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   "source": [
    "# Epidemiological Indicators\n",
    "In most epidemiological analyses we must start with simple measurements, or indicators about the raw data. In the `epigraphhub.epistats` module, some useful functions to calculate such indicators are provided."
   ]
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   "source": [
    "import pandas as pd\n",
    "from epigraphhub.analysis import epistats as es\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculating the posterior prevalence distribution\n",
    "The prevalence of a disease in a population can be modeled as a binomial random variable :math:`Bin(n,p)`, where a fraction of the cases in the population is the parameter :math:`p` and the population size is the parameter :math:`n`. If we have a prior guess on the proportion, which we can represent as a :math:`Beta(a,b)` distribution, we can obtain the posterior distribution of the prevalence for a point in time as a Beta(a+cases, b+population size-cases) as a result of a conjugate Bayesian analysis.\n"
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   "source": [
    "# Using a vague prior Beta(1,1)\n",
    "pdist = es.posterior_prevalence(pop_size=1e6,positives=10000,a=1,b=1)\n",
    "pdist.mean()"
   ]
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     "data": {
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       "9.950342051571256e-05"
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     "execution_count": 3,
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   "source": [
    "pdist.std()\n"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "## Incidence rate\n",
    "incidence is defined as the number of new cases in a population over a period of time, typically 1 year. The incidence rate is also usually scale to 100k people to facilitate comparisons between localities with different populations.\n"
   ]
  },
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   "execution_count": 4,
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    {
     "data": {
      "text/html": [
       "<div>\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>population</th>\n",
       "      <th>cases</th>\n",
       "      <th>incidence_ratio</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1000</td>\n",
       "      <td>5</td>\n",
       "      <td>500.0</td>\n",
       "    </tr>\n",
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       "      <th>1</th>\n",
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       "      <th>2</th>\n",
       "      <td>10000</td>\n",
       "      <td>5</td>\n",
       "      <td>50.0</td>\n",
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      "text/plain": [
       "   population  cases  incidence_ratio\n",
       "0        1000      5            500.0\n",
       "1        5000      5            100.0\n",
       "2       10000      5             50.0"
      ]
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   "source": [
    "ir = es.incidence_rate([1000, 5000, 10000], [5, 5, 5])\n",
    "pd.DataFrame({'population': [1000, 5000, 10000],\n",
    "              'cases': [5, 5, 5],\n",
    "              'incidence_ratio': ir\n",
    "              })"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Relative Risk or Risk ratio\n",
    "Is the risk of contracting a disease given exposure to a risk factor. It is calculated from the results of a controlled experiment with Exposed and control groups.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
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     "end_time": "2022-09-20T11:35:02.302470Z",
     "start_time": "2022-09-20T11:35:02.300045Z"
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "RelativeRiskResult(relative_risk=2.4495156482861398, exposed_cases=27, exposed_total=122, control_cases=44, control_total=487)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "result = es.risk_ratio(exposed_cases=27, exposed_total=122, control_cases=44, control_total=487)\n",
    "result"
   ]
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   "cell_type": "code",
   "execution_count": 6,
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     "end_time": "2022-09-20T11:35:03.472184Z",
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    {
     "data": {
      "text/plain": [
       "ConfidenceInterval(low=1.5836990926700116, high=3.7886786315466354)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
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   "source": [
    "result.confidence_interval(confidence_level=0.95)\n"
   ]
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
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   "source": []
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