examples/category_estimation.ipynb

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    "# Estimating Current Cases by Category\n",
    "This notebook explores a methodology to estimate current mild, severe and critical patients. Both mild and critical categories appear to be correlated to independently reported categories from Italy's ministry of health.\n",
    "\n",
    "Most of the reporting of COVID-19 data, including what is reported by the ECDC, focuses on the daily counts of new cases and deaths. While this is useful for tracking the general development of the disease, it provides little information about the capacity required by a health care system to cope with the case load. Here we explore a methodology to estimate total active cases (cases between onset and recovery / death) broken down by category."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Breakdown of cases\n",
    "Early data from China classified the cases into *mild*, *severe* and *critical* with 80.9%, 13.8% and 4.7% of occurrences respectively ([source](https://www.cnn.com/2020/03/20/health/covid-19-recovery-rates-intl/index.html)). While this might be useful for categorising cases, it does not appear to match some outcome-based data like hospitalization rate where, as of March 26, Italy reported 43.2%, Spain 56.80% and New York 15% of all confirmed cases.\n",
    "\n",
    "Such wild range in hospitalization rates is potentially due to different criteria being used across health care systems as well as hitting potential system capacity limits. Therefore, the estimations performed here cannot be used as a proxy for hospitalization rates unless a country-dependent correcting factor is applied. However, using an estimate of 5% of all cases appears to be a good predictor for ICU admission rates, and 15% of all cases seem to correlate to a rate of confirmed cases that only experience mild symptoms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Since reported numbers are approximate, they are rounded for the sake of simplicity\n",
    "severe_ratio = .15\n",
    "critical_ratio = .05\n",
    "mild_ratio = 1 - severe_ratio - critical_ratio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discharge time for severe vs critical cases\n",
    "Unfortunately, early data from Chinese sources only reported a median stay of 12 and a mean stay of 12.8 for *all hospitalizations* without specifying which of them required ICU resources.\n",
    "\n",
    "Since we know the ratio of severe vs critical cases, we only need to guess the discharge time of severe cases since there will only be one way to satisfy the constraint of overall hospitalization median and mean. Here, we plot the estimated discharge time for critical cases (y axis) given a discharge time for severe cases (x axis):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "\n",
    "# Data from early Chinese reports\n",
    "mean_discharge_time = 12.8\n",
    "severe_ratio_norm = severe_ratio / (severe_ratio + critical_ratio) \n",
    "critical_ratio_norm = critical_ratio / (severe_ratio + critical_ratio) \n",
    "\n",
    "def compute_icu_discharge_time(severe_discharge_time, mean_discharge_time: float = 12.8):\n",
    "    ''' Using mean discharge time from https://www.cnn.com/2020/03/20/health/covid-19-recovery-rates-intl/index.html '''\n",
    "    return (mean_discharge_time - severe_discharge_time * severe_ratio_norm) / critical_ratio_norm\n",
    "\n",
    "X = np.linspace(10, 15, 100)\n",
    "y = np.array([compute_icu_discharge_time(x) for x in X])\n",
    "\n",
    "X_name = 'Hospitalization time for severe cases (days)'\n",
    "y_name = 'Hospitalization time for critical cases(days)'\n",
    "df = pd.DataFrame([(x, y_) for x, y_ in zip(X, y)], columns=[X_name, y_name]).set_index(X_name)\n",
    "df.plot(figsize=(16, 8), grid=True, ylim=(0, max(y)));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because the data is reported daily, we can only pick an estimated whole number for both variables. The only possible value for *hospital discharge days* that would result in a median discharge time of 12 days is, unsurprisingly, 12. Then, the estimated *ICU discharge days* is 15 days."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "severe_recovery_days = 12\n",
    "critical_recovery_days = 15"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Recovery time for mild cases\n",
    "In order to estimate the current number of mild cases, there is one more number that we must guess: how many days it takes for recovery, on average, for all cases that are not severe or critical. Reported recovery times from a COVID-19 infection range from 2 weeks ([source](https://www.who.int/docs/default-source/coronaviruse/who-china-joint-mission-on-covid-19-final-report.pdf)) to \"a week to 10 days\" ([source](https://www.webmd.com/lung/news/20200324/the-other-side-of-covid-19-milder-cases-recovery#1)). After experimenting with several choices, using a median recovery time of 7 days appears to match empirical data from multiple official reports."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "mild_recovery_days = 7"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimating new cases breakdown\n",
    "Using Italy's data up to March 26, assuming the proportion of each category remains constant for every new case, daily breakdowns can be estimated by multiplying the number of new cases by the ratios of the respective categories:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "            new_confirmed  new_deceased  new_mild  new_severe  new_critical\ndate                                                                       \n2020-03-23           4789           601    3831.2      718.35        239.45\n2020-03-24           5249           743    4199.2      787.35        262.45\n2020-03-25           5210           683    4168.0      781.50        260.50\n2020-03-26           6153           662    4922.4      922.95        307.65\n2020-03-27           5959           969    4767.2      893.85        297.95",
      "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>new_confirmed</th>\n      <th>new_deceased</th>\n      <th>new_mild</th>\n      <th>new_severe</th>\n      <th>new_critical</th>\n    </tr>\n    <tr>\n      <th>date</th>\n      <th></th>\n      <th></th>\n      <th></th>\n      <th></th>\n      <th></th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>2020-03-23</th>\n      <td>4789</td>\n      <td>601</td>\n      <td>3831.2</td>\n      <td>718.35</td>\n      <td>239.45</td>\n    </tr>\n    <tr>\n      <th>2020-03-24</th>\n      <td>5249</td>\n      <td>743</td>\n      <td>4199.2</td>\n      <td>787.35</td>\n      <td>262.45</td>\n    </tr>\n    <tr>\n      <th>2020-03-25</th>\n      <td>5210</td>\n      <td>683</td>\n      <td>4168.0</td>\n      <td>781.50</td>\n      <td>260.50</td>\n    </tr>\n    <tr>\n      <th>2020-03-26</th>\n      <td>6153</td>\n      <td>662</td>\n      <td>4922.4</td>\n      <td>922.95</td>\n      <td>307.65</td>\n    </tr>\n    <tr>\n      <th>2020-03-27</th>\n      <td>5959</td>\n      <td>969</td>\n      <td>4767.2</td>\n      <td>893.85</td>\n      <td>297.95</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "# Load country-level data for Italy\n",
    "data = pd.read_csv('https://storage.googleapis.com/covid19-open-data/v2/IT/main.csv').set_index('date')\n",
    "\n",
    "# Estimate daily counts per category assuming ratio is constant\n",
    "data = data[data.index <= '2020-03-27']\n",
    "data['new_mild'] = data['new_confirmed'] * mild_ratio\n",
    "data['new_severe'] = data['new_confirmed'] * severe_ratio\n",
    "data['new_critical'] = data['new_confirmed'] * critical_ratio\n",
    "data = data[['new_confirmed', 'new_deceased', 'new_mild', 'new_severe', 'new_critical']]\n",
    "\n",
    "data.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimating current cases breakdown\n",
    "Now that we have an estimate for the category breakdown of new cases as well as for the discharge time per category, we can estimate the number of current cases per category by adding up each category over a rolling window:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "            new_confirmed  new_deceased  new_mild  new_severe  new_critical  \\\ndate                                                                          \n2020-03-23           4789           601    3831.2      718.35        239.45   \n2020-03-24           5249           743    4199.2      787.35        262.45   \n2020-03-25           5210           683    4168.0      781.50        260.50   \n2020-03-26           6153           662    4922.4      922.95        307.65   \n2020-03-27           5959           969    4767.2      893.85        297.95   \n\n            current_mild  current_severe  current_critical  \ndate                                                        \n2020-03-23       28757.6         7719.75           2827.60  \n2020-03-24       30136.0         8109.45           3000.20  \n2020-03-25       30938.4         8508.90           3211.85  \n2020-03-26       31603.2         8907.30           3403.85  \n2020-03-27       31581.6         9262.65           3569.25  ",
      "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>new_confirmed</th>\n      <th>new_deceased</th>\n      <th>new_mild</th>\n      <th>new_severe</th>\n      <th>new_critical</th>\n      <th>current_mild</th>\n      <th>current_severe</th>\n      <th>current_critical</th>\n    </tr>\n    <tr>\n      <th>date</th>\n      <th></th>\n      <th></th>\n      <th></th>\n      <th></th>\n      <th></th>\n      <th></th>\n      <th></th>\n      <th></th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>2020-03-23</th>\n      <td>4789</td>\n      <td>601</td>\n      <td>3831.2</td>\n      <td>718.35</td>\n      <td>239.45</td>\n      <td>28757.6</td>\n      <td>7719.75</td>\n      <td>2827.60</td>\n    </tr>\n    <tr>\n      <th>2020-03-24</th>\n      <td>5249</td>\n      <td>743</td>\n      <td>4199.2</td>\n      <td>787.35</td>\n      <td>262.45</td>\n      <td>30136.0</td>\n      <td>8109.45</td>\n      <td>3000.20</td>\n    </tr>\n    <tr>\n      <th>2020-03-25</th>\n      <td>5210</td>\n      <td>683</td>\n      <td>4168.0</td>\n      <td>781.50</td>\n      <td>260.50</td>\n      <td>30938.4</td>\n      <td>8508.90</td>\n      <td>3211.85</td>\n    </tr>\n    <tr>\n      <th>2020-03-26</th>\n      <td>6153</td>\n      <td>662</td>\n      <td>4922.4</td>\n      <td>922.95</td>\n      <td>307.65</td>\n      <td>31603.2</td>\n      <td>8907.30</td>\n      <td>3403.85</td>\n    </tr>\n    <tr>\n      <th>2020-03-27</th>\n      <td>5959</td>\n      <td>969</td>\n      <td>4767.2</td>\n      <td>893.85</td>\n      <td>297.95</td>\n      <td>31581.6</td>\n      <td>9262.65</td>\n      <td>3569.25</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 6
    }
   ],
   "source": [
    "data['current_mild'] = data['new_mild'].rolling(round(mild_recovery_days)).sum()\n",
    "data['current_severe'] = data['new_severe'].rolling(round(severe_recovery_days)).sum()\n",
    "data['current_critical'] = data['new_critical'].rolling(round(critical_recovery_days)).sum()\n",
    "data.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparing with Italy's home care, hospitalizations and ICU counts\n",
    "Italy categorises the cases into home care, hospitalizations and ICU admission, which appear to map well into *mild*, *severe* and *critical* categories. From Italy's ministry of health, this is the breakdown [as of March 26](https://web.archive.org/web/20200325181518/http://www.salute.gov.it/portale/nuovocoronavirus/dettaglioContenutiNuovoCoronavirus.jsp?lingua=italiano&id=5351&area=nuovoCoronavirus&menu=vuoto) of cases compared to our model estimates:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "                 Estimated  Reported Difference\nCategory                                       \ncurrent_mild      31581.60     30920      2.14%\ncurrent_severe     9262.65     23112    -59.92%\ncurrent_critical   3569.25      3489      2.30%",
      "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>Estimated</th>\n      <th>Reported</th>\n      <th>Difference</th>\n    </tr>\n    <tr>\n      <th>Category</th>\n      <th></th>\n      <th></th>\n      <th></th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>current_mild</th>\n      <td>31581.60</td>\n      <td>30920</td>\n      <td>2.14%</td>\n    </tr>\n    <tr>\n      <th>current_severe</th>\n      <td>9262.65</td>\n      <td>23112</td>\n      <td>-59.92%</td>\n    </tr>\n    <tr>\n      <th>current_critical</th>\n      <td>3569.25</td>\n      <td>3489</td>\n      <td>2.30%</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "source": [
    "estimated = data.iloc[-1]\n",
    "reported = pd.DataFrame.from_records([\n",
    "    {'Category': 'current_mild', 'Count': 30920},\n",
    "    {'Category': 'current_severe', 'Count': 23112},\n",
    "    {'Category': 'current_critical', 'Count': 3489},\n",
    "]).set_index('Category')\n",
    "\n",
    "pd.DataFrame.from_records([\n",
    "    {\n",
    "        'Category': col, \n",
    "        'Estimated': '{0:.02f}'.format(estimated[col]),\n",
    "        'Reported': reported.loc[col, 'Count'],\n",
    "        'Difference': '{0:.02f}%'.format(100.0 * (estimated[col]  - reported.loc[col, 'Count']) / reported.loc[col, 'Count']),\n",
    "    }\n",
    "    for col in reported.index.tolist()\n",
    "]).set_index('Category')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While the severe category does not match what was estimated by the model, both mild cases and critical cases were very accurate predictors for home care and ICU patients, respectively."
   ]
  }
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