ELSO Survival.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      ":0: FutureWarning: IPython widgets are experimental and may change in the future.\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import pymc3 as pm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "flu = pd.read_csv('data/flu.csv', index_col=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1406, 60)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flu.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Turn into table of unique patients, with appropriate organism columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "flu_only = flu.groupby('PatientID')['OrganismName'].apply(lambda s: \n",
    "                        len([x for x in s if str(x).startswith('Influenza')])==len(s)).astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "coinfections = flu.groupby('PatientID')['OrganismName'].apply(lambda s: \n",
    "                        [x for x in s.dropna() if not str(x).startswith('Influenza')])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "MRSA coinfection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mrsa = coinfections.apply(lambda x: x.count('Staphylococcus aureus, meth resist') > 0).astype(int)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Any coinfection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "any_coinf = coinfections.apply(lambda x: int(len(x)>0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.4/site-packages/pandas/util/decorators.py:81: FutureWarning: the 'cols' keyword is deprecated, use 'subset' instead\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    }
   ],
   "source": [
    "flu_unique = flu.drop_duplicates(cols=['PatientID']).set_index('PatientID')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "flu_unique['flu_only'] = flu_only\n",
    "flu_unique['mrsa'] = mrsa\n",
    "flu_unique['any_coinf'] = any_coinf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Add time from admission to time on ECMO"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "admit_through_emco = flu_unique.AdmitToTimeOnHours.add(flu_unique.HoursECMO, fill_value=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See how many have no time information from admission, and drop these"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "missing = admit_through_emco.isnull()\n",
    "missing.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.4/site-packages/pandas/computation/expressions.py:190: UserWarning: evaluating in Python space because the '-' operator is not supported by numexpr for the bool dtype, use '^' instead\n",
      "  unsupported[op_str]))\n"
     ]
    }
   ],
   "source": [
    "flu_complete = flu_unique[missing-True]\n",
    "admit_through_emco.dropna(inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Confirm no null here\n",
    "admit_through_emco.isnull().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Time off ECMO through to event (death or discharge)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "off_ecmo_to_event = flu_complete.TimeOffToDCDateHours.add(flu_complete.TimeOffToDeathDateHours, \n",
    "                                                          fill_value=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "51"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "off_ecmo_to_event.isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.4/site-packages/IPython/kernel/__main__.py:2: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  from IPython.kernel.zmq import kernelapp as app\n"
     ]
    }
   ],
   "source": [
    "# Not sure why add() does not work here\n",
    "flu_complete['time_to_event'] = (admit_through_emco.values + off_ecmo_to_event.fillna(0).values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flu_complete.time_to_event.isnull().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clean covariates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "W    554\n",
       "A    102\n",
       "B     83\n",
       "H     82\n",
       "O     56\n",
       "dtype: int64"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flu_complete.Race.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.4/site-packages/IPython/kernel/__main__.py:1: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  if __name__ == '__main__':\n"
     ]
    }
   ],
   "source": [
    "flu_complete['non_white'] = (flu_complete.Race!='W').astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.4/site-packages/IPython/kernel/__main__.py:1: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  if __name__ == '__main__':\n"
     ]
    }
   ],
   "source": [
    "flu_complete['male'] = (flu_complete.Sex=='M').astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.4/site-packages/IPython/kernel/__main__.py:1: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  if __name__ == '__main__':\n"
     ]
    }
   ],
   "source": [
    "flu_complete['OI'] = flu_complete.FiO2 * flu_complete.MAP / flu_complete.PO2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.4/site-packages/IPython/kernel/__main__.py:2: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  from IPython.kernel.zmq import kernelapp as app\n",
      "/usr/local/lib/python3.4/site-packages/pandas/core/indexing.py:415: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  self.obj[item] = s\n"
     ]
    }
   ],
   "source": [
    "# ECMO Type\n",
    "flu_complete['VA'] = flu_complete.Mode.isin(['VA', 'VV-VA'])\n",
    "# Set \"Other\" type to NA (there are only a couple)\n",
    "flu_complete.loc[flu_complete.Mode=='Other', 'VA'] = None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# covariates = ['male', 'AgeYears', 'non_white', 'HoursECMO', 'pH', 'PCO2', 'PO2', 'HCO3', \n",
    "#               'SaO2', 'mrsa', 'any_coinf']\n",
    "covariates = ['male', 'AgeYears', 'non_white', 'pH', 'PCO2', 'HCO3', 'PO2', 'OI', \n",
    "              'SaO2', 'mrsa', 'any_coinf', 'AdmitToTimeOnHours', 'VA', 'PEEP']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get counts of missing values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "male                   0\n",
       "AgeYears               0\n",
       "non_white              0\n",
       "HoursECMO              0\n",
       "pH                    11\n",
       "PCO2                  10\n",
       "HCO3                  19\n",
       "PO2                    9\n",
       "OI                    43\n",
       "SaO2                  16\n",
       "mrsa                   0\n",
       "any_coinf              0\n",
       "AdmitToTimeOnHours    13\n",
       "VA                     2\n",
       "PEEP                  38\n",
       "dtype: float64"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flu_complete[covariates].isnull().mean().round(2)*100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['RunNo', 'AgeDays', 'HoursECMO', 'SupportType', 'PrimaryDx', 'Mode', 'Discontinuation', 'DischargedAlive', 'DischargeLocation', 'YearECLS', 'VentType', 'Rate', 'FiO2', 'PIP', 'PEEP', 'MAP', 'HandBagging', 'pH', 'PCO2', 'PO2', 'HCO3', 'SaO2', 'Venttype24', 'Rate24', 'Fio224', 'PIP24', 'PEEP24', 'MAP24', 'Handbagging24', 'SBP', 'DBP', 'MapHemo', 'SVO2', 'PCWP', 'SPAP', 'DPAP', 'MPAP', 'CI', 'Race', 'Sex', 'AdmitToTimeOnHours', 'TimeOffToExtubationDateHours', 'TimeOffToDeathDateHours', 'TimeOffToDCDateHours', 'ExtubationToDCDateHours', 'ExtubationToDeathDateHours', 'year', 'HoursVent', 'AgeYears', 'age_class', 'RunID', 'OrganismNo', 'OrganismName', 'CultureSite', 'CultureTimeIsApproximate', 'OrganismTiming', 'Type', 'has_flu', 'fate', 'flu_only', 'mrsa', 'any_coinf', 'time_to_event', 'non_white', 'male', 'OI', 'VA'], dtype='object')"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flu_complete.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>HoursECMO</th>\n",
       "      <th>AdmitToTimeOnHours</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fate</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Died</th>\n",
       "      <td> 324.935754</td>\n",
       "      <td> 101.009709</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Survived</th>\n",
       "      <td> 293.647280</td>\n",
       "      <td>  60.439914</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           HoursECMO  AdmitToTimeOnHours\n",
       "fate                                    \n",
       "Died      324.935754          101.009709\n",
       "Survived  293.647280           60.439914"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flu_complete.groupby('fate')[['HoursECMO', 'AdmitToTimeOnHours']].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are going to drop the missing values for some of the covariates, and not use some covariates with many missing values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "drop_subset = ['HoursECMO', 'pH', 'PCO2', 'PO2', 'VA']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "flu_complete = flu_complete.dropna(subset=drop_subset)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "ApZ93ScIAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ac36da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "flu_complete[['pH', 'PCO2', 'PO2', 'HCO3', \n",
    "              'SaO2']].hist(bins=25);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Survival Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Surivival time, in days"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "obs_t = flu_complete.time_to_event.values/24."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "SeXbJNNV6zXhTG92938KeHpG1qlXpqmuU3dfPwZOdjPc3m//E1yrXpmmvlbr9nkfv3kxdKr3q00y\n",
       "7XitvFyCJDXAD1VJUgMse0lqgGUvSQ2w7CWpAZa9JDXAspekBlj2ktQAy16SGvC/ij538o0uYn4A\n",
       "AAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b4976d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(obs_t, bins=25);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fate of each patient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "died = (flu_complete.fate=='Died').astype(int).values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kaplan-Meier Curves"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from lifelines import KaplanMeierFitter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "iDQANeYiIg1AjbmISANQYy4i0gDUmIuINID/D/gAL5UofpYxAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b8b1940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "km = KaplanMeierFitter()\n",
    "km.fit(obs_t, event_observed=died)\n",
    "ax = km.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mrsa_ind = flu_complete.mrsa.astype(bool).values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x10b8d1ba8>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "A/5/J2cBqyDzsp0AAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b8e49b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "km = KaplanMeierFitter()\n",
    "km.fit(obs_t[~mrsa_ind], event_observed=died[~mrsa_ind], label='non-MRSA')\n",
    "ax = km.plot()\n",
    "\n",
    "km.fit(obs_t[mrsa_ind], event_observed=died[mrsa_ind], label='MRSA')\n",
    "km.plot(ax=ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cumulative Hazard"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x10ba0d748>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "MRcRGQZUzEVEhgEVcxGRYUDFXERkGFAxFxEZBlTMRUSGgf8B4Jqur14MV1EAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b932b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from lifelines import NelsonAalenFitter\n",
    "na = NelsonAalenFitter()\n",
    "\n",
    "na.fit(obs_t, event_observed=died)\n",
    "na.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unique failure times"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,  10,  11,  12,\n",
       "        13,  14,  15,  16,  17,  18,  19,  20,  21,  22,  23,  24,  25,\n",
       "        26,  27,  28,  29,  30,  31,  32,  33,  34,  35,  36,  37,  38,\n",
       "        39,  40,  41,  42,  43,  44,  45,  46,  47,  48,  50,  53,  54,\n",
       "        55,  59,  61,  62,  63,  67,  68,  73,  77, 108, 121, 125, 126,\n",
       "       133, 142, 150, 201, 227, 235, 301])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "times = np.unique((flu_complete.time_to_event[flu_complete.fate=='Died'].values/24).astype(int))\n",
    "times"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "N_obs = len(obs_t)\n",
    "T = len(times) - 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate risk set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1, 1, ..., 0, 0, 0],\n",
       "       [1, 1, 1, ..., 0, 0, 0],\n",
       "       [1, 1, 1, ..., 0, 0, 0],\n",
       "       ..., \n",
       "       [1, 0, 0, ..., 0, 0, 0],\n",
       "       [1, 1, 1, ..., 0, 0, 0],\n",
       "       [1, 1, 1, ..., 0, 0, 0]])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y = np.array([[int(obs >= t) for t in times] for obs in obs_t])\n",
    "Y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Counting process. Jump = 1 if $\\text{obs}_t \\in [ t_j, t_{j+1} )$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dN = np.array([[Y[i,j]*(times[j+1] >= obs_t[i])*died[i] for i in range(N_obs)] for j in range(T)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Process for one patient\n",
    "dN[:,1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Covariates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "standardize = lambda x: (x - x[np.isnan(x)-True].mean()) / x[np.isnan(x)-True].std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "analysis_covariates = ['male', 'AgeYears', 'non_white', 'HoursECMO', 'pH', 'PCO2', 'PO2', 'mrsa', 'any_coinf', 'VA']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "male         0\n",
       "AgeYears     0\n",
       "non_white    0\n",
       "HoursECMO    0\n",
       "pH           0\n",
       "PCO2         0\n",
       "PO2          0\n",
       "mrsa         0\n",
       "any_coinf    0\n",
       "VA           0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flu_complete[analysis_covariates].isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "male, AgeYears, non_white, HoursECMO, pH, PCO2, PO2, mrsa, any_coinf, VA= \\\n",
    "    flu_complete[analysis_covariates].values.T\n",
    "\n",
    "\n",
    "HoursECMO_std = standardize(HoursECMO)\n",
    "AgeYears_std = standardize(AgeYears)\n",
    "pH_std = standardize(pH)\n",
    "PCO2_std = standardize(PCO2)\n",
    "PO2_std = standardize(PO2)\n",
    "# HCO3_std = standardize(HCO3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import theano.tensor as tt\n",
    "from pymc3 import Model, Normal, Poisson, DensityDist, T as StudentT, Uniform, Deterministic, HalfCauchy, Laplace, Exponential\n",
    "from pymc3 import Bernoulli, Gamma, MvNormal, BinaryMetropolis\n",
    "from pymc3.distributions.timeseries import GaussianRandomWalk\n",
    "from pymc3 import sample, NUTS, Slice, Metropolis, forestplot, find_MAP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n_kernels = 5\n",
    "kernels = np.linspace(AgeYears_std.min(), AgeYears_std.max(), n_kernels)\n",
    "\n",
    "def rbf(s, x):\n",
    "    return [tt.exp( ((x - k)/ s)**2) for k in kernels]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "with Model() as model:\n",
    "    \n",
    "    sigma = Uniform('sigma', 0, 100)\n",
    "    \n",
    "    alpha_sd = Uniform('alpha_sd', 0, 100)\n",
    "\n",
    "    alpha = GaussianRandomWalk('alpha', sd=alpha_sd, shape=n_kernels)\n",
    "\n",
    "    a = tt.dot(alpha, rbf(sigma, AgeYears_std))\n",
    "    \n",
    "    X = np.c_[[male, pH_std, PCO2_std, PO2_std, HoursECMO_std, non_white, mrsa, any_coinf]].T\n",
    "    \n",
    "    # Intercept for survival rate\n",
    "    beta0 = Normal('beta0', 0.0, 0.001)\n",
    "    # Treatment effect\n",
    "    beta = Normal('beta', 0, 0.001, shape=X.shape[1])\n",
    "\n",
    "    # Survival rates\n",
    "    lam = tt.exp(beta0 + tt.dot(X, beta) + a)\n",
    "\n",
    "    def exp_logp(failure, value):\n",
    "        # Exponential survival log-likelihood\n",
    "        return tt.sum(failure * tt.log(lam) - lam * value)\n",
    "\n",
    "    surv_like = DensityDist('surv_like', exp_logp, observed=(died, obs_t))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 2000 of 2000 complete in 821.2 sec"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    trace = sample(2000, step=NUTS(), njobs=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.gridspec.GridSpec at 0x10dcbffd0>"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ee44898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "forestplot(trace, vars=['alpha'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.gridspec.GridSpec at 0x10fae6b70>"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "AABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1100c5860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "forestplot(trace, vars=['beta'], ylabels=['male', 'pH', 'PCO2', 'PO2', 'HoursECMO', 'non_white', 'mrsa', 'any_coinf'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['RunNo', 'AgeDays', 'HoursECMO', 'SupportType', 'PrimaryDx', 'Mode', 'Discontinuation', 'DischargedAlive', 'DischargeLocation', 'YearECLS', 'VentType', 'Rate', 'FiO2', 'PIP', 'PEEP', 'MAP', 'HandBagging', 'pH', 'PCO2', 'PO2', 'HCO3', 'SaO2', 'Venttype24', 'Rate24', 'Fio224', 'PIP24', 'PEEP24', 'MAP24', 'Handbagging24', 'SBP', 'DBP', 'MapHemo', 'SVO2', 'PCWP', 'SPAP', 'DPAP', 'MPAP', 'CI', 'Race', 'Sex', 'AdmitToTimeOnHours', 'TimeOffToExtubationDateHours', 'TimeOffToDeathDateHours', 'TimeOffToDCDateHours', 'ExtubationToDCDateHours', 'ExtubationToDeathDateHours', 'year', 'HoursVent', 'AgeYears', 'age_class', 'RunID', 'OrganismNo', 'OrganismName', 'CultureSite', 'CultureTimeIsApproximate', 'OrganismTiming', 'Type', 'has_flu', 'fate', 'flu_only', 'mrsa', 'any_coinf', 'time_to_event', 'non_white', 'male', 'OI', 'VA'], dtype='object')"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flu_complete.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2009    338\n",
       "2011    186\n",
       "2010    115\n",
       "2012     73\n",
       "2008     31\n",
       "2007     25\n",
       "2003     24\n",
       "2005     19\n",
       "2006     17\n",
       "2000     14\n",
       "1998     10\n",
       "1999      9\n",
       "2002      8\n",
       "2001      8\n",
       "2004      6\n",
       "1997      3\n",
       "1996      2\n",
       "1995      1\n",
       "1994      1\n",
       "1993      1\n",
       "1992      1\n",
       "dtype: int64"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flu_complete.year.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.gridspec.GridSpec at 0x125108850>"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "l5eHTz75BJMmTQIAnDt3DosWLcLly5fRqlWrKkvTa6P9m/R6PTZu3Ig333yzxm2b2v6RI0fw7rvv\n",
       "olWrVoZTiM8+++xdH3nr9XosX77cUPIcHR2NH374AQDQt29fAMDq1atx8OBB2NnZ4ZVXXoGnp6dZ\n",
       "tteU9hcvXoz9+/fDzc0NQFnhTUJCQp21f6uPPvoInTt3NnvJ+53a37JlCzZt2oSioiI8+uijePjh\n",
       "h+us/atXr+LLL7/EkSNH4OTkhKioKAQHB5ut/dowd+5c/Prrr/j777/h7OyMp59+GmFhYXXS5uXL\n",
       "l+Hi4oKnnnoKJSUlAMpex82bN+OHH36ASqVC69atER0dDS8vL7P2wZR9w5gxY7Bw4UKT1sfQIiIi\n",
       "afD0IBERSYOhRURE0mBoERGRNBhaREQkDYYWERFJg6FFRETSYGgREZE0GFpERCSN/w85j9572TW8\n",
       "gAAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12528d250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "forestplot(trace, vars=['beta'], ylabels=['male', 'pH', 'PCO2', 'PO2', 'HoursECMO', 'non_white', 'mrsa', 'any_coinf'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Same model above, but with a Weibull hazard function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "with Model() as model_weibull:\n",
    "    \n",
    "    X = np.c_[[male, pH_std, PCO2_std, PO2_std, HoursECMO_std, non_white, mrsa, any_coinf]].T\n",
    "    \n",
    "    # Intercept for survival rate\n",
    "    beta0 = Normal('beta0', 0.0, 0.001)\n",
    "    # Treatment effect\n",
    "    beta = Normal('beta', 0, 0.001, shape=X.shape[1])\n",
    "\n",
    "    # Survival rates\n",
    "    lam = tt.exp(beta0 + tt.dot(X, beta))\n",
    "\n",
    "    alpha = Exponential('alpha', 1)\n",
    "    def weibull_logp(failure, times):\n",
    "        # Weibull survival log-likelihood\n",
    "        return tt.sum(failure*(tt.log(alpha) + (alpha-1)*tt.log(times*lam) + tt.log(lam)) - (lam*times)**alpha)\n",
    "\n",
    "    surv_like = DensityDist('surv_like', weibull_logp, observed=(died, obs_t))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "PositiveDefiniteError",
     "evalue": "Scaling is not positive definite. Simple check failed. Diagonal contains negatives. Check indexes [0 1 2 3 4 5 6 7 8]",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mPositiveDefiniteError\u001b[0m                     Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-52-4e1716b5764d>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mwith\u001b[0m \u001b[0mmodel_weibull\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m     \u001b[0mtrace_weibull\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msample\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2000\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstep\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mNUTS\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/usr/local/lib/python3.4/site-packages/pymc3/step_methods/nuts.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, vars, scaling, step_scale, is_cov, state, Emax, target_accept, gamma, k, t0, model, **kwargs)\u001b[0m\n\u001b[1;32m     67\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     68\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 69\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpotential\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mquad_potential\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mscaling\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mis_cov\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mas_cov\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     70\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     71\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mstate\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.4/site-packages/pymc3/step_methods/quadpotential.py\u001b[0m in \u001b[0;36mquad_potential\u001b[0;34m(C, is_cov, as_cov)\u001b[0m\n\u001b[1;32m     33\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mQuadPotential_SparseInv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mC\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     34\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 35\u001b[0;31m     \u001b[0mpartial_check_positive_definite\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mC\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     36\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mC\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     37\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mis_cov\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mas_cov\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.4/site-packages/pymc3/step_methods/quadpotential.py\u001b[0m in \u001b[0;36mpartial_check_positive_definite\u001b[0;34m(C)\u001b[0m\n\u001b[1;32m     56\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     57\u001b[0m         raise PositiveDefiniteError(\n\u001b[0;32m---> 58\u001b[0;31m             \"Simple check failed. Diagonal contains negatives\", i)\n\u001b[0m\u001b[1;32m     59\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     60\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mPositiveDefiniteError\u001b[0m: Scaling is not positive definite. Simple check failed. Diagonal contains negatives. Check indexes [0 1 2 3 4 5 6 7 8]"
     ]
    }
   ],
   "source": [
    "with model_weibull:\n",
    "    trace_weibull = sample(2000, step=NUTS())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following incorporates a spline for the age effect."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def interpolate(x0, y0, x):\n",
    "    \n",
    "    x = np.array(x)\n",
    "\n",
    "    idx = np.searchsorted(x0, x)\n",
    "    dl = np.array(x - x0[idx - 1])\n",
    "    dr = np.array(x0[idx] - x)\n",
    "    d=dl+dr\n",
    "    wl = dr/d\n",
    "\n",
    "    return wl*y0[idx-1] + (1-wl)*y0[idx]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'interpolate' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-37-db5cbe3c3dee>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      9\u001b[0m     \u001b[0mspline\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mNormal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'spline'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcoeff_tau\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mshape\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnknots\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     10\u001b[0m     \u001b[0mknots\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinspace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mAgeYears\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mAgeYears\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnknots\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m     \u001b[0mbeta1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mDeterministic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'beta1'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minterpolate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mknots\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mspline\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mAgeYears\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     12\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m     \u001b[0;31m# Intercept for survival rate\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'interpolate' is not defined"
     ]
    }
   ],
   "source": [
    "nknots = 10\n",
    "\n",
    "with Model() as model_spline:\n",
    "    \n",
    "    #X = np.c_[[male, non_white, mrsa, any_coinf]].T\n",
    "    \n",
    "    coeff_sd = Uniform('coeff_sd', 0, 100)\n",
    "    coeff_tau = coeff_sd**-2\n",
    "    spline = Normal('spline', 0, coeff_tau, shape=nknots)\n",
    "    knots = np.linspace(AgeYears.min(), AgeYears.max()+1, nknots)\n",
    "    beta1 = Deterministic('beta1', interpolate(knots, spline, AgeYears))\n",
    "    \n",
    "    # Intercept for survival rate\n",
    "    beta0 = Normal('beta0', 0.0, 0.001)\n",
    "    # Treatment effect\n",
    "    #beta = Normal('beta', 0, 0.001, shape=X.shape[1])\n",
    "\n",
    "    # Survival rates\n",
    "    lam = tt.exp(beta0 + beta1)# + tt.dot(X, beta))\n",
    "    \n",
    "    def exp_logp(failure, value):\n",
    "        # Exponential survival log-likelihood\n",
    "        return tt.sum(failure * tt.log(lam) - lam * value)\n",
    "\n",
    "    surv_like = DensityDist('surv_like', exp_logp, observed=(died, obs_t))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "with model_spline:\n",
    "    trace_spline = sample(1000, step=NUTS())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.gridspec.GridSpec at 0x11bb06a90>"
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     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11bf197d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "forestplot(trace_spline, vars=['beta'], \n",
    "           ylabels=['male', 'non_white', 'mrsa', 'any_coinf'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.gridspec.GridSpec at 0x11da06210>"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "ZMHAISIiWTBwiIhIFv8PpEZZIFL6F1IAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d95b1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "forestplot(trace_spline, vars=['spline']) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Log-logistic model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "with Model() as log_logistic_model:\n",
    "    \n",
    "    sigma = Uniform('sigma', 0, 100)\n",
    "    \n",
    "    alpha_sd = Uniform('alpha_sd', 0, 100)\n",
    "\n",
    "    alpha = GaussianRandomWalk('alpha', sd=alpha_sd, shape=n_kernels)\n",
    "\n",
    "    a = tt.dot(alpha, rbf(sigma, AgeYears_std))\n",
    "    \n",
    "    X = np.c_[[male, pH_std, PCO2_std, PO2_std, HoursECMO_std, non_white, mrsa, any_coinf]].T\n",
    "    \n",
    "    # Intercept for survival rate\n",
    "    beta0 = Normal('beta0', 0.0, 0.001)\n",
    "    # Treatment effect\n",
    "    beta = Normal('beta', 0, 0.001, shape=X.shape[1])\n",
    "\n",
    "    # Survival rates\n",
    "    lam = tt.exp(beta0 + tt.dot(X, beta) + a)\n",
    "\n",
    "    def exp_logp(failure, value):\n",
    "        # Exponential survival log-likelihood\n",
    "        return tt.sum(failure * tt.log(lam) - lam * value)\n",
    "\n",
    "    surv_like = DensityDist('surv_like', exp_logp, observed=(died, obs_t))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Radial basis function model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 248.,  106.,   75.,  103.,   79.,   64.,   66.,   40.,    7.,    4.]),\n",
       " array([  0.        ,   8.13123288,  16.26246575,  24.39369863,\n",
       "         32.52493151,  40.65616438,  48.78739726,  56.91863014,\n",
       "         65.04986301,  73.18109589,  81.31232877]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111210610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(AgeYears)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.,  0.,  0.,  0.],\n",
       "       [ 0.,  3.,  0.,  0.],\n",
       "       [ 0.,  0.,  4.,  0.],\n",
       "       [ 0.,  0.,  0.,  5.]])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.eye(4)*[2,3,4,5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "gaussian_basis = lambda x, h, l: np.exp(-(np.abs(x - h) / l)**2)\n",
    "\n",
    "n_rbf = 20\n",
    "centers = np.linspace(AgeYears.min(), AgeYears.max()+1, n_rbf)\n",
    "l = 3\n",
    "# Weights\n",
    "w = [[gaussian_basis(x, h, l) for h in centers] for x in AgeYears]\n",
    "w_pred = [[gaussian_basis(x, h, l) for h in centers] for x in np.linspace(AgeYears.min(), AgeYears.max()+1, 100)]\n",
    "\n",
    "with Model() as model_rbf:\n",
    "    \n",
    "    # Prior on number of basis functions\n",
    "    z = Bernoulli('z', 0.5, shape=n_rbf)\n",
    "    \n",
    "    # Prior for non-zero coefficients\n",
    "    sigma = HalfCauchy('sigma', 25)\n",
    "    #kappa = Gamma('kappa', 0.5, 0.5, shape=n_rbf)\n",
    "    #Tau = tt.diag(kappa) #* sigma**-2\n",
    "    \n",
    "    #beta = MvNormal('beta', [0]*n_rbf, Tau, shape=n_rbf)\n",
    "    beta = GaussianRandomWalk('beta', sd=sigma, shape=n_rbf)\n",
    "\n",
    "\n",
    "    # Intercept for survival rate\n",
    "    beta0 = Normal('beta0', 0.0, 0.001)\n",
    "\n",
    "    # Hazard rates\n",
    "    lam = Deterministic('lam', tt.exp(beta0 + tt.dot(w, z*beta)))\n",
    "    lam_pred = Deterministic('lam_pred', tt.exp(beta0 + tt.dot(w_pred, z*beta)))\n",
    "    \n",
    "    def exp_logp(failure, value):\n",
    "        # Exponential survival log-likelihood\n",
    "        return tt.sum(failure * tt.log(lam) - lam * value)\n",
    "\n",
    "    surv_like = DensityDist('surv_like', exp_logp, observed=(died, obs_t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Library/Python/2.7/site-packages/theano/scan_module/scan_perform_ext.py:85: RuntimeWarning: numpy.ndarray size changed, may indicate binary incompatibility\n",
      "  from scan_perform.scan_perform import *\n"
     ]
    }
   ],
   "source": [
    "with model_rbf:\n",
    "    start = {'z': [1]*n_rbf, 'sigma': 10, 'beta': [0]*n_rbf, 'beta0': 0}\n",
    "    step1 = BinaryMetropolis(vars=[z])\n",
    "    step2 = NUTS(vars=[sigma, beta, beta0], scaling=start)\n",
    "    trace_rbf = sample(2000, step=[step1, step2], start=start)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from pymc import traceplot\n",
    "\n",
    "forestplot(trace_rbf[5000:], vars=['lam_pred'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "_ = traceplot(trace_rbf[5000:], vars=['sigma'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from pymc import summary\n",
    "summary(trace_rbf, vars=['z'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  }
 ],
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