notebook.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
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   "source": [
    "# Hypothesis Testing in Healthcare: Drug Safety\n",
    "\n",
    "A pharmaceutical company GlobalXYZ has just completed a randomized controlled drug trial. To promote transparency and reproducibility of the drug's outcome, they (GlobalXYZ) have presented the dataset to your organization, a non-profit that focuses primarily on drug safety.\n",
    "\n",
    "The dataset `drug_safety.csv` was obtained from [Hbiostat](https://hbiostat.org/data/) courtesy of the Vanderbilt University Department of Biostatistics. It contained five adverse effects: headache, abdominal pain, dyspepsia, upper respiratory infection, chronic obstructive airway disease (COAD), demographic data, vital signs, lab measures, etc. The ratio of drug observations to placebo observations is 2 to 1.\n",
    "\n",
    "For this project, the dataset has been modified to reflect the presence and absence of adverse effects `adverse_effects` and the number of adverse effects in a single individual `num_effects`.\n",
    "\n",
    "The columns in the modified dataset are: \n",
    "\n",
    "| Column | Description |\n",
    "|--------|-------------|\n",
    "|`sex` | The gender of the individual |\n",
    "|`age` | The age of the individual |\n",
    "|`week` | The week of the drug testing |\n",
    "|`trx` | The treatment (Drug) and control (Placebo) groups | \n",
    "|`wbc` | The count of white blood cells |\n",
    "|`rbc` | The count of red blood cells |\n",
    "|`adverse_effects` | The presence of at least a single adverse effect |\n",
    "|`num_effects` | The number of adverse effects experienced by a single individual |\n",
    "\n",
    "The original dataset can be found [here](https://hbiostat.org/data/repo/safety.rda)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from statsmodels.stats.proportion import proportions_ztest\n",
    "import pingouin\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    .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>age</th>\n",
       "      <th>sex</th>\n",
       "      <th>trx</th>\n",
       "      <th>week</th>\n",
       "      <th>wbc</th>\n",
       "      <th>rbc</th>\n",
       "      <th>adverse_effects</th>\n",
       "      <th>num_effects</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>62</td>\n",
       "      <td>male</td>\n",
       "      <td>Drug</td>\n",
       "      <td>0</td>\n",
       "      <td>7.3</td>\n",
       "      <td>5.1</td>\n",
       "      <td>No</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>62</td>\n",
       "      <td>male</td>\n",
       "      <td>Drug</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>No</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>62</td>\n",
       "      <td>male</td>\n",
       "      <td>Drug</td>\n",
       "      <td>12</td>\n",
       "      <td>5.6</td>\n",
       "      <td>5.0</td>\n",
       "      <td>No</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>62</td>\n",
       "      <td>male</td>\n",
       "      <td>Drug</td>\n",
       "      <td>16</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>No</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>62</td>\n",
       "      <td>male</td>\n",
       "      <td>Drug</td>\n",
       "      <td>2</td>\n",
       "      <td>6.6</td>\n",
       "      <td>5.1</td>\n",
       "      <td>No</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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16098</th>\n",
       "      <td>78</td>\n",
       "      <td>male</td>\n",
       "      <td>Placebo</td>\n",
       "      <td>16</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Yes</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16099</th>\n",
       "      <td>78</td>\n",
       "      <td>male</td>\n",
       "      <td>Placebo</td>\n",
       "      <td>2</td>\n",
       "      <td>7.5</td>\n",
       "      <td>4.9</td>\n",
       "      <td>No</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16100</th>\n",
       "      <td>78</td>\n",
       "      <td>male</td>\n",
       "      <td>Placebo</td>\n",
       "      <td>20</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Yes</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16101</th>\n",
       "      <td>78</td>\n",
       "      <td>male</td>\n",
       "      <td>Placebo</td>\n",
       "      <td>4</td>\n",
       "      <td>6.4</td>\n",
       "      <td>4.8</td>\n",
       "      <td>No</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16102</th>\n",
       "      <td>78</td>\n",
       "      <td>male</td>\n",
       "      <td>Placebo</td>\n",
       "      <td>8</td>\n",
       "      <td>7.8</td>\n",
       "      <td>4.8</td>\n",
       "      <td>No</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>16103 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       age   sex      trx  week  wbc  rbc adverse_effects  num_effects\n",
       "0       62  male     Drug     0  7.3  5.1              No            0\n",
       "1       62  male     Drug     1  NaN  NaN              No            0\n",
       "2       62  male     Drug    12  5.6  5.0              No            0\n",
       "3       62  male     Drug    16  NaN  NaN              No            0\n",
       "4       62  male     Drug     2  6.6  5.1              No            0\n",
       "...    ...   ...      ...   ...  ...  ...             ...          ...\n",
       "16098   78  male  Placebo    16  NaN  NaN             Yes            1\n",
       "16099   78  male  Placebo     2  7.5  4.9              No            0\n",
       "16100   78  male  Placebo    20  NaN  NaN             Yes            1\n",
       "16101   78  male  Placebo     4  6.4  4.8              No            0\n",
       "16102   78  male  Placebo     8  7.8  4.8              No            0\n",
       "\n",
       "[16103 rows x 8 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "drug_safety = pd.read_csv(\"drug_safety.csv\")\n",
    "drug_safety"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Count the adverse_effect column values for each trx group"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "trx      adverse_effects\n",
       "Drug     No                 9703\n",
       "         Yes                1024\n",
       "Placebo  No                 4864\n",
       "         Yes                 512\n",
       "Name: count, dtype: int64"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "adv_eff_by_trx = drug_safety.groupby(\"trx\").adverse_effects.value_counts()\n",
    "adv_eff_by_trx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute total rows in each group"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "trx\n",
       "Drug       10727\n",
       "Placebo     5376\n",
       "Name: count, dtype: int64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "adv_eff_by_trx_totals = adv_eff_by_trx.groupby(\"trx\").sum()\n",
    "adv_eff_by_trx_totals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create an array of the \"Yes\" counts for each group"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1024, 512]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yeses = [adv_eff_by_trx[\"Drug\"][\"Yes\"], adv_eff_by_trx[\"Placebo\"][\"Yes\"]]\n",
    "yeses"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create an array of the total number of rows in each group"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[10727, 5376]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = [adv_eff_by_trx_totals[\"Drug\"], adv_eff_by_trx_totals[\"Placebo\"]]\n",
    "n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Perform a two-sided z-test on the two proportions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0452182684494942, 0.9639333330262475)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "two_sample_results = proportions_ztest(yeses, n)\n",
    "two_sample_results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Store the p-value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9639333330262475"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "two_sample_p_value = two_sample_results[1]\n",
    "two_sample_p_value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Determine if num_effects and trx are independent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/egifermana/anaconda3/lib/python3.11/site-packages/pingouin/contingency.py:150: UserWarning: Low count on observed frequencies.\n",
      "  warnings.warn(\"Low count on {} frequencies.\".format(name))\n",
      "/Users/egifermana/anaconda3/lib/python3.11/site-packages/pingouin/contingency.py:150: UserWarning: Low count on expected frequencies.\n",
      "  warnings.warn(\"Low count on {} frequencies.\".format(name))\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(trx                 Drug      Placebo\n",
       " num_effects                          \n",
       " 0            9703.794883  4863.205117\n",
       " 1             960.587096   481.412904\n",
       " 2              58.621126    29.378874\n",
       " 3               3.996895     2.003105,\n",
       " trx          Drug  Placebo\n",
       " num_effects               \n",
       " 0            9703     4864\n",
       " 1             956      486\n",
       " 2              63       25\n",
       " 3               5        1,\n",
       "                  test    lambda      chi2  dof      pval    cramer     power\n",
       " 0             pearson  1.000000  1.799644  3.0  0.615012  0.010572  0.176275\n",
       " 1        cressie-read  0.666667  1.836006  3.0  0.607131  0.010678  0.179153\n",
       " 2      log-likelihood  0.000000  1.922495  3.0  0.588648  0.010926  0.186033\n",
       " 3       freeman-tukey -0.500000  2.001752  3.0  0.572043  0.011149  0.192379\n",
       " 4  mod-log-likelihood -1.000000  2.096158  3.0  0.552690  0.011409  0.199984\n",
       " 5              neyman -2.000000  2.344303  3.0  0.504087  0.012066  0.220189)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_effects_groups = pingouin.chi2_independence(\n",
    "    data = drug_safety, x = \"num_effects\", y = \"trx\")\n",
    "num_effects_groups"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Extract the p-value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6150123339426765"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_effects_p_value = num_effects_groups[2][\"pval\"][0]\n",
    "num_effects_p_value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create a histogram with Seaborn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/egifermana/anaconda3/lib/python3.11/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.\n",
      "  with pd.option_context('mode.use_inf_as_na', True):\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='age', ylabel='Count'>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.histplot(data = drug_safety, \n",
    "             x = \"age\", \n",
    "             hue = \"trx\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Confirm the histogram's output by conducting a normality test\n",
    "### To choose between unpaired t-test and Wilcoxon-Mann-Whitney test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/egifermana/anaconda3/lib/python3.11/site-packages/scipy/stats/_morestats.py:1882: UserWarning: p-value may not be accurate for N > 5000.\n",
      "  warnings.warn(\"p-value may not be accurate for N > 5000.\")\n",
      "/Users/egifermana/anaconda3/lib/python3.11/site-packages/scipy/stats/_morestats.py:1882: UserWarning: p-value may not be accurate for N > 5000.\n",
      "  warnings.warn(\"p-value may not be accurate for N > 5000.\")\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>W</th>\n",
       "      <th>pval</th>\n",
       "      <th>normal</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>trx</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Drug</th>\n",
       "      <td>0.976785</td>\n",
       "      <td>2.190318e-38</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Placebo</th>\n",
       "      <td>0.975595</td>\n",
       "      <td>2.224615e-29</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                W          pval  normal\n",
       "trx                                    \n",
       "Drug     0.976785  2.190318e-38   False\n",
       "Placebo  0.975595  2.224615e-29   False"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "normality = pingouin.normality(\n",
    "    data = drug_safety,\n",
    "    dv = 'age',\n",
    "    group = 'trx',\n",
    "    method = 'shapiro', # the default\n",
    "    alpha = 0.05) # 0.05 is also the default\n",
    "normality"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Select the age of the Drug group"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0        62\n",
       "1        62\n",
       "2        62\n",
       "3        62\n",
       "4        62\n",
       "         ..\n",
       "16074    60\n",
       "16075    60\n",
       "16092    68\n",
       "16093    68\n",
       "16094    68\n",
       "Name: age, Length: 10727, dtype: int64"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "age_trx = drug_safety.loc[drug_safety[\"trx\"] == \"Drug\", \"age\"]\n",
    "age_trx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Select the age of the Placebo group"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "32       73\n",
       "33       73\n",
       "34       73\n",
       "35       73\n",
       "36       73\n",
       "         ..\n",
       "16098    78\n",
       "16099    78\n",
       "16100    78\n",
       "16101    78\n",
       "16102    78\n",
       "Name: age, Length: 5376, dtype: int64"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "age_placebo = drug_safety.loc[drug_safety[\"trx\"] == \"Placebo\", \"age\"]\n",
    "age_placebo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Since the data distribution is not normal, conduct a two-sided Mann-Whitney U test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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>U-val</th>\n",
       "      <th>alternative</th>\n",
       "      <th>p-val</th>\n",
       "      <th>RBC</th>\n",
       "      <th>CLES</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>MWU</th>\n",
       "      <td>29149339.5</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>0.256963</td>\n",
       "      <td>-0.01093</td>\n",
       "      <td>0.505465</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          U-val alternative     p-val      RBC      CLES\n",
       "MWU  29149339.5   two-sided  0.256963 -0.01093  0.505465"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "age_group_effects = pingouin.mwu(age_trx, age_placebo)\n",
    "age_group_effects"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Extract the p-value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MWU    0.256963\n",
       "Name: p-val, dtype: float64"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "age_group_effects_p_value = age_group_effects[\"p-val\"]\n",
    "age_group_effects_p_value"
   ]
  }
 ],
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