Simple Logistic Regression-Alcohol & Fertility Diagnosis.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import io\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import scipy.stats\n",
    "import scipy.special\n",
    "import seaborn as sns\n",
    "sns.set_style('white')\n",
    "sns.set_context('notebook')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Alcohol Consumption (frequency)</th>\n",
       "      <th>FertilityDiagnosis</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.8</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.8</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.8</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.8</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.8</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.6</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.8</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1.0</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Alcohol Consumption (frequency)  FertilityDiagnosis\n",
       "0                              0.8               False\n",
       "1                              0.8                True\n",
       "2                              1.0               False\n",
       "3                              1.0               False\n",
       "4                              0.8                True\n",
       "5                              0.8               False\n",
       "6                              0.8               False\n",
       "7                              0.6               False\n",
       "8                              0.8               False\n",
       "9                              1.0               False"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "\n",
    "PROBLEM STATEMENT:\n",
    "\n",
    "What impact does alcohol consumption have on the fertility diagnoses (sperm concentration) \n",
    "of males (keeping in mind that sperm concentration are related to socio-demographic and \n",
    "environmental factors, health status, as well as habits accosicated with individual lifestyle)?\n",
    "\"\"\"\n",
    "\n",
    "##################################################################################################\n",
    "##################################################################################################\n",
    "\n",
    "\"\"\"Stripped down dataset to include just relevant data: alcohol consumption and diagnosis outcome.\"\"\"\n",
    "\n",
    "data = \"\"\"Alcohol Consumption (frequency)\tFertilityDiagnosis\n",
    "0.8\tN\n",
    "0.8\tO\n",
    "1\tN\n",
    "1\tN\n",
    "0.8\tO\n",
    "0.8\tN\n",
    "0.8\tN\n",
    "0.6\tN\n",
    "0.8\tN\n",
    "1\tN\n",
    "0.8\tN\n",
    "0.6\tN\n",
    "0.8\tN\n",
    "1\tN\n",
    "0.2\tN\n",
    "1\tN\n",
    "1\tN\n",
    "0.8\tO\n",
    "1\tN\n",
    "0.8\tO\n",
    "0.8\tN\n",
    "0.6\tN\n",
    "0.8\tN\n",
    "1\tO\n",
    "1\tN\n",
    "1\tN\n",
    "0.6\tO\n",
    "0.6\tO\n",
    "1\tN\n",
    "0.6\tO\n",
    "1\tN\n",
    "1\tN\n",
    "1\tN\n",
    "0.8\tN\n",
    "1\tN\n",
    "0.6\tN\n",
    "1\tN\n",
    "1\tN\n",
    "0.6\tO\n",
    "1\tN\n",
    "0.8\tN\n",
    "0.8\tN\n",
    "0.8\tN\n",
    "1\tN\n",
    "1\tN\n",
    "1\tN\n",
    "1\tN\n",
    "0.6\tN\n",
    "0.8\tN\n",
    "0.6\tN\n",
    "0.8\tN\n",
    "1\tN\n",
    "0.8\tN\n",
    "0.8\tN\n",
    "1\tN\n",
    "0.8\tN\n",
    "0.8\tN\n",
    "1\tN\n",
    "0.4\tN\n",
    "0.8\tN\n",
    "0.8\tN\n",
    "1\tN\n",
    "0.6\tN\n",
    "1\tN\n",
    "0.8\tN\n",
    "1\tN\n",
    "0.8\tN\n",
    "1\tN\n",
    "0.8\tN\n",
    "0.8\tN\n",
    "0.8\tO\n",
    "1\tN\n",
    "0.6\tN\n",
    "0.8\tN\n",
    "0.8\tN\n",
    "1\tN\n",
    "0.6\tN\n",
    "0.8\tN\n",
    "0.8\tN\n",
    "0.6\tN\n",
    "1\tN\n",
    "0.8\tN\n",
    "0.6\tN\n",
    "1\tN\n",
    "1\tO\n",
    "0.6\tN\n",
    "0.6\tN\n",
    "0.8\tN\n",
    "1\tN\n",
    "1\tN\n",
    "0.8\tN\n",
    "1\tN\n",
    "0.8\tN\n",
    "0.8\tO\n",
    "0.6\tN\n",
    "1\tN\n",
    "0.8\tN\n",
    "1\tN\n",
    "1\tN\n",
    "0.6\tN\n",
    "\"\"\"\n",
    "df = pd.read_table(io.StringIO(data))\n",
    "df.FertilityDiagnosis = df.FertilityDiagnosis == 'O'\n",
    "df.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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MkydPeipqpSobxyUffPCBMWTIEGPu3LnujldlZuOYMGGC8c0333gi2q9S2Tjs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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b3babdb240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "\n",
    "Frequency of alcohol consumption is measured (0, 1) with the following criteria: \n",
    "    \n",
    "    1. Several times a day\n",
    "    2. Every day\n",
    "    3. Several times a week\n",
    "    4. Once a week\n",
    "    5. Hardly ever or never\n",
    "    \n",
    "\n",
    "Fertility Output s as follows: \n",
    "    \n",
    "    1. Diagnosis normal (N)\n",
    "    2. Altered (by the aforementioned factor) (O) \n",
    "\n",
    "\"\"\"\n",
    "\"\"\"Plot the Data\"\"\"\n",
    "\n",
    "df.plot.scatter('Alcohol Consumption (frequency)', 'FertilityDiagnosis')\n",
    "plt.ylabel('Impact On Fertility Diagnosis')\n",
    "sns.despine()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import sklearn.linear_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.03588022] [[-2.42830288]]\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "Address unpenalized OLS, etc. associated with regression. \n",
    "C=1e12 is effectively no regularization - see https://github.com/scikit-learn/scikit-learn/issues/6738.\n",
    "\"\"\"\n",
    "\n",
    "clf = sklearn.linear_model.LogisticRegression(C=1e12, random_state=0)\n",
    "clf.fit(df['Alcohol Consumption (frequency)'].values.reshape(-1, 1), df['FertilityDiagnosis'])\n",
    "print(clf.intercept_, clf.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_log_reg(x, y, data, clf, xmin=None, xmax=None, alpha=1, ax=None):\n",
    "    if ax is None:\n",
    "        fig, ax = plt.subplots()\n",
    "    else:\n",
    "        fig = ax.figure\n",
    "    ax.scatter(data[x], data[y], color='black', zorder=20, alpha=alpha)\n",
    "    if xmin is None:\n",
    "        xmin = x.min()\n",
    "    if xmax is None:\n",
    "        xmax = x.max()\n",
    "    X_test = np.linspace(xmin, xmax, 300)\n",
    "\n",
    "    loss = scipy.special.expit(X_test * clf.coef_ + clf.intercept_).ravel()\n",
    "    ax.plot(X_test, loss, linewidth=3)\n",
    "\n",
    "    ax.set_xlabel(x)\n",
    "    ax.set_ylabel(y)\n",
    "    fig.tight_layout()\n",
    "    sns.despine()\n",
    "    return fig, ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IiEjEzN5yEgQBa9aswcaNG1FZWQkACAwMxBNPPIFnnnmmVQq0tr0n8vCv5AyEB3rgzxN7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\nwYMHY9GiRZg0aRJmzpyJ/Px8bNmyBZm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      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b3bfa570b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"Plot Data\"\"\"\n",
    "\n",
    "plot_log_reg(x='Alcohol Consumption (frequency)', y='FertilityDiagnosis', data=df, clf=clf, xmin=0, xmax=1.5);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def log_reg_null_model(y):\n",
    "    clf = sklearn.linear_model.LogisticRegression(C=1e12)\n",
    "    clf.fit(np.zeros_like(y).reshape(-1, 1), y)\n",
    "    return clf\n",
    "\n",
    "clf0 = log_reg_null_model(df['FertilityDiagnosis'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import sklearn.metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def log_reg_lik_ratio_test(X, Y, clf0, clf1, df=1):\n",
    "    if X.ndim == 1:\n",
    "        X = X.values.reshape(-1, 1)\n",
    "    y_prob0 = clf0.predict_proba(X)\n",
    "    loss0 = sklearn.metrics.log_loss(Y, y_prob0, normalize=False)\n",
    "    y_prob1 = clf1.predict_proba(X)\n",
    "    loss1 = sklearn.metrics.log_loss(Y, y_prob1, normalize=False)\n",
    "    D = 2 * (loss0 - loss1)\n",
    "    return scipy.stats.distributions.chi2.sf(D, df=df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.16248345977701148"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_reg_lik_ratio_test(df['Alcohol Consumption (frequency)'], df['FertilityDiagnosis'].astype(np.float64), clf0, clf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "35.7170192231 35.7170192231\n"
     ]
    }
   ],
   "source": [
    "_ = clf.predict_proba(df['Alcohol Consumption (frequency)'].values.reshape(-1, 1))\n",
    "df['prob_absent'], df['prob_present'] = _[:,0], _[:,1]\n",
    "lik = df.loc[df['FertilityDiagnosis'], 'prob_present'].prod() * df.loc[~df['FertilityDiagnosis'], 'prob_absent'].prod()\n",
    "print(\n",
    "    -np.log(lik), \n",
    "    sklearn.metrics.log_loss(\n",
    "        df['FertilityDiagnosis'], \n",
    "        clf.predict_proba(df['Alcohol Consumption (frequency)'].values.reshape(-1, 1)), \n",
    "        normalize=False\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "CONCLUSIONS:\n",
    "\n",
    "The frequency of alcohol consumption has no particular bearing on the fertility diagnois (sperm concentration) in males.\n",
    "\n",
    "###############################################################################\n",
    "\n",
    "Predicting Fertility Diagnosis in Drinkers\n",
    "\n",
    "Abstract: \n",
    "\n",
    "100 volunteers provide a semen sample analyzed according to the WHO 2010 criteria. Sperm concentration are related to socio-demographic data, environmental factors, health status, and life habits.\n",
    "Problem Statement: \n",
    "What impact does alcohol consumption have on the fertility diagnoses (sperm concentration) of males (keeping in mind that sperm concentration are related to socio-demographic and environmental factors, health status, as well as habits accosicated with individual lifestyle)?\n",
    "\n",
    "###############################################################################\n",
    "\n",
    "Data Set Information:\n",
    "\n",
    "The data associated with this analysis (http://archive.ics.uci.edu/ml/datasets/Fertility) contains the following information:\n",
    "0. Season in which the analysis was performed. 1) winter, 2) spring, 3) Summer, 4) fall. (-1, -0.33, 0.33, 1)\n",
    "1. Age at the time of analysis. 18-36 (0, 1)\n",
    "2. Childish diseases (ie , chicken pox, measles, mumps, polio) 1) yes, 2) no. (0, 1)\n",
    "3. Accident or serious trauma 1) yes, 2) no. (0, 1)\n",
    "4. Surgical intervention 1) yes, 2) no. (0, 1)\n",
    "5. High fevers in the last year 1) less than three months ago, 2) more than three months ago, 3) no. (-1, 0, 1)\n",
    "6. Frequency of alcohol consumption 1) several times a day, 2) every day, 3) several times a week, 4) once a week, 5) hardly ever or never (0, 1)\n",
    "7. Smoking habit 1) never, 2) occasional 3) daily. (-1, 0, 1)\n",
    "8. Number of hours spent sitting per day ene-16 (0, 1)\n",
    "9. Output: Diagnosis normal (N), altered (O) \n",
    "\n",
    "###############################################################################\n",
    "\n",
    "Relevant Papers:\n",
    "\n",
    "David Gil, Jose Luis Girela, Joaquin De Juan, M. Jose Gomez-Torres, and\n",
    "Magnus Johnsson. Predicting seminal quality with artificial intelligence\n",
    "methods. Expert Systems with Applications, 39(16):12564 - 12573, 2012.\n",
    "\n",
    "###############################################################################\n",
    "\n",
    "Citations:\n",
    "\n",
    "David Gil, Jose Luis Girela, Joaquin De Juan, M. Jose Gomez-Torres, and\n",
    "Magnus Johnsson. Predicting seminal quality with artificial intelligence\n",
    "methods. Expert Systems with Applications, 39(16):12564 - 12573, 2012.\n",
    "\n",
    "\"\"\""
   ]
  }
 ],
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