Correlation/2020_02_11a_correlation_and_paf.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# This file is a practical example and test of approaches to change the population attributable fraction (PAF) for risk factors in Vivarium such that they account for observed correlation in exposure between risks.\n",
    "\n",
    "This file will investigate the approach that Vivarium currently uses to calculate the PAF for multiple risk factors, which we will call the *multiplicative* approach. In comparison, Abie and Chris and proposing a *joint* approach. \n",
    "\n",
    "The first part of the file looks at how we will jointly estimate exposure probabilities from copulae. The second part of the file proposes our alternative formulation of a *joint* PAF. The last part of the file tests our assumptions in a very simple step by step model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#import numpy as np, matplotlib.pyplot as plt, pandas as pd\n",
    "#pd.set_option('display.max_rows', 8)\n",
    "#!date\n",
    "\n",
    "#%load_ext autoreload\n",
    "#%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib as matplot\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "import scipy.stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gaussian copula to correlation two risk factor exposures\n",
    "\n",
    "And then some investigation of how much error this introduces in the PAF.\n",
    "\n",
    "This part of our file shows how we can introduce correlation from a multivariate normal distribution. All we need is correlation (variance/covariance) in our exposures."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "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>SBP</th>\n",
       "      <th>LDL-C</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>125.905847</td>\n",
       "      <td>5.723323</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>139.578867</td>\n",
       "      <td>3.322323</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>119.611226</td>\n",
       "      <td>3.089911</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>118.885394</td>\n",
       "      <td>3.845074</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>169.315611</td>\n",
       "      <td>5.091290</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9995</th>\n",
       "      <td>112.742931</td>\n",
       "      <td>3.499870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9996</th>\n",
       "      <td>173.045882</td>\n",
       "      <td>8.809667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9997</th>\n",
       "      <td>129.865889</td>\n",
       "      <td>5.465636</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9998</th>\n",
       "      <td>105.705538</td>\n",
       "      <td>3.818431</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9999</th>\n",
       "      <td>143.099773</td>\n",
       "      <td>7.605454</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             SBP     LDL-C\n",
       "0     125.905847  5.723323\n",
       "1     139.578867  3.322323\n",
       "2     119.611226  3.089911\n",
       "3     118.885394  3.845074\n",
       "4     169.315611  5.091290\n",
       "...          ...       ...\n",
       "9995  112.742931  3.499870\n",
       "9996  173.045882  8.809667\n",
       "9997  129.865889  5.465636\n",
       "9998  105.705538  3.818431\n",
       "9999  143.099773  7.605454\n",
       "\n",
       "[10000 rows x 2 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Simulate for testing purposes\n",
    "\n",
    "N = 10_000  # number of individuals\n",
    "\n",
    "# set random seed for reproducibility\n",
    "np.random.seed(12345)\n",
    "\n",
    "# simulate data (to be replaced with real data, e.g. from NHANES, eventually)\n",
    "df = pd.DataFrame(index=range(N))\n",
    "df['SBP'] = np.random.normal(130, 20, size=N)\n",
    "df['LDL-C'] = np.random.normal(4+(df.SBP-130)/20, 1, size=N)  # intentionally include correlation between SBP and LDL-C\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.JointGrid at 0x1c8a1169188>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.jointplot(df['SBP'], df['LDL-C'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# What we want from the microdata is simply the Spearman R value, which captures the correlation of SBP and LDL-C as continuous variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6942625526106255"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rho, p_val = scipy.stats.spearmanr(df['SBP'], df['LDL-C'])\n",
    "rho"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# What will we use that for?\n",
    "\n",
    "We will generate a multivariate normal with that rho, and then use that to generate a distribution that is marginally uniform, but with that rho, and then use that to generate a distribution that in its margins matches the SPB and LDL-C from GBD, but also has Spearman correlation rho:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6797538355495384"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "probit_propensity = np.random.multivariate_normal([0,0], [[1, rho],\n",
    "                                                         [rho, 1]], size=N)\n",
    "sns.jointplot(probit_propensity[:,0], probit_propensity[:,1])\n",
    "rho, p_val = scipy.stats.spearmanr(probit_propensity[:,0], probit_propensity[:,1])\n",
    "rho"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6797538355495384"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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dAhVJRA+9wwnCyz9P5g7BuXvxQFCTWCdLJFnpuNMxX714w7c4xV0xbegadm5aiww1/xI+WdEmNlxJhgQqQbj55wFyd4i7CqIRJEJoNu0VxN4njoV8jbHa+7dvWx4nLhXIiojwjVfDOtE8lOJLECqj153WjGTl4la8nMGdaDbtJRtO2GoqnOPaUvXVjtGzTa89Pbe9F+eu3KI0WoeRawOPyKRDEVSCcPPPc2PnprWuj2cYML+w6Hu0RhBREwhX8yS6HFhfVxhrT+Nv38Dc/cWm99MsOUPHjkfWtPo0OoZf3ltsegAo4Q4JVIQEnbnkd/9epcMVXi2c8DtaI+i4C40xvPjUFhwZ3OJpLBs3eobVRaTNiLDALHPltbkoKZZM/NhSrEJEi7WBnIiGZF092ghZOfb+8WnkJaXfXmXmbtv6QUyjFft162taqWd8HcPeOJy0PL0wqwWqr33nprVt1RuUvIRqe0Np3WghgYoI2Wh0QC48fhpxwyhgEKXgJy4VHPuafnL9bt0xVErGhTgJ0WvlBVPmLC7MaPePT8d/UkRbQaNfooUEKiK81jachMdtTtOO0bN1EY7q2ombqIhScHshg72vyfp7MYTQ6c4xvzRkMOxxGBkAmsZglv3JXQLrM4g2I4lFQO0ErUFFhMrahl1kZM9hQF0vktedv7iry+cMPLu913Udye8XTIxi17X6O0ddY9i5aS12jJ7F/vHppsXJWijyr4b6MPbVrTVxTBKruqkXppNJ4meynaAIKiJUvN3sguT0HFkE5PQ7mXHswINr8PzxGUcx8lsKXjtn21PKFY7xv74RyuiHfM7A+ZFdABqdLJLG3EJ72iMR3mQY6gpuCDUcjGKlkEBFhNWItVAseY6wsD9HeOp5edlpjKHCuadpKwCpc7nTFF0nxCj2sTNXG4Sowqv9Rc0i3peJqUKD0azT+0ikj3ZwVs/qGfzxU4/RRN2IIYGKEPuYclUHcOs6jhfWplOvcwHkzuUqIrWquwuD/XkciLC4YN+2PCY/uC09n2aua0ltHE4aDMAXHlnjuA4ZBr/x8BpcuHYH5RSrVM+qFa0+hY6ABCom/LqGq1bp+Ul7OZ3DxFQB567cAof3BVxYKslMa2XkDB1/d89Uumt+c+Yj3C2ZoUdJ1vTnxFQBh07O1vUu5Qw9Eb1MSWC1oePpgd7IBCqq/cZJsybMhBpUJJFQVKv05u47d7OrNAnbR6iXOYeha8gZzhYuGcYwMVVwbODVNdbgGiF+WrWiC19/vFe6XyvFCMSpK8OwoiuDA+PT2DF6FgAwfXA33h/dW/s3fXA3esi6BkD1bzD8+kyrTyPxBDVhJtShCCqhyKIUe29PsWQ23MmpNvzK+q5W6hkYutbwWJlzDL82A11jKJnLc2cZqm4KPUtzqEQkYu37OnGpUItg+g6/FThaCbIGtVhZdnqwjgKx++cl0JWpZfgt6e9U2n1MS6uhCCpmVO2PhvdsbIhI9AxzjELsd3JuDb9WZF+u4ryJF5/a4tiEaFY45s36oejiUnZn3sTcgrMnnfX4br2N3Zr8wZyhe5bNq1Ayy3j5wvWGG4AUL4kQLSKJlaXtBAlUjDjNV3L1xbNfqxmkVX1WsZGtD6n2XYnfBykocLvzFpN/3SoTFyTP3/HIGqxa0YWXL1xv2eRb6nkirDhV4hLhQgIVExNTBTx/fEYpsgGqUZD9Yu928ReiMjFVaNA1gVhDEsgGIO7ctFapgtAvqw090NrGqm4NP7l+t+W+Z7qW8YzeKEvYOahMGiCagwQqBkTkJItInFJtfnLb1js5N/+7Muc4MD6NFyaW16NefGqLrTiA45WL0UQpZrkSaG1jbqHcsqjJyt2SPPUpoCxhZyBsvYhoIYGKAa+ScadUm2pu2z4zykvYOKo9T9ZI6p5lTalkViLxsFvVraXedSHDGA6MT+NjK7sarJ6IzsJrBhsRDiRQMeAmGrI8tsosJgbg/Miuuju51Qql3BzA//CX1SjKjyt6M5fkf/HbW5p4drxoknK+MufgqFYpmmVO6bwO5tyVW60+hY6AysxjQFYyLgb7WcvDrQ2kq7o16cgIoHpHv2HkdM0VAoC0is7O3EIZL0xc9pVKbCawGuzPNzTHJpVypVoyn+3uqr4/kr8BpfM6FyovjwcSqIiZmCo4jgO3G7tOTBUw/NpMncfd3EIZGQZkMszRFkasaRWKJQy/PoPFCveVnnv14g2sjsFBQQQkh57cjD8Yn0bFffNEcGfeRLa7C0eH+mhuFNEAlZer48cc1k7Hp/iiHMsuiiOcBGClXv/WOxmwAtXenI+t6KorZHBKLZllf+IEVAVONeJywyvVJV7WYH8eq5twa4g7pWZtcCYIgTBNJqJHSaAYY19kjF1ljL3LGBtxeHw1Y+wUY2yGMTbLGPtH4Z9q+PjuS/KJ2/rOnXmz7lhuKYNiyURx3kQ+Z+DYUF8o5yZwqqpj8CcG1kGGXni5s8swdA1dirdThp5BVg/n3isJ1YNEshj69fVUwRcTnt9ixpgG4E8BfAnAZwE8wxj7rG2zfwbgbzjnWwH8JoDvMsa6Qz7X0FF1XAiK6lRdwDtlYBVQlUIIgaFr2PHIGuXtxbGODvX5Gmd9s1iSeu2J37v1aLkhKhVNj9xgVs8gnzNwz6ygZ9UKPLe9l/z1iNChAon4ULnN/DyAdznnP+OcLwD4IYCv2LbhAD7GGGMAHgBwG0DzuaOIkQlIWAugfqbqOlkbOVEyy2AMSnY/ogjjld/7DTy3vbcmOBpjeG57r2vUM3bmqu9Bhl/e+inHx8Tv3Xq07GT1DI4N9dUiRq8RHxkGzJuVumj4lQvXA0dsBCGjsOSIQkSPikDlAdyw/Pzh0u+s/GsAjwK4CeAygP+ec574tXAvq59mUSkVtx7rgZVqNSvCK0+MRe/J6g3iZugavvu1rbVUxJHBLXjvxd/CsaE+/OrqlXjlwnXH4g1BoVhSTtuJUvnT73zk+Lj4vR/hv7dY/fhYU7BuOPnoUZUdERVhLgUQclSuiE639fbv/h4A0wB2AXgEwP/OGPv3nPO/q9sRY98A8A0A6O0NXtnhF9mwQKcR60H9tdwGEsrGrQPVhj+7+7g4j5V6xjECWLfUxW7Ng6sMRLQfx616jwFSAcsAWJ3VUZw3644lq3YTr8HPHKkKB1XPEYlFpOejXIuyXi8/8auduealIlAfAlhv+fnTqEZKVv4RgFHOOQfwLmPsGoBNAP7auhHn/CUALwHAwMBALDe4KqMnVCbdBj0GAPyK0SVNNZ24VMCbMx85roWt6GoceyETUJWBiH6ackVDqhMVANnuLkx9e7fSvgQ7N61VHi+vAo1/J1pJ1L1Q1uvlw48+1pEfdRWBehvAZxhjGwAUAPwOgK/btrkO4L8C8O8ZY/8AwEYAPwvzRIPiVgghLurN3gXJjnFgfBpdGnP1nyuZcp+5uyUTR4f6AgmoU0QV5hfKaV+yqbQ5Q8fEVAEnLhVCFZSO/MY6oGeYY4sCES3UCxU9ngLFOV9kjP0+gDMANAB/zjmfZYx9c+nx7wH45wC+zxi7jOqN7R9yzn8R4XkrE3UhhNu+OJob/OaUylNBFtGF2ZTr9OU89OTmhmZjPcPw5a2fkqY5vcbME+7kcwbmFxapGKQFUC9U9CitynPOfwTgR7bffc/y/zcB+Mv3xIRs3SPMux8/aytO9GR13DMrdZEUQ3BDSrdJuWHgtk63akVXTQR7sjr2PvYpnLhUkIoQiVNw9AzDzk1r8fKF660+lY4jZ+jUCxUDbe8kIZt5FObdj0q1ngxD13Dwic3Yty1fV43CUV2fClIpJIvo7sybrhNrVXESOifXjOK82dIBg+2OWeEkTi3A0DUcenJzq0+jI2h7gRIzj0RJtn08RZjH8NPYCtu5nLtyq2FNJWjTsFt0KJtYa8ftg2F3wZANY6TYiGhHaFBhfHSEWWwYhRAqxwDQUC7uhN0oFgh3rcypfN6OWwWcsAmad7FusIrn8OvyMvqk8Nz2Xvzg4nXHfimC8MP+8Wk8f3wGzzy+HkcG0zNGplX84GJjlK9qINsRAmVHpWcoCPay9VxWxy/vLdYVDTAAn+tdjbEzV3FgfLp2fNk61mpDx47Rs7X9cV6t7nM7b/E7tz4ijqpnHcDqhEzPMNxbrChdyAvFEv7g+HQqLvphlrfL0DNAl6ZRSrMDKPPl9CqJVHR0nECp9EWp7sdJ5KzR2o7Rsw3VVRzAj9+7XbtYiuN/rnc1btocE/QMw9zCYm1dx7ove6+V/VxUKJkVPLe9F+eu3Ko9129FWBrECYgn3bhYAcae3oKxM1ebKpoh0sOrF2+QQEVIxwmUV1+UCqoi51Z+bj++VbSAaqTV3ZVxHZNeMsv41hvvwBoFiXNRrdg7d+UWzo/sqgluVOXKDMCz23ubXtTP5wzcnruPkpdzbAvgqHoGpkSziRBIemo77bR9kYSdMNZ6VF3Q/ZSy2z/mHHAVp+XjVhzPRVVohPGl8LyLAgbg1z65Cq80IU5ahiFn6LhZLGFlwIrJOKDLVWfhtzCK8EfHCVQYBrGqIudUfp7Ej7NTBV5YMFaNnN79+Vzgi7fGqh/UYskER/CZUgQRNs88vt57IyIwHSdQYfRFqYqcU4n7F3zMZsoZemBBk81mciLKNAXnwMtNFihUOMjKJ2SSeKOUNnY8sobWnyKm4wQqjL4oPyI32J/H+ZFduDa6F+dHduH9v1VLo+kaw6EnN+PZ7b2+LyaikfC57fE5xkcJSVP4cPi7iSEaeeX3fqPVp9D2dFyRBNB8X1QzLujKa11LV+Ujg1sw8OAaHD41q5TaYgD2bVuuJhx4cA3+6I13XHuaiM4kLF/GTkR1VhrRHB0pUEEJo39K1bfPrHDsH5/G2JmrGN6zEdlu+cgOKxz1I6mFUE1MFXDo5GyiLkpahqFs6xFLWrTUszT3KmnnRbSW+YVFTEwVyFEiYjpWoPyKjVdpuerAwPkF+RRbJ8Rx/BQxOEVp4lySUgadYagTJyB54gQAv7y3mMjzIlqLsPsC/PVPEv7oSIEK0qzrVVrutT+nqbnA8jqAW2RTMsu+xlLIijjGzlxNzMU2LTUPVJxByIhjqm6n07ZFEhNTBewYPYsNI6exY/RsnSu4ah+TFbfScq/9ycxUgep4ikNPbvZ0Qy9z3rCNrjHomfoSCreKxKgngBJEp0HfqWhpS4GyNp5yLEc0QqSCNOu6lZa77U+ciyz6uVks1VUWyhDVhtbqw7GvbsXY01trv8sZOlbqGRwYn24Q5YmpAjLUVEgQoUJTdaOlLVN8XnZGQYYYOjmEi2hF5r22Lmc4not9G+v6Vc7QMbewWDeJVxxHVn0o1sBkaUYAriKZZnY8sgZ/fe0OpeKI2Al7rlw7oupaLqMtIyivCClIs65b/5TMMWLnprWuUZmha3jo4wYOjE/Xor1iyQR4tXrMT5+WmyjLRFJjDDt8NA7LXsNz23tbVnZ7/r3bGPr8eurpIWIjqrlyRCNtGUF5RUhB+5jcIpjJD27XjXQQE3FzWd2xPFxjDPu25R3HQJgVjmx3F6a+vRvA8npaoViqFUvkbeccJG1Z4Vy5cdiJfM7Azk1rceJSoaUjJt6c+QjTB3fXfhbvlR8YgGy3puR/SLQnOUPHl7d+Cqff+Uja0tGT1WvfSyJ62lKg3NJxgrCHGMom4pbMckN/j64xrOrucnX2FsJiT92JNJ29UtBLlGWPBV3kzecMnB/ZhR2jZ1s+/8heAakysNGOqjkv0b4USyZevnAdboMAiiUTG0ZOhzpHjpDTlim+OMa823G70HMse5/1ZHWAe3fxC2FxW8Oqm2rrkrZ0egyoNhuuDpgaE2KflComa7Wm098/LtunfM7AsaG+plOnROtwM13hHI6FV0Q0tGUEBcQz5t2Kl0MEx7I9ioojRKFYUkpViUpBIWSyFCCABsujO/NmrVTdb5GBEEZVZ4yoEReN4ddnADT+/V+YuCx5ZjjkDB2HntyMwf48Xpi4jPPv3Y70eO1AkM9dkqA+qOhpywgqLNx6qezIohQrN4slXxFHoVjyNIpdbeh1s5zKnIMtPXfszNW6c3Ya8meWOR5Y2eW7yEHcQe7ctNbX86LGLFctoqx/r4mpQtODEr0olszaHZ53vowAACAASURBVHUzc686Cas45Qwdq7qTO+dLRlIyCO1K20ZQzRLEbWKlnvEsKZ+7v+jLD0+kB53uMw1dA2NoOKZ9nDzg7iJRnDcx9e3dUrcLGSWzjHNXbsHQM4mbcGt/7XEg7qjTGxO0jiR5RPqB+qCihSIoCX7cJsSF3St1t3PTWgTplbWmB63PX6lnPI8pztkr/bhj9CwmP7itPCpeUCiWcC9h4iRQee1hk4R0J+FNV6b5pnXqg4qejhQoldSdn7Jtr2Zcwbkrt1B0EZSerHPBgqiYOzbUh5Vdy2mQO/Om0qyom0vl6W4UiiW8fOG672m1DAhcaBEHKmlSovNYDLj2FWfhFdGBAuVlgyTwMxpeNQ8teq6cyOcMHHyi0ZPPepfmJITWCkEZ63JGZC4SHNWozu4JmCQo5Ub4weujfHSoD+dHdpE4xUDHCZRq6s6P24RqBMEBzN1fhK7JDV5XdC3/SXqyet1dmkwI3aaj6hmG4T0bpdFZGNyZN1NdjUV0Diq3UW4f5UKxhP3j0+j/zltUYh4DHVckoZq683KbEKXdftcciiUTeobVBuGtNnQwBuwfn27Y9pf36mdHyUq6xfqU00LzAyurf+K7KV2EJogwCes2iuZBxUPHCZQfo1hZL5VKtVtWz6Bn1QrHYwkro4NPbHbdj1nhOHRytnYOMoeE+YVF6drRnXkTzx+fSc38JYJIC9QH5c0PLspbLlSMZDsuxRfEKNaOSlFEyazg/MguaUpBNkfKjjUqEg4J9nSeV2FDWlzMGYDntvfiH3ysO9Dzsz4rENudnqyOnLFsOmxNHxPhQH1Q0dJxEZQwdn314g2UOa+Ztvq5C1L5UIqIzC1iU/1wb/72X2F+oQyOqsms31LwJCN6vITx7Lkrt/D//f1CoH3Nh1DunmHpmfbrxZ15E4au4dntvXhz5iPcX0xmO0CaoT6oaGmfK50iE1MFnLhUqEUVZc5x4lLB14Kn14fSGpHJIjY/PVFzS+IkzredTE05qoUcwhW91X1E7SJOgpJZxssXrqe2ETbJUB9U9HScQAUZ925HNv8JqKZVVnQtT7UF0GBc+rne1Xj5wvW2uxgGxaxwvHzhestd0Ynm6ISBzeIlUh9UPHScQAWZm2THyS376FAfjg314Z5ZQbFk1vVYAcD5kV24NroXw3s24scRGIl2wLWBSDAMwOqVyW3YJtJJx61BeVXxWcevy0rLZUMOnWYj2St9wvRqyy+9FrtXn3Vdp9UpM6IzqE2DbnOcfC4pioqOjoughvdsbGiU1bVqM6uby4SKA4VKdBZW1U9Wz+D8yC7kDL1B8IQ4nR/Z1bJR7ATR7vhdGiD803ECBaCxW2/pZ7f1KZW1KxV7pLCqfv74qccwMVWQ3rUKIVQZAxI1lH4k2hUqM4+WjhOosTNXG2x5zAqvpe6ccJvjZE2h7dy01vFiPHd/sRZpNTs/KWfoODbUh8H+vOvdmxBC63pZnGQY6tbn4hQpQ8/g2FCfp0GunQTbCRIJhcrMo6Xj1qDcRMhrfUq2ntP/nbdqzuJO60timB1QdTT3CwPw7PZeHBnc0nDOMqzlr8IR46GR076PHRTOq6aaY2eu4sD4NDJLk37joGRW8EdvvOP7eFqGYWWGhdJPRbQ/DKAy84jpuAjKLQ3n5jIxvGejNAoQTg5ul8OSWcahk7OBihY44NirJXstPVm9buFWjBeJk2y3VrdmF7ebRRCRMcsc9xep9p9Qg4MKJKKm4wTKTYScysdFr8Ngf77p6rtmqpycFmRl6cK9j32q9v/W4o44mVsop7KvKS22UEQ8aEvGzk5QAVL0dFyKz8ulXGYQC7S+bLtQLGHDyOnaOf/lT5zdL6xpRNVhigRBNPIrK7uw97FP4cSlQt33iFwkgqNiEivoOIEC3EXIDZmbeJyIEvfnX5tBWWJFEUVZO9FIO/n2Ec7cmTcx/vYNDP36epy7ckvaA0lEQ0cKlBWv5lsr9uhrtaFjbmERZnn5KiUrlAgbmTgBQIaxWqS12tA7ooGyFZA4dQZmmeP0Ox9h6tu7W30qHUdHCpR12KBVUKzd4YBzGtAefTkJHAA8f3ym6fWMoHfo4riFYgm6xqBnGE28JYgm8BppQ0QD4y1aFB4YGOCTk5OxH1dl2GBPVsc9s9KwTU9Wx8EnNruG9ir790M+Z7gOJFShJ6uD82Ra0WiMocJ5LFEnQTSD6D8MEeXOu4cffYwf+f6bYR67ZUjWoBzfi46LoFSKBtym0zr5b1mjKFm/T9DUX6FYgp5h0DVWl0rUMsw1zWelOG/i2uheTEwVHEfLN0vQ12boGl58qtrbFcV5EY10L32O6IbAPzQ9N346rsy82aIBe7m33aNPltZr5oJgVjgWyxw92eXpqN99eqvy8zOM4aGR03j++EwTZyEnyGuzlvCTn1l8/E9f3Ypro3tbfRqphIyX46fjIiiZW4SVnEdhwc1iCRNTBRw6ORta2swrCuEA7pkVHB3qAwBfF3XrcMYkICyFDoxP19YCiXiwrrES/mCoTiygSr74UIqgGGNfZIxdZYy9yxgbkWzzm4yxacbYLGPs/wz3NMPDyzy1J6vj0JObXbfJZXUMvzYT6pqOcCB3Q7hReDXesqV/fr3o4qLCUecKn8yzbE/a1YFbpMH94ucZ4vMqm2ZAhI+nQDHGNAB/CuBLAD4L4BnG2Gdt2+QA/BsAT3LONwN4OoJzDQXhFpEznLvDRZAh28bQNXCO0KvixHiM57a7N7EVS6bnGhoHcG10LyoJiZi8SMdZtg/tGLEOfX49VnX7SwgJj8ugjhDtKvZJQiWC+jyAdznnP+OcLwD4IYCv2Lb5OoA3OOfXAYBz/vNwT7M5hBfdhpHTNU+66YO7cWyor8HGxGrseujJzQ4ixSOphpu7v4gNI6fx6sUbTe+LofqayWmZ6BROXJKPnpEhDJibGUlDjfDRonLLkQdgvWp+COBx2zb/EIDOGPt3AD4G4E84539h3xFj7BsAvgEAvb3qdhfNYC/7tk/CHDtztaFqr2SWcfjUrGOpeSkip2vx5QpjnYiDquKIziJIW8eJSwUMPLimrgHfb3QZ5U2g9Xr5iV/tzLUulQjKKU1rv4p2AdgGYC+APQD+R8bYP2x4Eucvcc4HOOcDa9c2NxdJFa9Bg7I7oDvz3qk0FaJYX6E1G4JoHut1YLA/j/Mju3BsqE85mop63Ib1evmx3JrIjpNkVCKoDwGst/z8aQA3Hbb5Bed8DsAcY+z/ArAVwH8M5SybwGsMu0pVXzNwVIsVnCIj2e9V9pnPGa59VwTR7oRhKyauA9ZexlxWx4quDO6WTNfvF43b8Icfk1iBSgT1NoDPMMY2MMa6AfwOgJO2bf5XAP8FY6yLMZZFNQX4H3yfTQR4jWGXjd+QFVE44RXROH3AdY3hYyubq/I/OtSH735NvR+KIPwQoCguNp7b3htKcQ0H8NDIaRwYn65V6N2ZN3F/sYJnt/e63vzRuI3o8bxCcs4XGWO/D+AMAA3An3POZxlj31x6/Huc8//AGPsrAO8AqAD4M875/xvliavi5EButcqXjd8AoGRZFPQurlxurtiiUCzhwPg0fu2TqwLvgyDcKCc0MNcYww8uXg91n/aXWjLLeOWC/Bg0TTcelG7hOec/AvAj2+++Z/t5DMBYeKcWDl7zn8Q2slDdrRm3mflQYZRacAA//flcCHsiiNbD2HKbhxtxpbRlRxHl6ZTei56OcJIIOv9JPOfwqdlapV/OqDbyisd2jJ6NvK+kJ6ujOG9SvxCRaPQMkMlkcH8x2O1XWpZSj4ZvGktI6DgvPj9MTBUw/PpMXRn63MJi3TbN9FDYyRm6dF+rfayJEUQrMCtQFqcVXRkYevouP/mcQeIUI+n7hMTI4VOzdQ7iQHV42YHj03VNvy8+tQX5nFG1GGpiYdksV7BvW76hQOPOvNkgjK0miK0MQQjuL1Yi6ykMC/snnMa8x09HpPickE3Stf5elnEQqQjR9PviU1twfmRXbb9B50HNLZTx8oXrjlWBZpljVbeG+YVyMlJ9iTiJ1lCNcnniL7CdjJgzFrQNw9A17NuWpzHvLaYjBUrmLjH5wW2cuFTwJS4ls4z949PYPz5d62vqsfRRBBm5Lvs6zS+UcXSoLxEO4GaFB+7j8ktPVk/MRFMxtPLwqVkSqIQi5owN9uexYeR0oH2I5xOtpS1TfHbvPavj8MRUAc8fn3F0l3j14o2m3CPExVr0URwd6sOqFeHeAxw+NZsY/6+oxUnXWHX0SULECaj+bSc/uJ2ocyLqsYpLECsiWmdKDm0XQbl57wHV3ibZhTXMC66wUQlTTEQTYSewqlvDwmIlkWPqX75wHYaeoQgqgdjT48N7NvrypaR1pmTRdhGUm/ee17j3sOcnFZZy1+1I1CUScwvl0EeahEmniVN3SopiOFA3p0klEhKvzDrlmUgGbSdQbt57btGMoWt45vH1DWXezXwtGYCdm+IxxY2TfM7o5BqJjmQhqbYSDtjnNHnZlglvy/MjuxzFyW3JgIiWthEo8SGSfY3W5QzXaGbftjyODG6pKxnP5ww86zFA0A0O4NyVW6ns95AhvsjpuJ8mkkgcnx3rzeihJzdDz7gftVAsOQqPWDKgSbqtoS3WoLxKu615Zdl2wnfryGBjiH/6nY8Cr/0UiiX0ZPW2SQmJ6sH03E8TSUI4sbhZiIWBtbFdfJ+9jjn82kzd9oD7kgGlAv0h/BP9uJq3xa2929qSNa8sxr07rTVxVEXK6c7o4BObPd0i3O7P2qmwQUzrJYggFEtmrWjBI6hpirv3zIaUnJfLhVnh2D8+Xfccr3E9RLS0hUDJPiwMaMgrD/bnUXGZ72LNXVufs29b3lWEOiWiENN6Q64nSQxeqaB2IAmvUEQyURVfcI66lNyhk7PKLSTWNJ7MYqxdi5+SRlsIlOzDstrQHRc33T5cslz0uSu3OkaEVEiLsadfklw5GAaGruHZ7b2J+OJXeDzFFyWz7DudWDLLOHxq1tFiTM8wKkWPiSR8TpvGybBVzzDMLSw6Lm4O79noehc5/PoM+g6/VSdsrXZuIIigMFaNmnKGjgyr9nGlYUX0ue29LY1o78ybDV6cAPDAyi5af4qJthAosbZkrb57YGVXw4fLurj57PZeqUiZS8MEhbAdGJ9ORFrEjaSfH9EcGQRfs+G8OiJibmERcwvBnVLiJJ8zcGRwC8ae3oqebPNO/j1Z+aQAv5CLSHy0hUABVZE6P7IL10b34vzILumHSKxXHRncgqNDfUr75kj+GlMSzi9n6A0u5ySc4cAYQzPZRydnfv/nUHX4iBrrtNrB/jyy3c0VGxu6hoNPbK67ifUSPUPXpP1TtP4UH20jUHZkHyLr7wf786HcnRHVL/z0wd0Y+vX1daKUBOFslvdH97b8c9KsDVcYlaScA/ea8KpUwT6tttn0ur2KV9zETn17t+vN04tPbcGhJxurd8kKKV7aog9KYB2VsXrpbt561+j04QprsT8uZ++k8st7i3hh4jJevXijLUTJyo7Rs23VKtAMUdc0cFTXyE6/8xH2PvYpnLjk3dKgZ6qLbE4RokjRT35wG0cGt9R+PzFVkI7isJvFOo3lIeKhbQTK3qxbLJnQMwyrurVa3r1klnHo5CyA5Wa8uyE0CzIA2x/uwfn3bje9r6DHb7UomBWOl5eanZOA9e/eLFQgEz935k2lz5No/AUgHUMjRA+opvbFtcJJnOw3sSLyIlpD2wiUU7OuWeEwbRepYsms6xhflzOavgBxoKXi9IVH1rTs+EmllJJiAKI5GFu+2Rzsz2PH6Fnp9/nlC9dx7sotzN1fdOyJYozmQCWNtlmD8tPZbVZ4rSHXqUQ9TXAAF67dafVpJI40lFETzWNPvXpdBwrFkrQninM0OEkQraVtIii/kZD4IIu7JZEeSEK6zC/lNm8uJQhVwsiIFIolDL8+g0MnZ3G3ZNLaUwthvEUL+wMDA3xycjK0/TkZxnqJTd7hgzcxVfA14IwgiNaSM/SakOzctBY/uHi9qZJ8J6xj5ENEuQvj4Ucf40e+/2aYx245NtNYx/eibVJ8Ts26z27vbejLsVIoljD82gz6v7PsGjH5wW3q3SGIGMig6hbRbAm/tal+/O0boYsT0DhjioiHtknxAc4VNwMPrsHhU7PSMmGzwmuPFYolvHLheupSfER6yYeQkmoVGYbAYiCq7wb7q3PYXpi4HEoVaLPNyG6Qg3n8tE0EJWOwP680LkMQhzjlDB156kbveMTwx2OKjiZJI6g45XNGTZyAalrdrd+pJ5uM7ws5SMRP2wsU4D4vKm4YgC9v/RTOj+xquTsB0VoKxRIeGjmN54/PtPpUYqVQLGH/+DT6v/NWrbnebdjowSc24/zILrw/utdzfHsYrOrWGkxqGYCdm9ZGfmyino4QqChSKFk9E2gmEgcw/vYNTEwVIreNcUNrkUu03hGfOH90qgPJnXmzNk5dhr0wIY45ZLlsN4Y+32jZdeJSgcrPY6btLxcTU4VIih7mzQpWdmk4NtTnOxIyyxx/9MY7LR0DH9WgOC8++SsG3h/di2NDfbHcDRPJpmSWpaLTk9Ub1pTjcBK/WSw5zn+jQon4aasiCSfGzlyNbF2pZJZxYHw60P7nQxSnIL1bJbPS1CJ3UKx3y6tWdPkeJEe0H7IA8r5ZxsRUAYdOztY+J3HcVq3LGTTqPSG0vUBF/YFKQnKmK8PQ3ZXx7T3Xqv7eh0ZOp7IhmoiXebOC4ddm6qYcO31m7KbQzWDoGnZuWotXL95wTL1SoUS8tH2KrxM+UGaF455ZAUN65i+1uzi1cBBsW2Eq3EWt6u5CNuDipq4x5Ay91ju5b1seJy4VlIxkiehpe4Ea3rPRtVm3XShznorBih0D/SFi427JxB8/9Zjvm4J8zsDYV7di+uDu2qDTc1duOVYUaoyRkWwLaMsUn3UuVC6roxz1EBuCsEFmtfEhsiSrDd11bhdb2tbNV0+2JFDhnMSpBbSdQNk9+ZI2aI6x8IYkEkSnI/qThl+f8VyHuja613N/MrPZTlgqSCJtJ1BJasp1gooDCCI8VuoZZYukzd/+K8wvlF2jqOE9Gx1Np6lJNxxsBrGetN0aVNLLQGkyBtFqvGy/klrgkTN09GSrBQ09WR16hvnqJZxbKNdMZb/1xmXHptvB/jz2bctTk25CaDuBolC8dWiMtawBmFDn3mLZ1dEj6psoUTW3osvf5adYMnHPrODoUB+y3V1KFX4ySmZZOpyQmnSTQ9sJVNon5KYZLQMsUEFK4uEcMCvAZz65qiXR0vTB3Tg61IeFRf+lJEIowsqUOEVT1KSbHNpOoKxzoYh4IXFKFz/9+VzLUs7NOLzcLJZCzZTYoynZvik7Ez+pLpKwlpOLaZrnrtwK/QNMEES4NBONiCIHezFDs4hoSjTrWvdNTbqtIbURlCgnLxRLtYXPly9cr/vZjThckYn00+kfkyhGwuwYPRs4ehJCITIlmo8vssqWJbOMc1du4cWnttSZGa8kG/6WkNp3vdlycupFIgh3erI6st1dNRugHY+s8SUIMoKMvxHnYHVzGOzPo6L4RTZ0DUeH+nBsqM/TWUZEd/cta2RiNAhV8sVLalN8aViw1Bhrm1k/OUPvSOfx9vjr+SfDqhdl0eheKJZaNppeTB52QtZYayXD6udKWd3RZft0ugEWBRrkKBEfqY2gVNeYxHh1cQcWJ+0iTgA6Upw6DWE2nDP0RPXruTXJqlTt2qO+uy6fZZFClIleGm6M24nUCpRqOTlj1W2FGSRV9xGEHBU7oLh5c+Yj7Bg9iw0jpxv6lqxVuwzOa8tmhdf1MMlubhmqa037x6el50LFV/GS2hSfCLOtprB3S2bDnZ/IHYvn7Ny0VtkahSDSRGbJRyuoUe26nIGJqULiouViyaydU6FYwoHxaewfn0beYlkkrgcbRk477qNQLGHDyOlata+9Sk/PMIC5e3cygCr5Yia1ERRQFZzzI7twbXQvst1d0rREySzj+eMz2DByGq9evBHvSRJETFQ4oC3NN/KLSG0dPjUbwZkts+ORNU3vQ3zNnZps3SIcUd174lIB+7bl61L/D6zs8jSb5QCtP8WMkkAxxr7IGLvKGHuXMTbist2vM8bKjLGvhneKanjlhsW8pHZaFyIIO2aZ+46ArNVxUbv/X/jZnVD3Z7cgUkn9l8wyXr14o9YvObxnI4oKr5uWB5rnBxf9Za88BYoxpgH4UwBfAvBZAM8wxj4r2e5fAjjj6wxCgnLDBBGMhz5erVqTpcfCJIobROvNqX1Nyu08rMaxOY9+L2rUbQ0qEdTnAbzLOf8Z53wBwA8BfMVhu/8OwAkAPw/x/JQhDz6CCMb5927XGtzTiP3m1Jr6V4l6SmYZnDe6vAuBs/dfEfGhIlB5ANaFmw+XfleDMZYH8NsAvue2I8bYNxhjk4yxyVu3bvk9V1fEnZO9873TnQAIot1xi2xUb1zvlsy6yCufM3B0qA/vL1X/tkKcrNfLvy/ejv34SUClis/pGm+/2ToG4A8552Xm0mnOOX8JwEsAMDAwEMkN2z3bfBiOqgrTCG6CaE/cxMNe7ZuRNM+vyxl11YBJwHq9fPjRx9Ia4DaFikB9CGC95edPA7hp22YAwA+XxOkTAH6LMbbIOZ8I5SwVkdkfVQBk9QzmfQw3iwI9w6BrrOXnQRBRwVi8NmIq1ktW4REenmQEmw5UUnxvA/gMY2wDY6wbwO8AOGndgHO+gXP+EOf8IQCvA/incYsT4F7J52fyZmRQvrEtSHVvhoUwfPWsGLoWqMS9Gcqc+/LHsxdR0PpSsvGMoDjni4yx30e1Ok8D8Oec81nG2DeXHnddd4qT1S5+cUmIj80y9+y1IJLNsaE+AN5+bknHj09kT1YH59V1mtWGDsaA4ryJnOX3olz7gIsLQzMs9SA7MvzaTO3/reN3RBOvHZVUnn2Uj2xfRLQoOUlwzn8E4Ee23zkKE+f8d5s/Lf9MTBUwt7DYikMTHQAD8Oz23jon7YmpQmqFyk+5N+fLFkKrVnTV0mHiAr7a0DG/sIgD49PSNZ4gaIyhwrnU/UFgVjj+6I13wMFqj4vyccB5jcpJgMRrKhRLdYLotS8iOhhvUePqwMAAn5ycDG1/O0bPRu62rGcYzCS5aBKxIC5WuaULcRonB4tkXpgCEiWGrjWk3iamCq4+eU70ZHVMfXt33T6cbip0jQEcrt9vN1f1gCjnWB9+9DF+5PtvhnnslvH1x3udfu34XqTWi8/KxFQhcnHSGMPY01trd1jEMu00VsQJ8crSGCkJxGuI6+8kop9cVsd9s+y7MGjftnwtSrX6bfrlzryJialCbV+yKbwqqXdyMo+f1AuU+NBFTZlzHBifDvQlaXfKnCPDkKgRDURrKXOOfM4IfFE/calQ+68QlKA2TGKGU7NDTsmtJn5SL1DNfuj8wBH8S9LukDgRdprJNAi/vDAiPiGSzURAVIreGlIvUG4fuue29+LclVuuDXpEOsnnDDz0cQPn3+vMDvtmyStMom01YX1fReTjNn3XaQ1KrD3mqYqvaSTrTp6kXqBkH7p8zsCRwS21nx+KwQiTiI9CsYT/9Hf3oGeAJLS4pY3zI7vwwsTlRM9GC2Nt0xr5DO/Z6LgG1ZPVcfCJzQDUytSJ+Ei9QMkGENrHRLf7Qn4nUq5wxJPcbU/EDdwPLl5vSNHqGsPYV7disD8fS4WsHQbgmcfXS0vLVcgZOg49ubmuNQBwFyESpGSReoE6/c5Hjr8/d6VqRiuqgEicCKKKcHuYmCrg3JVbjuuHZpnXhhfKIo+oED1nRwa3YODBNYEqZ3NGdcK2mBVlFSl76fqO0bMUNSWUVLu2TEwVpEULN4slTEwVMPz6TOJz7QQRJ3dLJl6YuIxvvXHZ9btxZ96sVcgKeyCgsWHF0DU8tz3YGkM+Z+C57b0NLuIiuhOjM/wMC2SotgRY5z052SGJCmAxasRtW6I1pFqgrJM07eSyOg6fmiVrIYKwwQG8fOG6UkQkJtYKoXh/dC+ODvXVBCVn6FipZ/BKgLUshupa2MCD3mPgncZm6BqDnmns77R/4+1TdwVOFcCybYnWkGqBcqvg++W9xUAl4eKOTtfI2ZWIjyR/Ee3fs8H+PIb3bEQuW/W+vDNvBvK6XJczlKOYwf489m3L1wxuNcYw9OvrMfb01jqxlFEolrBh5DR2jJ6t7Vt2/aCG3OSQ6jUot7LRIJZEVisTv7lvNzNLgnAjA+BfDfXhtcnriSybtzeoujky+GF+YRGHT826RjFWv7+5hcXaWnKZc5y4VMDAg2tq39kdo2dd3T6sAihel9P3mxpyk0OSb9w8CXvMe6FYwo7Rs9gwchpjZ65ieM9G7HjEO/0AkDgRwVmd1THYn8crv/cbeG57b+hjMJqBoXFibVjN8XfmTWmWQwiJiKyKJbMhXW9Px6lGPuJ5TtcPashNFqk3i52YKuD54zORVOnpGqM1LCIW8h6O3a3iM59chV/8cqEmJDmXkTZh4qcthKEa9czdX1Q+Nwbg2ujeVo/V6BizWIVG3fY0ixUfpuHXZ0IXExInIi4KxRJeuXA9cZH4T38+V/dzHOLk98ZQpO5E0YSTG4QdkcZL2ph3op5Up/gEg/35eOdME0QE0Ce4ymKZB5rMa5Y5HljZVVey/uz2XkrjpZjUR1BANc3XCXY3WoahTK6syuQMHatWdFEfXMoQa04ZANavtf1nJ4rzZt38J2C54Mk+nJAadJNPWwhUp/QtfGxFV6pnEsVNu79XYt1q/K9vpGqQpnB58DJwrli2XZczML/g3TriVIHn5B5hrUKkibnJpS1SfJ3St3C3zS+4UdCuIiWaXN+c+ahpcQqzZjBn6NIeQobqhIHpg7txbXQvvvu1rZ5VuKtWdOHa6F6cH9mFooc4qabuqEE3XoI6mQNtEkGtjqmyqJWQ2W1y6cnquGdWxpY35gAAIABJREFUYq2+E02uYXzun7WMpVlt6Lh7z3Rd0jX0DEqSnPrdkomjQ321HkLxuXUaWSH+360K13rz6db36DYSw16pJ9tHp9zopolUC9TEVAGHT822vTgB8Y3qJvxTnK9elN0utCrrJ6pkWNWt32uSdM7QsbDoPm49g+oajXU0jVcjbsmsSKvjMks9XKJ51gm7YDzz+HppBaM1ZedkWmvoGl58aos0NeeUzvOq7COSQ2oFqpludo0xVDgHozHlREjsH592fTzMGp4KB05c+lAaxQisoyYAoO/wWw03cxUsj0QX2MdSOK0VcTiXcJc5d13PcRKME5cK+MIja/Dj927X7c+eslMZl2HHKZ3ndO5U2ZdMUitQQbvZMwA4ODioMr0dybTgpqMVHyMvcQKAA+PT2D8+XUt/ydYw7amtiakCDp1czkzIokIO59Sz1WDWjmz95/2/LdVSg3bxaaaZVpa2E5NyqYov2aRWoIKWDlcA31eUnqweyHiWiB+66VhGvBWiSk22VmtNbU1MFTD82oxS4YW4wDsR5PdOTbPNVty5Tdx2S0MSySC1AhVn0cC9TmiyahM6RZ8yDFjRpSlnEUpmGSv1DAxda1jDsaa2xs5cVa4KfOjjcnshp/WciamCtLTcyZBWZtZsjdC8oivZupVTOq/FtkeEA6kVqDiLBpLkjUYQwHLp7ss+5jCJYg6nptX+77zlO0tw/r3bcBjHBD3DGgRAREJO31tdq99eZX1ZDCT1iq6c1q12blqLsTNXcWB8uu49oN6o5JFagcq7lIsSRNJgzD39mM8ZuD13X2ltSTQvnrjkb/Lrupzh2LTajI+lU7C16PBCXdeMLZurmj+vyxmu/Uz2og/xs0zUVnRllPZFxEtqG3WH92wMtcGQIKIiq2dw9Gt90sc1xnB+ZFetRNuLCoBXL97wFdnL0lpjZ66GborMORqGDrr1GJkVjrEzV12jLCvitQQZOCgTNVmrCvVGtZbUCtRgfx5fUJzVRBCtZN6s4LVJeSquzDkmpgqYW1AXHD8p7nzOkPYKRXUBtjszePUY3SyWlCpzNcZq+14tMZR1O5bf10u9Ua0ltSk+AJi9+fetPgWCUMJtUm4+Z+DwqdlIjmutVnMrPAiKm4GxVQycihWsrHOpCASq61pgyyNwZOM1vPqZZFV9Tm4g1BvVelIbQQHt67NGdBbDezZG0sZgvcCK9JkfcVrRJb88aIzhue29+O7TW6UTgK3Rx2B/Hi8+tcVxjIY4T1m0ojGGB1Z2NaQizTJHmVdHc4jxGm6uEoDzFG5D13Dwic148aktdaM6vPZFRE+qIyiiNcisYohgDPbnPZ0oVBEuKfYy6cOnZn1Xo2oMjmXpThdulVJuUazgVs4tszI6IHl/Khy4v1jB0aE+JTHxcqMgQQqfH1xcTm/7NY5NtUBRA21rIHEKD4ZqdBPWKPWPrexqsDiamCoE+p7MmxU8ZzGSlfUG2S/6qw0djFWdLMbOXHU0iXUSApl4AHAdzVEyy9jvcCyZENIU3fTAeIta7wcGBvjk5GRT+2i2RJYgkoCha/hc72rXdSpAPXK1Rzk7Rs8GXndyWsNyEyunHiYvQ1c3/HpuimMB8mgsQeKkXIj88KOP8SPffzPKc4kFlwjK8b1I7RqU+LKYZV7LgTs1DRJE0imZZfz4Z+7ilDN0PLu9V+mKZq+ga6ZSTzzXuobFsdw/ZC0lB8KfteTXc1Mc69DJxpQmzXxKH6lM8dnvqsqcw9A17NuW99VZTxBJwSuRsWpFFwYeXIPxv74OFeetQrFUG2nezKJhhrHazaDTBf/54zN1jgwyMRTns3PTWs+UoZUg4uoWLVJfU7pIpUDJviznrtxq0RkRRLQUiqUlE1d/zwHQ1KKhGJ8hi2LEulChWML+8WkwFzEsFEt1N5AqdkJuAwZluPl0Ul9Tukhlis/tLk1P5SsiOp2sxwdXY6zp0e5BKZllaSm5Hb9L2l5pN6eycDcMXXNtYqa+pnSRyst5LuvcQQ7A1x0mQSQFt6m3eiYa534/S7ZlzqFr6s9QFTTAPe0m+qdU9id6l/KSKKknqyepQIJQIJUCRTN/iE4hZ+gYe3qrY4Nrs3zhkTXSi7mdfM7Aqm71FYEy58r79kq7DfbnUXH50hu6hmNDfTg/sguD/XnXZlwiXaRSoGSTQQmiHcjnDLw/uhfvj+7F9MHdAIC5hcXQj3P+vdvYuWmtp5CIpls/3zuNMezctNZzO1U7ITeXCXvpuIi6yBUi/aSySCLIwilBpIXC0qwja+NqkF4/rxEfAPDKheuuNRQaY/hc72qMnbnqq9aizDlOv/OR42OZpfPyMxRQNnhQJjzUjNsepFKgvIwnCSLtWKvbgt6MqaTCOdyr3sqcezYQO+E2r63CgfdH9/ran5dFEdGepFKgrB/WQrFE3nARQO9pa7FWt0X9twhagJHPGXjo4wZ+/N7tuvMzdA07N60NvSeRoqLOI5UCBdR/WJuxciGcIXFqPYWlGUlJ/FswoM4C6dDJ2ZqX4Eo9gzdnnNN7ACIp+FBFxa6JCB+/JrGC1AqUFeoODx+3tA8RDwzurgiq9GR1cO48niZodGYvWri/uFwm72VMe+jJ1lTTyca9A+RinlTaQqBWh+QETSxD4tR6wvgLiPJqmcN3EAHUNYa5+4vYMHIa63IG5hcWldeDc0brepHcfAJJoJJJagXK+kXz0RNIEB3Fvm35OnGypuLmFxaVx3yIOVO5rI5f3lusPcevwDGGugrFOJFlWigDk1xS2Qdld1ZukQMM0QF0+3BPSCLCn3JiqoDh12bqxOjOvKmceahwjmuje5Ht7lK2XOrJ6g3rTXfmTUcX9DiQ9VKRP19yURIoxtgXGWNXGWPvMsZGHB5/ljH2ztK/HzPGtoZ/qsv4teAniKBku7ug2ea46Fp13LmuMN8lZ+gNz48TEeGMnbnalJefcDVXjTZEanHVisYkTavGXsgcJsifL7l4ChRjTAPwpwC+BOCzAJ5hjH3Wttk1AP8l5/wxAP8cwEthn6gVCsmJuCiWTJQrvDZrLJ8zMPbVrRh4cI2ymV05gDD48bJT2U+z3xnhau7mg2lFNNAmKa1GDhPpQ2UN6vMA3uWc/wwAGGM/BPAVAH8jNuCc/9iy/QUAnw7zJO2QkwQRNxW+XBxwYHwaUHBpAJwr57wwdC20DIEodgnjO1Myy1jRlfGs/MvnDAz256tpPNnGDOj/zlsozpuxlntTL1W6UEnx5QHcsPz84dLvZPxjAP+b0wOMsW8wxiYZY5O3bgWf3eTXgp8gwsAscxRLJjjcxalHMcpwgjGEmr4WPnvDezYqpSS9uLv0+mWIlJlY85K9T5xX16PcpvMGYWKqgB2jZ7Fh5DR2jJ5tyVpXWFivl39f9O/m0Q6oRFBOn2rHjx1jbCeqAvWfOz3OOX8JS+m/gYGBwAlxcQf0/PGZti+H7tYYFsscaZ8iouIL1w70ZHUUPfqAZOgaC+S5J8O6viK+M9YqPjdkfXCioMApGsswYEVXBgfGp5Hx2UdnXZcK2kjbbn1O1uvlw48+1gHfnkZUIqgPAay3/PxpADftGzHGHgPwZwC+wjn/23BOT46XBX+7wAF8fXuwLuwkcfRrfb7mD6UVERV4IYIZsUbkd5yFDLf1lcH+PKYP7sb7o3s9o7wy59KCAqcMhq4xaIzVIswgN45CUER1rt/Iyq3PiUgnKgL1NoDPMMY2MMa6AfwOgJPWDRhjvQDeAPDfcM7/Y/in6czqFlqmxIVZ5vjLn6Q3TQEsN2cm6Xbiue29ODbUByPGEcxs6biGrtVaI8qc1xwjmm02z+cMnB/ZhWuje2uzkWQcfGKz6w2DdfifXfDsxQY5Q8dihYcy8bcZgUlSQQYRDp63bJzzRcbY7wM4A0AD8Oec81nG2DeXHv8egG8D+DiAf8Oqd4SLnPOB6E67Gs5HMSMnicwtpLuk/stbP4WJqUKiDGhPXCpg4ME1WLNqhVLxwKpurem/w7Pbe3Huyq2Gi3BYjhFe5dLW5vZcVnc97s5Na10LCsRjIq0WZTJDVWBkhSDU55RelHIKnPMfAfiR7Xffs/z/PwHwT8I9NXeCzsgh4ufclVs4d+VWaOIUhtCVzDL2j08rb9/dlWlKoHqyOo4MbsGGkdOBnp8zdMwtLNZ95sX7kFdYq7Gvz3j55YkGXy/89CSu6tagaxlppOi17uWFbGYU9Tmll9RaHVHYnh7CbAloVRTmdUH3Qowb91vurWcYxp7eWotWrAUEOzetxbkrt3BzyfUckBcD+G1uV/1+eW2nawxjX91ad14vTFxuGJRo6Br2bcvjxKVCYIGhmVHtR2oFinqhOpO0xsziIul32KZZ4TUzU2vKzW/Fmt8bunU5Q2k0hdf30CzzOjPWiakCTlwq1P0dGaqegUcGt2DgwTVNCQz1ObUXqfTiA6gXqp1pN/NfbckmCKh3MwDUzCgKxVJDT8/hU7O+Cgr8rMPoGsPOTWuVKupUvodWcXSK5DiWU4qD/XnlQg+i/UmtQNm/6ET70G7dA8ImyCpS50d24f3RvTg61FerhnOzNyoUSzgwPo0XJqr7kaUcZZGS6g1dT1bH2Fe3OhZzOAmgyvfQKo5UaUf4IbUpPmA5nHfKaRNEVIj1Ej8jzd0aUa2Tad3SfxzAKxeu4/Q78mm1skjJq7m9J6tj6tu7az8fkBSQOAmJvaLPbQ2JKu0IP6RaoADnnDbRenSNARyh9MYkCY2xWj/QuSu3fK2DFoolDL8+U6vEs68bDfbnMfnBbbx68Ya00ZXDvWDDqaDAupYk+2vcmTexY/RsTThlQ0DdhESlSIEq7Qg/pF6gaPRG8sgvVZiduPRh2wlUmXPXggcGwNAzmDedzansrRGi3H3/+DQMPYPFCg9s3+U0rdYrKrOetxDbQrEEXWPQM6zu76ciJPZCjrEzV3FgfLpBrFQLIVQKNYj2JfUCRbnrZNGT1TG8ZyP+4Ph02w6StEYan+tdjR+/d7sWmXBURSiIr15JImoqGLqGQ09ubvi9yg2cU+m+WV4eMQJUxe/Qk5uVxcGrylBlP+3mrUf4J7VFEoI4rWoIb+7Mm20tTgDqKtus4iQwKzwUXz0/rOhy/h643cAJCyPZn8r6N7y/6E88w/DFI289ItVX94mpgjSVQrSOdhYnO7KXerdkxlphWiw5j1KXrRnlc0atlFvlPP0Iw8RUQbo25yfjQRV/RKoFiu6kCCvNzGEKG7FeEmevnpOIqIw5Vz1PFWEQaTkZVsH0mt0kE9dOMIkmqqRaoMhJgrByz6zU3MLjxN69JARA9AjlYryg2r8TKmPO7dvI+rFUSsHd1rz0DKsJoxAyt0Zg2ZDFuYXF2nbtNKCQaCS1RRL0QSTslMwyzl25hRef2oKxM1dRKJYi9+4TPVHCE8+p0szv+k2zTEwVGgTIqbrPTz+WoWvYuWltXYGIU0WdW5T1wMquuio+2fqSdZ9OFY3CPgkAFVG0OakUKK80AtG53CyWGkqdVafIqpJh1nU2jtPvfITivOl40W5FG8Tzx2cAyC/S9sZ2WYWd3ZjWauQqEwM3bz7rpGGv9SXxHZetZwqDXBWRI1rH1x9vbthqKgWKep8IGU4mp2F7+2mM1aY5l8xKrTzcftF2KxaIEmGtJM7DygsTlx0dMOwXdnvUtWP0rJIYDO/ZiAPj045RqzVF6OUo4fUdX23ooRRiEMkmlQJFH8B4YQAyklk9SUKkoexpn7Bxaz4umWUcPjUbetTmF6t4CMH2ei/cvleyx5zWvCY/uO04TsNemOHmKOF2LnqGuQ4rJduk9iGVRRJUxRMfWT2Da6N78czj61tyfI0xPLe917MUWiz+O5mcxs2deVNJnKIu5rhZLNUVI3iRsbiu25Fd9Bka14OPDG6pM8FVKcywbyM7nsYYHljZJW2CJtuk9oLxFt0VDwwM8MnJyUDP7f/OW00PkCP8wVjrXMZlw+ysj4uL24aR06nxZTw21Cc1bw2DfM7A3P1FX5Gc9b20MjFVkKbu8jmjVmARFrJCjRef2iI9D6D6nqZo/Uk5+fzwo4/xI99/M8pziQQfa1CO70UqI6giiVPsxCFOhp5x/JSWzDLenPkIKyWuISKdNTFVQCYlw6SEb953v7bVsZTa776cep12blrrO80oa8gd7M9LRSGKlLtbhOXWfJwicSIUSOUaFE3TbU/cvOi8LrSiQCGKaMTQtVDThhmg5ps32J/H4VOzgTMCVg8+e9l40EZ2meDkYx6VIfPsI0f0ziGVAuVWKUR0Jhpjkaw95S0Xe9lNkeazgETT6iOmoBkB6+gPoLFiTzbTyQuZ4CRFGPw6ohPpJZUCNdifx/6AXz6i/WBwbuhsBqe1mOdfm0HZVsFnH0lhx0m8zDLH88dnamModI1hQbLoL2s0ZgC++7WtrhflIJkGN8FJkjCoOqIT6SaVAgVU8+6tLOMlkgOHPP2kSs7QwRikDbdANTVnj9GGPr8ep9/5yDFF15PVpdGREK2g58zh7Zawc9NaX1N/VUZqkDAQcZJagTLL5GKeRHqyOjivunnnsjrum+XIHec1xhqcDvygUvk1duaqY6T08oXr0kbgO/Om7/SfnVxWdxQ/FQfyc1duqR/H0DF9cLf3hgQRI6kVqLkFcpJIInfmTegaw9Gli/6O0bOYj7igpcw5TlwqYN+2vK+IAagKqopPnVulmpv+NJt6vG+WHdN8xfkFbBg57Zpm81Ndd7dF2QiamEu4kcoyczKKTTZmmePwqVkAzZcgq35AhVGsnxlMeobh4BP1U2hlLtvNNodrjLk6hcuYNyuOa1BzC2WpC7hw+PYjja1wX1BxNCc6m1QKFM2BSj535k1MTBWauvDlDB2rfcx4ulks+ZrBZFZ4rX9KIDMgZaw554cK57g2uhff/dpWx56lZgZDW3uX/DhHWBneszH20RU0Mbf9+cHF6w3//JBKgaIeqHSwf3wat+fuQ9f8N6IeG+rD9MHdvkqwc0vpOj8zmOx37bKIrzhv1hpHZbhFR1ahtjYc5wy9Oh7k6b6mBFCcdxAjZXHWcUczNDGX8CKVAuU3TUK0jpJZkfqmuSHWIfyk1qzLPX5mMJXMMp4/PoOHXGyS1i25FJwf2YVjQ41iYugavvu1rY6PAcDc/UW8MHEZ33rjcl3RgzhPJ+cEP4MOhQAGubhztCaakUXXZPZKCFJZJJF0V22iOcTtx8RUwdW12o5Y6D98atZ3FOH2mbL3Bqn0A9ndIYols8HhG6h3HbeXcNvnNqmcX1CXlbiiGWtRRC6rN/SRkSMEYSWVApXVM5GXLhOtgwPYMHLa94iPDGN4aOR0qOdid2sQuPUDDfbnMXbmakN5uB8vu4mpAk5cKigVOljPT+b2sFLPSO2UcoaOVSu6IrcxshvAiorPnKHjbknef0Z0LqkUKBKn9ofDf6QcRWRd5tzxgmkvj965aW3d2Hc/UYyTCKiuJdkNUmXRHQAMvz7TkG61+gJGbWPk9JrMMseqFV3Ug0U4kkqBIghgebJtM8MUZVZC1mPYsUcChWKprv/KjzjJREAltSZ7rlt0Z0092p0jJj+4jVcv3kCZc2iMYd+2cF0jqCiC8AsJFBE7IqXT7JTeMueBLY4YgGe390ptiqzHsBOkUs5KPmd4NqZ6RWFBBMRNuERKUbzeMud4ZUl0jwxuUT6GG15j3gnCTiqr+Ih0M31wd60nqBkYgrccHB3qw5HBLZ5jLpzKypu54xfD/a6N7sX5kV1SwfDq5xLuGWGVgTuJLgfwyoXroR3D6TVRUQThBgkUoUyTc/UAoK50erA/j1XdwXp/vFJzboh1m4mpgutIU9nFU/WO375vPxdje9m5U6oxzDJwmeiKEvQw8BrzThB2UilQQS9qRHO4TJVQhrF6q6rf/pz/i1M+ZwQWJwbURGLszFXpfkQDrWxgnldTraFreHZ7b50giwZdVccG0Xd1bXQvKpJUaKFYCiXCcRPdMNeIrK/JLYIkCCClAvUvfjucnDgRP3fmzTqHAj+O2wDw3PZenB/Z5ctzz4qICDaMnHZND04f3O1aRm6PBJ7b3tsQGQw8uKauYfjOvInh12Yw/PqMb8cGNwEJw/FheM9GaTRJa0REq0hlkcTkB7dbfQpEE1ibU/3cnRt6Bq9cuI5zV241NV7Da91KRfxU5iLtGD3bWFbtEIZa3w8ZTv1Nfp7vxWB/HpMf3G5oDKY1IqKVpFKgXvE5UoFIHkKYVHuGGKq2ScByWXczBqsymr0gW/uj/KQhvYRaiI9sknQYabgjg9Woj8ZfEFHx9cd7fW2fOoGamFLrrifiRxQuqBQwiLSRW2RgxWl/UfRr318sY//4NMbOXPV9cbb3R/lBJY0mHCqiLNWmiblEkkjdGhRZ8SeTfM7A0aE+vD+6F0eH+jwNfQvFEh4aOY3Dp2axb1trL4jWMxUZuCBu3ir9UXqGNbi7+4naqFSb6CRSF0FR13kyOT+yq/b/XukoK3fmTYy/fQM5Q0cxgqmuXtGc2+Mls4xvvfGOcsrL7bPJgDrboaBpNBWjWoJoF1InUEHdmol4EYvuKiPYzTKvDQRsxqHBCQ7Uid+qbg26lqmZk3p9lkpmpbaNiKoAOAqCbH+iOddKswUNJEhEJ5C6FB+lMpJHj2Tq7ZHBLTg21Fcrv3ZDDAT0MwNJ9dyspd5zC2XcX6zg6FBfoHJ1t+ZYSr8RRLikTqDozjFZ6BrDwSc2Sx+3Nma6iYEYCLhqRXhBvZ5h4Byug/j8jIgXiFSeveEWADklEESIpC7FR7QesW6TV1z/EKXXsnSalmG1KCOs9K1w6j7gUZZtXdNRPfa6nOHoaH5gfLr2vhwd6iNhIogmIYEifOOnzF9lKqw1jNeadDi3r/eolGWLNR2VMnGRspOZqwLea1UEQaiRuhQf4R9D16TrRM1gL8W2p7xUR5abFY7949PYMXq26aGD9ko6P+tCqhZGKg4YYRq5EkSnohRBMca+COBPAGgA/oxzPmp7nC09/lsA5gH8Luf8JyGfK2HBj5v3i09tkaa6msV6IbanvFTEyUqhWGrKpRxobFj1W5atWiGnUgFILREE0RyeAsUY0wD8KYD/GsCHAN5mjJ3knP+NZbMvAfjM0r/HAfzbpf+GzgsTl6PYbepQvYiL0RJ+1lj8crNYck15+UHVicKJIBNmg6LigEEmqwTRHCopvs8DeJdz/jPO+QKAHwL4im2brwD4C17lAoAcY+xTIZ8rAODVizei2G3LUfWV8zOSyXrBdkp1iX2JVJbuMPApw4Adj6zxrMALM1oQhQYM1TLxnKHXpdycqu56svLxGFFgTQcCzc1+IgjCGZUUXx6AVRU+RGN05LRNHsBH1o0YY98A8A0A6O31ZxooaHaNIqn89I/3YsfoWccoR2MMFc59NSn3ZHUcfGJz7YKtkuryMgp1KiKwFg04nVuQaMipsdVKUgxNrZGZ1SSW3B2IMLBfL/0arbYDKgLldNNuv+aobAPO+UsAXgKAgYGBQErTbJVXK9AYwzOPr8ebMx852vmIu3CntJGha3WRgYqIyS6OXqkulccBucg5nfu+bXmcu3ILN4slZBT+diqRRxKdFJJ4TkS6CeN6mXZUBOpDAOstP38awM0A24TCM4+vV7LPiQO7bc5DHzdw4Wd3UOa8JkpHBpeHKw48uEYagQBqUY6KiEWJ7EKscu5OEZiuMazq7qq9hxR5EAQhUBGotwF8hjG2AUABwO8A+Lptm5MAfp8x9kNU0393Oef/f3v3FyJVGYdx/PukLSRFSlaEJlr09yLBtpKosLpI90YCL6JIkG6kP3RpdFFEBHUnIbGESHSTFyWlYEYQZWBbbeDfpNiMTBLMkgK9kNVfF2eEbVndd5mZc9535vnAwMycl9nfszO8v3POvHv2OF1wYcKfSZMSMGdgFmfOnvvfBTtf23GIU2emvkDpZaqubL1gbvsX+LwgZRJv9yimSSXXbmb5USScLpM0BGykWma+JSLekLQeICKGW8vMNwErqZaZr4uI0Uu95uDgYIyOXnKImVkvS17z1Afz5ZS/i6S/g4qIncDOSc8NT7gfwHPtVGdmZjaRryRhZmZZcoMyM7MsuUGZmVmW3KDMzCxLblBmZpYlNygzM8uSG5SZmWXJDcrMzLLkBmVmZllygzIzsyy5QZmZWZbcoMzMLEtJVzPvyg+W/gR+a/Nl5gMnO1BO7vohpzP2jn7I2YmMJyNiZcpASbtSx/aSxhpUJ0gajYjBpuvotn7I6Yy9ox9y9kPGHPgUn5mZZckNyszMslR6g3q36QJq0g85nbF39EPOfsjYuKK/gzIzs95V+hGUmZn1KDcoMzPLUhENStJKST9JGpP00hTbJent1vb9kpY1UWc7EjI+1cq2X9IeSUubqLNd0+WcMO4eSeckramzvk5IyShphaS9kg5J+qruGtuV8Hm9WtIOSftaGdc1UWc7JG2RdELSwYtsL37eyV5EZH0DZgG/ADcBA8A+4M5JY4aATwEBy4Fvm667CxnvB+a17q8qLWNqzgnjvgB2AmuarrsL7+Vc4EdgUevxdU3X3YWMLwNvte5fC/wNDDRd+wxzPgQsAw5eZHvR804JtxKOoO4FxiLiSEScBbYCqyeNWQ28H5URYK6kG+outA3TZoyIPRFxqvVwBFhYc42dkPJeArwAfAScqLO4DknJ+CSwLSKOAkREaTlTMgZwlSQBV1I1qPF6y2xPROymqvtiSp93sldCg1oA/D7h8bHWczMdk7OZ1v8M1Z5baabNKWkB8DgwXGNdnZTyXt4KzJP0paQfJK2trbrOSMm4CbgD+AM4ALwYEefrKa82pc872ZvddAEJNMVzk9fGp4zJWXL9kh6malAPdLWi7kjJuRHYEBHnqp3v4qRknA3cDTwKXAF8I2kkIn7udnEdkpLxMWAv8AhwM/C5pK8j4t9uF1ej0ued7JXQoI4BN054vJBqr2w8SZViAAABWElEQVSmY3KWVL+ku4DNwKqI+Kum2jopJecgsLXVnOYDQ5LGI+LjekpsW+rn9WREnAZOS9oNLAVKaVApGdcBb0b1Zc2YpF+B24Hv6imxFqXPO9kr4RTf98AtkpZIGgCeALZPGrMdWNtaVbMc+CcijtddaBumzShpEbANeLqgPe3Jps0ZEUsiYnFELAY+BJ4tqDlB2uf1E+BBSbMlzQHuAw7XXGc7UjIepTpCRNL1wG3AkVqr7L7S553sZX8EFRHjkp4HPqNaPbQlIg5JWt/aPky12msIGAPOUO29FSMx4yvANcA7raOL8SjsasqJOYuWkjEiDkvaBewHzgObI2LKpcw5SnwfXwfek3SA6lTYhogo6l9wSPoAWAHMl3QMeBW4HHpj3imBL3VkZmZZKuEUn5mZ9SE3KDMzy5IblJmZZckNyszMsuQGZWZmWXKDMjOzLLlBmZlZlv4D/m4c/KGYoywAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "propensity = scipy.stats.norm().cdf(probit_propensity)\n",
    "sns.jointplot(propensity[:,0], propensity[:,1])\n",
    "rho, p_val = scipy.stats.spearmanr(propensity[:,0], propensity[:,1])\n",
    "rho"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# HACK: instead of loading marginals from GBD, I'm going to re-use the ones\n",
    "# I synthesized above\n",
    "\n",
    "exposure1_vals = df['SBP'].sort_values().values\n",
    "exposure2_vals = df['LDL-C'].sort_values().values\n",
    "\n",
    "def exposure1_from_propensity(p):\n",
    "    p = np.array(p)\n",
    "    i = np.array(np.floor(p*len(exposure1_vals)), dtype=int)\n",
    "    return exposure1_vals[i]\n",
    "\n",
    "def exposure2_from_propensity(p):\n",
    "    p = np.array(p)\n",
    "    i = np.array(np.floor(p*len(exposure2_vals)), dtype=int)\n",
    "    return exposure2_vals[i]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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>SBP</th>\n",
       "      <th>LDL-C</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>134.011378</td>\n",
       "      <td>5.192848</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>116.002529</td>\n",
       "      <td>3.155872</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>120.862054</td>\n",
       "      <td>1.630903</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>110.848538</td>\n",
       "      <td>2.214022</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>133.763781</td>\n",
       "      <td>4.926610</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9995</th>\n",
       "      <td>135.609528</td>\n",
       "      <td>5.082792</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9996</th>\n",
       "      <td>91.988864</td>\n",
       "      <td>3.282778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9997</th>\n",
       "      <td>90.701909</td>\n",
       "      <td>1.307473</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9998</th>\n",
       "      <td>122.352818</td>\n",
       "      <td>4.338779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9999</th>\n",
       "      <td>136.862764</td>\n",
       "      <td>3.626774</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             SBP     LDL-C\n",
       "0     134.011378  5.192848\n",
       "1     116.002529  3.155872\n",
       "2     120.862054  1.630903\n",
       "3     110.848538  2.214022\n",
       "4     133.763781  4.926610\n",
       "...          ...       ...\n",
       "9995  135.609528  5.082792\n",
       "9996   91.988864  3.282778\n",
       "9997   90.701909  1.307473\n",
       "9998  122.352818  4.338779\n",
       "9999  136.862764  3.626774\n",
       "\n",
       "[10000 rows x 2 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# now map from propensity to value\n",
    "df_synthetic = pd.DataFrame(index=range(N))\n",
    "df_synthetic['SBP'] = exposure1_from_propensity(propensity[:,0])\n",
    "df_synthetic['LDL-C'] = exposure2_from_propensity(propensity[:,1])\n",
    "df_synthetic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6797565466113832"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.jointplot(df_synthetic['SBP'], df_synthetic['LDL-C'])\n",
    "rho, p_val = scipy.stats.spearmanr(df_synthetic['SBP'], df_synthetic['LDL-C'])\n",
    "rho"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The anticipated problem with this approach: how does correlation affect the joint PAF?\n",
    "\n",
    "This is not relevant to the material above---using the Gaussian Copula to capture the correlation between risk-factor exposure will be fine.  The problem is when we then layer at RiskEffect component into our model, to make the risk have a effect on the incidence or mortality rate of our cause model.  Without loss of generality, suppose the risk effect will change the incidence of first MI.\n",
    "\n",
    "We have traditionally handled this by calculating a risk-deleted incidence:\n",
    "$$\n",
    "i_0 = \\left(1-\\text{PAF}\\right) \\cdot i_{\\text{GBD}}\n",
    "$$\n",
    "\n",
    "If we _just_ include one risk effect, I think we're still ok, even with correlation.  But if we have two risk effects, we have previously used assumption\n",
    "$$\n",
    "1 - \\text{PAF}_{\\text{joint}} = \\left(1 - \\text{PAF}_{\\text{SBP}}\\right)\\cdot\\left(1 - \\text{PAF}_{\\text{LDL-C}}\\right).\n",
    "$$\n",
    "\n",
    "The more correlated the risk exposure, the more wrong this assumption.\n",
    "\n",
    "I propose we continue to assume that the relative risks have a \"log linear\" relationship with incidence:\n",
    "$$\n",
    "i_{e_1, e_2} = i_0 \\cdot \\left(\\text{RR}_1\\right)^{e_1}\\cdot \\left(\\text{RR}_2\\right)^{e_2},\n",
    "$$\n",
    "where I have written $e_1$ and $e_2$ as \"standardized\" exposures, after scaling and shifting so that the TMREL is 0.0 and a one unit increment gives the relative increase in disease burden reported by GBD.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the log-linear assumption, we can calculate the PAF from first principles as a double integral (below $p_{e_1,e_2}$ denotes the joint probability density of exposure level $(e_1,e_2)$ in the population:\n",
    "\n",
    "\\begin{align*}\n",
    "i_{\\text{GBD}} &= \\int_{e_1} \\int_{e_2} i_{e_1, e_2} p_{e_1,e_2} de_1 de_2\\\\\n",
    "&= \\int_{e_1} \\int_{e_2} i_0 \\cdot \\left(\\text{RR}_1\\right)^{e_1}\\cdot \\left(\\text{RR}_2\\right)^{e_2}\n",
    "p_{e_1,e_2} de_1 de_2\\\\\n",
    "&= \\int_{e_1} \\int_{e_2} \\left(1-\\text{PAF}\\right) \\cdot i_{\\text{GBD}} \\cdot \\left(\\text{RR}_1\\right)^{e_1}\\cdot \\left(\\text{RR}_2\\right)^{e_2}\n",
    "p_{e_1,e_2} de_1 de_2\\\\\n",
    "\\end{align*}\n",
    "\n",
    "Dividing through and cancelling terms yields a solution:\n",
    "$$\n",
    "\\frac{1}{1-\\text{PAF}} = \\int_{e_1} \\int_{e_2} \\left(\\text{RR}_1\\right)^{e_1}\\cdot \\left(\\text{RR}_2\\right)^{e_2}\n",
    "p_{e_1,e_2} de_1 de_2,\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.936944660107624"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# there are lots of ways to approximate this integral, but here is a cool one:\n",
    "rr_1 = 1.5\n",
    "rr_2 = 3\n",
    "\n",
    "e1 = np.clip((df['SBP'] - 120)/10, 0, np.inf)  # rescale exposures \n",
    "e2 = np.clip((df['LDL-C'] - 4), 0, np.inf)\n",
    "\n",
    "one_over_one_minus_paf = np.mean(rr_1**e1 * rr_2**e2)\n",
    "paf = 1 - 1/(one_over_one_minus_paf)\n",
    "paf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8708098034918508"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# how does this compare to multiplicative approx of paf?\n",
    "ooomp_1 = np.mean(rr_1**e1)\n",
    "paf_1 = 1 - 1/ooomp_1\n",
    "\n",
    "ooomp_2 = np.mean(rr_2**e2)\n",
    "paf_2 = 1 - 1/ooomp_2\n",
    "\n",
    "1 - (1 - paf_1) * (1 - paf_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These values are somewhat different, reflecting the impact of the correlation in SBP and LDL-C in our simulated data. If we used the *multiplicative* PAF, our estimated rate would be quite different. Let's look at a simpler model of categorical risks."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chris is adding an example of categorial risk exposures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# simulate categorical data (to be replaced with real data, e.g. from MALED/Surveys, eventually)\n",
    "df = pd.DataFrame(index=range(N))\n",
    "# Uncorrelated, binomial \n",
    "df['bin_a'] = np.random.binomial(1, 0.3, size=N)\n",
    "df['bin_b'] = np.random.binomial(1, 0.1, size=N)  \n",
    "\n",
    "rr_1 = 2.5\n",
    "rr_2 = 5\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define what I will call a joint PAF:\n",
    "\n",
    "$$\n",
    "PAF_{joint} = 1 - \\frac{1}{RR_1^{e_1} \\cdot RR_2^{e_2}}\n",
    "$$\n",
    "   \n",
    "And also what I will call a multiplicative PAF:\n",
    "\n",
    "$$\n",
    "PAF_{multiplicative} = 1 - (1 - \\frac{1}{RR_1^{e_1}}) \\cdot (1 - \\frac{1}{RR_2^{e_2}})\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5127418018808165"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "one_over_one_minus_paf = np.mean(rr_1**df['bin_a'] * rr_2**df['bin_b'])\n",
    "paf = 1 - 1/(one_over_one_minus_paf)\n",
    "paf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5145153501895934"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# how does this compare to multiplicative approx of paf?\n",
    "ooomp_1 = np.mean(rr_1**df['bin_a'])\n",
    "paf_1 = 1 - 1/ooomp_1\n",
    "\n",
    "ooomp_2 = np.mean(rr_2**df['bin_b'])\n",
    "paf_2 = 1 - 1/ooomp_2\n",
    "\n",
    "1 - (1 - paf_1) * (1 - paf_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The approaches give nearly the same estimate of the combined PAF when the exposures are independent."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Now I am making it a bit more complicated, sim some data for continuous exposures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I have made two pairs of random distributions with the same means and standard deviations. First, I sim without correlation (nml_a, nml_b). Next, I sim with some correlation (cor_a, cor_b). I have continuous distributions at this point so I create four new variables that are binary if they are below -2. The variables \"exp_na\" and \"exp_nb\" are for the normal uncorrelated distributions while \"exp_ca\" and \"exp_cb\" are for the correlated distributions. This is just intended as an exercise based on the height-for-age z-score definitions of stunting (stunted is <= -2 SD). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\ctroeger\\AppData\\Local\\Continuum\\miniconda3\\lib\\site-packages\\ipykernel_launcher.py:25: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "C:\\Users\\ctroeger\\AppData\\Local\\Continuum\\miniconda3\\lib\\site-packages\\ipykernel_launcher.py:32: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "C:\\Users\\ctroeger\\AppData\\Local\\Continuum\\miniconda3\\lib\\site-packages\\ipykernel_launcher.py:30: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "C:\\Users\\ctroeger\\AppData\\Local\\Continuum\\miniconda3\\lib\\site-packages\\ipykernel_launcher.py:28: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n"
     ]
    },
    {
     "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>bin_a</th>\n",
       "      <th>bin_b</th>\n",
       "      <th>nml_a</th>\n",
       "      <th>nml_b</th>\n",
       "      <th>cor_a</th>\n",
       "      <th>cor_b</th>\n",
       "      <th>exp_na</th>\n",
       "      <th>exp_nb</th>\n",
       "      <th>exp_ca</th>\n",
       "      <th>exp_cb</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.057584</td>\n",
       "      <td>-0.950021</td>\n",
       "      <td>-1.818019</td>\n",
       "      <td>-0.826437</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.382862</td>\n",
       "      <td>0.206593</td>\n",
       "      <td>0.126023</td>\n",
       "      <td>-1.564974</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.287244</td>\n",
       "      <td>-0.582161</td>\n",
       "      <td>1.631291</td>\n",
       "      <td>-0.496486</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-2.595732</td>\n",
       "      <td>-0.208823</td>\n",
       "      <td>0.671197</td>\n",
       "      <td>0.529351</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-0.603832</td>\n",
       "      <td>-0.572606</td>\n",
       "      <td>0.681999</td>\n",
       "      <td>-0.739108</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9995</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.413890</td>\n",
       "      <td>0.426929</td>\n",
       "      <td>-0.502449</td>\n",
       "      <td>-1.987269</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9996</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.182369</td>\n",
       "      <td>-0.633904</td>\n",
       "      <td>0.503280</td>\n",
       "      <td>-1.297071</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9997</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-0.937989</td>\n",
       "      <td>-0.543358</td>\n",
       "      <td>0.014530</td>\n",
       "      <td>-1.185948</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9998</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1.806999</td>\n",
       "      <td>0.142196</td>\n",
       "      <td>-0.099585</td>\n",
       "      <td>-0.248132</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>9999</th>\n",
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       "      <td>-1.193765</td>\n",
       "      <td>0.860961</td>\n",
       "      <td>-0.972553</td>\n",
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       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 10 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      bin_a  bin_b     nml_a     nml_b     cor_a     cor_b  exp_na  exp_nb  \\\n",
       "0         0      1 -0.057584 -0.950021 -1.818019 -0.826437       0       0   \n",
       "1         1      0  0.382862  0.206593  0.126023 -1.564974       0       0   \n",
       "2         0      0  0.287244 -0.582161  1.631291 -0.496486       0       0   \n",
       "3         0      0 -2.595732 -0.208823  0.671197  0.529351       1       0   \n",
       "4         0      0 -0.603832 -0.572606  0.681999 -0.739108       0       0   \n",
       "...     ...    ...       ...       ...       ...       ...     ...     ...   \n",
       "9995      0      0  1.413890  0.426929 -0.502449 -1.987269       0       0   \n",
       "9996      0      0  0.182369 -0.633904  0.503280 -1.297071       0       0   \n",
       "9997      0      0 -0.937989 -0.543358  0.014530 -1.185948       0       0   \n",
       "9998      0      1  1.806999  0.142196 -0.099585 -0.248132       0       0   \n",
       "9999      0      0 -1.193765  0.860961 -0.972553 -1.269407       0       0   \n",
       "\n",
       "      exp_ca  exp_cb  \n",
       "0          0       0  \n",
       "1          0       0  \n",
       "2          0       0  \n",
       "3          0       0  \n",
       "4          0       0  \n",
       "...      ...     ...  \n",
       "9995       0       0  \n",
       "9996       0       0  \n",
       "9997       0       0  \n",
       "9998       0       0  \n",
       "9999       0       0  \n",
       "\n",
       "[10000 rows x 10 columns]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Uncorrelated, continuous normal\n",
    "mean_a = 0\n",
    "sd_a = 1.3\n",
    "\n",
    "mean_b = -0.5\n",
    "sd_b = 1\n",
    "\n",
    "rho = 0.8\n",
    "\n",
    "df['nml_a'] = np.random.normal(mean_a, sd_a, size=N)\n",
    "df['nml_b'] = np.random.normal(mean_b, sd_b, size=N)\n",
    "\n",
    "# Correlated continuous normal\n",
    "cor_nml = np.random.multivariate_normal([mean_a,mean_b], [[sd_a**2, rho],[rho, sd_b**2]], size=N)\n",
    "#cor_nml\n",
    "df['cor_a'] = cor_nml[:,0]\n",
    "df['cor_b'] = cor_nml[:,1]\n",
    "\n",
    "# For this example, I am thinking about HAZ, so I will set 'exposed' to less than -2\n",
    "\n",
    "## Does this work how I am expecting it to in Python?!\n",
    "df['exp_na'] = 0\n",
    "df['exp_nb'] = 0\n",
    "df['exp_ca'] = 0\n",
    "df['exp_cb'] = 0\n",
    "for i in range(0,N):\n",
    "    if (df['nml_a'][i] < (-2)):\n",
    "        df['exp_na'][i] = 1\n",
    "for i in range(0,N):\n",
    "    if(df['nml_b'][i] < (-2)):\n",
    "        df['exp_nb'][i] = 1\n",
    "    if(df['cor_a'][i] < (-2)):\n",
    "        df['exp_ca'][i] = 1\n",
    "    if(df['cor_b'][i] < (-2)):\n",
    "        df['exp_cb'][i] = 1\n",
    "df\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0573 0.069 0.0611 0.0721\n"
     ]
    }
   ],
   "source": [
    "# Does this do what I expected it to?\n",
    "print(np.mean(df['exp_na']), np.mean(df['exp_nb']),\n",
    "      np.mean(df['exp_ca']), np.mean(df['exp_cb']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0.98, 'Uncorrelated exposures')"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compare just to make sure I got what I expected\n",
    "sns.jointplot(df['nml_a'], df['nml_b'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.JointGrid at 0x1c8a2698848>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.jointplot(df['cor_a'], df['cor_b'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## When the exposures are independent, it seems that the PAFs from the multiplicative and joint risk approaches are similar."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2772216399840989"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# What is the value of the joint risk approach?\n",
    "one_over_one_minus_paf = np.mean(rr_1**df['exp_na'] * rr_2**df['exp_nb'])\n",
    "paf_j_ind = 1 - 1/(one_over_one_minus_paf)\n",
    "paf_j_ind"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2783285974850329"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# how does this compare to multiplicative approx of paf?\n",
    "ooomp_1 = np.mean(rr_1**df['exp_na'])\n",
    "paf_1 = 1 - 1/ooomp_1\n",
    "\n",
    "ooomp_2 = np.mean(rr_2**df['exp_nb'])\n",
    "paf_2 = 1 - 1/ooomp_2\n",
    "\n",
    "paf_m_ind = 1 - (1 - paf_1) * (1 - paf_2)\n",
    "paf_m_ind"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## However, when the exposures are correlated, it seems that the PAFs from the the joint risk approach are higher than the multiplicative approach which returns similar values to the independent exposures. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3420403329275915"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# What is the value of the joint risk approach?\n",
    "one_over_one_minus_paf = np.mean(rr_1**df['exp_ca'] * rr_2**df['exp_cb'])\n",
    "paf_j_cor = 1 - 1/(one_over_one_minus_paf)\n",
    "paf_j_cor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2890061162964448"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# how does this compare to multiplicative approx of paf?\n",
    "ooomp_1 = np.mean(rr_1**df['exp_ca'])\n",
    "paf_1 = 1 - 1/ooomp_1\n",
    "\n",
    "ooomp_2 = np.mean(rr_2**df['exp_cb'])\n",
    "paf_2 = 1 - 1/ooomp_2\n",
    "\n",
    "paf_m_cor = 1 - (1 - paf_1) * (1 - paf_2)\n",
    "paf_m_cor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Now, calculate individual incidences for the individuals in our simulated data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I am proposing that we leave the general approach to risk deleted incidence the same:\n",
    "\n",
    "$$\n",
    "i_0 = \\left(1-\\text{PAF}\\right) \\cdot i_{\\text{GBD}}\n",
    "$$\n",
    "\n",
    "But now we can compare two different approaches to calculating this PAF, multiplicative and joint:\n",
    "\n",
    "$$\n",
    "i_{multi,0} = (1-{PAF_{multi}}) \\cdot i_{{GBD}}  \n",
    "$$\n",
    "$$\n",
    "i_{joint,0} = (1-{PAF_{joint}}) \\cdot i_{{GBD}}\n",
    "$$\n",
    "\n",
    "\n",
    "And we can continue to find an individual's rate the same way:\n",
    "\n",
    "$$\n",
    "i_{e_1, e_2} = i_0 \\cdot \\left(\\text{RR}_1\\right)^{e_1}\\cdot \\left(\\text{RR}_2\\right)^{e_2},\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "rate = 0.8\n",
    "\n",
    "# Independent draws\n",
    "multi_rate0 = (1-paf_m_ind) * rate\n",
    "joint_rate0 = (1-paf_j_ind) * rate\n",
    "df['ind_multi_rate'] = multi_rate0 * rr_1**df['exp_na'] * rr_2**df['exp_nb']\n",
    "df['ind_joint_rate'] = joint_rate0 * rr_1**df['exp_na'] * rr_2**df['exp_nb']\n",
    "\n",
    "# Correlated draws\n",
    "multi_rate0 = (1-paf_m_cor) * rate\n",
    "joint_rate0 = (1-paf_j_cor) * rate\n",
    "df['cor_multi_rate'] = multi_rate0 * rr_1**df['exp_ca'] * rr_2**df['exp_cb']\n",
    "df['cor_joint_rate'] = joint_rate0 * rr_1**df['exp_ca'] * rr_2**df['exp_cb']\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7987747751596663"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(df['ind_multi_rate'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(df['ind_joint_rate'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8644832433174788"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(df['cor_multi_rate'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7999999999999998"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(df['cor_joint_rate'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### My interpretation of these results is that the _Joint PAF_ approach produces (near) exact matches for both independent and correlated exposures. When the exposures are independent, the _Multiplicative PAF_ approach seems to be very close. However, when the exposures are correlated, the _Multiplicative PAF_ returns a rate that is too high."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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