incubator/logistic-regression-amputation.ipynb

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   "source": [
    "import pymc3 as pm\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import theano.tensor as tt\n",
    "import theano\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'retina'"
   ]
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_csv(\"../datasets/antiseptic-amputation.csv\", header=None)\n",
    "data.columns = [\"subject\", \"year\", \"antiseptic\", \"limb\", \"outcome\"]\n",
    "data.set_index(\"subject\", inplace=True)\n",
    "\n",
    "# Data normalization\n",
    "data[\"year\"] = data[\"year\"] - data[\"year\"].min()\n",
    "data = pm.floatX(data)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The logistic function is defined as\n",
    "\n",
    "$$ p = \\frac{1}{1 + e^{-k}}$$\n",
    "\n",
    "Here, the $k$ term refers to:\n",
    "\n",
    "$$ k = \\beta_{n}x_{1} + \\beta_{2}x_{2} + ... + \\beta_{n}x_{n} $$\n",
    "\n",
    "Therefore, we will write it in as such"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import theano.tensor as tt\n",
    "\n",
    "# data = pm.floatX(data)\n",
    "\n",
    "\n",
    "def logit(x):\n",
    "    return np.exp(x) / (1 + np.exp(x))\n",
    "\n",
    "\n",
    "with pm.Model() as model:\n",
    "    pm.glm.linear.GLM(x=data[[\"year\", \"antiseptic\", \"limb\"]], y=data[\"outcome\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "with model:\n",
    "    trace = pm.sample(draws=2000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pm.traceplot(trace)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Posterior predictive check."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ppc = pm.sample_ppc(trace, model=model, samples=500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ppc[\"y\"].mean(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "preds = np.rint(ppc[\"y\"].mean(axis=0)).astype(\"int\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scikitplot.plotters import plot_confusion_matrix\n",
    "\n",
    "plot_confusion_matrix(preds, data[\"outcome\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "accuracy_score(preds, data[\"outcome\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pm.forestplot(trace,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There's a baseline probability of survival, and a little bit of an error term that governs whether a limb will survive or not. Beyond that, antiseptics have the biggest effect on limb survival."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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