Subclassification on propensity score.ipynb

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   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import pyAgrum as gum\n",
    "import pyAgrum.lib.notebook as gnb"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## We are given this database coming from the historical records of a hospital"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>smoker</th>\n",
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       "        smoker  treatment  dead\n",
       "0            0          0     0\n",
       "1            1          1     0\n",
       "2            1          1     0\n",
       "3            0          1     0\n",
       "4            0          0     0\n",
       "...        ...        ...   ...\n",
       "999995       0          0     0\n",
       "999996       1          1     0\n",
       "999997       0          0     0\n",
       "999998       0          0     0\n",
       "999999       0          0     0\n",
       "\n",
       "[1000000 rows x 3 columns]"
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     "execution_count": 32,
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   "source": [
    "df = pd.read_csv(\"sample\")\n",
    "df"
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   "source": [
    "## And we are asked: \n",
    "## Question: How much will number of deads change if we decide treat everybody from now on with respect to not treating anyone? "
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "## We can use subclassification on propensity score\n",
    "### We start computing the propensities of each sample. \n",
    "### Recall that \n",
    "\\begin{align}\n",
    "e(x)=p(z=1|x)\n",
    "\\end{align}\n",
    "### in our case:\n",
    "\\begin{align}\n",
    "e(smoker)=p(treatment=1|smoker)\n",
    "\\end{align}"
   ]
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   "cell_type": "code",
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     "text": [
      "0.551550247155304\n"
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   "source": [
    "n_smokers = len(df[df[\"smoker\"]==1])\n",
    "n_treated_smokers = len(df[(df[\"smoker\"]==1) & (df[\"treatment\"]==1)])\n",
    "e_smoker = n_treated_smokers/n_smokers\n",
    "print(e_smoker)"
   ]
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   "cell_type": "code",
   "execution_count": 34,
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      "0.20002946321174753\n"
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   "source": [
    "n_non_smokers = len(df[df[\"smoker\"]==0])\n",
    "n_treated_non_smokers = len(df[(df[\"smoker\"]==0) & (df[\"treatment\"]==1)])\n",
    "e_non_smoker = n_treated_non_smokers/n_non_smokers\n",
    "print(e_non_smoker)"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute the propensity score for each patient. "
   ]
  },
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   "cell_type": "code",
   "execution_count": 35,
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   ],
   "source": [
    "df[\"propensity\"]=df[\"smoker\"]*e_smoker + (1-df[\"smoker\"])*e_non_smoker\n",
    "df.hist(\"propensity\")\n",
    "pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.699177, 0.300823])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "high_propensity = df[df[\"propensity\"]==e_smoker]\n",
    "low_propensity = df[df[\"propensity\"]==e_non_smoker]\n",
    "counts = np.array([len(low_propensity),len(high_propensity)])\n",
    "percentages= counts / np.sum(counts)\n",
    "percentages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.30154970389303043"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "high_propensity_treated = high_propensity[high_propensity[\"treatment\"]==1]\n",
    "high_propensity_untreated = high_propensity[high_propensity[\"treatment\"]==0]\n",
    "ATE_high_propensity = high_propensity_treated[\"dead\"].mean()-high_propensity_untreated[\"dead\"].mean()\n",
    "ATE_high_propensity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.010967865389731754"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "low_propensity_treated = low_propensity[low_propensity[\"treatment\"]==1]\n",
    "low_propensity_untreated = low_propensity[low_propensity[\"treatment\"]==0]\n",
    "ATE_low_propensity = low_propensity_treated[\"dead\"].mean()-low_propensity_untreated[\"dead\"].mean()\n",
    "ATE_low_propensity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "ATE = percentages[0] * ATE_low_propensity + percentages[1] * ATE_high_propensity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.0830446073546166"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ATE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Response: The percentage of deads is estimated to decrease!!!\n",
    "## Consequently, we should treat our population."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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