vukosim/AUC Approximation Tests

## AUC Approximation Tests
{
 "metadata": {
  "name": "AUC Scratchboo"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "import numpy as np\nimport scipy as sp\nfrom scipy import stats\nfrom scipy import interpolate",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 25
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": "T-Tests"
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": "First lets do a T-Test with two independent sets of data with same mean and variance."
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "np.random.seed(12345678)\na  = stats.norm.rvs(loc=5,scale=10,size=1000)\nb  = stats.norm.rvs(loc=5,scale=10,size=1000)\n\n# Now do t-test\nresult = stats.ttest_ind(a,b)\n\np_value = result[-1]\n\nprint \"p-value: \", p_value\n",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "p-value:  0.782578705472\n"
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": "As we can see the p-value is greater than 0.05 meaning there is a very small chance that the means of the two actually being different. So we cant reject the hypothesis that the means are the same"
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": "Creatig Data for AUC calculation"
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": "We are interested in the process that data is collected from a process (patients visiting a doctor) and random intervals and having measurements taken. I am assuming that the measurements are randomly distributed (mean 5) and that the days of visiting are random too. \n\nI am going to create a 120 day process with guaranteed measurements on day 1 and day 120 but random days in between. Patients will not have the same measurements. Lets assume the patients have 8 - 12 measurements in the time (including the start and end measurements)"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "def get_data():\n    data =[]\n    day_range = xrange(1,119)\n    for i in range(1000):\n        days = [0,120] # Add the first and last day\n        sample_size = randint(6,10) #How many days to sample?\n        days.extend(list(np.random.choice(day_range,size=sample_size,replace=False)))\n    \n        days = list(np.sort(days))\n    \n        measurements = list(stats.norm.rvs(loc=5,scale=10,size=sample_size+2))\n        \n        data.append([days,measurements])\n    return data\n\nprocess_data = get_data()",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": "Now lets calculate AUC for each data point"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "def calculate_auc(data,start_day,end_day):\n    auc =[]\n    for days,measurements in data:\n        tck = interpolate.splrep(days, measurements, s=0, k=1)\n        temp_auc = interpolate.splint(start_day, end_day, tck)\n        auc.append(temp_auc)\n    return auc",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "original_process_auc = calculate_auc(process_data,0,120)",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 28
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": "Lets look at the distribution of the AUC"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "pyplot.hist(original_process_auc)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 29,
       "text": "(array([  4,  28,  88, 195, 275, 231, 133,  36,   8,   2]),\n array([ -914.27695876,  -587.87472991,  -261.47250106,    64.9297278 ,\n         391.33195665,   717.7341855 ,  1044.13641436,  1370.53864321,\n        1696.94087206,  2023.34310092,  2349.74532977]),\n <a list of 10 Patch objects>)"
      },
      {
       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": "Now lets set 30 day intervals for measurements using the linear spline and see how that AUC matches up"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "def calculate_interval_auc(data,start_day,end_day,interval):\n    auc =[]\n    for days,measurements in data:\n        tck = interpolate.splrep(days, measurements, s=0, k=1)\n        new_days = range(start_day,end_day,interval)\n        new_days.append(end_day)\n        new_measurements = []\n        for day in new_days:\n            new_measurements.append(interpolate.splev(day,tck))\n        new_tck = interpolate.splrep(new_days, new_measurements, s=0, k=1)\n        temp_auc = interpolate.splint(start_day, end_day, new_tck)\n        auc.append(temp_auc)\n    return auc",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 42
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "interval_process_auc = calculate_interval_auc(data,0,120,30)",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "pyplot.hist(interval_process_auc)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 32,
       "text": "(array([  6,  27,  79, 171, 243, 240, 155,  54,  21,   4]),\n array([-1067.19503284,  -728.22618587,  -389.25733889,   -50.28849192,\n         288.68035506,   627.64920203,   966.61804901,  1305.58689598,\n        1644.55574296,  1983.52458993,  2322.49343691]),\n <a list of 10 Patch objects>)"
      },
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAD9CAYAAAC7iRw+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n"
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": "Now lets see the T-Test :)"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "# Now do t-test for 30 days\nt_result = stats.ttest_ind(original_process_auc,interval_process_auc,equal_var=False)\nt_p_value = t_result[-1]\nprint t_p_value",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "0.347322142161\n"
      }
     ],
     "prompt_number": 50
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "interval_60_process_auc = calculate_interval_auc(data,0,120,60)\npyplot.hist(interval_60_process_auc)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 36,
       "text": "(array([  6,  21,  64, 166, 245, 232, 156,  75,  27,   8]),\n array([-1545.455439  , -1123.48193243,  -701.50842587,  -279.53491931,\n         142.43858725,   564.41209381,   986.38560037,  1408.35910694,\n        1830.3326135 ,  2252.30612006,  2674.27962662]),\n <a list of 10 Patch objects>)"
      },
      {
       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "# Now do t-test for 60 days\nt_result = stats.ttest_ind(original_process_auc,interval_60_process_auc)\nt_p_value = t_result[-1]\nprint t_p_value",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "0.33965966423\n"
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "interval_120_process_auc = calculate_interval_auc(data,0,120,120)\npyplot.hist(interval_120_process_auc)\n# Now do t-test for 120 days\nt_result = stats.ttest_ind(original_process_auc,interval_120_process_auc,equal_var=False)\nt_p_value = t_result[-1]\nprint \"p-value 120 day intervals: \", t_p_value",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "p-value 120 day intervals:  0.394243496552\n"
      },
      {
       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 49
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "interval_15_process_auc = calculate_interval_auc(data,0,120,15)\npyplot.hist(interval_15_process_auc)\n# Now do t-test for 15 days\nt_result = stats.ttest_ind(original_process_auc,interval_15_process_auc,equal_var=False)\nt_p_value = t_result[-1]\nprint \"p-value 15 day intervals: \",t_p_value",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "p-value 15 day intervals:  0.458344635524\n"
      },
      {
       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "t_result = stats.ttest_ind(original_process_auc,original_process_auc,equal_var=False)\nt_p_value = t_result[-1]\nprint \"p-value Original: \",t_p_value",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "p-value Original:  1.0\n"
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}