph_name, len(mrg[mrg[ph_name] == 1])))\n",
    "        nLess.append(ph_name)\n",
    "        print('---')\n",
    "    else:\n",
    "        print(\"WOW! It is enought samples for phenotype {}. We found {} cases!\".format(ph_name, len(mrg[mrg[ph_name] == 1])))\n",
    "        nMore.append(ph_name)\n",
    "        print('...')\n",
    "\n",
    "        # fill NA values with mean\n",
    "        mrg['BMI'].fillna(mrg['BMI'].mean(), inplace=True)\n",
    "        mrg['gender'].fillna(mrg['gender'].mean(), inplace=True)\n",
    "        mrg['Age_at_MBsample'].fillna(mrg['Age_at_MBsample'].mean(), inplace=True)\n",
    "\n",
    "        # create a df with results for each phenotype\n",
    "        df = pd.DataFrame(columns=['bacteria', 'p-value', 'betta'])\n",
    "\n",
    "        n = len(mrg.columns)-5\n",
    "        bac = mrg.columns[1:n]\n",
    "        len(bac)\n",
    "\n",
    "        for b in bac:\n",
    "            # Create a design matrix by adding the covariates to the model\n",
    "            X = mrg[covariates + [ph_name]]\n",
    "            X = sm.add_constant(X)\n",
    "\n",
    "            y = mrg[b]\n",
    "\n",
    "            # Fit the linear regression model\n",
    "            model = sm.OLS(y, X).fit()\n",
    "            # Fit the logistic regression model\n",
    "            #model = sm.Logit(y, X).fit(method='bfgs', maxiter=1000) \n",
    "            #model = sm.Probit(y, X).fit(method='bfgs', maxiter=1000)\n",
    "\n",
    "            if model.pvalues[ph_name] < alpha:\n",
    "                print(b)\n",
    "                #print(model.pvalues[ph_name])   \n",
    "\n",
    "                # fill out separete table for phenotype\n",
    "                rows_to_append = []\n",
    "                new_row = {'bacteria': b, 'p-value': model.pvalues[ph_name], 'betta': model.params[ph_name]}\n",
    "                rows_to_append.append(new_row)\n",
    "                new_data = pd.DataFrame(rows_to_append)\n",
    "                df = pd.concat([df, new_data], ignore_index=True)\n",
    "\n",
    "                # fill out AllCor table\n",
    "                rows_to_append = []\n",
    "                new_row = {'pheno': ph_name, 'bacteria': b, 'p-value': model.pvalues[ph_name], 'betta': model.params[ph_name]}\n",
    "                rows_to_append.append(new_row)\n",
    "                new_data = pd.DataFrame(rows_to_append)\n",
    "                allCor = pd.concat([allCor, new_data], ignore_index=True)\n",
    "\n",
    "            df.sort_values(by=['p-value'], inplace=True)\n",
    "            df.to_csv('results/sm-Probit/Pval_'+str(ph_name)+'.csv', index=False)     \n",
    "        \n",
    "        if df.empty:\n",
    "            print('There are no significant correlations')\n",
    "            new_row = {'phenotype': ph_name, 'ass_found': 'no','ass_bact': '-','cases': len(mrg[mrg[ph_name] == 1]),'controls':len(mrg[mrg[ph_name] == 0])}\n",
    "        else:\n",
    "            bct = ', '.join(df['bacteria'].to_list())\n",
    "            new_row = {'phenotype': ph_name, 'ass_found': 'yes','ass_bact': bct,'cases': len(mrg[mrg[ph_name] == 1]),'controls':len(mrg[mrg[ph_name] == 0])}\n",
    "\n",
    "        rows_to_append = []\n",
    "        rows_to_append.append(new_row)\n",
    "\n",
    "        new_data = pd.DataFrame(rows_to_append)\n",
    "        res = pd.concat([res, new_data], ignore_index=True)\n",
    "\n",
    "        print('---')\n",
    "\n",
    "# Write the results!\n",
    "allCor = allCor.merge(ph_names, left_on='pheno', right_on='code', how='left')\n",
    "allCor = allCor[['pheno','name','bacteria','p-value', 'betta']]\n",
    "allCor.to_excel('results/allCorrelation_table_v2.xlsx', index=False) \n",
    "\n",
    "res = res.merge(ph_names, left_on='phenotype', right_on='code', how='left')\n",
    "res = res[['code','name','ass_found','ass_bact','cases','controls']].sort_values(by='ass_found', ascending=False)\n",
    "res.to_excel('results/aggrCorrelation_table_v2.xlsx', index=False) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture captured_output\n",
    "k = len(res[res['ass_found'] == 'yes'])\n",
    "\n",
    "# print current date\n",
    "from datetime import datetime\n",
    "\n",
    "current_date = datetime.now()\n",
    "print(current_date, '\\n')\n",
    "\n",
    "print(f\"Bacteria filter: sp. with prevalence <1%\")\n",
    "print(f\"Initial bacteria species count is {len(abud)}.\")\n",
    "print(f\"Final sp. number after filtering is {fspNumb}.\")\n",
    "print(f\"{str(perc)[0:5]}% of bacteria species were filtered out.\\n\")\n",
    "\n",
    "print(f\"Data preparation: SLR transformation\")\n",
    "print(f\"Significance level: Bonferoni correction\")\n",
    "print(f\"Significance level after is {alpha}. \\n\")\n",
    "\n",
    "print(f\"Phenotype filter: filter out phenotypes with less then 100 cases\")\n",
    "print(f\"It was analised 66 phenotypes\")\n",
    "print(f\"Fot {len(nMore)} phenotypes with enought cases\")\n",
    "print(f\"Among them {k} phenotypes had {len(allCor)} associations \\n\")\n",
    "\n",
    "print(f\"Phenotypes with associations:\")\n",
    "a = ', '.join(res[res['ass_found'] == 'yes']['name'].to_list())\n",
    "print(a, '\\n')\n",
    "\n",
    "print(f\"Phenotypes without associations:\")\n",
    "b = ', '.join(res[res['ass_found'] != 'yes']['name'].to_list())\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open('results/log.csv', 'w') as f:\n",
    "    f.write(captured_output.stdout)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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