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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<h1><center> Inferential statistics on the I-SPY1 Clinical Trial</center></h1>"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/Julio/anaconda/lib/python3.5/site-packages/statsmodels/compat/pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n",
+      "  from pandas.core import datetools\n"
+     ]
+    }
+   ],
+   "source": [
+    "# import custom modules wrote by julio\n",
+    "import seaborn as sns\n",
+    "import pandas as pd\n",
+    "%matplotlib inline\n",
+    "#from capstone_01 import clean_data\n",
+    "from ispy1 import inferential_statistics\n",
+    "\n",
+    "# reload modules without restartign the kernel (makes development easier)\n",
+    "# import importlib\n",
+    "#importlib.reload(inferential_statistics);"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 0. load clean data"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style>\n",
+       "    .dataframe thead tr:only-child th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: left;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>SUBJECTID</th>\n",
+       "      <th>age</th>\n",
+       "      <th>White</th>\n",
+       "      <th>ER+</th>\n",
+       "      <th>PR+</th>\n",
+       "      <th>HR+</th>\n",
+       "      <th>Bilateral</th>\n",
+       "      <th>Right_Breast</th>\n",
+       "      <th>MRI_LD_Baseline</th>\n",
+       "      <th>MRI_LD_1_3dAC</th>\n",
+       "      <th>MRI_LD_Int_Reg</th>\n",
+       "      <th>MRI_LD_PreSurg</th>\n",
+       "      <th>Alive</th>\n",
+       "      <th>Survival_length</th>\n",
+       "      <th>RFS</th>\n",
+       "      <th>RFS_code</th>\n",
+       "      <th>PCR</th>\n",
+       "      <th>RCB</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>1001</td>\n",
+       "      <td>38.73</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>No</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>No</td>\n",
+       "      <td>No</td>\n",
+       "      <td>88.0</td>\n",
+       "      <td>78.0</td>\n",
+       "      <td>30.0</td>\n",
+       "      <td>14.0</td>\n",
+       "      <td>No</td>\n",
+       "      <td>1264</td>\n",
+       "      <td>751</td>\n",
+       "      <td>1</td>\n",
+       "      <td>No</td>\n",
+       "      <td>2.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>1002</td>\n",
+       "      <td>37.79</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>No</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>29.0</td>\n",
+       "      <td>26.0</td>\n",
+       "      <td>66.0</td>\n",
+       "      <td>16.0</td>\n",
+       "      <td>No</td>\n",
+       "      <td>1155</td>\n",
+       "      <td>1043</td>\n",
+       "      <td>1</td>\n",
+       "      <td>No</td>\n",
+       "      <td>3.0</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "   SUBJECTID    age White  ER+  PR+  HR+ Bilateral Right_Breast  \\\n",
+       "0       1001  38.73   Yes  Yes   No  Yes        No           No   \n",
+       "1       1002  37.79   Yes  Yes  Yes  Yes        No          Yes   \n",
+       "\n",
+       "   MRI_LD_Baseline  MRI_LD_1_3dAC  MRI_LD_Int_Reg  MRI_LD_PreSurg Alive  \\\n",
+       "0             88.0           78.0            30.0            14.0    No   \n",
+       "1             29.0           26.0            66.0            16.0    No   \n",
+       "\n",
+       "   Survival_length   RFS  RFS_code PCR  RCB  \n",
+       "0             1264   751         1  No  2.0  \n",
+       "1             1155  1043         1  No  3.0  "
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df = pd.read_csv('./data/I-SPY_1_clean_data.csv')\n",
+    "df.head(2)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 1. Inferential_statistics: Categorical vs Categorical (Chi-2 test)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 1. 1 Effect of categorical predictors on Pathological complete response (`PCR`)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style>\n",
+       "    .dataframe thead tr:only-child th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: left;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th>ER+</th>\n",
+       "      <th>Yes</th>\n",
+       "      <th>No</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>PCR</th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>Yes</th>\n",
+       "      <td>17.0</td>\n",
+       "      <td>28.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>No</th>\n",
+       "      <td>81.0</td>\n",
+       "      <td>42.0</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "ER+   Yes    No\n",
+       "PCR            \n",
+       "Yes  17.0  28.0\n",
+       "No   81.0  42.0"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# example of contingency table\n",
+    "inferential_statistics.contingency_table('PCR', 'ER+',df)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style>\n",
+       "    .dataframe thead tr:only-child th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: left;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>p-value</th>\n",
+       "      <th>Relative_Risk</th>\n",
+       "      <th>RR_lb</th>\n",
+       "      <th>RR_ub</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>White</th>\n",
+       "      <td>0.833629</td>\n",
+       "      <td>0.8878</td>\n",
+       "      <td>0.5076</td>\n",
+       "      <td>1.5528</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>ER+</th>\n",
+       "      <td>0.001988</td>\n",
+       "      <td>0.4337</td>\n",
+       "      <td>0.2582</td>\n",
+       "      <td>0.7285</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>PR+</th>\n",
+       "      <td>0.000198</td>\n",
+       "      <td>0.3219</td>\n",
+       "      <td>0.1707</td>\n",
+       "      <td>0.6069</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>HR+</th>\n",
+       "      <td>0.000307</td>\n",
+       "      <td>0.3831</td>\n",
+       "      <td>0.2286</td>\n",
+       "      <td>0.6422</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Right_Breast</th>\n",
+       "      <td>0.851883</td>\n",
+       "      <td>1.0965</td>\n",
+       "      <td>0.6649</td>\n",
+       "      <td>1.8080</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "               p-value  Relative_Risk   RR_lb   RR_ub\n",
+       "White         0.833629         0.8878  0.5076  1.5528\n",
+       "ER+           0.001988         0.4337  0.2582  0.7285\n",
+       "PR+           0.000198         0.3219  0.1707  0.6069\n",
+       "HR+           0.000307         0.3831  0.2286  0.6422\n",
+       "Right_Breast  0.851883         1.0965  0.6649  1.8080"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Perform chi-2 test on all categorical variables\n",
+    "predictors = ['White', 'ER+', 'PR+', 'HR+','Right_Breast']\n",
+    "outcome = 'PCR'\n",
+    "inferential_statistics.categorical_data(outcome, predictors, df)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<h3><center> 1.1.2 Conclusion: Only `ER+` , `PR+`, and `HR+` have an effect on `PCR`</center></h3>\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 1. 2 Effect of categorical predictors on Survival (`Alive`)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style>\n",
+       "    .dataframe thead tr:only-child th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: left;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>p-value</th>\n",
+       "      <th>Relative_Risk</th>\n",
+       "      <th>RR_lb</th>\n",
+       "      <th>RR_ub</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>White</th>\n",
+       "      <td>0.439359</td>\n",
+       "      <td>1.0935</td>\n",
+       "      <td>0.9032</td>\n",
+       "      <td>1.3239</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>ER+</th>\n",
+       "      <td>0.001135</td>\n",
+       "      <td>1.3095</td>\n",
+       "      <td>1.1025</td>\n",
+       "      <td>1.5554</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>PR+</th>\n",
+       "      <td>0.162557</td>\n",
+       "      <td>1.1266</td>\n",
+       "      <td>0.9739</td>\n",
+       "      <td>1.3031</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>HR+</th>\n",
+       "      <td>0.038917</td>\n",
+       "      <td>1.1950</td>\n",
+       "      <td>1.0094</td>\n",
+       "      <td>1.4148</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Right_Breast</th>\n",
+       "      <td>0.729139</td>\n",
+       "      <td>0.9602</td>\n",
+       "      <td>0.8287</td>\n",
+       "      <td>1.1125</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>PCR</th>\n",
+       "      <td>0.070860</td>\n",
+       "      <td>1.1796</td>\n",
+       "      <td>1.0333</td>\n",
+       "      <td>1.3467</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "               p-value  Relative_Risk   RR_lb   RR_ub\n",
+       "White         0.439359         1.0935  0.9032  1.3239\n",
+       "ER+           0.001135         1.3095  1.1025  1.5554\n",
+       "PR+           0.162557         1.1266  0.9739  1.3031\n",
+       "HR+           0.038917         1.1950  1.0094  1.4148\n",
+       "Right_Breast  0.729139         0.9602  0.8287  1.1125\n",
+       "PCR           0.070860         1.1796  1.0333  1.3467"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "predictors = ['White', 'ER+', 'PR+', 'HR+','Right_Breast','PCR']\n",
+    "outcome = 'Alive'\n",
+    "inferential_statistics.categorical_data(outcome, predictors, df)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<h3><center> 1.2.2 Conclusion: Only `ER+` and `HR+` have an effect on `Alive`</center></h3>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 2. Inferential_statistics: Continous vs Categorical (ANOVA)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 2.1 Effect of Age on PCR "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "---------------------------------------------\n",
+      "             sum_sq     df         F    PR(>F)\n",
+      "age        0.256505    1.0  1.302539  0.255394\n",
+      "Residual  32.689923  166.0       NaN       NaN\n",
+      "---------------------------------------------\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x113ce0898>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "predictor= ['age']\n",
+    "outcome = 'PCR'\n",
+    "anova_table, OLS = inferential_statistics.linear_models(df, outcome, predictor);\n",
+    "sns.boxplot(x= outcome, y=predictor[0], data=df, palette=\"Set3\");"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 2.2 Effect of Age on Survival "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "---------------------------------------------\n",
+      "             sum_sq     df         F    PR(>F)\n",
+      "age        0.062227    1.0  0.399719  0.528104\n",
+      "Residual  25.842534  166.0       NaN       NaN\n",
+      "---------------------------------------------\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x1142b6ef0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "predictor= ['age']\n",
+    "outcome = 'Alive'\n",
+    "anova_table, OLS = inferential_statistics.linear_models(df, outcome, predictor);\n",
+    "sns.boxplot(x= outcome, y=predictor[0], data=df, palette=\"Set3\");"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 2.3 Explore interactions between age, survival, and PCR"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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N7L2NrptjZmMzLEsiZ2Z3mdm0RpdLzMzNbHCWdcVGod99vQncamYt/oKOSCeb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\nYII=\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x114382390>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# create a boxplot to visualize this interaction\n",
+    "ax = sns.boxplot(x= 'PCR', y='age', hue ='Alive',data=df, palette=\"Set3\");\n",
+    "ax.set_title('Interactions between age, survival, and PCR');"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "---------------------------------------------\n",
+      "             sum_sq     df         F    PR(>F)\n",
+      "age        0.637369    1.0  3.674443  0.057611\n",
+      "Residual  20.988648  121.0       NaN       NaN\n",
+      "---------------------------------------------\n"
+     ]
+    }
+   ],
+   "source": [
+    "# create dataframe only for patients with PCR = Yes\n",
+    "df_by_PCR = df.loc[df.PCR=='No',:]\n",
+    "df_by_PCR.head()\n",
+    "\n",
+    "# Anova age vs Alive\n",
+    "predictor= ['age']\n",
+    "outcome = 'Alive'\n",
+    "anova_table, OLS = inferential_statistics.linear_models(df_by_PCR, outcome, predictor);"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style>\n",
+       "    .dataframe thead tr:only-child th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: left;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>Effect Size</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Predictor of Alive</th>\n",
+       "      <th></th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>age</th>\n",
+       "      <td>-0.409422</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "                    Effect Size\n",
+       "Predictor of Alive             \n",
+       "age                   -0.409422"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# estimate the effect size\n",
+    "mri_features = ['age']\n",
+    "outcome = 'Alive'\n",
+    "# Effect Size\n",
+    "inferential_statistics.effect_size( df_by_PCR, mri_features, outcome)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Conclusion."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "1. `age` has an important effect on `Alive` for patients with `PCR` = Yes\n",
+    "2. To quantitify this effect a logistic regression is needed"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 2.4 Effect of MRI measurements on PCR ANOVA"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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0oAt2dnqXs1V1dq5g7tyFVYfRFrp/jofr59VXAtpnItagGqUkNVxmTu7vmIg4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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x114525a90>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "R = inferential_statistics.anova_MRI('PCR', df);"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "** Estimate the effect size **"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style>\n",
+       "    .dataframe thead tr:only-child th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: left;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>Effect Size</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Predictor of PCR</th>\n",
+       "      <th></th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>MRI_LD_Baseline</th>\n",
+       "      <td>0.191798</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>MRI_LD_1_3dAC</th>\n",
+       "      <td>0.304774</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>MRI_LD_Int_Reg</th>\n",
+       "      <td>0.502345</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>MRI_LD_PreSurg</th>\n",
+       "      <td>0.590352</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "                  Effect Size\n",
+       "Predictor of PCR             \n",
+       "MRI_LD_Baseline      0.191798\n",
+       "MRI_LD_1_3dAC        0.304774\n",
+       "MRI_LD_Int_Reg       0.502345\n",
+       "MRI_LD_PreSurg       0.590352"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "mri_features = ['MRI_LD_Baseline', 'MRI_LD_1_3dAC', 'MRI_LD_Int_Reg', 'MRI_LD_PreSurg']\n",
+    "outcome = 'PCR'\n",
+    "# Effect Size\n",
+    "inferential_statistics.effect_size( df, mri_features, outcome)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 2.5 Effect of MRI measurements on Survival ANOVA"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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GsP7t1y7AbykSrSnAJ4EDKapiANcAs+kjEZs2bRLjyur2QHR0jIU16xmtGqqj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\nwgAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x1146327f0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "outcome = 'Alive'\n",
+    "R = inferential_statistics.anova_MRI(outcome, df);"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style>\n",
+       "    .dataframe thead tr:only-child th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: left;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>Effect Size</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Predictor of Alive</th>\n",
+       "      <th></th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>MRI_LD_Baseline</th>\n",
+       "      <td>0.375046</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>MRI_LD_1_3dAC</th>\n",
+       "      <td>0.357002</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>MRI_LD_Int_Reg</th>\n",
+       "      <td>0.678682</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>MRI_LD_PreSurg</th>\n",
+       "      <td>0.469548</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "                    Effect Size\n",
+       "Predictor of Alive             \n",
+       "MRI_LD_Baseline        0.375046\n",
+       "MRI_LD_1_3dAC          0.357002\n",
+       "MRI_LD_Int_Reg         0.678682\n",
+       "MRI_LD_PreSurg         0.469548"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "mri_features = ['MRI_LD_Baseline', 'MRI_LD_1_3dAC', 'MRI_LD_Int_Reg', 'MRI_LD_PreSurg']\n",
+    "outcome = 'Alive'\n",
+    "# Effect Size\n",
+    "inferential_statistics.effect_size( df, mri_features, outcome)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### stratify analysis by PCR"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Outcome = Alive | PCR = No\n",
+      "---------------------------------------------\n",
+      "                    sum_sq     df         F    PR(>F)\n",
+      "MRI_LD_Baseline   0.081585    1.0  0.484431  0.487791\n",
+      "MRI_LD_1_3dAC     0.019421    1.0  0.115317  0.734774\n",
+      "MRI_LD_Int_Reg    0.423490    1.0  2.514580  0.115474\n",
+      "MRI_LD_PreSurg    0.143688    1.0  0.853186  0.357537\n",
+      "Residual         19.872834  118.0       NaN       NaN\n",
+      "---------------------------------------------\n",
+      "                    Effect Size\n",
+      "Predictor of Alive             \n",
+      "MRI_LD_Baseline        0.314555\n",
+      "MRI_LD_1_3dAC          0.362579\n",
+      "MRI_LD_Int_Reg         0.582373\n",
+      "MRI_LD_PreSurg         0.484103\n",
+      "\n",
+      "\n",
+      "\n",
+      "Outcome = Alive | PCR = Yes\n",
+      "---------------------------------------------\n",
+      "                   sum_sq    df         F    PR(>F)\n",
+      "MRI_LD_Baseline  0.128853   1.0  1.966383  0.168546\n",
+      "MRI_LD_1_3dAC    0.240330   1.0  3.667597  0.062650\n",
+      "MRI_LD_Int_Reg   0.543712   1.0  8.297407  0.006352\n",
+      "MRI_LD_PreSurg   0.404720   1.0  6.176300  0.017228\n",
+      "Residual         2.621118  40.0       NaN       NaN\n",
+      "---------------------------------------------\n",
+      "                    Effect Size\n",
+      "Predictor of Alive             \n",
+      "MRI_LD_Baseline        0.597109\n",
+      "MRI_LD_1_3dAC          0.037712\n",
+      "MRI_LD_Int_Reg         0.804525\n",
+      "MRI_LD_PreSurg        -0.234776\n",
+      "\n",
+      "\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "# predictors and outcomes\n",
+    "predictors= ['MRI_LD_Baseline', 'MRI_LD_1_3dAC', 'MRI_LD_Int_Reg', 'MRI_LD_PreSurg']\n",
+    "\n",
+    "# split data and run anova\n",
+    "PCR_outcomes = ['No','Yes']\n",
+    "\n",
+    "for out in PCR_outcomes:\n",
+    "    df_by_PCR = df.loc[df.PCR == out,:]\n",
+    "    print('Outcome = Alive' + ' | ' + 'PCR = ' + out)\n",
+    "    # Anova\n",
+    "    anova_table, OLS = inferential_statistics.linear_models(df_by_PCR, 'Alive', predictors);\n",
+    "    # Effect Size\n",
+    "    print(inferential_statistics.effect_size( df_by_PCR, predictors, 'Alive'))\n",
+    "    print('\\n' * 2)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Conclusion "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "1. The largest tumor dimension measured at baseline (`MRI_LD_Baseline`) is not a statistically different between patients who achieved complete pathological response (`PCR`)and those who did not. While all other MRI measurements are statistically different between `PCR = Yes`, and `PCR = No`\n",
+    "2. All MRI measurements of the tumor dimension are different between patients who are Alive at the end of the trial and those who did not. These results do not indicate anything about the size of these effects. An statistically significant effect is not always clinically significant\n",
+    "3. The estimated effect sizes are very small, and most likley not clinically significant\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "## 3. Inferential_statistics: Continous vs Categorical (ANOVA)"
+   ]
+  }
+ ],
+ "metadata": {
+  "anaconda-cloud": {},
+  "kernelspec": {
+   "display_name": "Python [conda root]",
+   "language": "python",
+   "name": "conda-root-py"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}