araastat/leuk.py

## leuk.py
{
 "metadata": {
  "name": "Survival Example"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Cox regression in PyMC\n",
      "\n",
      "This example implements the Cox model using the counting process notation introduced by Andersen and Gill (1982) "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Leukemia data"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Survival times in weeks\n",
      "obs_t = (1, 1, 2, 2, 3, 4, 4, 5, 5, 8, 8, 8, 8, 11, 11, 12, 12, 15, 17, 22, 23, 6, \n",
      "    6, 6, 6, 7, 9, 10, 10, 11, 13, 16, 17, 19, 20, 22, 23, 25, 32, 32, 34, 35)\n",
      "# Failure (1) or censored (0)\n",
      "fail = (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, \n",
      "    0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0)\n",
      "# Indicators for placebo or treatment\n",
      "Z = (0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, \n",
      "    0.5, 0.5, 0.5, 0.5, 0.5, -0.5, -0.5, -0.5, -0.5, -0.5, -0.5, -0.5, -0.5, -0.5, -0.5, \n",
      "    -0.5, -0.5, -0.5, -0.5, -0.5, -0.5, -0.5, -0.5, -0.5, -0.5, -0.5)\n",
      "# Unique failure times\n",
      "t = (1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 15, 16, 17, 22, 23, 35)\n",
      "N = len(obs_t)\n",
      "T = len(t) - 1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Calculate risk set"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Y = np.array([[int(obs >= time) for time in t] for obs in obs_t])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Counting process. Jump = 1 if $\\text{obs}_t \\in [ t_j, t_{j+1} )$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dN = np.array([[Y[i,j]*(t[j+1] >= obs_t[i])*fail[i] for i in range(N)] for j in range(T)])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Model using Poisson trick:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pymc import Normal, Lambda, Poisson, MCMC\n",
      "\n",
      "beta0 = Normal('beta0', 0, 0.001, value=np.zeros(T))\n",
      "beta1 = Normal('beta1', 0, 0.00001, value=0)\n",
      "\n",
      "# Poisson trick: independent log-normal hazard increments\n",
      "Idt = Lambda('Idt', lambda b0=beta0, b1=beta1: [[Y[i,j]*np.exp(b0[j] + b1*Z[i]) for i in range(N)] for j in range(T)])\n",
      "\n",
      "# Likelihood\n",
      "dN_like = Poisson('dN_like', Idt, value=dN, observed=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 43
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Initialize MCMC sampler."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "M = MCMC([beta0, beta1, Idt, dN_like])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 44
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "M.sample(10000, burn=5000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " \r",
        "[****************100%******************]  10000 of 10000 complete"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "beta1.summary()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "beta1:\n",
        " \n",
        "\tMean             SD               MC Error        95% HPD interval\n",
        "\t------------------------------------------------------------------\n",
        "\t1.428            0.294            0.013            [ 0.853  1.97 ]\n",
        "\t\n",
        "\t\n",
        "\tPosterior quantiles:\n",
        "\t\n",
        "\t2.5             25              50              75             97.5\n",
        "\t |---------------|===============|===============|---------------|\n",
        "\t0.878            1.224           1.422          1.63          2.026\n",
        "\t\n"
       ]
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pymc import Matplot\n",
      "\n",
      "Matplot.plot(beta1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Plotting beta1\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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4s7adE9xHfmk96nnyl9hBi3XNKNPP7DwjRxxrG0l0dGo173Yd9py3Ds64weCb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\npZegVCrh4+ODfv36uTxGIiKiG7HA6qEOHz4MrVYLrVaLo0ePQqlU4te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       "text": [
        "<matplotlib.figure.Figure at 0x109f62c10>"
       ]
      }
     ],
     "prompt_number": 47
    }
   ],
   "metadata": {}
  }
 ]
}