C2_W3_Lab_1_counting_patients__M.ipynb

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   "source": [
    "# Count Patients\n",
    "\n",
    "Welcome to the first practice lab of this week!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import Packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll work with data where:\n",
    "- Time: days after a disease is diagnosed and the patient either dies or left the hospital's supervision.\n",
    "- Event: \n",
    "    - 1 if the patient died\n",
    "    - 0 if the patient was not observed to die beyond the given 'Time' (their data is censored)\n",
    "    \n",
    "Notice that these are the same numbers that you see in the lecture video about estimating survival."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Time</th>\n",
       "      <th>Event</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>8</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>60</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>20</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>12</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>30</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>15</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "   Time  Event\n",
       "0    10      1\n",
       "1     8      0\n",
       "2    60      1\n",
       "3    20      1\n",
       "4    12      0\n",
       "5    30      1\n",
       "6    15      0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
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    }
   ],
   "source": [
    "df = pd.DataFrame({'Time': [10,8,60,20,12,30,15],\n",
    "                   'Event': [1,0,1,1,0,1,0]\n",
    "                  })\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Count Number of Censored Patients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    False\n",
       "1     True\n",
       "2    False\n",
       "3    False\n",
       "4     True\n",
       "5    False\n",
       "6     True\n",
       "Name: Event, dtype: bool"
      ]
     },
     "execution_count": 3,
     "metadata": {},
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   ],
   "source": [
    "df['Event'] == 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Patient 1, 4 and 6 were censored."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Count how many patient records were censored\n",
    "\n",
    "When we sum a series of booleans, `True` is treated as 1 and `False` is treated as 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
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     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "sum(df['Event'] == 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Count Number of Patients Who Definitely Survived Past Time $t$\n",
    "\n",
    "This assumes that any patient who was censored died at the time of being censored ( **died immediately**).\n",
    "\n",
    "If a patient survived past time `t`:\n",
    "- Their `Time` of event should be greater than `t`.  \n",
    "- Notice that they can have an `Event` of either 1 or 0.  What matters is their `Time` value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    False\n",
       "1    False\n",
       "2     True\n",
       "3    False\n",
       "4    False\n",
       "5     True\n",
       "6    False\n",
       "Name: Time, dtype: bool"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = 25\n",
    "df['Time'] > t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
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     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "sum(df['Time'] > t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Count Number of Patients Who May Have Survived Past Time $t$\n",
    "\n",
    "This assumes that censored patients **never die**.\n",
    "- The patient is censored at any time and we assume that they live forever.\n",
    "- The patient died (`Event` is 1) but after time `t`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    False\n",
       "1     True\n",
       "2     True\n",
       "3    False\n",
       "4     True\n",
       "5     True\n",
       "6     True\n",
       "dtype: bool"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = 25\n",
    "(df['Time'] > t) | (df['Event'] == 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "sum( (df['Time'] > t) | (df['Event'] == 0) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Count Number of Patients Who were Not Censored Before Time $t$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If patient was not censored before time `t`:\n",
    "- They either had an event (death) before `t`, at `t`, or after `t` (any time)\n",
    "- Or, their `Time` occurs after time `t` (they may have either died or been censored at a later time after `t`)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     True\n",
       "1    False\n",
       "2     True\n",
       "3     True\n",
       "4    False\n",
       "5     True\n",
       "6    False\n",
       "dtype: bool"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = 25\n",
    "(df['Event'] == 1) | (df['Time'] > t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum( (df['Event'] == 1) | (df['Time'] > t) )"
   ]
  }
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