Untitled.ipynb

FRS.ipynb

{
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    {
      "metadata": {
        "collapsed": true,
        "trusted": true,
        "editable": true,
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      },
      "cell_type": "code",
      "source": "import numpy as np",
      "execution_count": 1,
      "outputs": []
    },
    {
      "metadata": {
        "editable": true,
        "deletable": true
      },
      "cell_type": "markdown",
      "source": "I will implement the 10-year risk equation for women. Here are the betas."
    },
    {
      "metadata": {
        "collapsed": true,
        "trusted": true,
        "editable": true,
        "deletable": true
      },
      "cell_type": "code",
      "source": "betas = np.array([2.72107, # log age\n0.51125,          # log BMI\n2.81291,          # log SBP (not treated)\n2.88267,          # log SBP (treated)\n0.61868,          # smoking\n0.77763,          # diabetes\n])",
      "execution_count": 2,
      "outputs": []
    },
    {
      "metadata": {
        "editable": true,
        "deletable": true
      },
      "cell_type": "markdown",
      "source": "Here is the formula. The `dot` function is the dot product, or inner product of the coefficients and the data array (i.e. multiply them element-wise, and add the products)"
    },
    {
      "metadata": {
        "collapsed": true,
        "trusted": true,
        "editable": true,
        "deletable": true
      },
      "cell_type": "code",
      "source": "def frs(X, b, surv, const):\n    return 1 - surv** np.exp(X.dot(b) - const)",
      "execution_count": 16,
      "outputs": []
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "Below are special cases of the general formula, using the survival and constants specified for men and women:"
    },
    {
      "metadata": {
        "trusted": true,
        "collapsed": true
      },
      "cell_type": "code",
      "source": "def frs_women(X, b):\n    return frs(X, b, 0.94833, 26.0145)",
      "execution_count": 17,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true,
        "collapsed": true
      },
      "cell_type": "code",
      "source": "def frs_men(X, b):\n    return frs(X, b, 0.88431, 23.9388)",
      "execution_count": 18,
      "outputs": []
    },
    {
      "metadata": {
        "editable": true,
        "deletable": true
      },
      "cell_type": "markdown",
      "source": "Here is some sample data"
    },
    {
      "metadata": {
        "collapsed": false,
        "trusted": true,
        "editable": true,
        "deletable": true
      },
      "cell_type": "code",
      "source": "x_sample = np.array([np.log(30), np.log(22.5), 0, np.log(125), 0, 0])\nx_sample",
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([ 3.40119738,  3.11351531,  0.        ,  4.82831374,  0.        ,  0.        ])"
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "metadata": {
        "editable": true,
        "deletable": true
      },
      "cell_type": "markdown",
      "source": "Here is the corresponding risk scores (men and women)"
    },
    {
      "metadata": {
        "collapsed": false,
        "trusted": true,
        "editable": true,
        "deletable": true
      },
      "cell_type": "code",
      "source": "frs_women(X=x_sample, b=betas)",
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": "0.015094153510678776"
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "metadata": {
        "trusted": true,
        "collapsed": false
      },
      "cell_type": "code",
      "source": "frs_men(X=x_sample, b=betas)",
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": "0.24491217871245496"
          },
          "metadata": {},
          "execution_count": 21
        }
      ]
    }
  ],
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