notebooks/3-Logistic-Regression-Model.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logitic regression on ICAN clinical data\n",
    "\n",
    "**Objective:** implement a logistic regression model with the simulated ICAN clinical data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Library importation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "library(ggplot2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data loading"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>2505</li>\n",
       "\t<li>28</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 2505\n",
       "\\item 28\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 2505\n",
       "2. 28\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 2505   28"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ican <- read.csv(\"simulated_ican_clinical_data.csv\", sep = \"#\", encoding = \"utf8\")\n",
    "dim(ican)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "ican[\"adjusted_size_ratio\"] <- as.factor(ifelse(is.na(ican$adjusted_size_ratio), NA, \n",
    "                                                ifelse(ican$adjusted_size_ratio < 3, \"<3\", \n",
    "                                                       ifelse(ican$adjusted_size_ratio >= 3, \">=3\", \"Other\"))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "ican[\"age\"] <- as.factor(ifelse(is.na(ican$age), NA, \n",
    "                                ifelse(ican$age < 50, \"<50\", \n",
    "                                       ifelse(ican$age < 60, \"50-59\", \n",
    "                                              ifelse(ican$age < 70, \"60-69\", \n",
    "                                                     ifelse(ican$age >= 70, \">=70\", \"Other\"))))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "ican$IA_location <- factor(as.character(ican$IA_location), levels = c(\"ICA\", \"MCA\", \"ACA\", \"PCA\"))\n",
    "ican$tobacco <- factor(as.character(ican$tobacco), levels = c(\"Non-smoker\", \"Minor_smoker\", \"Regular_smoker\"))\n",
    "ican$adjusted_size_ratio <- factor(as.character(ican$adjusted_size_ratio), levels = c(\"<3\", \">=3\"))\n",
    "ican$age <- factor(as.character(ican$age), levels = c(\"<50\", \"50-59\", \"60-69\", \">=70\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Univariable Logistic Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "format_values <- function(x, dec) {\n",
    "  return(formatC(x, format = 'f', digits = dec))\n",
    "}\n",
    "\n",
    "write_pvalue <- function(val) {\n",
    "  ifelse(val < 0.001, return(\"<0.001\"), return(paste0(\"=\", val)))\n",
    "}\n",
    "\n",
    "\n",
    "res_glm_uni <- function(df, var_dependant, var_explanatory) {\n",
    "    # Univariate\n",
    "    univ_formulas <- sapply(var_explanatory, function(x){as.formula(paste(var_dependant, '~', x))})\n",
    "    univ_models <- lapply(univ_formulas, function(x){glm(x, data = df, family=\"binomial\")})\n",
    "    univ_results <- lapply(univ_models,\n",
    "                           function(x){\n",
    "                               x <- summary(x)\n",
    "                               Pvalue <- format_values(x$coefficient[-1,4], 3)\n",
    "                               HR <- format_values(exp(x$coefficient[-1,1]), 2)\n",
    "                               HR.confint.lower <- format_values(exp(x$coefficient[-1,1] - 1.96*x$coefficient[-1,2]), 2)\n",
    "                               HR.confint.upper <- format_values(exp(x$coefficient[-1,1] + 1.96*x$coefficient[-1,2]), 2)\n",
    "                               HR <- paste0(HR, \" (\", HR.confint.lower, \"-\", HR.confint.upper, \", P\", write_pvalue(Pvalue),\")\")\n",
    "                               if (length(Pvalue) != 1) {\n",
    "                                   res <- cbind(HR)\n",
    "                                   colnames(res)<-c(\"OR (univariate)\")\n",
    "                                   return(as.data.frame(res))\n",
    "                               } else {\n",
    "                                   res <- HR\n",
    "                                   names(res)<-c(\"OR (univariate)\")\n",
    "                                   return(t(as.data.frame(res)))\n",
    "                               }\n",
    "                           })\n",
    "    res = NULL\n",
    "    for (i in 1:length(univ_results)) {\n",
    "        if (length(res) == 0){\n",
    "            ifelse(nrow(univ_results[[i]]) == 1, rownames(univ_results[[i]]) <- names(univ_results)[i],\n",
    "                   rownames(univ_results[[i]]) <- paste0(c(paste0(names(univ_results)[i], \" (\", \n",
    "                                                                 levels(df[,names(univ_results)[i]])[1], \")          \"), \n",
    "                                                          rep(\" \", (length(levels(df[,names(univ_results)[i]]))-2))), \n",
    "                                                        levels(df[,names(univ_results)[i]])[-1]))\n",
    "            res <- univ_results[[i]]\n",
    "        } else {\n",
    "            ifelse(nrow(univ_results[[i]]) == 1, rownames(univ_results[[i]]) <- names(univ_results)[i], \n",
    "                   rownames(univ_results[[i]]) <- paste0(c(paste0(names(univ_results)[i], \" (\", \n",
    "                                                                 levels(df[,names(univ_results)[i]])[1], \")          \"), \n",
    "                                                          rep(\"\", (length(levels(df[,names(univ_results)[i]]))-2))), \n",
    "                                                        levels(df[,names(univ_results)[i]])[-1]))\n",
    "            res <- rbind(res, univ_results[[i]])\n",
    "        }\n",
    "    }\n",
    "    res <- cbind(rownames(res), res)\n",
    "    rownames(res) <- NULL\n",
    "    colnames(res) <- c(\"Explanatory variables\", \"OR (univariate)\")\n",
    "    return(as.matrix(res))\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 32 × 2 of type chr</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>Explanatory variables</th><th scope=col>OR (univariate)</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>sex                                       </td><td>1.14 (0.96-1.36, P=0.147)</td></tr>\n",
       "\t<tr><td><span style=white-space:pre-wrap>age (&lt;50)          50-59                  </span></td><td>0.64 (0.53-0.78, P&lt;0.001)</td></tr>\n",
       "\t<tr><td><span style=white-space:pre-wrap>60-69                                     </span></td><td>0.47 (0.38-0.59, P&lt;0.001)</td></tr>\n",
       "\t<tr><td><span style=white-space:pre-wrap>&gt;=70                                      </span></td><td>0.30 (0.21-0.42, P&lt;0.001)</td></tr>\n",
       "\t<tr><td>bmi                                       </td><td>0.99 (0.97-1.00, P=0.105)</td></tr>\n",
       "\t<tr><td>sporadic_case                             </td><td>1.32 (1.07-1.62, P=0.008)</td></tr>\n",
       "\t<tr><td>multiple_IA                               </td><td>1.22 (1.03-1.45, P=0.022)</td></tr>\n",
       "\t<tr><td><span style=white-space:pre-wrap>IA_location (ICA)          MCA            </span></td><td>2.47 (1.91-3.20, P&lt;0.001)</td></tr>\n",
       "\t<tr><td><span style=white-space:pre-wrap>ACA                                       </span></td><td>4.11 (3.21-5.26, P&lt;0.001)</td></tr>\n",
       "\t<tr><td><span style=white-space:pre-wrap>PCA                                       </span></td><td>4.14 (3.15-5.44, P&lt;0.001)</td></tr>\n",
       "\t<tr><td><span style=white-space:pre-wrap>adjusted_size_ratio                       </span></td><td>1.91 (1.62-2.26, P&lt;0.001)</td></tr>\n",
       "\t<tr><td>tobacco (Non-smoker)          Minor_smoker</td><td>1.10 (0.91-1.33, P=0.333)</td></tr>\n",
       "\t<tr><td>Regular_smoker                            </td><td>0.91 (0.74-1.13, P=0.393)</td></tr>\n",
       "\t<tr><td>alcohol                                   </td><td>1.20 (0.94-1.54, P=0.137)</td></tr>\n",
       "\t<tr><td>hta                                       </td><td>0.93 (0.79-1.10, P=0.384)</td></tr>\n",
       "\t<tr><td>headaches                                 </td><td>0.84 (0.69-1.04, P=0.113)</td></tr>\n",
       "\t<tr><td>diabetes                                  </td><td>0.66 (0.44-0.99, P=0.043)</td></tr>\n",
       "\t<tr><td><span style=white-space:pre-wrap>dyslipidemia                              </span></td><td>0.64 (0.52-0.78, P&lt;0.001)</td></tr>\n",
       "\t<tr><td><span style=white-space:pre-wrap>ischemic_stroke_history                   </span></td><td>0.23 (0.15-0.36, P&lt;0.001)</td></tr>\n",
       "\t<tr><td><span style=white-space:pre-wrap>ischemic_heart_disease_history            </span></td><td>0.32 (0.19-0.54, P&lt;0.001)</td></tr>\n",
       "\t<tr><td>pad_history                               </td><td>0.56 (0.30-1.03, P=0.062)</td></tr>\n",
       "\t<tr><td>carotid_artery_stenosis_history           </td><td>0.67 (0.41-1.09, P=0.107)</td></tr>\n",
       "\t<tr><td>aortic_aneurysm_history                   </td><td>0.44 (0.12-1.57, P=0.206)</td></tr>\n",
       "\t<tr><td>statin_ttt                                </td><td>0.63 (0.48-0.83, P=0.001)</td></tr>\n",
       "\t<tr><td><span style=white-space:pre-wrap>platelet_aggregation_inhibiting_ttt       </span></td><td>0.59 (0.46-0.77, P&lt;0.001)</td></tr>\n",
       "\t<tr><td>vka_or_anticoagulant_ttt                  </td><td>0.63 (0.39-1.03, P=0.065)</td></tr>\n",
       "\t<tr><td>anti_inflammatory_ttt                     </td><td>1.06 (0.64-1.77, P=0.817)</td></tr>\n",
       "\t<tr><td>hormone_therapy_ttt                       </td><td>0.40 (0.23-0.71, P=0.002)</td></tr>\n",
       "\t<tr><td>allergy                                   </td><td>0.89 (0.74-1.09, P=0.261)</td></tr>\n",
       "\t<tr><td>asthma                                    </td><td>1.07 (0.77-1.47, P=0.686)</td></tr>\n",
       "\t<tr><td>atopy                                     </td><td>0.62 (0.42-0.93, P=0.019)</td></tr>\n",
       "\t<tr><td>eczema                                    </td><td>0.91 (0.64-1.30, P=0.610)</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 32 × 2 of type chr\n",
       "\\begin{tabular}{ll}\n",
       " Explanatory variables & OR (univariate)\\\\\n",
       "\\hline\n",
       "\t sex                                        & 1.14 (0.96-1.36, P=0.147)\\\\\n",
       "\t age (<50)          50-59                   & 0.64 (0.53-0.78, P<0.001)\\\\\n",
       "\t 60-69                                      & 0.47 (0.38-0.59, P<0.001)\\\\\n",
       "\t >=70                                       & 0.30 (0.21-0.42, P<0.001)\\\\\n",
       "\t bmi                                        & 0.99 (0.97-1.00, P=0.105)\\\\\n",
       "\t sporadic\\_case                              & 1.32 (1.07-1.62, P=0.008)\\\\\n",
       "\t multiple\\_IA                                & 1.22 (1.03-1.45, P=0.022)\\\\\n",
       "\t IA\\_location (ICA)          MCA             & 2.47 (1.91-3.20, P<0.001)\\\\\n",
       "\t ACA                                        & 4.11 (3.21-5.26, P<0.001)\\\\\n",
       "\t PCA                                        & 4.14 (3.15-5.44, P<0.001)\\\\\n",
       "\t adjusted\\_size\\_ratio                        & 1.91 (1.62-2.26, P<0.001)\\\\\n",
       "\t tobacco (Non-smoker)          Minor\\_smoker & 1.10 (0.91-1.33, P=0.333)\\\\\n",
       "\t Regular\\_smoker                             & 0.91 (0.74-1.13, P=0.393)\\\\\n",
       "\t alcohol                                    & 1.20 (0.94-1.54, P=0.137)\\\\\n",
       "\t hta                                        & 0.93 (0.79-1.10, P=0.384)\\\\\n",
       "\t headaches                                  & 0.84 (0.69-1.04, P=0.113)\\\\\n",
       "\t diabetes                                   & 0.66 (0.44-0.99, P=0.043)\\\\\n",
       "\t dyslipidemia                               & 0.64 (0.52-0.78, P<0.001)\\\\\n",
       "\t ischemic\\_stroke\\_history                    & 0.23 (0.15-0.36, P<0.001)\\\\\n",
       "\t ischemic\\_heart\\_disease\\_history             & 0.32 (0.19-0.54, P<0.001)\\\\\n",
       "\t pad\\_history                                & 0.56 (0.30-1.03, P=0.062)\\\\\n",
       "\t carotid\\_artery\\_stenosis\\_history            & 0.67 (0.41-1.09, P=0.107)\\\\\n",
       "\t aortic\\_aneurysm\\_history                    & 0.44 (0.12-1.57, P=0.206)\\\\\n",
       "\t statin\\_ttt                                 & 0.63 (0.48-0.83, P=0.001)\\\\\n",
       "\t platelet\\_aggregation\\_inhibiting\\_ttt        & 0.59 (0.46-0.77, P<0.001)\\\\\n",
       "\t vka\\_or\\_anticoagulant\\_ttt                   & 0.63 (0.39-1.03, P=0.065)\\\\\n",
       "\t anti\\_inflammatory\\_ttt                      & 1.06 (0.64-1.77, P=0.817)\\\\\n",
       "\t hormone\\_therapy\\_ttt                        & 0.40 (0.23-0.71, P=0.002)\\\\\n",
       "\t allergy                                    & 0.89 (0.74-1.09, P=0.261)\\\\\n",
       "\t asthma                                     & 1.07 (0.77-1.47, P=0.686)\\\\\n",
       "\t atopy                                      & 0.62 (0.42-0.93, P=0.019)\\\\\n",
       "\t eczema                                     & 0.91 (0.64-1.30, P=0.610)\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 32 × 2 of type chr\n",
       "\n",
       "| Explanatory variables | OR (univariate) |\n",
       "|---|---|\n",
       "| sex                                        | 1.14 (0.96-1.36, P=0.147) |\n",
       "| age (&lt;50)          50-59                   | 0.64 (0.53-0.78, P&lt;0.001) |\n",
       "| 60-69                                      | 0.47 (0.38-0.59, P&lt;0.001) |\n",
       "| &gt;=70                                       | 0.30 (0.21-0.42, P&lt;0.001) |\n",
       "| bmi                                        | 0.99 (0.97-1.00, P=0.105) |\n",
       "| sporadic_case                              | 1.32 (1.07-1.62, P=0.008) |\n",
       "| multiple_IA                                | 1.22 (1.03-1.45, P=0.022) |\n",
       "| IA_location (ICA)          MCA             | 2.47 (1.91-3.20, P&lt;0.001) |\n",
       "| ACA                                        | 4.11 (3.21-5.26, P&lt;0.001) |\n",
       "| PCA                                        | 4.14 (3.15-5.44, P&lt;0.001) |\n",
       "| adjusted_size_ratio                        | 1.91 (1.62-2.26, P&lt;0.001) |\n",
       "| tobacco (Non-smoker)          Minor_smoker | 1.10 (0.91-1.33, P=0.333) |\n",
       "| Regular_smoker                             | 0.91 (0.74-1.13, P=0.393) |\n",
       "| alcohol                                    | 1.20 (0.94-1.54, P=0.137) |\n",
       "| hta                                        | 0.93 (0.79-1.10, P=0.384) |\n",
       "| headaches                                  | 0.84 (0.69-1.04, P=0.113) |\n",
       "| diabetes                                   | 0.66 (0.44-0.99, P=0.043) |\n",
       "| dyslipidemia                               | 0.64 (0.52-0.78, P&lt;0.001) |\n",
       "| ischemic_stroke_history                    | 0.23 (0.15-0.36, P&lt;0.001) |\n",
       "| ischemic_heart_disease_history             | 0.32 (0.19-0.54, P&lt;0.001) |\n",
       "| pad_history                                | 0.56 (0.30-1.03, P=0.062) |\n",
       "| carotid_artery_stenosis_history            | 0.67 (0.41-1.09, P=0.107) |\n",
       "| aortic_aneurysm_history                    | 0.44 (0.12-1.57, P=0.206) |\n",
       "| statin_ttt                                 | 0.63 (0.48-0.83, P=0.001) |\n",
       "| platelet_aggregation_inhibiting_ttt        | 0.59 (0.46-0.77, P&lt;0.001) |\n",
       "| vka_or_anticoagulant_ttt                   | 0.63 (0.39-1.03, P=0.065) |\n",
       "| anti_inflammatory_ttt                      | 1.06 (0.64-1.77, P=0.817) |\n",
       "| hormone_therapy_ttt                        | 0.40 (0.23-0.71, P=0.002) |\n",
       "| allergy                                    | 0.89 (0.74-1.09, P=0.261) |\n",
       "| asthma                                     | 1.07 (0.77-1.47, P=0.686) |\n",
       "| atopy                                      | 0.62 (0.42-0.93, P=0.019) |\n",
       "| eczema                                     | 0.91 (0.64-1.30, P=0.610) |\n",
       "\n"
      ],
      "text/plain": [
       "      Explanatory variables                      OR (univariate)          \n",
       " [1,] sex                                        1.14 (0.96-1.36, P=0.147)\n",
       " [2,] age (<50)          50-59                   0.64 (0.53-0.78, P<0.001)\n",
       " [3,] 60-69                                      0.47 (0.38-0.59, P<0.001)\n",
       " [4,] >=70                                       0.30 (0.21-0.42, P<0.001)\n",
       " [5,] bmi                                        0.99 (0.97-1.00, P=0.105)\n",
       " [6,] sporadic_case                              1.32 (1.07-1.62, P=0.008)\n",
       " [7,] multiple_IA                                1.22 (1.03-1.45, P=0.022)\n",
       " [8,] IA_location (ICA)          MCA             2.47 (1.91-3.20, P<0.001)\n",
       " [9,] ACA                                        4.11 (3.21-5.26, P<0.001)\n",
       "[10,] PCA                                        4.14 (3.15-5.44, P<0.001)\n",
       "[11,] adjusted_size_ratio                        1.91 (1.62-2.26, P<0.001)\n",
       "[12,] tobacco (Non-smoker)          Minor_smoker 1.10 (0.91-1.33, P=0.333)\n",
       "[13,] Regular_smoker                             0.91 (0.74-1.13, P=0.393)\n",
       "[14,] alcohol                                    1.20 (0.94-1.54, P=0.137)\n",
       "[15,] hta                                        0.93 (0.79-1.10, P=0.384)\n",
       "[16,] headaches                                  0.84 (0.69-1.04, P=0.113)\n",
       "[17,] diabetes                                   0.66 (0.44-0.99, P=0.043)\n",
       "[18,] dyslipidemia                               0.64 (0.52-0.78, P<0.001)\n",
       "[19,] ischemic_stroke_history                    0.23 (0.15-0.36, P<0.001)\n",
       "[20,] ischemic_heart_disease_history             0.32 (0.19-0.54, P<0.001)\n",
       "[21,] pad_history                                0.56 (0.30-1.03, P=0.062)\n",
       "[22,] carotid_artery_stenosis_history            0.67 (0.41-1.09, P=0.107)\n",
       "[23,] aortic_aneurysm_history                    0.44 (0.12-1.57, P=0.206)\n",
       "[24,] statin_ttt                                 0.63 (0.48-0.83, P=0.001)\n",
       "[25,] platelet_aggregation_inhibiting_ttt        0.59 (0.46-0.77, P<0.001)\n",
       "[26,] vka_or_anticoagulant_ttt                   0.63 (0.39-1.03, P=0.065)\n",
       "[27,] anti_inflammatory_ttt                      1.06 (0.64-1.77, P=0.817)\n",
       "[28,] hormone_therapy_ttt                        0.40 (0.23-0.71, P=0.002)\n",
       "[29,] allergy                                    0.89 (0.74-1.09, P=0.261)\n",
       "[30,] asthma                                     1.07 (0.77-1.47, P=0.686)\n",
       "[31,] atopy                                      0.62 (0.42-0.93, P=0.019)\n",
       "[32,] eczema                                     0.91 (0.64-1.30, P=0.610)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "res_glm_uni(ican, \"rupture\", colnames(ican[,-dim(ican)[2]]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multivariables Logistic Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "fit <- glm(rupture ~ sex + age + tobacco + hta + IA_location + adjusted_size_ratio + multiple_IA + headaches + statin_ttt\n",
    "                      + platelet_aggregation_inhibiting_ttt + hormone_therapy_ttt + allergy, \n",
    "           family = binomial, data = ican)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Waiting for profiling to be done...\n",
      "\n",
      "Waiting for profiling to be done...\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Odds Ratio and confidence interval\n",
    "Odds <- as.vector(round(exp(coef(fit)),2))\n",
    "CILow <- as.vector(round(exp(confint(fit)),2)[,1])\n",
    "CIHigh <- as.vector(round(exp(confint(fit)),2)[,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "boxLabels = c(\"(Intercept) \", \"Sex (M) \", \"Age (<50)           50-59 \", \"60-69 \", paste0(\"\\U2265\", \"70 \"), \n",
    "              \"Tobacco (Non-smoker)           Minor smoker \", \"Regular smoker \", \n",
    "              \"HTA (Yes)\" , \"IA location (ICA)           MCA \", \"ACA \", \"PCA \", \n",
    "              paste0(\"Adjusted size ratio (\\U2265\", \"3) \"), \"Multiple IA (Yes) \", \"Headaches (Yes) \", \n",
    "              \"Statin treatment (Yes) \", \"Platelet aggregation inhibiting treatment (Yes) \", \n",
    "              \"Hormone therapy treatment (Yes) \", \"Allergy (Yes) \")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "df <- data.frame(yAxis = length(boxLabels):1,\n",
    "                 boxOdds = Odds,\n",
    "                 boxCILow = CILow,\n",
    "                 boxCIHigh = CIHigh)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/roWcSi6N6lEcKCKTOUsIpRVGM4tZ0FH/XWnUBYXRohLJgyvy2sOAhm783mXUBY\nXRohLJgyvy6s+CmYbZvtO4CwujRCWDBlfn9KmH7Mgl5jLIruXRohLJgyIwgrfe9XdUdYXRoh\nLJgyw90l1Guu0s/mXcK+6xoQVpdGCAumzHDrsMy0791ZhzULvmxShPWD5ggLHpfhVrqbkVXs\nPEy4sM/k/LWr4C+EonuXRggLpsxvPkv4Ye4P9l2IhbC6NEJYMGUGE9ab+7YGOweU3uDQHYTV\npRHCgikz3PuwtnGmpoWpZOVFqw/1jqyXz34dIqwujRAWTBneODpoRoQlg7CgHwhr0IwISwZh\nQT8Q1qAZEZYMwoJ+IKxBMyIsGYQF/UBYHii6iwGEBaOBsEoaC/Avv5jqXSAsGYQF/UBYJQir\nJYaw4FZAWCUIqyWGsOBWQFglDWFVM34bLuoCYckgLOgHwirxCuu75IIuEJYMwoJ+IKwSn7C+\nvzsZC2G1pa+CsKAfCKukXVjfdbp2gbBkBhJW6CLtvVaiXZiYDjdX77rG+Z6TcHfFZGF4yL4c\nin/B4X5ZmfOS5girpL3ojrC6bj6GsE6RvqyzDqNrd13nfM+HMDpdL5lx8AZh/ZzxhNXwVaux\nEFZb+ip3LqxVOM/Tra7cdZ0OPc/D5fWSmV+0Qlg/ZzRhCb5qMxbCaktfZcgaVusVcLVr72in\ngvqqPl616wYdet6Yadx1koWhelVwLCt/CBBWbxBWSwxhVVnZjvRVnVy16wZdes7HeddIFut8\n+hNh/Yyxiu6ir1qMhbDa0lf5NWGtswtv/lrueI3CuS2Ur+dKN3uzcVpF2UW6EzYqXeQdJXmH\nWR97N2c931r1tK+c32mlE2+KJvNwvk6Py7JhvRNV5A8jNZQ7LqMwWh3zPce5PpPkWm7Julyq\n4dpBf7pTwsZvqZ2jPZOBfqADwipBWC2xuxXWMTLlrCift8VFlcbOekJzi+1gG64aG9UuNNnF\ntc4zZZf2vMzZki90jZW30VOvokkSFQ0bnZSX8849Z6NLdSbr8Eo3CrMu16rLjf6sCcv9LY1z\nnOf/JoP8QAeEVRLItAirpfWPzhlhXQFHWJEuNm3MtaNv6h20jvbqIo9P+lKPTcNszyk2V0pt\nw+1Cs8prRipToi8pm7OZL+ti6R6rRZmlV92b47LTUHKYH/KTaXRSXM6n/Afo24LmWMXhWnNC\nZeAkXGannBwawnJ/S+Mc4/JG5QA/0GAusH+QcxVhjf0j7oPfEdbG/v/ntSmS2//PnV0dS3Vr\nzamWZw1fzfUyb264XWgSW2nXB5/00oaiGyHfKazM2MroXG/YGWUxsRQ6ycc1K3Po3pxgWIyr\njlUl/uif7vCandc8fG0Ky/kt8g8d7gc6MMIqaSm6MyW81xFWbpZjmK/zVFunfPXUaf9qS8uJ\ne5+tvuF2UU2gv7yq4U3RjZCvVlae6wnS+ujucj+anYT5vAugP/wAACAASURBVGhedGhnW/n4\no5qhP0pYmU+yf6FNU1hOpuY5OiOhIX5gCcIqQVgtsXsVVtUstYtunxex0toFL2840Vosm+Ec\na91I+fJse/tlfkzF67nZSZgPoMKSljP6IUpYB12/OniF1fJDDUP8wBKEVYKwWmJTFJaahiw3\nddOkrRvtwsqGJMkFwjL3IBW77tdzUYUeXlgmS9pfWEP8wBKEVcI6rJbYvQpLnrmY4so8zJ+u\nSS+dEkY1iRWrLL1TwvJCzBps1DUdiddzs5PVwU5i55UruCKsqO+/VgUtrLke8Fw4Jax1dO0f\nWIKwStoefkZY3TdvSljN8q7a3Ol7aqbVsRgkqdtsRZ29suEvuqfOk8LNfLUTUsxtZcYdbbgf\nUidLE1sV5ey40q1r05/+0x1VsnCZ/8vIwmr5oYP9QAeEVdL6tobOvkJYNyUsYZnBXi9rOOjL\nap0e8vXceqmDvRPf2Kgva3jNF1blmZZh2U3thn3thFLty/ioGy3F61nsJNISOOkfcIpri1Xz\nu2pX+qdbh+5KDVFYLT90sB/ogLBKeL1MS+xuhZUvUZw3F47u7R4z/7NbZjlTZaPaRWr3ryuZ\nTrmwGvnqJ6RY2e7VWiPpepY6saO+nXtmZbfr6tLUH/7T7fXE0C8s+YcO9gMdEFYJwmqJ3a2w\nzEMg8brcsSoezVF3CePdMTSvOjiqmkuSr2tyNypdGKLy0RzbpPxWy9c4oYydGpGZRrIVhE5i\n+56qZXlmZbfJlUpYpkul3xbVuD9Z+KGD/UAHhFXi+yMUnXSFsG5BWMOzkq6kEbnaw893AMIq\n8f7VnE6+QlgPIazTtZ7duw47aYHlVEFYJWf+zNd5XSGsxxBWNsS6zqMw1yF5oAEWwnLg7xK2\nxBBWnehar8y7AodrVbDuAoRVcubvEvbpAmHJ3Luw9lda+HQNkivdIrwPEFYJwmqJISy4FRDW\noBkRlgzCgn4grEEzIiwZhAX9QFgefn4xISwZhAX9QFgeEJYYQFgwGgjLA8ISAwgLRgNheUBY\nYgBhwWggrEEzIiwZhAX9QFiDZkRYMggL+oGwemT8I/yrVWLFBsKSQVjQD4R1ecZtY0l8LVZu\nICwZhAX9QFge5Itp2/j7zrWYs4GwZBAW9ANheRAvpj/BrCGsSszdQFgyCAv6gbA8SBfTLHj6\nrAurEqtsICwZhAX9QFgepIspeGu+k6ESq2wgLBmEBf1AWD0yCkX3agxhnQFhQT8QVo+MCKt1\nE2HBoCCsHhkRVusmwoJBQVg9MiKs1k2EBYOCsDy0XUwIq3UTYcGgICwPCEsMICwYDYTlAWGJ\nAYQFo4GwPCAsMYCwYDQQVo+MCKt1E2HBoCCsHhlzH7mSQlj+9FUQFvQDYfXIiLBaNxEWDArC\nGjQjwpJBWNAPhOWBP0IhBhAWjAbC8oCwxADCgtFAWB4QlhhAWDAaCMsDwhIDCAtG43GEJS2e\n6pmxe1cISwZhQT8QVo+MCKt1E2HBoCCsHhkRVusmwoJBQVgu34ZzGRFW6ybCgkFBWCXfJSZw\nycPPMghLBmFBPxBWwfd33VgISwwgLBgNhGX5rpMirJYAwrp3wpxk3ePQq5/LJc0RlgVhtccQ\n1sQIS+LLD736uVzSHGEZGr5SxqLoLgYQ1r3jCCu8cIyFsDozpLAEX2XGQlhiAGHdO7kkTqsw\nnPc79Orn0hGEpUFYvhjCmhilJC72D8LqzIDCEn31/Y2wxADCuneawjouozBaHU1wM8++57vy\nFrXN9VzV7Pf5ruM8TPLeTyu9b5M3z5rO11mGMIxN+3QdZyO7V/cMdmEYHWvnUevWgLAULcKi\n6C4GENa9U2oqNELY2YLWTm2sTDXeK6zYPSD7nJfFsGPk1PNtR1kaE907DbShTIe5r3bt3Voe\nSVjttAir/YCBzhlhwW/gFt2VQk6ZLw7pIRvcnNL0kG94hLUO45P6r7nJqKx0KjqPdZ+nWLvG\n7For9xzy9lnP2ehrUx5c+KpyHrVu8yv436NwVWGN/WPuHYQ1Ko6v8jGV+tyHYTZPW5qNjU9Y\n8/BYje0qnautk67nWyOWH7pjPWpaa2/p5nZ39Txq3VoeaYTVvo8poTfGCGtiFLp6NSOYeSGl\nWG+o6Mlfw0pP+1dn1uiMhOZ6Brg+CkfpjyQ0tjua6ai7uKJyHrVuLQhLQdHdG0NYE0OL4xjn\nZSR3xNVqqOrmPi7a12/07e2e+bFxVKV/+6Wsd9XOQ75/iLAUCMsbQ1gTIywq54IoughLTeKW\nm6MorPS0iorpZldhFWV2hJXDOqyuUYQ1dawKjqb8XU7FUrtxdkqYtTnUYy7HjZJW1HFKuDro\ntrXzQFienQjLF0NYEyNXwcaKYlXUyeOi6L6uFqj2FfWY/8ojLCu8ynDK/WgW3XXOdf08EJZv\nr+QrHn6WAwjr3ilUYNYe6OUEe70SYZ8va9jnyxqyAdEqLTeLEdY6PdSXahmy6WJ81F5aisIS\nljXo2Kl2HgjLu1vwFcKSAwjr3ilUcLDjp3zB5koFqwtHbQ29KicbrM4Mc1a2M7WYShJWvnB0\n7iyN2JjclfNAWD4QVnsMYU2MUgUru9T9sMwskthlT+ZZmryRGkiVm7nGVMF+d9SjqIZZdktl\nuLXTvDYUU4/mxOvKucTGfe55ICw/dV0hrJYAwnoIRF+MDsIqqfuKorscQFgPQVh/7vgmQFgu\nFV0hrJYAwpo0oS55H5cXv9vvV0BYPTIirNZNhHX3vOZrNy99e/KvgLB6ZERYrZsI6/7ZqcJ3\nURS/MRCWB4ruYgBhwWg8jrB68POLCWHJICzoB8LygLDEAMKC0UBYHhCWGEBYMBoIa9CMCEsG\nYUE/ENagGRGWDMKCfiCsQTMiLBmEBf1AWINmRFgyCAv6gbA8UHQXAwgLRgNhNXlfBMFs8VG5\nmD6y2NOb3fj7HATPb+KxNRCWDMKCfiCsBlv7twe3zsVkY0+fauPZbDx36AthySAs6AfCajAL\nFl/p1yKYlRfTRxC8fWUjKy2pt+DpPQs9Bx3GWAhLBmFBPxBWnW2w0J9x8F5kXFg5vWTDrvQp\n0OOsj8xoZ0FYMggL+oGw6mgppUpcL0XGWfClPz+tzDRdHoFGWDIIC/qBsOrEwYf+/AjiImPh\nJqdw9dGliIWwZBAW9ANh1SnlFDSE9VWOqrYzKzYvCEsGYUE/EFYdR1jFxbSw08S3fGccBLP3\nDp0hLBmEBf1AWHUkYb0Hs8xYX5mvcmHFTzp0DoQlg7CgHwirjiSs9MUuzXIK7R+z4PwYC2HJ\nICzoB8KqIworfX8OgsVHGjw5oQ5Vd4Qlg7CgHwirTmyWWaWfzl3CnPfA/UsiHdY1ICwZhAX9\nQFh1XuxM791Zh5XzRy0gzRdlISxhE2HBoCCsOls7ioqDbWPh6JP6zJe9/3VXkbaAsGQQFvQD\nYTUonyUsMr4Ezx/ZmCsO/qT6mRx1f7DTQiyEJYOwoB8Iq8Gb+7YGO+2zL2gwY6/ydQ5nQVgy\nCAv6gbCabOPMRov31BFW+vYUBM+5odTLsWYvnx26QlgyCAv6gbA88MZRMYCwYDQQlgeEJQYQ\nFowGwho0I8KSQVjQD4Q1aEaEJYOwoB8Ia9CMCEsGYUE/Hk5YXd4TKme85Ei5h+s0R1jwuCAs\nD9WLCWF12ERYMCgIywPCEgMIC0YDYZV8G8oAwhIDCAtGA2HlfJfkIYQlBhAWjAbCsnx/N41F\n0V0MICwYDYSl+a4jZERYHTYR1sMQhmHlW+hi96yyr8v6gbswOWbxg908ZN+P7WmScOduIiwN\nwvLFEBY06SIs/f1UPe4UZa5ah2H+8t44DNeeNIcwcjtAWIqGr4yxEJYYQFiQdhLWTn/fVI9b\nhfPU0ZSjLpl5ZYyGsFLRV9pYFN3FAMKCtCms+tdUWymbFM4rhx2NwbIPPXLKxlu+CWHGppw9\npghLg7D8MYQFTc4L66hkNa/4Rpe19OfaVLcS/4TQ9LkqNxBWi6+UsRCWGEBYkHYR1msYvqr/\nrKqHJeZLNvzap/tiAHZcRmG0MoOt0yrTXJjYuWTi9omwENbZGMKCJueFFamC+ymb+zlH7YoR\n1SFz1akYf+1s8UvdEjxGdsMUt9ahc6PwAYXVoEVYzYaDnzPCgrtBuitYEdbODKYS1zdqRpjP\nELOx11yNwRRKa4f0EOnClh57pae8Ln+wYzRzEf57MH4irLHPfTogrPvnrLCWxlS7YhKoSJwa\nu5r32QnhyrTda4HZgdbJ7j269xEfcITVCLVOCVnWIAYYYUF6XljFXDByl2K5RjuUy0fnNqzd\npEQWJuujdAzCQlhnYwgLmpyrYa0dn70KR9W7KN23t9/mx+YxCIui+9kYwoIm54Q1dyQ0F46q\nd+EM1k6rqCzBI6wGLb5CWHIAYUF6VliHypRxnzeIZGHN3bDiuFHSimyz8j4jwkoR1rkYwoIm\nZ4S1KtdfuUux3KJ7tbWts5sa1snZfXSr9ghLIfsKYckBhAXpWWGFZan95DR4dUZbTmtVod/r\nlQx7fV8xPupncvRThHu3BoawNKKvKLrLAYQF6TlhVRYzxOUT0Hv3URznwHzhqB6KreyGeU/D\n2nUcwtIgLF8MYUETv7Bid7nozllJFTkiq6xxWEaZ4+wxu2W2K7ZmS9yl8gjL0tQVwmoJICzo\nz6peXj8LDz+LNH2FsOQAwoL+nMLqK0TPsqu8AhBhldR0RdG9JYCw4Aeszrywr05SedsDwvKA\nsMQAwoKfEFVfkHWGQ+VlDwjLB8ISAwgLfsLefRj6LIlzizBFWF4QlhhAWDAaDyes382IsGQQ\nFvQDYQ2aEWHJICzoB8IaNCPCkkFY0A+ENWhGhCWDsKAfCMvDzy8mhCWDsKAfCMsDwhIDCAtG\nA2F5QFhiAGHBaCAsDwhLDCAsGA2EVed9EQSzxUcl40cWe3orNmZBEG87dYawZBAW9ANh1dja\nv0G4dTLa2NOn2nixDV669IawZBAW9ANh1ZgFi6/0axHMyowfQfD2laZ/g+dy4y0I/nboDWHJ\nICzoB8Kqsg0W+jMO3ouMi8DMBl/UsGthRfU3eOrQHcKSQVjQD4RVRUspVeJ6KS6mWfClPz+V\nzGb5v1inZ6ERlgzCgn4grCpxoMvt2cwvLi6mQk16TpijJ43nQFgyCAv6gbCqBO4AqiasL3dQ\nlc8d/SAsGYQF/UBYVSRhLew08c0V1tPss0N3CEsGYUE/EFaVirBsxvdglhnrK/NV+a8Vd/IV\nwmoBYUE/EFYVSVj50qttKayX569O3SEsGYQF/UBYVURhpe/PQbD4SIuVDC/dxlcIqw2EBf1A\nWFXiwKjoU90lrGV8D+K80VvaDYQlg7CgHwiryotaMJoqOb00LqY/xlOfs86+QlgtICzoB8Kq\nsrWjqFjdGawtHH3Sn9tg9t65O4Qlg7CgHwirhvssob2YXoLnj2zMFQd/UjW+6lq/UiAsGYQF\n/UBYNd6ctzX8x5bgn01Ij70WQUGH3hCWDMKCfiCsOts4c9FCz/r+5VJ6ewqCZ7N6NEBYCAtG\nA2ENmhFhySAs6AfCGjQjwpJBWNAPhDVoRoQlg7CgHwjLA3+EQgwgLBgNhOUBYYkBhAWjgbA8\n/Kaw9E3H6wurvJeJsGACICwPCEsMICwYDYQ1aEaEJYOwoB8Ia9CMAwjr29AxI8KCSYGwBs14\ndWF9l3TKiLBgUiCsQTNeW1jf3+eMhbBgyiAsD7dWdP+ucz4jwrpRwjC031bZ12Xbzp59nmcX\nJs4B++U8DKNkU+53zyoJd31Op+UUw/CQfTnob2mX9BUQlgeEJQYQ1hUor1Z95Z5adnZkeelh\np0hpIz8gCS3R3jmF4qwOYXQSe7kc3a0S08YR1pn0FRCWhxsTVsNXkrEQ1n1QXK274hoWdnZj\nH4WXHrYK5+UBcVhykM5qLo92eqC7XaVmCGVP92x6F4Tl4baEJfhKMBbCug8KuWSXa3bxzuWd\nF/bVmaOxgTkwG+BE62w0c1xn24l0VpvCJD9FiyhOc0ulndK7IKxBMyIsGYSVS+aorst5TQiD\nC2tljtAHHjJhHE34MH89imdlRkVXQOlK59af6kuX9A4Ia9CMVxSW6KumsRDWfZBL5jUMX9V/\nVtLOdJ1d1fNXGz2touwyt/Xv9VyNR/apHbRYCQiHqeBaHbivJEiKPJm81vWzq59V0u8uQBNV\nS1ciOuhP1WmX9A4Ia9CMCEsGYeVyiVRt+ZSNMoSdx8jWovW442C39FWc1312grCqh5kxjaI0\n1s5KQh+Q7T3Wz65+VuvwSjcKs4xrlXyjP8O0W3oHhDVoxkuEdYYWYZ09zn8qCGskrFx2ZqyT\nVIVgd0a60rQxRZ9sKzqkp1i3XIfxSWskdprLhylzZUcs7aZmZWdb+gBhQtk4q8O15oSqrp6E\ny+x0kkNtWOhJbzD/e/4HrfznF3MNJqxf/A3dQVj2Ol2ai3JXlJudnRs7DlrnAlKTvJOuRc/D\no9NJVVjVw1IzDFPHlWJIQud4wRiNszq6uvvhzz686gLVa7uw5H8UAyMsDzd1l5Ap4aQw12kx\n7Ykqq46Ku3daK0d94Sa1GvRp/xqLwqoeVh9+pY0DmsYQzuryur6MElZm1CzDplVYLf8oBoTl\nAWGJAYR1Bcx1unaWIL3WdxaXsuCVfV7EStO6k6qHnRdW826ccFbXFNZB168OVlid0pcgLA8I\nSwwgrCtQXK0F8/pOj7DUwsrl5ngVYTVv0wlndU1hmdsEqRVWp/QlCGvQjKzDkkFYoV0C5bCv\n7vRNCe2wpO+UMHJj+3Ih1F4vhJLOSrxj1+9nH7SR4lxYndKXIKxBMyIsGYSVD27ym2+VVUeh\nXHRXDUzR3TSQR1jNonvqNlJUiu7lUvPsHJTjhLM6SvXvnj/7qIrq4bI4+w7pHRDWoBl5llAG\nYeXTvLyqXLmLF8rLGrLhhlrWsNYjrHV6iMt26antMElYr3bkYmKnqBzQqMGOcFZ7oZrU/2er\nItW6OKMO6R0Q1qAZryos3tYwIdSlWLlvHzsP+4bVFaBzPRza24t6VX63M0MzYmk5TBLW3l04\nmmoLWmEcUvGs1s25Wf+frc/eeVfE+fQOCMvDTRXdU4Q1JdTVGrsrI3fOUqdCLuoZmzivSR/V\nozmJOULdJYx3R/vSqKRarqocJgkrG4QlldhuGRUvpJLOKrlSCctkPJlBVHlG59I7ICwPtyYs\n3jgK12F14U2/qz38/GMQlofbExbvdIdrcLrs2cCd/DK9MUBYHm5QWPzVHLgGq4setUluZoCF\nsIbNOICwzjRCWNCF6IJX8h2uVcG6Aghr0IwISwZhjc3+goVVyZVuEV4DhDVoRoQlg7CgHwhr\n0IwX9nB9YZ3bgbDgrkBYHn6z6N69OcKCxwVheUBYYgBhwWggLA8ISwwgLBgNhOUBYYkBhAWj\ngbAGzYiwZBAW9ANhDZoRYckgLOgHwho0I8KSQVjQD4Q1aMbBhPWxmAVBvHXjX5W/RPj3OQie\n3872jbDgrkBYHm636P5i3fTixN9dYT2br8/n+kZYcFcgLA83K6yPIHj7StO3IPhbxv/oDdPF\nW/D0njV7Dt7cwzpmRFhwsyAsDzcrrIUV1d/gqYzHwWfRxZP+noltdqZvhAV3BcLycLPCmuX/\nZwuc//sZOVW7cPYjLJgACGvQjEPfJXRGUB/B4u05CP7Hp7P7wyliISyYAAhr0IwDC2sbLIrv\nf/Oae3nrcDsLPs70jbDgrkBYg2YcWFhPs3I8tQhm79nH6yz4MoE4MBFv3wgL7gqENWjGYYUV\nO75KnwJtp3/bfK1DHD8Fs61w2LmMCAtuFoTl4WaL7oaX5y9h75db15oFxRgLYcEEQFgebltY\nL+74ytnr3jl8L6vuCAsmAMLycNPCioM3ea8rLN7pDtMCYXm4YWF9zuq+ssX2f59qUFVU3hEW\nTAqENWjGoYS1rdwA1CyMwf69qVXwdiP9W657QFgwARDWoBkHEtbnrFm/+jC3BP/op3XshrsQ\nC2HBBEBYg2YcSFiLIHBezZC/UMYEjMq2jVWkCAsmAMIaNONAwgokYaUfmcee/t+vcmP28lk5\nrGNGhAU3C8LycMNF98v3IiyYAAjLA8ISAwgLRgNheUBYYgBhwWggLA8ISwwgLBgNhDVoxtsR\nViD/X3o4YbUktDuLbwgLLgFhDZoRYbWcTfENYcElIKxBMyKslrMpviEsuASENWhGhNVyNsU3\nhAWXgLA8TKno3k9Y3wbvMQgLfg+E5eHRhfVd4jkGYcHvgbA8PLiwvr9lYyEsGA2E5eGhhfVd\np+0YhAUXsgrDcOls75fzMIySTXuLAoQ1aEaE1XI2xTeE9YCEilOxmYSWaN/SogRhDZrxfoXV\n8FVpLIQFP2KndVSMp+Kw5CC2cEBYg2a8W2EJviqMhbDgR2SGyqZ8c7uVja+idTaYOq4zRyVS\nCxeENWhGhNVyNsU3hPVwHJWK5vlo6pD56mh2HOavR6FFBYTl4XGL7qKvcmMhLPgJr2H4qv6z\n0lvZSGrtb1EBYXlAWAgLrk6kyumnbGClt7LZ39HfogLC8jAtYV1Ci7Au68RzlgjrcdmZSlUS\nhju1GYbhmRY55n9V/6CV/4x9AldkBGH5zqb4XyHCejSWxkPWSpKwai0qMMIaNOMtjbA6N2dK\nCMNRzPQis9CqKax6iwoIa9CMCKvlbIpvCOvBWDurrl6z7ebNwHqLCghr0IwIq+Vsim8I68GY\nOzpSC62adwnrLSogrEEz3quwWIcFw3AIXfZpui/XYe31OqxGiwoIy8O07hJ2bo6wYDBW5eoq\nu9CqWOn+ala6N1u4ICwPDywsniWEQXCeaT6ZevspKsdTaqzVbOGCsDw8srB4WwMMQGWpQmye\nbz4VTz9HB7mFA8LygLAQFlyV2F0MmrkpNl+WUfE+LLlFAcIaNOMdC4s3jsINgrAGzXjXwuKd\n7nBzIKxBM963sPirOXBrIKxBM967sMQAwoLRQFgeHrro3h5AWDAaCMsDwhIDCAtGA2F5mJKw\nWnYMJywvCAv6gbA8ICwxgLBgNBDWoBkRlgzCgn4grEEzIiwZhAX9QFiDZkRYMggL+oGwBs2I\nsGQQFvQDYXmg6C4GEBaMBsLygLDEAMKC0UBYHhBWGXgvF4Lq/R+LIHh6azRHWDAoCMsDwioD\ns6qwtuZPDz59Iiz4TRDWoBknI6w/QUVYH0Hw9pWmf4NnhAW/CcIaNONUhPURVEdYi0DPBtOX\nYIuw4BdBWINmnIqwnoJqDWsWfOmvn8ECYcEvgrAGzTgRYb0FcVoRVrGRzQkRFvweCMsDRXfD\n/wlmX7KwvrIvCAt+D4TlAWEZ/nvwN01rNayt/vqGsOBXQVgeEJZG3wusCus9mGXG+noLEBb8\nKgjLA8JSfM2Cz7QmrPTFrMPaIiz4VRDWoBmnIKxF8D/VR22l+/tzECw+0uAJYcEvgrAGzTgF\nYQUljf3vQYyw4BdBWINmnLqw/gRvCAt+EYQ1aMYpCMsGxIWjT9knwoLfA2F5oOjuBCrCegme\nP7IJYRz8SREW/CIIywPCcgJWWPa24LOZI8b15ggLBgVheUBYTqAqrPTtKQiet43mCAsGBWF5\nQFhiwLeJsGBQENagGRGWDMKCfiCsQTMiLBmEBf1AWINmRFgyCAv6gbAGzXgrwqo/8udtfgVh\nBWf+d4WwoB8Iy8N0iu4IC6YBwvKAsMQAwoLRQFgeEJYYQFgwGgjLw4ML69uAsOB2QFiDZrxj\nYX2XICy4FRDWoBnvV1jfLt5jEBb8Hghr0Iz3KqzvOp5jEBZcRGhJ1nlkv5yHYZRsyjarbP9S\nOhhhDZoRYckgrAcmLFiZQJJvR/tKm5NwMMLy8LBF94avKsZCWPATSmGFO7UdO4GDabLTGxvh\nYITl4VGFJfjKNRbCgp+QqUh97DNRJakeX0XrbDB1XIcmkGqHZZPCuXAwwvKAsBAWXB0rrPSo\nvxwyXx3NjsP89ZjvmafzYrzlgrA8PKiwRF85xkJY8BNyYZkv2UhqXW/xGoav6j+r5sEIa9CM\nCEsGYT0wubAO+ks2+zvWW0Sq4H7Khl7NgxHWoBlvR1gX0CKsi/pAWNCGU8NaOuOtkl1R3Nq5\nYfM/rH/wAPy+sM6cT/G/QoT1cFRvCgrCWhpT7YoavAMjrEEz3s4Iiykh3AjVdVhNYRVzwUhY\nioWwPFB0R1hwdfJVoku9TLR5M3DtDMFe6wcjLA8IC2HB1amOqZp3CeeOsBpLsRCWhwcVFuuw\nYEiqwtqX67D2eh3WIXTZ1w5GWB4QFsKCq1OrWhUr3V/NSvdVuf5KWIqFsAbNeJ/C4llCGJCa\nsE5ROZ5SYy3nqedTsyKPsAbNeKfC4m0NMBx1C52Kp5+jQ20xQ9x4AhphDZoRYckgrAemOWza\nLaPifVixu1w0s1dcbYqwBs14r8LijaNwmyAsD49adNf/dXzlMxTCgt8EYXl4aGHxV3PgBkFY\nHh5cWG0BhAWjgbA8ICwxgLBgNBDWoBkRlgzCgn4grEEz3oqwWncMJKxzICzoB8IaNCPCkkFY\n0A+ENWhGhCWDsKAfCMvDdIrurTsQFtwVCMsDwhIDCAtGA2F5QFhiAGHBaCAsDwhLDCAsGA2E\nNWhGhCWDsKAfCGvQjBMR1ntlIWi2/2UWzF7s5p/nIHh+63RyBQgL+oGwBs04EWHNasJ61n96\n8Flvme92A2HBsCCsQTNOQ1j/X/UvOf97CV6+0q9FoMZYb8F/e0/Tj+fgrcPJFSAs6AfC8kDR\nXfMR1EZYs+Ar+/gKZtl/n4L/Y9t0OLkChAX9QFgeEJbmKajVsOyW/fjX3DgLwoJ+ICwPCEvx\nFvz36tsX/j3ZEdZT2fzDFrEQFgwKwvKAsDI+g9l7TVh/dfXqxSlbbWfBR4eTK0BY0A+ENWjG\nCQgrDv7+qwkrfZsFQTB7yzfjQEmtw8kVICzoB8IaNOP9C+tvNterC+sz1isZ4k/bPI6fgtm2\nw8kVICzoB8IaNOPdC+trFnzWhfV/zHhqO5t9Fs0/NOgtAgAAIABJREFUZsH7+ZMrQFjQD4Q1\naMa7F9ZCFapqwvofxk3pNliUzd9N1R1hwaAgLA8U3dOgxIlVvvwTNs6BsKAfCMsDwjovLDsV\nRFjwKyAsDwgrD1SmhP9PYKrteha4CP6n3vjrzg/PgrCgHwjLA8LKAxVh/a/gafuV+UoPrj6C\n/1L3B/OFWAgLBgVhDZpxYsKy074XO0nUL5jZ2g2WNcAvgLAGzThNYaUfi8xQC7O2Pf3f2cbs\n5bPLyRUgLOgHwho041SE1XkTYcGgIKxBMyIsGYQF/UBYHii6iwGEBaOBsDwgLDGAsGA0Jims\n4Eq/qn4xXd4vwpJBWNAPhOUBYYkBhAWjgbAuyIiwzm4iLBgUhHVBRoR1dhNhwaA8uLC+DR0z\nIqyzmwgLBuWhhfVd0ikjwjq7ibBgUB5ZWN/fZ4xF0V0MICwYjccV1nedZhOEJQYQ1u+zCsNw\nWYtlIeejL+2H/7Dj833swiRN9rVYHIbxWn9Nwl3zGISFsM7GENbohIpTI+Z8+KnLrtHLRXu6\nsDzbxykKD1mDuaullf6hYay+H8Lo1DjoYYXV8JVgLIQlBhDWr7PTl/GmGuwurH3U3mQYYeUZ\nfX2swrkx8Xydh8zvzNCReWNQ+bjCEnzVNBZFdzGAsH6dbJ6UjT3m1WB3ofhaXmPi16vXozbw\nYan8FK3NWCrbSE5p/lM3YTYEq4GwENbZGMIamaO6guf1y/fOhbWyTU5mGrhSylolehaYH51F\n60c9qLBEXzWMhbDEAML6bV7D8FX9J798N/Mweq1NCcuLXH+eVpngwmST2vqXiR6XURitjkIv\nBueovKewoNFB3uo4D5Ps21ofu69kLHpfZ4PE+WtaOTDJs66jsHIa+WAyaWoPYSGsszGENTKR\nKrifspmT2TRDktgnrGMUFuXrUh95iWjX7EXjHiUKq9JBmueb65pTXO5rCCvvOCpVt7OFKs1p\n7pzGKfOUuXe4Dhs3CicqrHO0COvsccOdc/fmCOvR2JnBSGIv33124R/SQ+QTVqyv+VNsrJCP\nuvID1byr1otGPCo/hVWtA4vSm9pa6491RXbFZ6TrVRu7U7MqZ7h2Umi3klKIh8qc0FyC/ybI\ncMIa+5dNBYR1CUtzBVtvOZvtwrIX/clMruy+lQnu1QSz3kt+bPOo1LRa1juoHpPOw2Pr2Wzs\naGrt3OnMvGSGW24Ny3SUec247OgazjDREda5Ft2mhCxrEAOMsH6XYi4YmaVYUTFeaheWuurD\nZG1nYHbfvGgSN3pJ07ajUj3SiRsdpEWrXDWn/Wssnk0up2NZt8pbHBI9VSxnh+lJD/EOtVPI\nQVgI62wMYY3Kuiwj6ZFNbbolKmJv289rw56yHlXrRSMepStQUdrowFJ838fOrsZ4r9a4ck7z\n2gIzZdG4cXIGhEXR/WwMYY3K3PGEO1XzCSubaNk69y7tLizxKHUCtljuE5aaWy43x8uFNRce\nwBFPTvOgwmIdlieKsG6KQ+iy1wJTkzDvlFBx3Cj9RGVs7l7+tV4KGkfZUnyjA0veyi4TE89G\nmhLaKWn1WcIk1id1LA+PaukQFsI6G0NYY7Iqb5WZpVi29L1pCEtd6/swr2Gdyp1hpehuJly1\nXjTiUctybUGlA0tVTfIIy1t0d1nqW47H2D7p7QrO8qjC6vQsIcISAwjrVwmdqra+/g/isoZE\ny2xvo9kELT5qU6grX41mTqZ6v9cl7X2jF031KLNn5ayFqnRQnp7+1IuxDnnR3Wb0LGt4NZ1U\nZ5nlaFIX3ffu7UjDwwqLtzW0RhHWLbFzRxmxvvDFhaP7sBK1rz0wK6bU83rLtFz3uSpbVBaO\nVo8qxlmlUCodGPLjbX47M8wzhtWFo/NyULUvFns5/ddWpq5dMxoQFsI6G0NYIxK7q713Zoyi\nHqpZ1ctFanQzX5dFcOUM+2YpNfzS1jssM3Mktr9KL3kC5yhBWNUOnFapuUsY7452NmczFnvX\n5XuuLFHewO1fPwxdPPuTNEpYDyws3jjaFkVYd0XVOPfD6vx58/BzlTO+QlhyAGHdFPcqrFPz\nQcEau8Y7Cx9cWPzVHIR19+yad9LuhFXjuZsaSXOA9ejCuiwjwjq7ibB+F/36u/X5djdJ1Hw/\nn8uhWcFCWBdlRFhnNxHW75K4Lxi+N/b+sWHSuEWYIqyLMiKss5sICwZlksK6Fj+/mBCWDMKC\nfiAsDwhLDCAsGA2E5QFhiQGEBaOBsDwgLDGAsGA0ENagGRGWDMKCfiCsQTMiLBmEBf1AWINm\nRFgyCAv6gbAGzYiwZBAW9ANhZbwvgmC2+KgGX2bB//1ivn71/bOECKsFhAX9QFhpurU62rrB\nZx161t/fEVbXTYQFg4Kw0nQWLL7Sr0Uwc2IvwctX+n8tAj3G+hP87dk1wpJBWNAPhJUNsBb6\nMw7ey+As+Moupi8jsTj47Nk3wpJBWNAPhJUNpsxccBu8lEE9/ftnH3eujL0uAmHJICzoB8LK\nxk+m3P4ROO8Te1IjrH9fwZPesXh7DoJFj2EWwpJBWNAPhFW+NMYtqv9Vw61/L8Gb/i5V5TuB\nsGQQFvQDYcnCSt9mmaFmylfpIpip6tZW17UuA2HJICzoB8KShfUZ6zFVrKaBT7YaXylydQNh\nySAs6AfCEoX1qQdV/9nOZk7h6uvy4jvCkkFY0A+EJQproQdV/ymWPDQadARhySAs6AfCKlZZ\nfTp3CY2a/lNzFMI6u4mwYFAQVvpiS1TvTonKqOmf+ZIX2z/tkzoXgLBkEBb0A2Fl0z4zsoqd\nZQvPetT1L5PYs5of6puF6dvlT+ggLBmEBf1AWOKzhO/B0/Yr/fc+U6Ovj2CmVPZXryK9DIQl\ng7CgHwhLjZycdaG2TvViY3qWaFeOzi5f6o6wZBAW9ANhZWzVoquFqWTlhfWPhYp9lBtPLxcv\nG0VYbSAs6AfC8sBfzREDCAtGA2F5QFhiAGHBaCAsDwhLDCAsGA2ENWhGhCWDsKAfCMtDj5e4\n145FWDIIC/qBsDwgLDGAsGA0EJYHhCUGEBaMBsLygLDEAMKC0UBYHnzC+jacORZhySAs6AfC\n8tAurO8S77EISwZhQT8QlodWYX1/nzUWwvKBsKAfCMtDi7C+67Qfi7BkENZIhIpD9uWgv8kt\nPJueYHXHKvu6rO/ehcnR5k/tORzbzzUJd80gwvKAsMQAwrpftKY22ZfNWWEtq5tim/YduvtT\nde8pyly1DsP8zb5xGK4953oIo1MjiLA8yMJq+Eo0FsLygbBGQntklZoRkE9Y+yh0N8U2nh27\nwowOq3CeOppy1CUzb47REJYPUViCryRjISwfCGsktEeUJuIzwmp1kndnsSPrPlPivLLzaAyW\nfeiRUzbe8k0IUz0KPNRjCMsDwhIDCOt+UbrSUtGfgwnrqGQ1r/lmZXeuTXUr8U8ITXereghh\neZCEJfpKMBbC8oGwRkKVwpVHDvqzoiZ3MwzzAZgTXUXhfOM2TY/LKIxWx0r3+vM1DF/Vfyq+\nCcPEfMlUuU/3xQDM7eW0yjQXJnYumTTFiLA8ICwxgLDul8wGazWy2ejPi4QVF/WvPLizzXZu\n9/ozUgX3Uzb3c1LvihFVZsv5qRh/ub0cI7thilvrsHGjEGF5CARahCW07HHOCAuGRS0qSLIZ\n2TJMDh5hSdEoG5dFxjImeMpj5c280mRqMJVUfLMqZ4jZ2GuuxmBpvRc99kpPeV3+UBmjmcvq\nH7TyM2GNffa3DMIaCSWsV11fer1UWMo9O1N+MsGVie1z9ZStl0XrpEydODV2Ne+zE8JKLzbN\nye49Nu8jMsLywJRQDDDCul+UsLLpYGaEzaXC0nf2zCzPBOdFk9jpvmxlZ4bVfYZDuXy00osS\nWZisj9IxBoTlAWGJAYR1vyhRHHT96nCpsJzN4r85TvepLj0VFIOvqnzKjUove/ttfhSO0SAs\nDwhLDCCs+0WPbIwdhhPW3NlTLsXqIqz0tLJl913zGA3C8sA6LDGAsO4XLSwllPhiYalBjy0u\nVaeE1e7zxxRz9vm+SBZWo5fjRkkrss2i6k6E5QNhiQGEdb9o8agVWEtV0XbLU/tzwlL37Xbm\ntl3oFt1P9RrWqry35y7Fcovu1aeky17mtuhldx8rVXsNwvLAs4RiAGHdL9oEa6Mfa4VES2Uf\nVU2lxkOn1BVWtBeWNez1GoR9pfuwLLWfnDndq9POEVall0yI8VE/k6OfIty7NTADwvLA2xrE\nAMK6X4rS9qF8zNlM3eKqsMworLlw9NVpky/5XFW6ryxmiMsnoPfuoziOyCq9rOyGWdq1dh1n\nQFgeEJYYQFj3ixbFyYyBcmkcMqvM1/W5YGK840TXURjvU7fNYZkNuZJdtfvYXS66c+aLkSMy\nt5pe6WWnTBlbsyWNEhbC8sEbR8UAwno8mrfrLmd1cR88/HwZvNNdDCCsx+Mawjo1nwz0s2u8\nAhBheeGv5ogBhPV4XENY2RDL/8K+OklzgIWwfPB3CcUAwno8riKsNGq+kM/DoVnBQlheEJYY\nQFiPx3WEtW8sq/KRNG4RpgjLC8ISAwgLRgNhefj5xYSwZBAW9ANhDZoRYckgLOgHwho0I8KS\nQVjQD4Q1aEaEJYOwoB8Ia9CMCEsGYUE/EJYHiu5iAGHBaCAsDwhLDCAsGA2E5QFhiQGEBaOB\nsDx0u5j+1P4NPxazIIi3+vs/qUE7CAvAC8L6acZtbT38i/2zhC95D/UGP02IsOBxQVg/zLgN\nqj76CIK3rzR9C4K/pod6g58mRFjwwCCsn2X8E8yqPlpoUaXp3+BJ99Bo8MOECAseGYT1o4yz\n4Omz6qNZvqXD/5oNfpbwbCOEBVMGYXk4fzEFb63vdAhm2X/+eRoIICwALwjLQ7eLSfbRNlik\n9pwRVgOEBf1AWB5+Iqyn2WeKsNpAWNAPhOXhB8KKta8QVgsIC/qBsH6cUfLRy/NX2QPCaoCw\noB8I68cZBR+9mPEVwmoDYUE/ENaPMzZ9FKt7g2UPCKsBwoJ+IKwfZ6z76HNW+AphtYCwoB8I\ny0Ovovs2mL0XGwhLBmFBPxCWhz7C+pzl9SsFwpJBWNAPhOXhMmGZz0VQkCKsNhAW9ANheegj\nrABhdQBhQT8Q1qAZL+wBYQF4QViDZkRYMggL+oGwBs2IsGQQFvQDYQ2aEWHJICzox5SF1b3Y\n3UJ+MfXvCGHJICzoB8LygLDEAMKC0UBYHhCWGEBYMBoIywPCEgMIC0bjwYX1bTiTEWF13kRY\nMCgPLazvEm9GhNV5E2HBoDyysL6/zxgLYYkBhAWj8bjC+q7TnhFhdd5EWLdKGIaNb12P6Nug\nzi5MjtlBB7t5yL4f21sn4a4ZRFgeYVF0FwMI6x65AWGdosxV6zCM7XYchmtP80MYnRrBhxVW\nw1eCsRCWGEBY98gNCGsVzlNHU466ZObhshF7VGEJvmoaC2GJAYR1j4wvrGw2uDEfeuSUjbd8\nE8KMTTl7LEBYCOtsDGFNgPGFtbLNs5GVGjkl/gmhSbCqhx5UWKKvGsai6C4GENY90hTWcRmF\n0coOctbzLJzszcZmHkavRbvKrtMqGxjFu7yj0yrbubTjILdDvSNMNpUzSMyXbFK4T/ehniB6\nD0uaRkRYCOtsDGFNgIawdqFByyd2N1b6a2zbVXYdIrOxsh3ZzUO9w6Pd4VSpdsWI6pC56jTP\n53uew9Zh40bhtIXVSouwWtv/0jkjLBiK0CXbPmW2OSgBqYLSOoxPRRV8n+/R7Sq70kjtOsVG\nJEpYe+23Zb1DPYjSDYtp36qsSL1mxgrDV/3dd9ihMic0l+K/6XJFYY39U6YGwvp16sJaGens\ntTjmpvxt9izNnp3ZquzaGM2czHTODotOQoflrnl+AolTY1fzPrvDd9ixeR9x2iOs1l3dpoQU\n3cUAI6x7pC6suZ0i5k447V/tJDAye07FJLLclVTu24VFF40OlZHCZO3eBXRL9Iew6Mh7WLOs\nj7AQ1tkYwpoA9RpWVV/7uPxe9ZC4q9ql0OHefpsfG62bZ9N+GMKyICxPFGFNEa+w1PRvuTlK\nwhJ3VbuUDKjvJoahUzXvIqz6YQgrp4uvEJYcQFj3SF1Yc9cF9pZdsUcv7Cy2yl1dpoQFx42y\nT5RvRrKwvIc5h1sQlkdYLGsQAwjrHqkLa1XUt+M8dKzs2biDKrtrY27blUX3tg6t9Nwhklt0\nd+K+w47F0q2CRxVWp2cJEZYYQFj3SF1YJ70m4WQWEszVOoKDrawfKssaKrvUMGlfLDuoCqvS\nYTaRjI9acMXjgK96R+NsfIft87UPJQ8rLF4v0xpFWFOkLqxiwaYaMtlit53+VRaOVnftnYPq\n1Xm3Q9tH6LxwYe8+iuOMvDyHrV3HGRAWwjobQ1gToCGs9LDMxkuJqW6rW4Hx7mhHNurRnJV7\nl7DcdVyVB9WEVekw3S2V9NynBSNnfudW09sPSxolrAcWVoc3jlJ0FwMIC/qwciTVDR5+rnLG\nVwhLDiAs6MOp+WSgn50twbs8tLDO/dUchCUGEBb0YnXmhX11kuYA69GF5QdhiQGEBf2Imi/k\n83BoVrAQVqeMCKvzJsKCdvaNZVU+ksYtwhRhdcqIsDpvIiwYlCkL6wYyIiwZhAX9QFiDZkRY\nMggL+oGwPPz8YkJYMggL+oGwPCAsMYCwYDQQlgeEJQYQFowGwvKAsMQAwoLRQFiDZkRYMggL\n+oGwMt4XQTBbfFSDL7Pgv17M16/ef+0LYckgLOgHwkrTrdXR1g0+69Cz/v6OsLpuIiwYFISV\nprNg8ZV+LYKZE3sJXr7UyEuPsf4Ef3t2jbBkEBb0A2FlA6yF/oyD9zI4C76yi+nLSCwOPnv2\njbBkEBb0A2FlgykzF9wGL2VQT//+Y58irIy9LgJhySAs6AfCysZPptz+EThv63myI6wnvWPx\n9hwEix7DLIQlg7CgHwirfBeDW1T/q4Zb/3kJ3vR3qSrfCYQlg7CgHwhLFlb6NssMNVO+ShfB\nTFW3trqudRkISwZhQT8Qliysz1iPqWI1DXyy1fhKkasbCEsGYUE/EJYorE89qPq3nc2cwtXX\n5cV3hCWDsKAfCEsU1kIPqv4VSx4aDTqCsGQQFvQDYRWrrD6du4RGTf+pOQphnd1EWDAoCCt9\nsSWqd6dEVRFWXmz/tE/qXADCkkFY0A+ElU37zMgqdpYtPOtR138yiT2r+aG+WZi+Xf6EDsKS\nQVjQD4QlPkv4Hjxtv9L/vM/U6OsjmCmV/dWrSC8DYckgLOgHwlIjJ2ddqK1TvdiYniXalaOz\ny5e6IywZhAX9QFgZW7XoamEqWXlh/WOhYh/lxtPLxctGEVYbCAv6gbAGzYiwZBAW9ANhDZoR\nYckgLOgHwvLAH6EQAwgLRgNheUBYYgBhwWggLA8ISwwgLBiNmxVW8zGY6wqry2M2CEsMICwY\nDYTlgaK7GEBYMBoIywPCEgMIC0YDYXlAWGIAYcFoTENY34af9d8EYYkBhAWjMQVhfZf8pP8m\nFN3FAMKC0ZiAsL6/+xgLYbVGERbcLHcvrO86vftvgrDEAMIam90yCsP56nC+ZRiGw59OZ3Zh\ncszOKD/vQ/b92N46CXfNIMLygLDEAMIamVVoeTXbS6mRCfqFJR7446ath52izFXrMMxfRR6H\n4dpz7CGMTo3gvQur4auuxqLo3hpFWLfNOizYZ5v7SHBSHvQJSzzwx009h63CeepoylGXzDxs\navLOhSX4qqOxEFZrFGHdNvMwXGVDj2N25Sdpi5O6TAUvmC72nFlWD8tmgxvzoUdO2XjLNyHM\n2JSzxwKE5QFhiQGENS65Bk7my90Ia2W3spGVGjkl/gmhOX5VD923sERfdTMWwmqNIqzbJhuZ\nLIuhiZ0bqq/rbOgVJvtK0O5SH+vsuHifNg9Upe+5Hqwdl1EYrWzfQne6m3k4X2cti87cgyp5\nnFOzOxPzJVZz2X2oJ4i1Dk4rnXVj9iRNTyIsDxTdxQDCGhddw5qvjC5KK8T2604WVlxWvWoH\nqt70aGdX9iB3V3STREVnlYMqeWrC2hUjqkOW8DTP53tuB8fIbsT5L63fKLxhYXWgRVidjkVY\nbVGEdeNYJ0Tm+s/HV2F8KgvZuShKYUXZpb+slLmdNrEuKmWNDukh0iUmsTvTUglznt/uqxxU\nz1OZEq7KitSrVqS5x1npQI+90lNelz9U5oTmsv13owwvrPPn8J/hf+aDgrB+xDpyxiHWCnNT\nwXbmgNVNNVQ5VQzitNHjmJX53GuViN3ZQVX5UTuonqeSLnFq7GreZyeElQ7K4/XeY/M+4g2P\nsOoRpoRdGjHCegj2r+qa1+OQ0gqn/WvcKix3M01rQb3eaV5sxy3dCR/Vg1rSNnKrJaN2uFXp\nQP+oZH2UjjEgLA8U3cUAwroJTkszDskv6n1edUrTi4WVf4ZlF1J3wkf1oK7CcjYqHeztt/lR\nOEaDsDwgLDGAsEYlsgOi/HK2F7WqXS83x2sJS+xucGGlp5Wd7e6ax2juW1isw+q+F2FNhGV+\nt626DsvedfuBsObuTrE74aNykFdYkSysed1Jx42SVmSbRbVfj7A8ICwxgLBGRY191tkYaz83\nCzArcvjJCGtVVLzjlu6Ej8pBXmG5RXdnT6WDuR092t3HYulWwZ0La9hnCSm6iwGENS55cSk0\ngyA1cjnpa32dHvIquQ16hVVroxcY7PWagn1Ld4KwKgfV8+QZNK/OIjD3ToHbQSbj+KifydFP\nEe6L57sL7l1YvK2h616ENRWO89xXutCzDPXlbevVdipng15h1dqUSzjV2iexO2mg5R5Uz5Nn\n0OzdR3GcE6l0kL+IwrynYe06zoCwPCAsMYCwxmaTTa/CeGUHL4mZOKnbevHuaBWRVJ6MFoVV\na5NxUO/ZSky9W+pOnBm6B9XzJO6cLnK+uyfidpDulOTidX6C9RLW/QuLN4523IuwYFxWFVt2\nYXIPPxv6+Iqie3sUYcEQnJpPBvrZFQs4SqYgLP5qTpe9CAtGZnXmhX11kuYAayLCukr/TRCW\nGEBY0I+o+UI+D4dmBQtheUFYYgBhQT/2jWVVPpLGLcIUYXmh6C4GEBaMxs0Kq8l1hdUFhCUG\nEBaMBsLygLDEAMKC0UBYHhCWGEBYMBoIa9CMCEsGYUE/ENagGRGWDMKCfiCsQTMiLBmEBf1A\nWINmRFgyCAv6MSVhvS+CYLb4qAa3z0Hw9NYvI0V3MYCwYDQmJKyt/fNdWzcYm9hzr4wISwwg\nLBiNCQlrFiy+0q9FMHNif4LnbMT1/hT86ZMRYYkBhAWjMR1hbYOF/oyD9yL2FQRf6vOjYrHO\nICwxgLBgNKYjrBc7F9wGL0Xsr/P9+hmv3wPCAvAyHWHFgSm3fwRxIzZMxuv3gLAAvExHWMXr\nF5z3MDwF6cciCJ7f5UN+mPH6PSAsAC/TFlYQ2FuH/WaGCEsMICwYjakLK/jzlabbWdBrjEXR\nXQwgLBiNqQvLLBnN7yBeCMISAwgLRmPqwmrGLgBhiQGEBaMxHWHFwaf+/HTuEj4jrDM7EBbc\nFdMR1outU707FfYXK7G038JRiu5iAGHBaExHWFs7soqdhwnfbe1q2+82IcISAwgLRmM6whKf\nJXzWptrO8pHWdTNevQeEBeBlQsJ6c9/WYItWn0/CGxyulvHqPSAsAC8TEla6Ve+SWZhKVlFl\nf8uUVX9HVlcouosBhAWjMSVhXR2EJQYQFowGwvKAsMQAwoLRQFgeEJYYQFgwGghr0IwISwZh\nQT8Q1qAZEZYMwoJ+3KSw5AdpriGsyx7RQVhiAGHBaCAsDwhLDCAsGA2E5YGiuxhAWDAaCMsD\nwhIDCAtG496F9W34Wc9tICwxgLBgNO5bWN8lP+m5DYQlBhAWjMZdC+v7+1JjUXTvEEVYcLPc\nsbC+6/TuuQ2EJQZ+WVihJVnnm91ydG44IN3PQW5Zi9rNalRuc5PswuSYnd/Bbh6y78f21km4\nawYRlgeEJQZGElYYruym0GgpHtet4SAsPecgcQVhXZryon+Mnv9ulcNOUeaqdRjm7zCPw3Dt\nOfYQRqdG8H6F1fBVF2MhrA7RmxWW/v+40gW5j4SLtHPDAcjz/KKwLk95wT9Gz3+32mGrcJ46\nmnLUJTMPm5q8W2EJvupgLIruHaK3Jyz1sc/+h56k8gUpXqSdGw7AtfJ00ljflBcc0fP3VA/L\nZoMb86FHTtl4yzchzNiUs8cChOUBYYmBcYSl/ocepgirLXr7wlrZrWxkpUZOiX9CaI5f1UP3\nKizRV+eNhbA6RG9UWGlVWOu5KsTv02LOqILHZRRGq2PluDLmNExrfWRs5lmz4qjKlioOz/X4\nzk1QO0I6oSLbOhsfzl/L37HOhhfxvvkra/uyzdMq63d5qDd6jcL5pgw2UtaTVM+1fpLSrxN+\nj+50Hs7XWcui6/q/eZG1/s9tRsipnhTu032oJ4i1DvSvDRPzy5TT0hoIywPCEgMjCetQuSDj\nsqxVXhg7p9aVN9xJDQ2x23ylv8Z2f3Ur+5jr8cCu/QjxhHKPRiYSHW1vtrFjrDKTu08dYzYP\nUqPyLoQkLLej6rnaBuURwq+Tfk/RaRIVXdf/zcustX/uXTGiyv4vOT/N8/me20H+D2WLW+uw\ncaPwRoV1lhZhnT/wkvOg6C4GxqthLYvNdRifyrKtbXLKLu9DeohMjcQEpZil0schb6dbVLf0\ndXiqd1ZtI55Q/hnp6s2m3Bll1+GyUnMuM7n71OZe62ZZa2Qy7yvB9o5qv6eSUv514u8xLdfK\ncPntvsa/b+30y3SrsiL1qhVpBpyVDvTYKz3ldflDZU5oLuB/N8iQwhr7t4Gi513CQ3ERzMN8\nsOJ8rMz/Q96ba8EEpZil0sfStNtIW2lYjqnKzqptxBOynxt7/a1N1dn2dpLsUdvX3HSiO9fg\ngrCcI2u/p5JS/nXi7wkLRRambPz7CudrSJwau5r32QlhpYPyeL332LyPeKMjLCn6+1NCRlhi\n4EbWYZ32r3H1wpgXV2BcBKVYSdlH1s6OMppo7r2LAAAeJUlEQVRbupTUSFBrI52Q/cwv1WP1\nPmeLsM5vOgPKjkc2zrXWpPnrxN8jfMj/vpKw3I1DWAy36v+maoXwUTrGgLA8ICwxMI6wouU+\n31Qf+7zG4sScsVgRlGI5bh/VS6396i87q7WRTqjWm9x52pKpfVPs3XukL6X869r+gesf8r/v\nOWE5G5UO9vbb/Cgco0FYHii6i4Gx7hK6m6pSu9wcfySsSh8/FZZ4QncsrLZ/4PrHdYWVnla2\n7L5rHqO5V2GxDuvSvdMS1twtaOUf80rLomFbX/NqUcw/JcyPqBxePaJ5QvZzgCmhzTzveOS5\nKaH465q/R/iQ/30lYUWysKodqH+ljZJWZJtF1Z0IywfCEgO3ICzz39oAYFWUbMt6ihSr9GT7\nsGXptbRVHFbprNpGPCH72Sy6N3/YhcJS/e1MVa/LkbXfU/2HFX+d+HuED/nfVxKWW3R39lQ6\nsGLNdx+LpVsFdyus33iWEGGJgVsQll44dMhrwur/eZ9MFXqvb4rvi4bVmG1oqPRhbvzvI2mr\nOIVKZ9U24gml5WZ1WUPzh10orOw01CKFQyWHm7J6ZO33GGpHVH+d+HsEYUn/5o1z0ry6687K\nE6l0kDk4Pup/Kb2MY5+vfSi5X2HxtobL9k5LWHtT6bATl2wAof8Xnq9BdG8nVmJ5Q021jzML\nR80hlc4qbeQTykcKtjAzd5cK/EhY9YWjjZS1I5sLRxtHVH+d+HsEYYn/5vVzyv+5y0dxnBMR\n/k3t04ZqRFg6zoCwPCAsMXALwtI3seLd0V4QiZ07HJaZGpJqwdaNFQ3TZh/mmZP8qMpWeQqV\nziptxBMqDlSP5sTr6g/6ibDSVfXRnEbKepLqr0uFI2q/Tvo9krDEf/PaORki57t7IpV/052S\nXP4vlTRKWPcsLN44etHeuxXW71K9pGuy7HDEbTPqua4uTj6hh58Nl/oKYXWJPriwktatLkf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IAIT18rD6qefcmvexalnDUaw+MJIvtazh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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 600,
       "width": 600
      },
      "text/plain": {
       "height": 600,
       "width": 600
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(repr.plot.width = 10, repr.plot.height = 10)\n",
    "\n",
    "p <- ggplot(df, aes(x = boxOdds, y = reorder(boxLabels, yAxis)))\n",
    "\n",
    "p + geom_vline(aes(xintercept = 1), size = 0.5, linetype = \"dashed\") +\n",
    "  geom_errorbarh(aes(xmax = boxCIHigh, xmin = boxCILow), size = 0.6, \n",
    "                 height = 0.5, color = \"gray20\") +\n",
    "  geom_point(size = 6, color = \"orange\") +\n",
    "  theme_bw()  +\n",
    "  scale_x_continuous(breaks = c(1, 2, 3, 4, 5, 6, 7, 8)) +\n",
    "  coord_trans(x = \"log10\") +\n",
    "  ylab(\"\") +\n",
    "  xlab(\"Odds ratio (95% CI)\") +\n",
    "  annotate(geom = \"text\", y =17.5, x = Odds[1], label = Odds[1], size = 5, hjust = 0, col = \"gray20\") +\n",
    "  annotate(geom = \"text\", y =16.5, x = Odds[2], label = Odds[2], size = 5, hjust = 0, col = \"gray20\") +\n",
    "  annotate(geom = \"text\", y =15.5, x = Odds[3], label = Odds[3], size = 5, hjust = 0, col = \"gray20\") +\n",
    "  annotate(geom = \"text\", y =14.5, x = Odds[4], label = Odds[4], size = 5, hjust = 0, col = \"gray20\") +\n",
    "  annotate(geom = \"text\", y =13.5, x = Odds[5], label = Odds[5], size = 5, hjust = 0, col = \"gray20\") +\n",
    "  annotate(geom = \"text\", y =12.5, x = Odds[6], label = Odds[6], size = 5, hjust = 0, col = \"gray20\") +\n",
    "  annotate(geom = \"text\", y =11.5, x = Odds[7], label = Odds[7], size = 5, hjust = 0, col = \"gray20\") +\n",
    "  annotate(geom = \"text\", y =10.5, x = Odds[8], label = Odds[8], size = 5, hjust = 0, col = \"gray20\") +\n",
    "  annotate(geom = \"text\", y =9.5, x = Odds[9], label = Odds[9], size = 5, hjust = 0, col = \"gray20\") +\n",
    "  annotate(geom = \"text\", y =8.5, x = Odds[10], label = Odds[10], size = 5, hjust = 0, col = \"gray20\") +\n",
    "  annotate(geom = \"text\", y =7.5, x = Odds[11], label = Odds[11], size = 5, hjust = 0, col = \"gray20\") +\n",
    "  annotate(geom = \"text\", y =6.5, x = Odds[12], label = Odds[12], size = 5, hjust = 0, col = \"gray20\") +\n",
    "  annotate(geom = \"text\", y =5.5, x = Odds[13], label = Odds[13], size = 5, hjust = 0, col = \"gray20\") +\n",
    "  annotate(geom = \"text\", y =4.5, x = Odds[14], label = Odds[14], size = 5, hjust = 0, col = \"gray20\") +\n",
    "  annotate(geom = \"text\", y =3.5, x = Odds[15], label = Odds[15], size = 5, hjust = 0, col = \"gray20\") +\n",
    "  annotate(geom = \"text\", y =2.5, x = Odds[16], label = Odds[16], size = 5, hjust = 0, col = \"gray20\") +\n",
    "  annotate(geom = \"text\", y =1.5, x = Odds[17], label = Odds[17], size = 5, hjust = 0, col = \"gray20\") +\n",
    "  annotate(geom = \"text\", y =0.5, x = Odds[18], label = Odds[18], size = 5, hjust = 0, col = \"gray20\") +\n",
    "\n",
    "  theme(plot.title = element_text(face = \"bold\", colour = \"gray20\", size = 16, hjust = 0.5),\n",
    "        axis.title.x = element_text(colour = \"gray30\", size = 16, face = \"bold\"),\n",
    "        axis.text.y = element_text(color = \"gray30\", size= 14, face = \"bold\"),\n",
    "        axis.text.x = element_text(color = \"gray20\", size= 16))"
   ]
  }
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