{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Doubly Robust Methods\n",
    "### AIPW\n",
    "\n",
    "#### Background\n",
    "\n",
    "Augmented Inverse Propensity Weighting (AIPW) is a modification of standard Inverse Propensity Weighting to achieve double robustness. We first consider basic IPW, which considers a sample weight, or propensity score $\\hat \\pi (X_i)$, in the model.\n",
    "\n",
    "$$\\widehat{ATE}_{IPW} = \\frac{1}{N} \\sum_{i=1}^N \\left[\\frac{D_iY_i}{\\hat \\pi (X_i)} - \\frac{(1-D_i)Y_i}{1-\\hat \\pi (X_i)}\\right]$$\n",
    "\n",
    "The augmenteed IPW, AIPW, as presetned by Glynn and Quinn, 2009 includes the outcome model in such a way that ensures doubly-robust estimation. This equations below reqrites the AIPW formulation such the basic IPW is seen clearly first along with the ourcome model augmentation. \n",
    "\n",
    "$$\\widehat{ATE}_{AIPW} = \\frac{1}{N} \\sum_{i=1}^N \\left(\\left[\\frac{D_iY_i}{\\hat \\pi (X_i)} - \\frac{(1-D_i)Y_i}{1-\\hat \\pi (X_i)}\\right]-\\frac{(X_i - \\hat \\pi (X_i))Y_i }{\\pi (X_i)(1-\\pi (X_i))} \\right) [(1-\\hat \\pi (X_i))\\hat{\\mathbb{E}}(Y_i|D_i=1,X_i) + + \\hat{\\pi} (X_i) \\hat{\\mathbb{E}}(Y_i|D_i=0,X_i)]$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "# Hide Cell\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "pd.set_option(\"display.precision\", 3)\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('seaborn')\n",
    "import seaborn as sns\n",
    "\n",
    "from sklearn.linear_model import LogisticRegression, LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Dataset\n",
    "\n",
    "We will use a simulated dataset based on The National Study of Learning Mindsets. This was a randomized study conducted in U.S. public high schools, the purpose of which was to evaluate the impact of a nudge-like, optional intervention designed to instill students with a growth mindset. The study includes measured outcomes via an achievement score, a binary treatment of a growth mindset educational intervention, and 11 other potential confounding factors that could be parents of both the treatment and outcome. The first 5 rows of the dataset are shows in the table below. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>schoolid</th>\n",
       "      <th>intervention</th>\n",
       "      <th>achievement_score</th>\n",
       "      <th>success_expect</th>\n",
       "      <th>ethnicity</th>\n",
       "      <th>gender</th>\n",
       "      <th>frst_in_family</th>\n",
       "      <th>school_urbanicity</th>\n",
       "      <th>school_mindset</th>\n",
       "      <th>school_achievement</th>\n",
       "      <th>school_ethnic_minority</th>\n",
       "      <th>school_poverty</th>\n",
       "      <th>school_size</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>76</td>\n",
       "      <td>1</td>\n",
       "      <td>0.277</td>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>0.335</td>\n",
       "      <td>0.649</td>\n",
       "      <td>-1.311</td>\n",
       "      <td>0.224</td>\n",
       "      <td>-0.427</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>76</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.450</td>\n",
       "      <td>4</td>\n",
       "      <td>12</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>0.335</td>\n",
       "      <td>0.649</td>\n",
       "      <td>-1.311</td>\n",
       "      <td>0.224</td>\n",
       "      <td>-0.427</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>76</td>\n",
       "      <td>1</td>\n",
       "      <td>0.770</td>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>0.335</td>\n",
       "      <td>0.649</td>\n",
       "      <td>-1.311</td>\n",
       "      <td>0.224</td>\n",
       "      <td>-0.427</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>76</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.122</td>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>0.335</td>\n",
       "      <td>0.649</td>\n",
       "      <td>-1.311</td>\n",
       "      <td>0.224</td>\n",
       "      <td>-0.427</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>76</td>\n",
       "      <td>1</td>\n",
       "      <td>1.526</td>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>0.335</td>\n",
       "      <td>0.649</td>\n",
       "      <td>-1.311</td>\n",
       "      <td>0.224</td>\n",
       "      <td>-0.427</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   schoolid  intervention  achievement_score  success_expect  ethnicity  \\\n",
       "0        76             1              0.277               6          4   \n",
       "1        76             1             -0.450               4         12   \n",
       "2        76             1              0.770               6          4   \n",
       "3        76             1             -0.122               6          4   \n",
       "4        76             1              1.526               6          4   \n",
       "\n",
       "   gender  frst_in_family  school_urbanicity  school_mindset  \\\n",
       "0       2               1                  4           0.335   \n",
       "1       2               1                  4           0.335   \n",
       "2       2               0                  4           0.335   \n",
       "3       2               0                  4           0.335   \n",
       "4       1               0                  4           0.335   \n",
       "\n",
       "   school_achievement  school_ethnic_minority  school_poverty  school_size  \n",
       "0               0.649                  -1.311           0.224       -0.427  \n",
       "1               0.649                  -1.311           0.224       -0.427  \n",
       "2               0.649                  -1.311           0.224       -0.427  \n",
       "3               0.649                  -1.311           0.224       -0.427  \n",
       "4               0.649                  -1.311           0.224       -0.427  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_mindset = pd.read_csv('learning_mindset.csv')\n",
    "# print(df_mindset.info())\n",
    "df_mindset.head()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "## Hide cell for book\n",
    "# Convert categorical values to binary indicators (one-hot)\n",
    "categ = [\"ethnicity\", \"gender\", \"school_urbanicity\"]\n",
    "cont = [\"school_mindset\", \"school_achievement\", \"school_ethnic_minority\", \"school_poverty\", \"school_size\"]\n",
    "\n",
    "df_categ = pd.concat([\n",
    "    df_mindset.drop(columns=categ), # dataset without the categorical features\n",
    "    pd.get_dummies(df_mindset[categ], columns=categ, drop_first=False) # categorical features converted to dummies\n",
    "], axis=1)\n",
    "\n",
    "# df_categ.head()\n",
    "\n",
    "T = 'intervention'\n",
    "Y = 'achievement_score'\n",
    "X = df_categ.columns.drop([T, Y])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Understanding the data and potential bias\n",
    "\n",
    "We begin by visualizing the achievement scores of treated and untreated cohorts with no control or consideration for the other variables. It is clear form the plot below there is an impact of the treatment as the average of the treated group's achievement scores is clearly higher. But we can intuit a positive bias in this measurement. We should note again the intervention was an option to take a growth mindset course. So although the option was offered in a random fashion, *it is highly likely students who opt-in to the treatment are likely to have the features to provide higher achievement scores regardless*. Thus, we might hypothesize controlling for this bias would decrease the ATE from the *naive ATE* (meaning no adjustment or simple difference of means of the treated and untreated groups)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.histplot(df_mindset['achievement_score'][df_categ['intervention'] == 0], kde=True, stat=\"density\", linewidth=0)\n",
    "sns.histplot(df_mindset['achievement_score'][df_categ['intervention'] == 1], kde=True, stat=\"density\", linewidth=0,color='g')\n",
    "plt.title(\"Achievement Scores by Treatment\", fontsize=20, fontweight = 'bold')\n",
    "plt.xlabel('Achievement Score', fontsize=14, fontweight = 'bold', labelpad=5)\n",
    "plt.legend(['Untreated', 'Treated']);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Method Implementations\n",
    "\n",
    "The following code block implements the naive ATE, the standard IPW, and finally the AIPW methods as python functions. Note that propensity score, or the exposure model, is constructed as a *Logistic Regression problem*, and the outcome model is generated as a *Linear Regression problem*.\n",
    "\n",
    "We do this to allow us to readily run many iterations of each method. We will use a bootstrap subsample method, where we will sample 1% of the original data (~100 data points), 100 times. This will allow us to generate a distribution of ATEs with an empirical standard deviation. Thus we can report our results comparing each of the three methods using various exposure and outcome models with 95% confidence intervals as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#### Define Estimation methods ####\n",
    "\n",
    "### Linear Regression T on Y\n",
    "def naive_ATE(df, T, Y):\n",
    "    return df[Y][df_categ[T] == 1].mean() - df_categ[Y][df_categ[T] == 0].mean()\n",
    "\n",
    "### IPW\n",
    "def IPW(df, X, T, Y,true_ps = True):\n",
    "\n",
    "    if true_ps:\n",
    "        p_scores = LogisticRegression(C=1e6, max_iter=1000).fit(df[X], df[T]).predict_proba(df[X])[:, 1]\n",
    "    else:\n",
    "        p_scores = np.random.uniform(0.1, 0.9, df.shape[0])\n",
    "\n",
    "    df_ps = df.assign(propensity_score=p_scores)\n",
    "\n",
    "    weight = ((df_ps[\"intervention\"]-df_ps[\"propensity_score\"]) / (df_ps[\"propensity_score\"]*(1-df_ps[\"propensity_score\"])))\n",
    "\n",
    "    weight_t = 1/df_ps.query(\"intervention==1\")[\"propensity_score\"]\n",
    "    weight_nt = 1/(1-df_ps.query(\"intervention==0\")[\"propensity_score\"])\n",
    "\n",
    "    y1 = sum(df_ps.query(\"intervention==1\")[\"achievement_score\"]*weight) / len(df_ps)\n",
    "    y0 = sum(df_ps.query(\"intervention==0\")[\"achievement_score\"]*weight_nt) / len(df_ps)\n",
    "\n",
    "    return np.mean(weight * df_ps[\"achievement_score\"]), p_scores, df_ps\n",
    "\n",
    "### AIPW\n",
    "def AIPW(df, X, T, Y,true_ps = True,true_mus = True):\n",
    "    if true_ps:\n",
    "        p_scores = LogisticRegression(C=1e6,max_iter=500).fit(df[X], df[T]).predict_proba(df[X])[:, 1]\n",
    "    else:\n",
    "        p_scores = np.random.uniform(0.1, 0.9, df.shape[0])\n",
    "\n",
    "    if true_mus:\n",
    "        mu0 = LinearRegression().fit(df.query(f\"{T}==0\")[X], df.query(f\"{T}==0\")[Y]).predict(df[X])\n",
    "        mu1 = LinearRegression().fit(df.query(f\"{T}==1\")[X], df.query(f\"{T}==1\")[Y]).predict(df[X])\n",
    "    else:\n",
    "        mu0 = np.random.uniform(0, 1, df.shape[0])\n",
    "        mu1 = np.random.uniform(0, 1, df.shape[0])\n",
    "\n",
    "    return (\n",
    "        np.mean(df[T]*(df[Y] - mu1)/p_scores + mu1) -\n",
    "        np.mean((1-df[T])*(df[Y] - mu0)/(1-p_scores) + mu0)\n",
    "    ), p_scores, mu0, mu1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Experiments and Results\n",
    "\n",
    "The following  block shows our bootstrap sampling method results displayed (100 iterations for ~100 samples of 1% of dataset). In this initial experiment, we correctly specify both the exposure and outcome models. The results are displayed in the plot and table below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Mean ATE</th>\n",
       "      <th>Std Dev</th>\n",
       "      <th>[.025</th>\n",
       "      <th>.975]</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>AIPW</th>\n",
       "      <td>0.386</td>\n",
       "      <td>0.018</td>\n",
       "      <td>0.353</td>\n",
       "      <td>0.424</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>IPW</th>\n",
       "      <td>0.386</td>\n",
       "      <td>0.018</td>\n",
       "      <td>0.355</td>\n",
       "      <td>0.423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Naive</th>\n",
       "      <td>0.472</td>\n",
       "      <td>0.016</td>\n",
       "      <td>0.439</td>\n",
       "      <td>0.504</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Mean ATE  Std Dev  [.025  .975]\n",
       "AIPW      0.386    0.018  0.353  0.424\n",
       "IPW       0.386    0.018  0.355  0.423\n",
       "Naive     0.472    0.016  0.439  0.504"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Hide cell\n",
    "bootstrap_sample = 100\n",
    "AIPW_ates = []\n",
    "IPW_ates = []\n",
    "naives_ates = []\n",
    "for iSample in range(bootstrap_sample):\n",
    "    df_bootstrap = df_categ.sample(frac=1)\n",
    "    ate, ps, mu0, mu1 = AIPW(df_bootstrap, X, T, Y)\n",
    "    AIPW_ates.append(ate)\n",
    "    ate, ps,_ = IPW(df_bootstrap, X, T, Y,true_ps=False)\n",
    "    IPW_ates.append(ate)\n",
    "    naives_ates.append(naive_ATE(df_bootstrap, T, Y))\n",
    "\n",
    "sns.histplot(AIPW_ates, kde=True, stat=\"density\", linewidth=0,color='g')\n",
    "sns.histplot(IPW_ates, kde=True, stat=\"density\", linewidth=0,color='b')\n",
    "sns.histplot(naives_ates, kde=True, stat=\"density\", linewidth=0,color='r')\n",
    "# plt.vlines(np.percentile(AIPW_ates, 2.5), 0, 20, linestyles=\"dotted\")\n",
    "# plt.vlines(np.percentile(AIPW_ates, 97.5), 0, 20, linestyles=\"dotted\", label=\"95% CI\")\n",
    "plt.title(\"ATE Bootstrap Distribution\", fontsize=20, fontweight = 'bold')\n",
    "plt.xlabel('ATE', fontsize=14, fontweight = 'bold', labelpad=5)\n",
    "plt.legend(['AIPW', 'IPW', 'Naive'])\n",
    "\n",
    "Results = {\"AIPW\":{\"Mean ATE\":np.mean(AIPW_ates), \"Std Dev\":np.std(AIPW_ates), \"[.025\":np.percentile(AIPW_ates, 2.5), \".975]\":np.percentile(AIPW_ates, 97.5)},\n",
    "\"IPW\":{\"Mean ATE\":np.mean(IPW_ates), \"Std Dev\":np.std(IPW_ates), \"[.025\":np.percentile(IPW_ates, 2.5), \".975]\":np.percentile(IPW_ates, 97.5)},\n",
    "\"Naive\":{\"Mean ATE\":np.mean(naives_ates), \"Std Dev\":np.std(naives_ates), \"[.025\":np.percentile(naives_ates, 2.5), \".975]\":np.percentile(naives_ates, 97.5)}}\n",
    "\n",
    "df_results = pd.DataFrame(Results)\n",
    "df_results.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the results it is clear both IPW and AIPW account for a positive bias we hypothesized. They estimate the ATE at ~$0.39$, up from the naive ATE estimate of ~$0.47$. We also note the IPW and AIPW methods agree with very close estimates and with very similar 95% confidence intervals. This is unsurprising considering the exposure model is correctly specified using logistic regression for both methods.\n",
    "\n",
    "Now that we have propensity scores, we can also perform a quick positivity check visualizing the distribution of our propensity scores to ensure we meet the positivity/overlap assumption which the plot below demonstrates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vIiMYmgu3WbmlDME8u9swPZouxsScD4aRftbqkTQBCP3Cmom5viOr6F6pE4hbxn7eV0qVF3zqfa11uKTD24AryuQ4vYuS63l9SA0ymA3pIqAdcCHGcISyAxigtd4HoJTaiKkdgUly/TPGcCRY867UWk+2yo7EuH4yMC+HP8LovSoYwlYp5aMkBG87639KSNkFmJgte4FRSqnxmJfJojDbPYDlmvl7yKwftNa7g+cA8zICc/wTrelgcuvthE9GEbr9fVYCkpcwNURXyOJ4a7tnK6WGhYTrvQrz9QTGDfUKgFLqS0ys9dWUhBO+FGOkwSQ8OZDdSim1CvOS8GCuc2jmqyBXaa0XYRk5q5YczCR1ZjB2u1JqLOZLxoN5eRxp+0B+yHRqBWWD13kT5ktpPaZX2AxL6xLL1bVeKfVLyHpbgj58pVT7kPmHda/UFaTmHpsUYD6zwz3EANPKGHYwn9tg+l1/XmbZWyHT/cJs76egYbcYHTLd1fp/bMi8P5RSAcsPWoQx7GA+/8sSoKR2D6UbQhMAtNYrMbUwMLXLHUqpqUqpZzH+6UkRJJ8uF8tXHXzgh1lpAFuEHNPIsm0L5Wxnu9b6Ckw7yM2YDEqhuUUTgA9Cvo56hSw7EJ9da12otT5Ga32hFUcdSq4flL5eYBJtBPWFu367LcMeSuj12hByvXZS8tyHu16VJTFk+lBuLTBfJmC+5tYppRYrpd7CGP3frRwAhyTa90ptQoy7/byK+eQciunP2wtopLW+J4wBDxIut2ZD6//mYENfCJtCphuEWbdUo541+CeYjShY20qnYsJ9ludqrYtDfocmhA7NUToE04e8AJOOL9itcDyglVJHaoiCDb7NMA1/54csi6g3klIqXSnVWGu9RWv9ttb6QsyL7TxKkkpnYhoYwaTSC1JRPtSGIdOh1wtrYFRw/XDXL9y2D/d6VZYmIdNbKyh7P6a9KGh8O2EqMKOAjVb7RCRE+16pFYhbxn5KdYWMkPww87ZjPuubKaUcZQx8Vsh0uFpNqYdcKZVCiQtmt/U/tGZ/E+ENSrgodBXWiAGs2tY1SqnbMLXY/tbfsRj3zTdKqeaR1LDL4RPgKYw75QJKatUrtNYzD7Wi1YNFY9wvszA9hYK6fcBYy2Xzf9bsxtb/0MbwhpS8AIKNudkhaQm3h5TNIsRQWl8Cwa+jcNcv3P0QvF4+jEsu3LWJNO/roQhtRJ1+qIJWZeVRpdSTmK+GAZg2kFMwL8K3lFIztNYLK9hOtO+VWoHU3Gsm/jDzgvkyUzE+4VBC3Tu/h1n3TKVUaM3xvJDp+db/eSHzCrXWY6yX0u8YY9mRkhdBpVBKHauUel4p9SMmpdt31pfLcZjeLmBqiG3K3wpQ+ryEfhWgtd5MiXvockpq15HU2tdTYpiPVWVSyFk9cPqGzAq6F0K7Lg4JKe/B+P1zlFLBBs5pIWVvojQ3UPKshrt+4e6H4PVyATtCrtdSzFdiO8p8sVUWq/dV0J20jtI9Z8qWbaKUesxqb3hAaz1Za/2E1noQ8JBVzEnJyyLstazCe6XWIzX32sPrmEY9B8bv2xVT2zyXkl4hyyjpPRNKCqYL2cuYz/5/hiwLJoP+BPMQxgGvKxPzYyXG9xz0A99HeONTET7gbmv6WKXUcxhj0ZGShNoFVPzZH+rzvUMptb1MTJKPgDMwrpMgZRuXD0JrHVBKvYLpfufADLl/A2NA62EanYOugNDk3J9geh95MD1BGlvLL8d0VYWShtyRwKNAI+BmZcIY/AJ0w/QsAXMOIh3q/z5m/ALAl0qpEZha/93WNsH0Vok02cjRIV0VE4EuwK2UNCw/WkFNeRdwC5Yby+oCOhvzlXNLSLngizH0WvZSSl2F6ZmTQ9XcK7UeqbnXErTWEzEZ6P0Y98GDmF4iQcO+GTi/HD/+Ykzf67cxXSiDvR7e1FbSa631akq6sqVgDNGnlBj2PzDdBQ9H+zxKUtdlACMwftjhmC6TYGp7FQUCC/26eBR42epaF+QbSruXZoaONK2AF631wfQlvwdz/K9T8hWwC7gsZHBTsMtoAGPgH8AY/GAtfgGmeyTWYKbLgL3WsisxL6N7MJWwIuBqq0GxQrTWf2Di3YAxoM9j7oegYR+NaRCOlEswx/8N5oX4ICV+/de01odMN6i1LsR0zS3GvBDuwbzQ/k1JLXus1nq8VX4HJjk5GDfVR8AlVXiv1HrEuNcitNbPYoztF5gudkWYmtArQM9yulWCqT0OwfSVLgJWYR6+28ps/xWr3K8YQ1aA+Rp4BBiitQ7n+41U+0MYd8E4TIOiF+MK+QU4R2v9cgSbeQFz7DswI05nUdJ2gDVI6fuQ8hGHdbBeihdQ0k8929K4B2OkRwBHl/UXW71hTrfW2YOpkS4BnsC4FfaHlP0VY3xfxXSTLMT44r8AemutQ3sxRaL5LkvvFMxLLRfjZrsT05U2nDsnEooxNePvgLO01hENiLJGoB6HOe/B4wtep79jvjxDuQZTu8+39rfW2k5V3Cu1HsnEVEdRpcMPvKK1/rt9aqoHpZQb85VyFMYVlKUlKJtQSxGfu1DrsUbZxmNqsUdZs38Swy7UZsS4C3WBuykJowzGHTDcHimCUD2Iz12oC8zD+JyDERYHa60j7SUiCDUS8bkLgiDUQmLGLZOdvc/Wt0x6ehK7dlUUGqP6EV2VQ3RFTixqAtFVWTIyUh3h5otbxsLtdlVcyAZEV+UQXZETi5pAdFUVYtwFQRBqIWLcBUEQaiFi3AVBEGohUWtQtZLYfgi0xowGvEkS1wqCIFQP0ay5DwHcWuu+mDyJT1ZQXhAEQagiomnclwNupZQTk3W9uILygiAIQhURtUFMVo7KsZjwsI2As7XWU8sr7/X6AjWtq5EgCEIMELafezSN+4uYjD0PWIZ+AtBVa10Qrrzdg5gyMlLJzt5XccFqRnRVDtEVObGoCURXZbFjENMuSnJI5mAy+EjVXBAE25g7dzaPPPJAqXlvvPEqP/74XdjyW7duZfLkcrMHRsxXX42KuOyh9FSGaIYfeAl4Tyn1ByYLzYNa66pIyCsIh2TECE/Y+ffdV1TNSoSazty5s1i3bi0nndSv4sKH4MMP3+OCC8qmNo4uUTPuVoaZi6O1fUEQajbDh8fz3XcHmyCnE/z+5MPa5jnneBk+vPCw1r377r8RF+dmy5bNDBx4OldeeS2ffPIBBQUFdO3aja+/HkVSUir79u3juede5oUXnmHjxg34/X5uuulWjjnmWH777Ve+/no0QXf3E0+MYOzYr9i7dw/PP/8Mf//7PTz33FMHrTdx4ng+/PBd6tdPp7i4mFatWh/WMYQig5gEQajzOBwOtm3bwhNPjODNN9/ns88+wuVyceWV13L66YM56SSTe/v00wfzyiuv88MP31KvXn3+8593eOaZF3jxxREAbNiwnueee4XXXnubli1bMXPmNK655gbS0upxzz338913Y8Ku9/rr/+bll1/nxRdfIyEhoVydlSFmokIKglC3GD68MGwt2zRcRseDGx+fQFFR6V7Z+fl5eDzxtG3bHrfbjdvtJj4+vIFt2bIVAKtWrWTBgnksWbIIAJ/Py549u0lPb8ATTzxCUlIS69atpUuXbqXWD7deTs5OkpOTqVevPsBB6xwuYtwFQagztG7dmhUrNDt27KBRo0YUFhYyf/48OnRQOML0OXE4HAQCJXnEnU7j7GjVqjWNGzfm6quvp7CwgA8/fA+Xy827777FV1+ZHOx33XXbAfdM8H+49VJT09i/P5ddu3aRnp7OsmVLaNw484iPVYy7IAh1huTkFO644y7uu+9O4uMT8HqLueCCS8jKas7s2TMOKt+uXXs++ug9jjrq6FLzhw49n2effYLbb/8Lubn7GTbsIpKTk+natTvXX38liYmJpKamsmNHNgCtW7fhscce5v77Hz5ovbi4OB588F/cffftpKbWw+2uGrMcM5mYpJ97eERX5cjISOXee8M3qNnZWyYWz1csagLRVVkkWYcgCEIdQoy7IAhCLUSMuyAIQi1EjLsgCEItRIy7IAhCLUSMuyAIQi1E+rkLglBnePXVl9B6KTk5OykoKKBZsyzq10/niSeePaztjR37NWeddW5EfdPHjPmSnTt3csMNNx/WviqLGHdBEOoMd9xxFwA//vgd69at5dZb7zii7X388fsMHnxWlQ08qkpiT5EgRAkJBRxbDJ/6EN+tGnPQfKfTgd9/eGMaz2l3HsP7PlGpdZ58cjh79uxh7949jBjxMp999hHz58/F7w9wySVXMHDgacybN4dPPnmP4mIfBQUFPPTQoyxYMI+cnJ0MH/4gTz/9Am+++dpB682f/yevvPI8aWlpOJ0uOnfucljHdTiIcRdqFcMnDmeKx1vu8hOLHq5GNUJNoVevY7nkkiuYNm0KW7Zs4o033qOwsJCbb76O4447njVrVvPcc8/hdCbx0Ufv8dtvv3LNNTfwwQfvMnz4U+Wu9+qrLzJ8+JO0bNmK559/ulqPSYy7IAi2MLzvE2Fr2XYM8w9Ge1y9eiVaL+P22/8CgNfrZevWLWRkZPDkk0/idMaRnb2drl27l1q/vPWys7cf2HbXrt3ZuHFDtR2TGHdBEOo8DkdJtMeePY/lH//4J36/nw8++C9ZWVncdddfGT9+PPn5AZ544pFS6wUCgXLXa9iwIWvXrqF16zYsXbqE1NTUajsmMe6CIAgWJ57Yj3nz5vDXv95Ifn4e/fqdQlJSMoMGDeHiiy8mKSmZ9PSGB6I9du/eg3vu+RuvvvpW2PUefvhxnnzyEZKSkklKSqpW4x61qJBKqWuBa62fCUAPoInWene48hIVMjyiq3L8Z/EL/DKucj736mhQjcXzFYuaQHRVlvKiQkYzh+oHwAcASqn/AO+VZ9gFIVp4C+PZNud4ti/oicMRYGdDN717+2jSJDZCXQtCtIi6W0YpdSzQWWt9W7T3JQihFOclsviTG8nfkYkzrhCn28fynS6WL3fRo4ePU07x4nLZrVIQokN1+NwfBB6tqFB6ehJut71PWkZG9fnDKoPoqhyeODe+YjeLRl9D/o5MmvaaTdvTxuGKL6T12uH89BP8+aeLnTtdXH45ZGTEV4uuWDxfsagJRFdVEFXjrpSqDxyttf6torK7duVFU0qFxLA/TXRVkqJiLxsnn8S+Tc1p1Hk+rc4Yi98RwO+Fxo0Luewy+PlnN1q7eP99P1dfnUdGRnTdNLF4vmJRE4iuylLeCyfagcP6Ab9GeR+CUIqifalsmtaPuKT9tBn8LQ5HacPt8cDZZ3vp3t3H9u1Ohg5NZPPmsG1SglBjibZbRgGro7wPQSjFhj8G4i/20Pr0H3DHh8+n6nDAaad58XgCzJrl5pxzkvjyyzzatCl5EUi4AqEmE9Wau9b6Oa31y9HchyCEkrcnkexFPUhI30HjbnMPWdbhgH79fDzwQCEbNjg599wkli2TKNhC7UDuZKFWMe+nngS8cWT2monDWbEf3eGAu+4q4sknC9i2zcl55yXy55/yWAg1H7mLhVqDzwezxx6HM66Ixl0PXWsvy003FfPKK/ns3u1g6NAkRo6UwdtCzUbuYKHGUtYnvm6dg91bU2ncYzbuxIJKb++yy7w0aJDPbbcl8re/JdKtm4+BA73EYKhuQagQuW2FWsOyZWacRKPOfx72NgYN8jFuXC433JDIggUuNm+BM87aQ8NGPjykMtXzBCNm+sKue1/vBw97v4JQ1YhxF2oFPh+sWOHEk7KPtBbrjmhbDZrt4pqXP+ax0T+yI3Umn6VsByDB35AkGtFq37E0T21RFbIFIWqIcRdqBevWOSkocJDVe0lEDall8fl9/L7xN0Yt+5Qf13xPoa8QmkJiUUsKVw/G73VR3HQxOamakVrTvn4HBrUeQqI7MQpHIwhHjhh3oVawfLnpG5DReVGl1stxLOfJ6R/yhf6cLbmbAWiQ0IDeTU5g/5rOJJBOUf0UVv0wjN2rFM52E6h/xV9ZuVuzbcn7XNDhYholNqry4xGEI0WMu1DjCQRg1SonSUkB0lpspLj8iL8AFLIH7f6SRXEfs9k1HeZCmqceV3e6Hq+/mKbJzXA4HExZY3z4npT9HH3xx2ybdxzrfj2TnMcX0/jav7K91duM0p9x8VGXkpHUuBqOVBAiR4y7UOPZutVBfr6DLl18B4UaCKWAXfwSfxtL3J/hdeRDwEEr76k8cOblnNnmbBLdiYyY+VTYdR0OaHLMLOq1WsOW8Rey7f23SD69Pbkn/oMvV4zi8qOvitbhCcJhIcZdqPGsWmVcMu3a+dkdZrkfL5tcU9jknErA4aeevw1di66hk/cK0gItOL9D5OEEEhvu4LLn3uT3d4cw7/t7cea5yT39//hqxWj+0fufpMXXq5qDEoQjRIy7UONZvdqJyxWgVauDjXsxuSxzj2a/cxOeQCqnF7yK8l6Ek8MPL+2O83HqLd/RvMsafn7lVopS1pPT52VuG3crH531KQ5H6SBkI0Z4SE6G3NzS/fIlRo0QTWSEqlCj2bcPtm930rx5AE+ZOF+F7GVh3Afsd26ika8z3YtvpqP30iMy7KGokxZx1SuvkbHyLlgzgJ/Xf8/j41+tkm0LwpEiNXehRrNunamftGnjLzW/mDyWxn1OoWM3Wb4TaeHrj4OqCes7ZWroy2E3bS94j8Cke9nRSPPaskeYM7+IE08uqZVP8bjw4OY4HqiS/QtCJEjNXajRrF1rbuHWrUuMewA/y93fkO/YQVNf7yo17OFwur10GDiVE9w3ATDN+w5jXj6NvD1JUdunIFSEGHehxhIImJp7SkqAhg1LeslsdE5mr3Mt6f4OtPKdFlXDHspJJxdxXL3BkLqFlVlP8P7tt7Niaqdq2bcglEWMu1Bj2b7ddIFs1cpPsA1zLxvZ6JqMJ5BGO+851WbYg/Q7qgvt6h0FbSZScNxTjH3qKpaPuYjiPBnJKlQv4nMXaixlXTI+itB8C44AHYqHEsfBBnWK5/GD5pUXCOxwcDgcDGkzhI+XZrO77/PUD7Rm57jbmLWuHY1Pd9K+vb/ijQhCFSDGXaixBBtTW7Y0BnNW3IvkObLJ9B1DWqBlxNsp3UB65MS7Eziv/QV8tvQj9p/0d5okBNj24y2MGeOmVy8v/fr5cFXtLgXhIMS4CzWS3FzYtMlB48Z+kpNhv2ML0z0jiAsk09J3it3yaJTYiLPansM3K78i55h/0q3FfjaMvI85c9xkZzs599xiydEqRJWo+tyVUg8opaYppeYopW6I5r6EusX06S58PscBl8wUz2N4HXm04RTcJNisztCufgdOataPIsdeVmf8h4uv3EX79j7Wr3cycmQcubl2KxRqM1GruSulBgB9gROBJOCeaO1LqHtMnGhu3dat/WQ7F7HI/SENfZ1o4uxJMbHj1z6+aR+Wbchhh2sRP6ZdyHnnjuGP31KYN8/FF1/EcfHFxSQnm7LB9gBJBiJUBdF0ywwCFgLfAGnAvYcqnJ6ehNttryMyIyPV1v2Xh+g6mMmTwe2GDh08jHI/RMDhZ5DzeTYxA0+cPZ3AkpPDP06dnMNYEvCy3j2Rn1Kv4OJzviY+3sX06U7Gjo3nmmvA4wGP9TiWt51onG+5typHrOoKRzSNeyOgFXA20Ab4Vil1tNY6bNi+XbvyoiilYjIyUsnO3merhnCIroPZvNnB4sUptG7tR3t/ZGXc/2jlHUjTglPYlDyDoopi/kaJX8aVv6xj3AVs8M5khfsHvvBdwpATP2TfvmQWL3YxerSPoUO9FMUb3bm54WvuVX2+5d6qHLGsKxzRrOLsBH7WWhdprTVQAGREcX9CHWHCBMsl06aY3z0PQsBB/6Knq71Pe2Vw4mZowShaePuxwj2GsYkXcsoZe2nZ0s/KlS5mzpTuM0LVEk3jPhkYrJRyKKWaAckYgy8IR8SECcYQert8RLZrIZ29V9LY391mVRUTRxLnF4ylrfdM1rrH8U3K2Zx+zg5SUgJMnuxi74ZWdksUahFRM+5a6++BecBM4DvgNq111Y0WEeokxcXw++9umrfdx5/pw3EHEjmp6BG7ZUVMHIkMLRiFKr6ITa6pfN9gMKcN3WyySX0/DF9xnN0ShVpCVPu5a63vi+b2hZpHeZmOglTUI2T2bBf79jlod8NzbHRu5oSi+0kNNK9KiVHHhYezCj/AQwoL495nUrtT6Xrizyyc0ooNv58K/X+wW6JQC5DYMkKNYvx4F6RuYmn6CyT7m9C7qGb2sHXi4ozC1+lVdCc5Ts26gf3xtJ7Flll92LFO8rEKR44Yd6FGMWGCG+dpD1EYyOOkokfwkGK3pMPGgYMBRc/Qt/Bh9rrW4b/8TEjO5rf/nk2g/FSwghARYtyFGsO2bQ4W7ViAv9uHdGrYhc7eq+2WdMQ4cNC3+J/0LXwYr2cnrmtPZ92iLNbMVnZLE2o4YtyFGsP48U4YdDc4Ajza98kqS5cXC/QpfpAMX3d8jRbB4DuZ8tlpUnsXjggx7kKN4eN530Cb3+jbaDD9W9gfHKwqceCgrW8wyf5M6PVftnmmsHrW0XbLEmowYtyFGsH2/TuZm3kXDm8CL57xtN1yooITNx28w3DjgbP+yuSve0rtXThsxLgLNYLbvn2QQFI2vfY9Qtv67eyWEzUSachJzU+CpByy2/6bjYtb2y1JqKGIcRdingnrx/H77s9hcy/uPemvdsuJOsdkHkt9RxYc8y5TfkuzW45QQ5FkHULMMGWqixETSyewKGIfXzX5O/jcpP72X056JHbjx1QVToeTQR36M2r5Z2zMfJddmwaTniWRO4TKITV3Iab5w/MvNu3fAJPv56xenYmrA6Pzp0x1sX5RG5L2doe24/lmjKfKUwEKtR+puQsxyybnVObFvUl9r2L3pIcY8n5xqfAFUzwHGzxPLbql23iOZTHzyWk2Cr/3dLvlCDWM2vMkCLUKLwX8nHArAK7v3yEt2cMpp+xnwXybhR0BwUxLkZLmbEJ89vEUtpjKZn1WlFQJtRUx7kJMMt3zDDlOTfudf2XlnydzxRVFxMfbrar6ae7qwSpmsCVuGiNG3B22jCTUFsIhPnch5sh2LmRm3POk+lsQP9m4YS64wJ7sSnaTkdIQZ87ReFv/xObc9XbLEWoQYtyFmMKPl//F34Lf4eXUvP+wamkaTZr46dOnbqYCcOCg4e5Twenjj7wP7ZYj1CDEuAsxxZy4V9nmmkOn4ivwLhtMQYGDCy7w4qrDnUVaNGoABWlsyvgAX6BufsEIlUeMuxAzFLKXqZ4nSAw04pTCESxcaCz65ZcX26zMXuIT/MRvOBN/yibm5/5itxyhhiANqkLMsN71G8WOXAYWPE/RnoasW+cgK8tPhw5+u6XZTiZdWM8opjheJN8zp9SyETONy6qiLFZC3SKqxl0pNQ/YY/1co7W+Lpr7E2oum/ZtZIdrEZm+XnTxXsOUhS7AQdeu4oYAaJpVzPptXSlsNIPi4uOJcybYLUmIcaJm3JVSCQBa6wHR2odQO/AH/IzfMA6ADH8XJrueYe7Ce3AluMnpOoIRMwtsVmg/TreP5B39yM1cyKbsHbRuULPyxgrVTzR97t2BJKXUL0qpCUqpE6K4L6EGs3DHArbnbSPD15XUQHNylnWmODeVxt3m4Iqr2/72UJolG4O+w7nEZiVCTSCabpk84Hngv0AH4CellNJah/3OTk9Pwu22t0tERkaqrfsvj9qkKzm59EikYl8xUzf/gcfloV3gdDxON9vmmnpAi+Pn4olzk5wc/jb1lBNnxhMXm01JR6qractCVm7uTXHTWfi9p5DgTgQ4cH4O53rUpnurOohVXeGI5lOwHFiptQ4Ay5VSO4GmwIZwhXftyouilIrJyEglO3ufrRrCUdt05eYWlvo9c+sMcotzOaFpXxzrEtm1NYO9G1pSv53GlbqdomLIzQ3fx72oOExsmTg3RcWx56evKl2pu/qwt9lM1uzYTLuGrYCS81PZ61Hb7q1oE8u6whFNt8z1wAsASqlmQBqwJYr7E2oYhb5CZm2dTrwrnmMzewOwdc7xADTpNcNOaTFLs7Qm4HeSE7fAbilCjBNN4/4uUF8pNRkYBVxfnktGqJvMz/6TfG8+x2b2JsGdQHF+IjsWdyO+fg71266wW15MUr/xfhwbT8bbaAF53v12yxFimKi5ZbTWRcDl0dq+ULPx+X3M3TaLOKeHno17AZC9oCd+r4cmx8zA4ZTkoeFwOKDe3t7s5nc27dlKh4bt7ZYkxCgyQlWwhaU5i9lfvJ9uGd1JcCcQ8DvYNrc3DlcxGd3m2i0vpslKbwheD7sS5tktRYhhIjLuSql7lVJNoi1GqBsEAgFmbZ2J0+GkV+ZxAKyb346CXY1o1GkhcUn5NiuMbVIb7cO5oT++9OXsL4q9Bj4hNoi05p4ETFRK/aCUukgpVQeSnQnRYvWeVews2MHRDTqS5jEJoOf/aBpSM4+Zaae0GoHDAfXyegKwaU+2zWqEWCUi4661flRrfTTwNHAKMF8p9ZpSqkc0xQm1k1lbTU+Y4zKNQd+3I42VMzqSnLmZlGYb7ZRWY8hqWA98bvYkSK8ZITwRN6gqpZKBNkBbwA/kAK8opaZqrR+Ikj6hlrEldwsb92+gdVpbMpIaA7Dg5+MI+F1kHjMTh+PgdSQ59MGkNsjDuekkfC0nsj3nNBo3SLRbkhBjROpz/wRYCQwAntBad9Fa/ws4A7g5evKE2sa87Sai4bGWr93ndbLw5+PwJBXQqHMNTpBqA/XzewAwfVGOvUKEmCTSmvsE4GatdW5whlLKo7UuVEp1io40obaxM38nOmcp6fENaJXWGoDVM49mf049ep4zFZdH4shUhqz0dHL8LtYVLASy7JYjxBiRNqjeVMawO4E5AFrrrdEQJtQ+Pl36Eb6Aj3q5vZg6zc2UqS4mfWn6uPsy51SwtlCWlPpFuLYcT2GDP9m2Q8YHCqU5ZM1dKTUB44pBKRWaMcELfBs9WUJtw+f38eHid3E748jwdwOgOD+R3auOIiljK8mNt9mssGZSL78HOUxlxsIcGGK3GiGWOKRx11oPBFBKvaK1vrN6JAm1kV/X/8KGfevp1qgH7s0m0UTOss4EfG4adfnTXnE1mKz0BuQEHKwtlF4zQmkqqrmfrbX+HpirlLq67HKt9UdRUybUKt5b+DYAPRsfw/LNZl72ou6An0adF9onrIaTkhrAk30cRRmzWLhmG13bZNotSYgRKvK5H2f9H4Dp3x76NyBqqoRaxerdK/ltw3iOb9rnQPfHwj312behDWkt1xKftqeCLQiHonVCN3AEePnnH+yWIsQQFbllHrH+H8h9qpRKA1porRdHWZtQS3h/0X8BuL7LTazYtRyAHYuN371RF+n+eKQc3zWd5evgt21jMJG2BSHyfu43KKU+UEplAEuAL5VSkmpdqJDc4lw+X/YpGYmNOavtuQAEAsYl43B5aXi01BGOlMwMF/G7erC/4SSmzNtptxwhRoi0K+RfgQeAy4CxQFfg/GiJEmoPX68Yzd6iPVzd+To8Lg8AedubkL8jk/T2y3AnSPLrqqB9Wkdw+nn+p+/sliLECBGH/NVab8F0tvrBSroh452FQxIIBHhv4Tu4HC6u7nTAs2c1pIpLpirp07UhBBxMzxtFgbwvBSI37ouVUt9j4sr8qpQaBcyKniyhNjB9y1QW71zI2W2H0jSlGQB+n4OdS7rhSsgnvd1ymxXWHuonpZBV3B9fsyl89F3YNMVCHSNS4349MAI4wcqw9AlwQ9RUCbWCdxa8CcCN3W45MG/jojYU7atHw6MX4XSHT3wtHB7X9LwUgHdmfGmzEiEWiNS4p2D87Lcppf4F9AT+WdFKSqnGSqkNSqmjj0CjUAPZuG8DP675jm4ZPejd5PgD85f8ZuKQZ4hLpsq5oc/ZOHwJrEv7jHXr7FYj2E2kxn00pm+7C3CE/JWLldDjLUDS6tRB3l/0X/wBPzd2vRmHFcc3Px+WT+2CJ203qS3E+lQ1qZ40eiScDY00L42SgWF1nUijQjbRWp9eyW0/D7yJ6WUj1CHyivP4eMn7NEpsxHntLzgwf9w4N0V5CTTrMwOHQxJgR4PbTr6IGyd8yTerRvJsYVfi4+1WJNhFpMZ9nlKqm9Y6ogAWSqlrgWyt9c9KqYiMe3p6Em63vUkZMjJSbd1/edQ0Xe/MGcnuwt08dPJDtGiacWD+d1YvvWY9FuOJizhPTKWJ5raPhGjpSk42283ISOXqBsO4/deG5LcfybgJL3Dd1YfOiFnT7i27iVVd4Yj0buuCMfDbgAKMSyagtW5bTvnrgYBS6jSgB/CRUurcQ4UH3rUrL3LVUSAjI5Xs7NhLNlzTdPkDfl6c+hJup5uL2lx5oMyuXfDjjylktNlCXPpmiqIUut0T56aoOPbC30ZTV26uaZgOnutz2lzA6HVv83+v/Y/FC844KLvVffcVATXv3rKbWNYVjkiN+7DK7Exr3S84rZSaCNwicd/rBuPW/cyynKVceNQlB7o/Anz7bRzFxQ46DvgTSckRXf5y3BWMXvc2uzu8xebNg8jKEhdYXSTSBNnrgBOBvwDZQH9rniCU4tW5LwFwe8+/l5r/5ZduHI4AHftLL5lo071xT45KOg46/Mi0ZfKY1lUijS3zDGZ06vmY2v51SqkXIllXaz1Aa73s8CUKNYXpW6Yxc+t0zmg1mE4NOx+Yv369gxkz3Jx4oo/URnttVFh3uLPPTeAIsDbjLfbKKa+TRNoVchBwFVCgtd4LnA6cGTVVQo3k1bkvAnDHMf9Xav7XX5tGvQsvFIdMdXFu+2F4ijOg53vMnl9otxzBBiI17v4yv+PDzBPqMEt2Lmbcup85vmkfjm96woH5gQCMHu0mPj7A2WfHXkNnbSXeFU9333WQuIsF/tEUFdmtSKhuIjXuXwCjgHSl1N+BP4DPoiVKqHkEfe13lPG1z57tZMUKF0OGeElLs0FYHaan7yYIOPEe8x8WLoo4RqBQS4j0iv8AfAfsAE4GHtZaPxU1VUKNYuWuFXyz8ks6NujMaa0GlVo2cqRxyVx2mbhkqpu0QAvaFJ4DTecxc/NM/PKtXaeoKIdqY+BLoDOwAvACA4FEpdRkrbXkRxN4Yfaz+AN+7j3uAZyOkvrCE094GDUqjtTUANOnu5g508UUj70D1eoavf23sYax5PZ8lpUrv+Koo8TC1xUqqrk/DUzGhB84QWt9AtAYmA+8Em1xQuyzPEfz9YrRdG7YlSFtzy61bMUKJ0VFDjp39uEUr4AtNPefTOOCPqC+Y9rqRXbLEaqRih65vlrrB7XWB76prekHMZEhhTrOC7OfIUCA+3o/WKrWDrBokamld+kioX3twoGDkwL3A5B99DNs3nzIeH9CLaIi4x42p4vWOoD0lqnzLN25hDErv6ZbRg8Gtx5SatmaNQ42bHDSooWf+vXt0ScY2vjOID2/J3QezRS9wm45QjVRkXE/1LhlGdNcx3k+WGs/7oEDYX2DjBplGlKl1m4/DhyczP3gCLCuxQjWrpXae12gotgynZVSq8PMdwBNo6BHqCEs2LaA71aNoWfjYzi91eBSy4qK4JNP4vB4AtKAVw1MmWrcXyMmesot08F3Dil5ndjf7VNeeO8BXn0sq7rkCTZRkXE/qlpUCDWGETNND9jv144BoG299jw36+kDy+/r/SDffedm+3YnvXp5iTt0xFmhmnDg5GT+wU/Oa/hy+wge3/0KGRkVryfUXA5p3CU4mBCObblbWbZjGc2Ss2id1qbUshEzn+KTl/4Kjiz8vV9himeXTSqFsnT0X8jv+58lr8tHvPLxPbz2WCe7JQlRJDazGggxzdTNkwE4Mevkg3ztm5a2ZOvyFrQ7fgkJ6WLYY4lpnqdo6u3KKucS3lr6OOnjOlFQVJJH4b7eD9qoTqhqxLgLlWJL7hZW7VlJy7SWtExtddDyGV8MAODYYX+wXqIRxhwZ7nas29sOr/qCT997iSZtQ4KK9bZPl1D1iHEXDiLoVw/H1E1/ADCg9YCDau3bVzdh9ayOZHVaS/POa1k/TUajxhoOHLTwn8Qa5yo2uCeQGehyUKYmoXYg4waFiNm8fxNr9q6mRWpL2qS3OWj5jNGnAHD8RRPFYMQwmUlZuHI64m33LTuyxQTUVuTKChEzZbOptfdtdtJBy7avboL+oxuZ7TfS5lhd3dKESuDAQbP808ERYH1gmt1yhCghxl2IiE37NrJu71papbamRWrLg5ZP/vgMAE6++heptdcAmjVKwbmtJ0UtfmV3XuwlfRaOnKj53JVSLuAdQAE+4Dqt9apo7U+ILjO2mhpen2YnHrRsw6LWrJ7VkeZdVtOqpwxvrwk4HQ6a7B7K5sx5rCmaTc+kU+yWJFQx0WxQPQdAa32iUmoA8CIwNIr7E6JEdn42q/esollyFs1TW5Ra5vc5mfDmuQD0v+4nqbXbyBTP45Uq36a1i80bT6Cg+VT25Uuf99pG1NwyWusxwF+sn62AbdHalxBdZm+dAUDvkPR5Qeb/rzfZa5vS5fRZNFUbq1uacAS4PV4abL4EgNVFc21WI1Q1Ue0KqbX2KqU+BIYBFx6qbHp6Em63vV3nMjJSbd1/eVS3ruTk+APTewv3sjRnCY2SGtGtWedS3R8d3nSmfHIG8ckFDL51Yqn1ADw2hR7wxMVmD99Y1NWufYCctf3Ja/07qwqWcEKL4+2WBMizWBVE/W7TWl+jlPoHMEMp1UlrnRuu3K5deeFmVxsZGalkZ8dew5IdunJzSwa2TNowGX/AT6/Gx5GXV5JlOTk5nl/e6kfBvkROuel78OSQW+bKFhVX/8vaE+emqDj2EnHHoi5PnBt3yk5S5l7L/ta/c9fXj/Pt5Z/bLUuexUpS3gsnam4ZpdRVSqkHrJ95mPjvEv+1BlHgLWBB9nxS4lLo2KBzqWVbVjRh/v9607DlNnqcJd3pajItWvpgQx+m7/6BZTlL7ZYjVBHR7Ar5NdBTKTUJ+Bn4u9Y6bPIPITZZsGM+xf4ijml8LG5nyUdeIAA//XsIBJwM/Mt3uNwS1rcmU6/VGjzzbwFgxNSX7RUjVBlRc8tY7peLo7V9Ibr4A37mb5+L2+mmW0aPUsuWTuzBhkUt6dB3Ea16rDoQT1yomTgckNUolTXbO/ND4As27Ptn2LEMQs1CBjEJYVmzZzV7ivbQsUEnEtwJB+YX5Xn4/f0zcXuKGXDDDzYqFKqSjC4LSJx7HwGHj9fmvGq3HKEKiL3meyEm+HO76RrXo/ExpeZP/+IUcnPS6H/NROpl7rZBmRANXJ5iOjZrztzdLflw8fskxsWTFJdUqoyEBK5ZSM1dOIjdBbtYs3c1zZKzyExqUjJ/SwNmjzmJtMa7OPGyyTYqFKLBMUNmw7S78TuKmLt9tt1yhCNEjLtwEH9mzwMOrrX//v5g/F43/a77ibj42OrWJxw59Zvsoq2rL+Q2Yu6WeRT5CiteSYhZxC0jlCKvOI95WxfgJomduhNTMI2le9e3YsXUrqQ2X8cO5xImTnTb0o9diC7HnjWP1T/fSdHAh5mf/SfHNYmNQU1C5ZGau1CKb1d9g89RQKa/B07r3R8IOFg7/kwAWp0q8WNqMy26rabBlguhMIVZm+fg88vQlJqKGHehFJ8v+wSAxr6eB+btWNyN3C3NadhpPqlZEj+mNuNwQJ+hf8Kcv5Dn38vSnMV2SxIOEzHuwgHW7FnNtM1TSPO3IoH6APiK41j/2xk4XMW0OmWcvQKFakGdvIB6a64Cv4sZm+YQCATsliQcBmLchQN8oU1ckcb+bgfmbZnZl6J99Wjaeyrx9XbbpEyoTpyuAH3OXgGLLmVX8TbW7F1ttyThMBDjLgBmROoX+nOS41Jo4D8agKL9KWya1g930n6y+k6yWaFQnXTs/ycpy24CYPqGOTarEQ4HMe4CAFM2/cGGfesZ2m4YLjwAbJh0Kv6ieFr0G487XrrF1SVcbj99B+6EVaexuWA1W3O32i1JqCTSFVIAShpSL+14JU8vmETu9ky2z+9FYqNtZPaQmltdoGyMIH/yfNy/34q33a9MWzfPJlXC4SI1d4F9RXv5YfW3tKnXluObnEAgAOvGnwkBJ61O/R8Op0R9rIs4XT5atfHC1m6s2r+I9XvX2S1JqARi3AXGrvyGfG8+l6orcDgc7F7dgT1r2lOvzQrS20nC67pMRueFpK2+Hpw+Hv/1dbvlCJVA3DICI5d9igMHF6vL8Hph3a9ngsNPq1P/Z7c0wWYcjgCDToljdHYW3xZ/SNYUD0lxiWHLSmCx2EJq7nWcVbtXMHPrdPo1H0BWanM+/jiO/J2Nadx9DsmNJae5AK26bqDh5ksJxOUxYc5mu+UIESLGvY4zapnp237p0Vewaxc8+6wHl6eAFv3G26xMiCWG9K8PBWnoot8pkHxqNQJxy9RhfH4fo/RnpHrSOLPN2TzxSDw5OU5aDpyIJ2W/3fKEGCKzRS6ZC85iW+bn/G98IeedFX9Q75oRE00X2vvuKwq3CaGakZp7HWbSxolsyd3Mee0vYP2qFN5/P462bf00PU4SXgsHM+SkJuBzs9L1I3u2pdotR6iAqNXclVJxwHtAayAeeEJr/W209idUnlH6UwAuUZfz0B3x+HwOHnssn/8skUiAwsE0rBdPlq8vmxpN4odvU2nVOc9uScIhiGbN/Upgp9b6ZOBM4LUo7kuoBCNmPsVjU//FtyvH0CChAe+M3sSkSW5a99LMq/e43fKEGObU7h0A2Jz+JXvWtLVZjXAooulzHw18GfL7kKl70tOTcLvtTf6QkRGbn5pVrSs5OZ6lmxfiDXjp3rgXk/59Dk6Xj7P+No6UlHg8cZFtxxMXm002oityItGUnFxSpk1yc5qv7sTG1pNYNfoBerfbiNNlBrklx8UDkJERf8S66sqzGE2idrdprfcDKKVSMUb+oUOV37XL3k+8jIxUsrP32aohHNHQlZtbyNzN83DgIHfy1eza3IBeQyeT2HATublElGHJE+emqDj2Uu2JrsiJVFNubmk3XZ9W3Ri9fAmFnd5l/fTraNZ7qilXZOIPZWcfWYNqXXoWq4LyXjhRrUoopVoA3wCva60/i+a+hPIZMcJT6vc4zy62eDbTIvEo5n12EYlp++lzmXR9FCKjZWorGsU3ZUfHr9nw1qM06jQfT0qu3bKEMkTN566UygR+Af6htX4vWvsRKk+2awEA3pk3UlwQT79r/0dCinReFiLD4XBwfLNjwenH3+t11k8cZLckIQzRbFB9EEgHHlZKTbT+wo9bFqoNP16ynQtx+pLYMvYOmqr1dDltrt2yhBrGUelH4wmkQc93yV7Zkn2bmtstSShDNH3udwJ3Rmv7wuGx1vUrxY79uBZfh8Pv4bS/jsHhlDRqQuVwOV008x3P2rhxcOwbrPn5evyXg1NGzsQMcinqGIvcHwPgm34rPYZMJ7PdFpsVCTWVxv7uuALxOPq+RO6OBixaJOYkloi9vllC1Mgnh5Xu7yC7I67dR3PilS/aLUmoAZQNMxDEhYtMfy82J0zF0etd/vjjNo46SkIPxAryqq1DLI0bhd9RBPOuo/XAX6QRVThimvqOxRFw4RzwBPmFXqZPt3esilCC1NzrCAECzPa/Cz43ydkDyOg/ttwamSBEiodUGvt7sC1xDgnHfca82Vezdq2D1q2lHcdupOZeR9gYmMXexEWgh9Ku/3QcDrsVCbWFLF8fHAEnrgFP4fP7eeqpIx+hKhw5YtzrCBP3vg9A+z03SBIOoUqJpx6N/F3JTVxOvb6jGTMmjtmzxbTYjVyBOkBO7l62ZYzCsbs1g48aYLccoRaS5euLI+DEcfJTQIBHHkkgIJ4ZWxHjXgf438YvwZNHu73XkRAvl1yoehJpgPJeyO6EhfS6/BtmzXLx/ffSpGcn8qTXchYudLK56bvgdzEw/Sq75Qi1mBOK74eAg729huNy+3j88XiKpGekbYhxr8UEAnDPC4uh2Rya7R9CmqOZ3ZKEWkwjfyc6ei9hxb6F9Lt1JGvXOvnggwjjRwtVjhj3Wsyvv7qYF/cmACfE3WCzGqEucGLRw7idbla3eoTUesW88EI8u3fbrapuIsa9luL1wsPP7oKun5JW3IE2vjPsliTUAeoH2nFFx2tYt38VA+58l127HLz0knSNtAMx7rWUjz+OY3WDt8FdRG/fHTjkUgvVxP/1upcEVwJzUp+kees83n03jrVrZWBFdSNPfC3k8Ykv8Miz+6D368Q7E9nr3MAUz+MH/gQhmnz8emu65v+VzbkbSR34GkVFDq66SqJ9Vzdi3GshM74YQEHrMZC0gx6Ne+DCU+E6glCV9C66h4RAA1a1eIKMthvR2iUDm6oZOdu1jA0bHMwe2xfnSS/gdDjp2fgYuyUJdZBEGtCv8HGKHPtIPO9uAO6/PwFvbKWRrdWIca9FjBjh4corE/G3Go+/gaaBtzPzZ9e3W5ZQR+nqvY4mvuNYn/YFrQaMY8ECF2+8IV+R1YUY91rE5s0Oli514jztIQCa+XvbrEioyzhwclrhK2Zg00l30CizgBEjPCxdKmanOojqWVZKHa+UmhjNfQgGvx8mTHBDu1/wN5lLuv8okgNN7JYl1HGa+I+hR/Ff2OXW9P/n0xQWOrj55gTy8uxWVvuJWvAHpdR9wFVAbrT2IZQwerSbrVsdJNz+LwqAFr5+dksS6hjl9cSKI5kUfxZjdz/F0FvOZOybJ3D//Qm88kqBhJ6OItGsua8Czo/i9gWL/fvhiSficXYdTUGjmTTwH01yINNuWYIAgJtEzix8G6/fyyJ1NV177WHkyDjeeENCE0QTRyCKcTmVUq2BkVrrEyoq6/X6Am63ZAY6HP75T3jq2UIS7ulIUcJGjuUWEmlgtyxBOMAAhrOvz928OP1Fzml7MbPvH8nWLQ4++QQuv9xudTWesN8/MROTc9cue51wGRmpZGfvs1VDOCrStXixkxEjkkgb9BJ7E9fQq+gOXKRRRHT7nHni3BQVx16/NtEVOdWpKbeokLu7/5PJa6fy3eovuPGpLnzxt4e4+mrIyytg6NASHTX1WbSLjIzUsPOl2boG4/XC3/+egDdlLQXHP0aiP4MTih6wW5YghCXOFce7gz6iaXIz/rv2X9z82gckJsJNNyXyxhtxktyjihHjXoN588045s930uSGWykK5HNK0QhxxwgxTWZyEz4/+ytSPWm8vPZm/vHeaDIz/TzySAIPPRSPz2e3wtpDVN0yWuu1QIX+dqHyrFrlYMSIeJIHvM7W1J8Z0GIgHZdearcsQaiQTg078+mQL7j0+wt4bNmVPPluEe/dcxnvvONh5Uono0ebciNGhB/wdN99kgEkEmLG5y5ETnEx3H57IgWpS4kbcA/p8em8csrrfLxU+pUJsUtpYz2Ac5xj+DpxGPfNvop7nllF038/yG8T4jjmGHjnHXEqHClyBmsgTz4Zz5zFe0m5cSjFFPDiKa/RNEWyLAk1ixb+k7ksfwLNkrN4/s/hZN50PXfft48NG+Ccc5KYP98pfvgjQGruNYyxY928/hYk3nAx++NX8ree/8dZbc+xW5YgHJJDhZo+t90wpm+Zwkj9CT1bL+Gdr0dy7/XtGTcujs2bfZx2mpc46RJfacS41yDmzXNy+9/icFxwOfnNfqWd9yzcfzzOiD9kfIBQc5k/ux79i8ZTFH8H87Z/yq3betLn6hdYNvJGFi92sX27g6FDi6lf326lNQtxy9QQtHZy6RUuCs+6kkCn0TT3ncjZBR/jRAy7UPOZ6XmBeoHWdPCehx8vk9JvoeimTjTq8x3Z2U4+/tjDqlViriqDnK0agNZOLriigF1nngtdRpHl68uw/G+II8luaYJQpTTyd+ZYbiHN34rd7uXknHEBDa+/Hq/fxzffxPHHHy6JCR8hYtxjnGnTYMj1K9h+3vHQbhxntBrMhfnfE0+a3dIEISokUJ9O3ito5z0bBy52tnyftHt6kdzlN2bMcHPJJYlkZ0vPsIoQ4x6jBALw4ccOTv7Hc+y75HhosIo7j7mbD8/8XGrsQq3HgYPG/u70LL6FDF83dsUvIPfCgSRfP4w/lqzmtNOSJG1fBUQ1cFhlyM7eZ6uQWIobsWOHgxsfm8PU+n+DJguo58rgjcGvc1qrQQAMfflZmxXGZqwUEF2VIRY1QXhdbb1nMjH+Xja5puEIOAksuBL3lH/y+F0tuf764moJHRxLNiKUjIzUsEcvxt0iFi5cQQG89vEWnp/3OP4unwDQqPB4Wjv6xlxtvSYZhlggFnXFoiYIr+vEoocJEGCFawwrsh5nac4S8LtgyYWc4LyVroOmUi9zb7nbvK/3g0esKxZsRDjKM+7SFTIG2LcPXvsghzcXP09+p7ehSxHJxa1p7e9PI0/rmHwABaG6ceDgKN8w3r7kTL5fNZZnp49gRZdRTGcU02f1oK3zJE7r7yEtWfK0ghj3aiV0+LXPB2vXOlmwYQ3rsl7C2+UD6FZAmq81xzY+hh4t2jNtmozcEISyPP9cAnAJ53IxG5yT+L3gDbY1/pbVzj95e5Gb+vm96Nkmi6ObZZEcl2y3XNsQ415N+P3Gl75hg4O5G1awpzAHf+9/w5CvwOknvjiTPpmn0jOrEy6n9F0XhIpw4KClvz9XefozLu8h1mzKZW+9aexuMoPfsuG37Q4S8trRs00LlrRbTMcGnXDUobx+YtyjxJYtDubOdTFvnpN581z8+aeLfQX50Gk0nPwWtJgGQEJhC049+hhUA4XTIa3/gnA4JHni6dwmHl/ReWyadxPbcrfjbf4bBS0nM237SgaM6kNDV0vO6jCIIe3P5KSsfnhctdt9I8a9Cti1C/7808X8+SXGfOvWoKEOQOZC6p31Ds62n+D37IaAg/r+djTzHU+aozU52sE0Ow9AEGoJLk8xLTtvpkUA8rZfRPbEe9gT2ERe49/Z2eEnPlr2Dh8te4ckZ33ObDuYczsMZUCLgSS6E+2WXuVIbxmLQ7WEh/rK/X7Yvt3Bxo1O6tcPMG+ei3XrSte4k1P8NDh6PnT+kt3NvmJfvDbz/U3p6r2GQvaRQP2IdNWkHg2xgOiKnFjUBFWvq28fH2cmPsTXYwN8OWMG2xt8Cx2/hnobAYh3JHNGm0Gc2/5cTm11BilxKWG3U9N6y4hxtyjvwvl8cN998WzY4GTDBmPUCwtLzmV6eoDu3X106rmL+KMmkZ3yGz+s+IVdzhUAuAOJtPENplPxpbT1DcFF3CEj5JWlrjyAVYXoipxY1ATR1RUIwP4tWexY0pm9uUXkNR0Hnb6CBqsAiHMkMKDFKQxqM5gzWg+mSXLTA+uKcT9MYsW4FxfDwoVOpk93MX26i2nT3OzZU3Lu6tcP0LxFMQ06LMeVNY99qX+yyTWZrc45BBwmR5g7kEhb35kc5T2ftt7BeChdExDjHj1EV+TEoiaoPl2BgIP9m5qTvaQLO3eCt/XP0PEraLzkQJmM+Ga0b9CGu4/7B4M6n0L+ntiwl6FUu3FXSjmB14HuQCFwo9Z6ZXnl7TDuxcWwerWTpUudrF2byKRJXubMcZGfD3hyIWkHjTusJa7xGhKbrsHZYA374leQ7VyI15F3YDvOgJsm/mNp6RtAS98A1rl+w1lFzRl1/QGsLKIrcmJRE9ijK+B3sHdDa3Yu6cKenAQKmkwE9R20+h1cRosj4KK5uyvt0zrTKUPRpYmibaNmZKU1pVFiI9s6RNhh3M8HztVaX6uUOgF4QGs9tLzyh2vc9+6FefNc+Hzg9UJREUzZ9zk7izdR6CukyFdMbmEh+UXF5BcVUVBcRG5BMXmFheQXF4OrEFxF5s+zH3fqTvyJO/E7CsPuzxFwkRhoSHIgk6RAJsmBTFICTXERfzjyK0QewMohuiInFjWB/br6nuBn+5omrJvXgbVLM9havJKihnOh5WRoOgfcYXK4+l0485rgLErH5U3B6UsiMz2JHp0TSY1PJt4Vj9sZR5wzjjinG5fTTZwzDrczjoYJDbngqIsPu/eOHSNUTwL+B6C1nq6UOjYaO/nb3xL48ceQwT711sFdN5Yu5ADirb9ycARcOHHjIpH4QAPiAkm4A4l4SCMhUI/4QH3zR1qV1coFQYg9HM4Ame22kNluC70xfvrcXfWZ8sut7J+TRK53PwWu7RQnbMbn2YUvfgf+xGz8SdvxJ27C69kPrmLWAmtXRbbP9ukdOK7J8VV6HNG0UmnAnpDfPqWUW2sd9pVc3tunIn74oeycVkDs+cUEQajhXGW3gMoRTSfRXiA1dF/lGXZBEAShaommcZ8CDAGwfO4Lo7gvQRAEIYRoumW+AU5XSk3FeL2vi+K+BEEQhBBipp+7IAiCUHVIpCpBEIRaiBh3QRCEWogYd0EQhFpInRiNE0koBKVUEjAOuEFrvcyaN4+SvvprtNZV2ihckS6l1GXA3wEfsAD4q7Uo4rAO1aVLa+2P5vmKQNMFwP2YQQ5va63/W9kQGNWly5pv670VUu5tIEdrfX8snK9wuqzfdj+L/wfcAGRbs24GVkRyLHZRJ4w7cB6QoLXuY3XLfAE4EArBGj37JtA8ZF4CgNZ6gB26lFKJwBNAV611nlLqc+BszDUr91js0qWU+gWier4OpckFPAMcC+wHliilxgD9ylvHZl37wb57K4hS6magK/B7pOvYocvuZ9HiGOBqrfWcEJ3nV7COrdQVt0ypUAiYhy2UeGAYsCxkXncgSSn1i1JqgnXxqlNXIdBXax2MUOYGCipYx05d0T5f5WrSWvuAjlrrPUBDTNfb/RUch5267L63UEr1AU4A3op0HRt12X6+gF7AA0qpyUqpByJcx1bqinEPGwoh+ENrPUVrvaHMOnnA88Ag4Bbg09B1oq1La+3XWm8DUErdAaRg3EaHPBYbdUX7fFV0Db1WTWo+MAkormgdG3XZem8ppZoCw4HbIl3HZl22ni+Lkda+BwInKaXOjmAdW4kZIVHmcEIhLAdWaq0DwHKl1E6gKVD2JRA1XZYfcARwFHCB1jqglKqOsA6Hoyva56vC49Zaf225PT4Aro5kHZt0fYa999ZFQCPgR6AJpla8LJJjsUnX59h4vpRSDuBl6wsMpdQPQM8KjsV26krN/XBCIVyP8aGhlGqGeUtvqWZdbwEJwHkhbpDqCOtwOLqifb7K1aSUSlNK/a6Uitda+4FcwB/Bcdily9Z7S2v9b611L8uH/Qzwmdb6g0OtY7Muu5/FNGCRUirFMvQDgTkVrGM7dWKEakhLeDdKQiEcA6Rord8OKTcRuEVrvUwp5cHUtFpiejr8Q2s9tbp0AbOtvz8oCXP5CjC27DrB3j026/qBKJ6viq6hUuovmN4MxZgePHdYOmw7V4fQ5cLGe6vMPX8tcHSZ3jK2na9ydNn6LFrX8Srgb5g2p/Fa60eq43wdCXXCuAuCINQ16opbRhAEoU4hxl0QBKEWIsZdEAShFiLGXRAEoRYixl0QBKEWIsZdEAShFlJXRqgKVYhSKrT/bAAoAjYCj2mtP7JHVdVhjXfoD/SxYoaglBoGLNFa68Pc5inAo5iRjV5MHKOntdbfVoloQSiD1NyFw8WPGVD1A6CBdsAHSqkBdoqqIiZjji0HQCn1H+BrIP1wNqaU6oYJMHUSJsbMAqA3MFYpdWZVCBaEskjNXThcirXW5wV/KKVGARcD1wATbdJUJWitHyozq/MRbvJqwAPcp7V+DkApdQvwBnAj8NMRbl8QDkKMu1BV/IEx7s2glGvjQeBuYKnW+mSlVEPgOeBcIAkTn+MerfV8a70PMC+Ii4C7MKFWZwLXBxMhWPFFXgdOx0QM/By4V2tdaC2/FxPBLwvYAXwCPGglFLkWeB94GDOc/TJMnJLHtdYfl9Hex9pOf+sYpymlHgUuBzoAXbTWi611vgfOAk7TWo8vc26Krf/nKKV+1lovAD4EFgH7goWUUkdjQjmcjIlD8wNwZ0jAqh7As0Bfa5vfAndrrXdaywPAEuucXgq8bg3fPxd4GmgPrAQe1lp/ba3T1NrnACAZ4y56UGv9M0KNRtwywhFjxdgIuhc2lln8KMbgTLdihIzHxO3IwbgoTgMmKaXal1nvPYzxX48xdl8rpZxW4KZvMEkRFmEM8x0YY48VinWEte4EzD3+D8yLIpR7gVOAtRhD/aZSql6Yw5sL7LSmJ2GM3+fW7/OsfSYBpwLbCf/VMgpjjE8G5iulVmGMbU7ISy0R+Bk4A1iMeSldY50HlFLtMC/QM6zjDi7/1TqvQTpiXrILgVlKqa4Yl1IrTPKLTGC0Uir4wnoV8yJdD0zFxEkZo5TKCnMcQg1CjLtwuMQppcZYNdYlmOh4PuCdMuWe0Vr301rfizEi3TFGspPWug/GyKUBD5RZbwImcFMXjLHriqlBn4LxV3+utT5ea90NY5SuVko1ANpa67+LeQH0xaQE/K3M9ndZWnoC6zAvg45lD1Jr/W+MMQUTsGokJmQvWMYdY3ATgC+tBB1lt/GnVXa5NastcCfG0F9mzbsC8yXxmdb6OEvbz8BOpVQcJlVfCvCUdd46Yc5jD+CSkN05gPO11idqrb/CvMRc1rwzrPPhtPYf1OLFfBmdDlwI/AUTIEuowYhxFw4XJ8Z4DsGkJ5wJnBPsXRLCtJDpYAadz0PiXn9UZlmQ77TWAa11EfCLNe8oSvzflymlApYroi/GxdgDU0vdDPwT83XwGib7UdlwrH9orfMsHcG8l/EVHjVg9ZiZC/RSSjWnJLXaqEOs86PWWmHcTP/CfAG4gZetL59OVtHxVvkirfVgrfVftNbFlJyfj63lXkq+IMqeu9BzHjxfP1vnKtjbJ5g16DWM8Z+vlFqD+QJbrrXeUcFpEGIc8bkLh0uh1johgnJ7Q6b9YZY7rP9lw5N6yha01o+zppdRYqiC5GutNyqlOmNcE4MxeVTPsv7ODymbFzIdfNE4iJzPMF8Ww6xtb8b0sjkIpdSLmC+Qq7XWc4G5SqnnMS6lxkBGyL7dIeslaq3zrZ+RnjtvyDpQcr5+AULn5wNord9TSs3E1P4HYsIT36yUOk9rPbacYxdqAFJzF6JNqJtinvX/0pB0ZFdZ/0NrmwDDLB97HMafDcaYL7GmV1q9dYZZ8ycDC5VSVwL/BVZprc8HWlsaTi+z/crEug4a1tDnZaQ1/wGMcR5tJeQIRytr/3eGzGuKceXkY1xEweM6A8A67sVKqc2Wuyl47q6ylrsxjaZQ+tyVdQsFt/uOdb4exLQzjFJKeZRSrwCPAE9qrU/ExCwH0xYi1GDEuAvVyRcYQ9wfWKKUmoYxjnswvvdQBlLSJ7wbxg3yB6YGugw4WykVXH4fcLHWej/GWF6A6UP+P2AWxu0w6Qh0B10Ubyml7gbQWm+yttnUWlauSwZ4CtOger9Sar5Sapx1bPHAa5br6VNM7f8CpdRsa3kbYLbWOgeTQzQfeNA6b0swXyVzMee1PF7DvMg+VUqNx5zDO4Esa79tMX72RUqpnyi5DkdyvoQYQIy7UG1YKfn6YbLqpGMaDX8FTtZary5T/CFgN8bA/Q5caPng/Ri/8FiMYWoBfIXpWonViHgtsMbaV32MX/+6I5D+MrAaM1ArLWR+0Oe9Hijb1nAArfUcTFfDXzC5QU/G9Cp60PoLnptBmIbkzphcoh9iesSgtV5krfcLxsXTCHMeT7d88uXtezLG5bIcM4hqP6Zh+D9WkSsxaRMTLY1bgNu11qPLPx1CTUAyMQkxRUg/98usnikxi1LqZUwt+AWt9T02yxGEUkiDqiBUEiuf5iWYLwgfxscvCDGFuGUEofLEYxp5NwA3xlJSZEEIIm4ZQRCEWojU3AVBEGohYtwFQRBqIWLcBUEQaiFi3AVBEGohYtwFQRBqIf8Pp1NmkNxHjj0AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Hide Cell\n",
    "sns.histplot(ps[df_categ['intervention']==0], kde=True, stat=\"density\", linewidth=0,color='b')\n",
    "sns.histplot(ps[df_categ['intervention']==1], kde=True, stat=\"density\", linewidth=0,color='g')\n",
    "plt.title(\"Positivity Check\\nPropensity Score Dists\", fontsize=20, fontweight = 'bold')\n",
    "plt.xlabel('Propesnity Scores', fontsize=14, fontweight = 'bold', labelpad=5)\n",
    "plt.legend(['Untreated', 'Treated']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the second experiment, we specify a bad exposure model. Instead of using logistic regression, we simply sample a uniform random distribution: \n",
    "\n",
    "$$ \\hat \\pi (X_i) \\sim U(0.1,0.9) $$\n",
    "\n",
    "As we can see from the results below, the AIPE method is effectively stable, estimating a slightly lower ATE of about ~$0.38$. The standard deviation also increases slightly. On the other hand, the IPW method does far worse than the naive method, which again makes sense as we are feeding it random noise for the propensity scores. This is the first example of a doubly robust method showing how, since the outcome model is correctly specified, the estimation is still robust even to random noise for the exposure model.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Mean ATE</th>\n",
       "      <th>Std Dev</th>\n",
       "      <th>[.025</th>\n",
       "      <th>.975]</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>AIPW</th>\n",
       "      <td>0.385</td>\n",
       "      <td>0.026</td>\n",
       "      <td>0.334</td>\n",
       "      <td>0.435</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>IPW</th>\n",
       "      <td>0.567</td>\n",
       "      <td>0.035</td>\n",
       "      <td>0.498</td>\n",
       "      <td>0.638</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Naive</th>\n",
       "      <td>0.473</td>\n",
       "      <td>0.018</td>\n",
       "      <td>0.440</td>\n",
       "      <td>0.507</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Mean ATE  Std Dev  [.025  .975]\n",
       "AIPW      0.385    0.026  0.334  0.435\n",
       "IPW       0.567    0.035  0.498  0.638\n",
       "Naive     0.473    0.018  0.440  0.507"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Hide cell\n",
    "bootstrap_sample = 100\n",
    "AIPW_ates = []\n",
    "IPW_ates = []\n",
    "naives_ates = []\n",
    "for iSample in range(bootstrap_sample):\n",
    "    df_bootstrap = df_categ.sample(frac=1,replace=True)\n",
    "    ate, ps, mu0, mu1 = AIPW(df_bootstrap, X, T, Y,true_ps=False)\n",
    "    AIPW_ates.append(ate)\n",
    "    ate, ps,_ = IPW(df_bootstrap, X, T, Y,true_ps=False)\n",
    "    IPW_ates.append(ate)\n",
    "    naives_ates.append(naive_ATE(df_bootstrap, T, Y))\n",
    "\n",
    "sns.histplot(AIPW_ates, kde=True, stat=\"density\", linewidth=0,color='g')\n",
    "sns.histplot(IPW_ates, kde=True, stat=\"density\", linewidth=0,color='b')\n",
    "sns.histplot(naives_ates, kde=True, stat=\"density\", linewidth=0,color='r')\n",
    "# plt.vlines(np.percentile(AIPW_ates, 2.5), 0, 20, linestyles=\"dotted\")\n",
    "# plt.vlines(np.percentile(AIPW_ates, 97.5), 0, 20, linestyles=\"dotted\", label=\"95% CI\")\n",
    "plt.title(\"ATE Bootstrap Distribution\\nRandom Exposure Model\", fontsize=20, fontweight = 'bold')\n",
    "plt.xlabel('ATE', fontsize=14, fontweight = 'bold', labelpad=5)\n",
    "plt.legend(['AIPW', 'IPW', 'Naive'])\n",
    "\n",
    "Results = {\"AIPW\":{\"Mean ATE\":np.mean(AIPW_ates), \"Std Dev\":np.std(AIPW_ates), \"[.025\":np.percentile(AIPW_ates, 2.5), \".975]\":np.percentile(AIPW_ates, 97.5)},\n",
    "\"IPW\":{\"Mean ATE\":np.mean(IPW_ates), \"Std Dev\":np.std(IPW_ates), \"[.025\":np.percentile(IPW_ates, 2.5), \".975]\":np.percentile(IPW_ates, 97.5)},\n",
    "\"Naive\":{\"Mean ATE\":np.mean(naives_ates), \"Std Dev\":np.std(naives_ates), \"[.025\":np.percentile(naives_ates, 2.5), \".975]\":np.percentile(naives_ates, 97.5)}}\n",
    "\n",
    "df_results = pd.DataFrame(Results)\n",
    "df_results.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the third experiment, we now investigate the impact of a bad outcome model. We again sample from a uniform distribution to obtain the incorrect outcome data: $$\\mu_d(X_i) \\sim U(0,1) $$\n",
    " \n",
    "Here once again see the AIPW and IPW methods both agree and estimate ~$0.39$. AIPW again shows the doubly robust property against the completely random outcome model, while IPW is unimpacted since the exposure model is correct. Both hence perform similarly to the original experiment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Mean ATE</th>\n",
       "      <th>Std Dev</th>\n",
       "      <th>[.025</th>\n",
       "      <th>.975]</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>AIPW</th>\n",
       "      <td>0.388</td>\n",
       "      <td>0.016</td>\n",
       "      <td>0.356</td>\n",
       "      <td>0.417</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>IPW</th>\n",
       "      <td>0.387</td>\n",
       "      <td>0.015</td>\n",
       "      <td>0.357</td>\n",
       "      <td>0.413</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Naive</th>\n",
       "      <td>0.470</td>\n",
       "      <td>0.017</td>\n",
       "      <td>0.441</td>\n",
       "      <td>0.506</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Mean ATE  Std Dev  [.025  .975]\n",
       "AIPW      0.388    0.016  0.356  0.417\n",
       "IPW       0.387    0.015  0.357  0.413\n",
       "Naive     0.470    0.017  0.441  0.506"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Hide cell\n",
    "bootstrap_sample = 100\n",
    "AIPW_ates = []\n",
    "IPW_ates = []\n",
    "naives_ates = []\n",
    "for iSample in range(bootstrap_sample):\n",
    "    df_bootstrap = df_categ.sample(frac=1,replace=True)\n",
    "    ate, ps, mu0, mu1 = AIPW(df_bootstrap, X, T, Y,true_mus=False)\n",
    "    AIPW_ates.append(ate)\n",
    "    ate, ps,_ = IPW(df_bootstrap, X, T, Y)\n",
    "    IPW_ates.append(ate)\n",
    "    naives_ates.append(naive_ATE(df_bootstrap, T, Y))\n",
    "\n",
    "sns.histplot(AIPW_ates, kde=True, stat=\"density\", linewidth=0,color='g')\n",
    "sns.histplot(IPW_ates, kde=True, stat=\"density\", linewidth=0,color='b')\n",
    "sns.histplot(naives_ates, kde=True, stat=\"density\", linewidth=0,color='r')\n",
    "# plt.vlines(np.percentile(AIPW_ates, 2.5), 0, 20, linestyles=\"dotted\")\n",
    "# plt.vlines(np.percentile(AIPW_ates, 97.5), 0, 20, linestyles=\"dotted\", label=\"95% CI\")\n",
    "plt.title(\"ATE Bootstrap Distribution\\nRandom Outcome Model\", fontsize=20, fontweight = 'bold')\n",
    "plt.xlabel('ATE', fontsize=14, fontweight = 'bold', labelpad=5)\n",
    "plt.legend(['AIPW', 'IPW', 'Naive'])\n",
    "\n",
    "Results = {\"AIPW\":{\"Mean ATE\":np.mean(AIPW_ates), \"Std Dev\":np.std(AIPW_ates), \"[.025\":np.percentile(AIPW_ates, 2.5), \".975]\":np.percentile(AIPW_ates, 97.5)},\n",
    "\"IPW\":{\"Mean ATE\":np.mean(IPW_ates), \"Std Dev\":np.std(IPW_ates), \"[.025\":np.percentile(IPW_ates, 2.5), \".975]\":np.percentile(IPW_ates, 97.5)},\n",
    "\"Naive\":{\"Mean ATE\":np.mean(naives_ates), \"Std Dev\":np.std(naives_ates), \"[.025\":np.percentile(naives_ates, 2.5), \".975]\":np.percentile(naives_ates, 97.5)}}\n",
    "\n",
    "df_results = pd.DataFrame(Results)\n",
    "df_results.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the final experiment, we show the impact of a bad outcome and exposure model: $$\\mu_d(X_i) \\sim U(0,1),  \\hat \\pi (X_i) \\sim U(0.1,0.9) $$\n",
    " \n",
    "In this experiment, we see that AIPW performs very poorly, vastly over-estimating the ATE. In this instance, either naive or IPW would perform better, although the naive without any consideration for random models does best. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Mean ATE</th>\n",
       "      <th>Std Dev</th>\n",
       "      <th>[.025</th>\n",
       "      <th>.975]</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>AIPW</th>\n",
       "      <td>1.054</td>\n",
       "      <td>0.037</td>\n",
       "      <td>0.986</td>\n",
       "      <td>1.132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>IPW</th>\n",
       "      <td>0.575</td>\n",
       "      <td>0.032</td>\n",
       "      <td>0.515</td>\n",
       "      <td>0.630</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Naive</th>\n",
       "      <td>0.475</td>\n",
       "      <td>0.017</td>\n",
       "      <td>0.439</td>\n",
       "      <td>0.508</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Mean ATE  Std Dev  [.025  .975]\n",
       "AIPW      1.054    0.037  0.986  1.132\n",
       "IPW       0.575    0.032  0.515  0.630\n",
       "Naive     0.475    0.017  0.439  0.508"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Hide cell\n",
    "bootstrap_sample = 100\n",
    "AIPW_ates = []\n",
    "IPW_ates = []\n",
    "naives_ates = []\n",
    "for iSample in range(bootstrap_sample):\n",
    "    df_bootstrap = df_categ.sample(frac=1,replace=True)\n",
    "    ate, ps, mu0, mu1 = AIPW(df_bootstrap, X, T, Y,true_mus=False,true_ps=False)\n",
    "    AIPW_ates.append(ate)\n",
    "    ate, ps,_ = IPW(df_bootstrap, X, T, Y,true_ps=False)\n",
    "    IPW_ates.append(ate)\n",
    "    naives_ates.append(naive_ATE(df_bootstrap, T, Y))\n",
    "\n",
    "sns.histplot(AIPW_ates, kde=True, stat=\"density\", linewidth=0,color='g')\n",
    "sns.histplot(IPW_ates, kde=True, stat=\"density\", linewidth=0,color='b')\n",
    "sns.histplot(naives_ates, kde=True, stat=\"density\", linewidth=0,color='r')\n",
    "# plt.vlines(np.percentile(AIPW_ates, 2.5), 0, 20, linestyles=\"dotted\")\n",
    "# plt.vlines(np.percentile(AIPW_ates, 97.5), 0, 20, linestyles=\"dotted\", label=\"95% CI\")\n",
    "plt.title(\"ATE Bootstrap Distribution\\nRandom Outcome and Exposure Model\", fontsize=20, fontweight = 'bold')\n",
    "plt.xlabel('ATE', fontsize=14, fontweight = 'bold', labelpad=5)\n",
    "plt.legend(['AIPW', 'IPW', 'Naive'])\n",
    "\n",
    "Results = {\"AIPW\":{\"Mean ATE\":np.mean(AIPW_ates), \"Std Dev\":np.std(AIPW_ates), \"[.025\":np.percentile(AIPW_ates, 2.5), \".975]\":np.percentile(AIPW_ates, 97.5)},\n",
    "\"IPW\":{\"Mean ATE\":np.mean(IPW_ates), \"Std Dev\":np.std(IPW_ates), \"[.025\":np.percentile(IPW_ates, 2.5), \".975]\":np.percentile(IPW_ates, 97.5)},\n",
    "\"Naive\":{\"Mean ATE\":np.mean(naives_ates), \"Std Dev\":np.std(naives_ates), \"[.025\":np.percentile(naives_ates, 2.5), \".975]\":np.percentile(naives_ates, 97.5)}}\n",
    "\n",
    "df_results = pd.DataFrame(Results)\n",
    "df_results.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Concluding Thoughts for AIPE\n",
    "\n",
    "We clearly demonstrate AIPW's doubly robust properties using the simulated National Mindset dataset. But it is important to note, our 'incorrect' models were uniform random which would be about as poor as one could imagine. In reality, misspecified models contain more subtle biases or noise, and thus there is a whole host of literature investigating the sensitivity of doubly robust methods to various types and degrees of misspecification. For instance in the example where both models were incorrect, one could imagine scenarios where model misspecifications cancel out, and actually produce a relatively accurate ATE estimate. It is an area of active research on when doubly robust methods should be used when there might be uncertainty on both models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### TMLE\n",
    "\n",
    "#### Background and Setup\n",
    "Targeted Maximum Likelihood Estimation (TMLE) is a semi-parametric method with minimal assumptions on the underlying data distribution demonstrated by Van der Laan & Rubin in 2006. We will briefly walk through the steps of a TMLE estimation algorithm on the same data without diving too deep into the formulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "# Hide Cell\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "pd.set_option(\"display.precision\", 3)\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('seaborn')\n",
    "import seaborn as sns\n",
    "from scipy.special import logit, expit\n",
    "import statsmodels.api as sm\n",
    "\n",
    "# Super Learner Import\n",
    "from math import sqrt\n",
    "from numpy import hstack\n",
    "from numpy import vstack\n",
    "from numpy import asarray\n",
    "from sklearn.datasets import make_regression\n",
    "from sklearn.model_selection import KFold\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.linear_model import ElasticNet\n",
    "from sklearn.neighbors import KNeighborsRegressor\n",
    "from sklearn.tree import DecisionTreeRegressor\n",
    "from sklearn.svm import SVR\n",
    "from sklearn.ensemble import AdaBoostRegressor\n",
    "from sklearn.ensemble import BaggingRegressor\n",
    "from sklearn.ensemble import RandomForestRegressor\n",
    "from sklearn.ensemble import ExtraTreesRegressor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The TMLE algorithm begins by first estimating a model by training and predicting a super learning ensemble of algorithms. In the hidden code block below, we do so using 9 models from pre-built libraries. We report the root mean squared errors for all algorithms, demonstrating the super learner ensemble performs best. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train (5195, 31) (5195,) Test (5196, 31) (5196,)\n",
      "Meta  (5195, 9) (5195,)\n",
      "LinearRegression: RMSE 0.828\n",
      "ElasticNet: RMSE 0.990\n",
      "SVR: RMSE 0.849\n",
      "DecisionTreeRegressor: RMSE 1.023\n",
      "KNeighborsRegressor: RMSE 0.887\n",
      "AdaBoostRegressor: RMSE 0.827\n",
      "BaggingRegressor: RMSE 0.900\n",
      "RandomForestRegressor: RMSE 0.898\n",
      "ExtraTreesRegressor: RMSE 0.954\n",
      "Super Learner: RMSE 0.808\n"
     ]
    }
   ],
   "source": [
    "# Hide Cell\n",
    "# create a list of base-models\n",
    "def get_models():\n",
    "\tmodels = list()\n",
    "\tmodels.append(LinearRegression())\n",
    "\tmodels.append(ElasticNet())\n",
    "\tmodels.append(SVR(gamma='scale'))\n",
    "\tmodels.append(DecisionTreeRegressor())\n",
    "\tmodels.append(KNeighborsRegressor())\n",
    "\tmodels.append(AdaBoostRegressor())\n",
    "\tmodels.append(BaggingRegressor(n_estimators=10))\n",
    "\tmodels.append(RandomForestRegressor(n_estimators=10))\n",
    "\tmodels.append(ExtraTreesRegressor(n_estimators=10))\n",
    "\treturn models\n",
    " \n",
    "# collect out of fold predictions form k-fold cross validation\n",
    "def get_out_of_fold_predictions(X, y, models):\n",
    "\tmeta_X, meta_y = list(), list()\n",
    "\t# define split of data\n",
    "\tkfold = KFold(n_splits=10, shuffle=True)\n",
    "\t# enumerate splits\n",
    "\tfor train_ix, test_ix in kfold.split(X):\n",
    "\t\tfold_yhats = list()\n",
    "\t\t# get data\n",
    "\t\ttrain_X, test_X = X[train_ix], X[test_ix]\n",
    "\t\ttrain_y, test_y = y[train_ix], y[test_ix]\n",
    "\t\tmeta_y.extend(test_y)\n",
    "\t\t# fit and make predictions with each sub-model\n",
    "\t\tfor model in models:\n",
    "\t\t\tmodel.fit(train_X, train_y)\n",
    "\t\t\tyhat = model.predict(test_X)\n",
    "\t\t\t# store columns\n",
    "\t\t\tfold_yhats.append(yhat.reshape(len(yhat),1))\n",
    "\t\t# store fold yhats as columns\n",
    "\t\tmeta_X.append(hstack(fold_yhats))\n",
    "\treturn vstack(meta_X), asarray(meta_y)\n",
    " \n",
    "# fit all base models on the training dataset\n",
    "def fit_base_models(X, y, models):\n",
    "\tfor model in models:\n",
    "\t\tmodel.fit(X, y)\n",
    " \n",
    "# fit a meta model\n",
    "def fit_meta_model(X, y):\n",
    "\tmodel = LinearRegression()\n",
    "\tmodel.fit(X, y)\n",
    "\treturn model\n",
    " \n",
    "# evaluate a list of models on a dataset\n",
    "def evaluate_models(X, y, models):\n",
    "\tfor model in models:\n",
    "\t\tyhat = model.predict(X)\n",
    "\t\tmse = mean_squared_error(y, yhat)\n",
    "\t\tprint('%s: RMSE %.3f' % (model.__class__.__name__, sqrt(mse)))\n",
    " \n",
    "# make predictions with stacked model\n",
    "def super_learner_predictions(X, models, meta_model):\n",
    "\tmeta_X = list()\n",
    "\tfor model in models:\n",
    "\t\tyhat = model.predict(X)\n",
    "\t\tmeta_X.append(yhat.reshape(len(yhat),1))\n",
    "\tmeta_X = hstack(meta_X)\n",
    "\t# predict\n",
    "\treturn meta_model.predict(meta_X)\n",
    " \n",
    "# create the inputs and outputs\n",
    "X = df_categ[df_categ.columns.drop([Y])].to_numpy()\n",
    "y = df_categ[Y].to_numpy()\n",
    "# split\n",
    "X, X_val, y, y_val = train_test_split(X, y, test_size=0.50)\n",
    "print('Train', X.shape, y.shape, 'Test', X_val.shape, y_val.shape)\n",
    "# get models\n",
    "models = get_models()\n",
    "# get out of fold predictions\n",
    "meta_X, meta_y = get_out_of_fold_predictions(X, y, models)\n",
    "print('Meta ', meta_X.shape, meta_y.shape)\n",
    "# fit base models\n",
    "fit_base_models(X, y, models)\n",
    "# fit the meta model\n",
    "meta_model = fit_meta_model(meta_X, meta_y)\n",
    "# evaluate base models\n",
    "evaluate_models(X_val, y_val, models)\n",
    "# evaluate meta model\n",
    "yhat = super_learner_predictions(X_val, models, meta_model)\n",
    "print('Super Learner: RMSE %.3f' % (sqrt(mean_squared_error(y_val, yhat))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the second step we use the super learner algorithm to estimate the expected value of the outcome using the treatment and confounders as predictors. Within this, there are three steps:\n",
    "1. predict with the interventions\n",
    "2. predict with every sample receiving no treatment\n",
    "3. predict with every sample receiving treatment.\n",
    " \n",
    "We can take the difference of the last two as an ATE estimate, which is effectively the g-estimation approach. We see below this provides a decent 1st estimate. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4044480650676532"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_predict = df_categ.copy()\n",
    "X = df_predict[df_predict.columns.drop([Y])].to_numpy()\n",
    "Q_a = super_learner_predictions(X, models, meta_model)\n",
    "df_predict['intervention'] = 0\n",
    "X = df_predict[df_predict.columns.drop([Y])].to_numpy()\n",
    "Q_0 = super_learner_predictions(X, models, meta_model)\n",
    "df_predict['intervention'] = 1\n",
    "X = df_predict[df_predict.columns.drop([Y])].to_numpy()\n",
    "Q_1 = super_learner_predictions(X, models, meta_model)\n",
    "\n",
    "df_tmle = pd.DataFrame([df_categ[Y].to_numpy(),df_categ[T].to_numpy(), Q_a,Q_0,Q_1]).T\n",
    "df_tmle.columns = ['Y','D','Q_a','Q_0','Q_1']\n",
    "\n",
    "df_tmle['Q_1'].mean() - df_tmle['Q_0'].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the third step we obtain propensity scores (ps) and form a \"clever covariate\" from these values which will be used to refine our model. the inverse ps with indicator is added with the negative inverse of not being treated (1-ps) also multiplied with indicator if not being treated:\n",
    "\n",
    "$$H(D,X) = \\frac{I(D=1)}{\\hat \\pi (X_i)} - \\frac{I(D=0)}{1 - \\hat \\pi (X_i)}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "T = 'intervention'\n",
    "Y = 'achievement_score'\n",
    "X = df_categ.columns.drop([T, Y])\n",
    "ate, ps,_ = IPW(df_categ, X, T, Y)\n",
    "\n",
    "df_tmle['H_1'] = 1/ps\n",
    "df_tmle['H_0'] = -1/(1-ps)\n",
    "df_tmle['H_a'] = df_tmle['D'] * df_tmle['H_1'] + (1-df_tmle['D']) * df_tmle['H_0']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the fourth and fifth steps, we estimate the fluctuation parameter using the logit function:\n",
    " \n",
    "$$logit(\\mathbb{E}[Y|D,X]) = logit(\\hat{\\mathbb{E}}[Y|D,X]) = \\epsilon H(D,X)$$\n",
    " \n",
    "We then update out initial estimates with the fluctuation parameter adjustment.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "eps_fit = np.polyfit(df_tmle['H_a'], df_tmle['Y'] - df_tmle['Q_a'], 1)[0]\n",
    "df_tmle['Q_0_hat'] = df_tmle['Q_0'] + eps_fit * df_tmle['H_0']\n",
    "df_tmle['Q_1_hat'] = df_tmle['Q_1'] + eps_fit * df_tmle['H_1']\n",
    "df_tmle['Q_a_hat'] = df_tmle['Q_a'] + eps_fit * df_tmle['H_a']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TMLE TAE estimate: 0.3864\n"
     ]
    }
   ],
   "source": [
    "TMLE_ate = df_tmle['Q_1_hat'].mean() - df_tmle['Q_0_hat'].mean()\n",
    "print('TMLE TAE estimate: {:.4f}'.format(TMLE_ate))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see how the fluctuation adjusted outcomes estimates vastly improves the ATE to be more in line with AIPW. One major benefit of TMLE is a whole set of nice statistical and convergence properties. In this case, we can use something called the influence function to calculate a closed form standard error, unlike the empirical error estimates we gained by bootstrapping in the AIPW case.\n",
    " \n",
    "$$\\hat{IF} = (Y-\\hat{\\mathbb{E}}*[Y|D,X])H(D,X) + \\hat{\\mathbb{E}}*[Y|D=1,X] - \\hat{\\mathbb{E}}*[Y|D=0,X] - ATE_{TMLE}$$\n",
    "$$SE = \\sqrt{var(IF)/N}$$\n",
    " \n",
    "Using the above method, we see we get a SE very similar to our AIPW empirical methods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SE calculated from influcence function: 0.0166\n"
     ]
    }
   ],
   "source": [
    "IF = (df_tmle['Y'] - df_tmle['Q_a_hat']) * df_tmle['H_a'] + df_tmle['Q_1_hat'] - df_tmle['Q_0_hat'] - TMLE_ate\n",
    "print('SE calculated from influcence function: {:.4f}'.format(np.sqrt(IF.var()/df_tmle.shape[0])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### References  \n",
    "    \n",
    "    1. Glynn, A. N., & Quinn, K. M. (2010). An introduction to the augmented inverse propensity weighted estimator. Political analysis, 18(1), 36-56.\n",
    "\n",
    "    2. https://matheusfacure.github.io/python-causality-handbook/12-Doubly-Robust-Estimation.html\n",
    "\n",
    "    3. Gruber S, van der Laan MJ. Targeted minimum loss based estimator that outperforms a given estimator. Int J Biostat. 2012 May 18;8(1):Article 11. doi: 10.1515/1557-4679.1332. PMID: 22628356; PMCID: PMC6052865.\n"
   ]
  }
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