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   "source": [
    "# Survival Regression Model code"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook describes code for the Cox Proportional Hazards regression used for the conventional parameter model in our study. We define a simple function that accepts as arguments the input data (predictor variables and survival outcomes) and a training parameter.\n",
    "Below we describe each section of the code:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import required libraries:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np, pandas as pd\n",
    "import os, sys, time, pickle, copy, h5py\n",
    "import lifelines.utils\n",
    "from lifelines import CoxPHFitter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "def coxreg_single_run(xtr, ytr, penalty):\n",
    "    df_tr = pd.DataFrame(np.concatenate((ytr, xtr),axis=1))\n",
    "    df_tr.columns = ['status','time'] + ['X'+str(i+1) for i in range(xtr.shape[1])]\n",
    "    cph = CoxPHFitter(penalizer=penalty)\n",
    "    cph.fit(df_tr, duration_col='time', event_col='status')\n",
    "    return cph"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Function arguments:\n",
    "- `xtr` : $n \\times p$ matrix of predictor variables, where $n$ is sample size and $p$ is number of predictor variables. \n",
    "- `ytr` : $n \\times 2$ matrix of survival outcomes, where first column is censoring status and second is survival/censoring time\n",
    "- `penalty` : To control for high correlations among the variables, L2-norm regularization is used to restrict the size of the coefficient estimates, which improves their stability. The `penalty` coefficient controls the strength of the L2-norm regularization\n",
    "\n",
    "Function output:\n",
    "- A `CoxPHFitter()` object which stores the model structure, regression coefficient estimates, etc. This object can be used to make predictions on new (test/validation) data"
   ]
  }
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