CamDavidsonPilon/b_splines.ipynb

## b_splines.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from lifelines.datasets import load_rossi\n",
    "rossi = load_rossi()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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>week</th>\n",
       "      <th>arrest</th>\n",
       "      <th>fin</th>\n",
       "      <th>age</th>\n",
       "      <th>race</th>\n",
       "      <th>wexp</th>\n",
       "      <th>mar</th>\n",
       "      <th>paro</th>\n",
       "      <th>prio</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>20</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>27</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>17</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>18</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>25</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>19</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>52</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>23</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>52</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>19</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   week  arrest  fin  age  race  wexp  mar  paro  prio\n",
       "0    20       1    0   27     1     0    0     1     3\n",
       "1    17       1    0   18     1     0    0     1     8\n",
       "2    25       1    0   19     0     1    0     1    13\n",
       "3    52       0    1   23     1     1    1     1     1\n",
       "4    52       0    0   19     0     1    0     1     3"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rossi.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# let's b-spline age\n",
    "cph = CoxPHFitter().fit(rossi, \"week\", \"arrest\", formula=\"fin + bs(age, df=4) + wexp + mar + paro + prio\")"
   ]
  },
  {
   "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>week</th>\n",
       "      <th>arrest</th>\n",
       "      <th>fin</th>\n",
       "      <th>age</th>\n",
       "      <th>race</th>\n",
       "      <th>wexp</th>\n",
       "      <th>mar</th>\n",
       "      <th>paro</th>\n",
       "      <th>prio</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>52.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>17.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>52.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>17.551020</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>52.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>18.102041</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>52.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>18.653061</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>52.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>19.204082</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   week  arrest  fin        age  race  wexp  mar  paro  prio\n",
       "0  52.0     0.0  0.5  17.000000   1.0   1.0  0.0   1.0   2.0\n",
       "1  52.0     0.0  0.5  17.551020   1.0   1.0  0.0   1.0   2.0\n",
       "2  52.0     0.0  0.5  18.102041   1.0   1.0  0.0   1.0   2.0\n",
       "3  52.0     0.0  0.5  18.653061   1.0   1.0  0.0   1.0   2.0\n",
       "4  52.0     0.0  0.5  19.204082   1.0   1.0  0.0   1.0   2.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# now we need to \"extend\" our data to plot it\n",
    "# we'll plot age over it's observed range\n",
    "age_range = np.linspace(rossi['age'].min(), rossi['age'].max(), 50)\n",
    "\n",
    "# need to create a matrix of variables at their means, _except_ for age. \n",
    "x_bar = cph._central_values\n",
    "df_varying_age = pd.concat([x_bar] * 50).reset_index(drop=True)\n",
    "df_varying_age['age'] = age_range\n",
    "\n",
    "df_varying_age.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cph.predict_log_partial_hazard(df_varying_age).plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# compare to _not_ bspline-ing:\n",
    "cph = CoxPHFitter().fit(rossi, \"week\", \"arrest\", formula=\"fin + age + wexp + mar + paro + prio\")\n",
    "\n",
    "age_range = np.linspace(rossi['age'].min(), rossi['age'].max(), 50)\n",
    "\n",
    "# need to create a matrix of variables at their means, _except_ for age. \n",
    "x_bar = cph._central_values\n",
    "df_varying_age = pd.concat([x_bar] * 50).reset_index(drop=True)\n",
    "df_varying_age['age'] = age_range\n",
    "\n",
    "cph.predict_log_partial_hazard(df_varying_age).plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}