analysis-I.ipynb

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   "source": [
    "from cibin.permute_utils import hypergeom_conf_interval\n",
    "from cibin.utils import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data from Regeneron Press"
   ]
  },
  {
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   "execution_count": 2,
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "(11, 742, 59, 693)"
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     "execution_count": 2,
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   "source": [
    "n=753\n",
    "m=752\n",
    "N=n+m\n",
    "n01 = 59\n",
    "n11 = 11\n",
    "n00 = m-n01\n",
    "n10 = n-n11\n",
    "alpha=0.05\n",
    "n11, n10, n01, n00"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "## One-sided confidence intervals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Upper one-sided"
   ]
  },
  {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "(397, [-0.5, 0.2637873754152824])"
      ]
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     "execution_count": 3,
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   "source": [
    "N_dot_1 = hypergeom_conf_interval(n11*N/n, n11, N, 1-alpha, alternative='upper')\n",
    "N_1_dot = hypergeom_conf_interval(n01*N/m, n01, N, 1-alpha, alternative='lower')\n",
    "\n",
    "upper = (N_dot_1[1] - N_1_dot[0])/N\n",
    "\n",
    "ci = [-0.5, upper]\n",
    "N_dot_1[1] - N_1_dot[0], ci"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Lower one-sided"
   ]
  },
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   "execution_count": 4,
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "(395, [-0.26245847176079734, 0.5])"
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     "execution_count": 4,
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   ],
   "source": [
    "N_dot_1 = hypergeom_conf_interval(n11*N/n, n11, N, 1-alpha, alternative='lower')\n",
    "N_1_dot = hypergeom_conf_interval(n01*N/m, n01, N, 1-alpha, alternative='upper')\n",
    "\n",
    "lower = (N_dot_1[0] - N_1_dot[1])/N\n",
    "\n",
    "ci = [lower, 0.5]\n",
    "N_1_dot[1] - N_dot_1[0], ci"
   ]
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   "cell_type": "code",
   "execution_count": null,
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   "outputs": [],
   "source": [
    "tau_lower_oneside(n11, n10, n01, n00, alpha=0.05, nperm=1) # result around (-0.15, 0.42), span 858"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Two-sided"
   ]
  },
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   "execution_count": 5,
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "(515, 516, [-0.34219269102990035, 0.34285714285714286])"
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     "execution_count": 5,
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   ],
   "source": [
    "N_dot_1 = hypergeom_conf_interval(n11*N/n, n11, N, 1-alpha/2, alternative='two-sided')\n",
    "N_1_dot = hypergeom_conf_interval(n01*N/m, n01, N, 1-alpha/2, alternative='two-sided')\n",
    "lower = (N_dot_1[0] - N_1_dot[1])/N\n",
    "upper = (N_dot_1[1] - N_1_dot[0])/N\n",
    "ci = [lower, upper]\n",
    "N_1_dot[1] - N_dot_1[0], N_dot_1[1] - N_1_dot[0], ci"
   ]
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   "cell_type": "code",
   "execution_count": 6,
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   "outputs": [],
   "source": [
    "two_side = hypergeom_conf_interval(n, n01, N, 1-alpha/2, alternative='two-sided', method='Sterne')"
   ]
  },
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   "cell_type": "code",
   "execution_count": 7,
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    {
     "data": {
      "text/plain": [
       "49"
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     "execution_count": 7,
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   "source": [
    "two_side[1]-two_side[0]"
   ]
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   "execution_count": 8,
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     "data": {
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       "(0.06312292358803986, 0.09568106312292358)"
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     "execution_count": 8,
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   "source": [
    "(two_side[0]/N, two_side[1]/N)"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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     "end_time": "2021-05-15T04:40:26.581612Z",
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   },
   "outputs": [],
   "source": [
    "tau_twosided_ci(n11, n10, n01, n00, 0.05, exact=False, max_combinations=10**5, reps=100) # result around (-0.15, 0.42), span 858"
   ]
  }
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