power_samplesize_estimations_copula.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f3246374",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy import stats\n",
    "from matplotlib import pyplot as plt\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "from sklearn.metrics import average_precision_score, roc_auc_score\n",
    "pd.set_option('max_colwidth', 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d65e84d3",
   "metadata": {},
   "outputs": [],
   "source": [
    "from mixedvines.copula import GaussianCopula\n",
    "from mixedvines.mixedvine import MixedVine\n",
    "from scipy.stats import norm, bernoulli\n",
    "import itertools\n",
    "\n",
    "rng = np.random.default_rng()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3acc670a",
   "metadata": {},
   "outputs": [],
   "source": [
    "'''def gen_auc_boots(scores, truth, nboots=100, rng=None):\n",
    "    if rng is None:\n",
    "        rng = np.random.default_rng()\n",
    "    boot_res = []\n",
    "    for pp in range(nboots):\n",
    "        boot_ind = rng.choice(range(len(truth)), size=truth.size, replace=True)\n",
    "        boot_truth = truth[boot_ind]\n",
    "        boot_score = scores[boot_ind]\n",
    "        boot_res.append(roc_auc_score(boot_truth, boot_score))\n",
    "    return np.array(boot_res)'''\n",
    "\n",
    "def gen_auc_boots(scores, truth, nboots=100, rng=None):\n",
    "    if rng is None:\n",
    "        rng = np.random.default_rng()\n",
    "    boot_res = []\n",
    "    for pp in range(nboots):\n",
    "        boot_ind = rng.choice(range(len(truth)), size=truth.size, replace=True)\n",
    "        boot_truth = truth[boot_ind]\n",
    "        boot_score = scores[boot_ind]\n",
    "        while len(np.unique(boot_truth)) == 1:\n",
    "            boot_ind = rng.choice(range(len(truth)), size=truth.size, replace=True)\n",
    "            boot_truth = truth[boot_ind]\n",
    "            boot_score = scores[boot_ind]\n",
    "        boot_res.append(roc_auc_score(boot_truth, boot_score))\n",
    "    return np.array(boot_res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "dadb2a99",
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 0.05"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "5d3c09ed",
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "parameter theta out of bounds",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[15], line 12\u001b[0m\n\u001b[1;32m     10\u001b[0m vine\u001b[38;5;241m.\u001b[39mset_marginal(\u001b[38;5;241m0\u001b[39m, norm(\u001b[38;5;241m0\u001b[39m,\u001b[38;5;241m1\u001b[39m))\n\u001b[1;32m     11\u001b[0m vine\u001b[38;5;241m.\u001b[39mset_marginal(\u001b[38;5;241m1\u001b[39m, bernoulli(case_rate))\n\u001b[0;32m---> 12\u001b[0m vine\u001b[38;5;241m.\u001b[39mset_copula(\u001b[38;5;241m1\u001b[39m, \u001b[38;5;241m0\u001b[39m, \u001b[43mGaussianCopula\u001b[49m\u001b[43m(\u001b[49m\u001b[43mcorr\u001b[49m\u001b[43m)\u001b[49m)\n\u001b[1;32m     13\u001b[0m population \u001b[38;5;241m=\u001b[39m vine\u001b[38;5;241m.\u001b[39mrvs(population_size)\n\u001b[1;32m     14\u001b[0m pop_y_score \u001b[38;5;241m=\u001b[39m population[:, \u001b[38;5;241m0\u001b[39m]\n",
      "File \u001b[0;32m~/Library/Python/3.9/lib/python/site-packages/mixedvines/copula.py:86\u001b[0m, in \u001b[0;36mCopula.__init__\u001b[0;34m(self, theta, rotation)\u001b[0m\n\u001b[1;32m     85\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m__init__\u001b[39m(\u001b[38;5;28mself\u001b[39m, theta\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m, rotation\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[0;32m---> 86\u001b[0m     \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m__check_theta\u001b[49m\u001b[43m(\u001b[49m\u001b[43mtheta\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     87\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m__check_rotation(rotation)\n\u001b[1;32m     88\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mtheta \u001b[38;5;241m=\u001b[39m theta\n",
      "File \u001b[0;32m~/Library/Python/3.9/lib/python/site-packages/mixedvines/copula.py:109\u001b[0m, in \u001b[0;36mCopula.__check_theta\u001b[0;34m(cls, theta)\u001b[0m\n\u001b[1;32m    107\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m theta\u001b[38;5;241m.\u001b[39msize \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m1\u001b[39m:\n\u001b[1;32m    108\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m theta \u001b[38;5;241m<\u001b[39m bnds[\u001b[38;5;241m0\u001b[39m][\u001b[38;5;241m0\u001b[39m] \u001b[38;5;129;01mor\u001b[39;00m theta \u001b[38;5;241m>\u001b[39m bnds[\u001b[38;5;241m0\u001b[39m][\u001b[38;5;241m1\u001b[39m]:\n\u001b[0;32m--> 109\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mparameter theta out of bounds\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m    110\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m    111\u001b[0m     \u001b[38;5;28;01mfor\u001b[39;00m i, bnd \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28menumerate\u001b[39m(bnds):\n",
      "\u001b[0;31mValueError\u001b[0m: parameter theta out of bounds"
     ]
    }
   ],
   "source": [
    "population_size = 100000\n",
    "sample_size = 300\n",
    "case_rate = 0.10\n",
    "target_auc = 0.8\n",
    "dim=2\n",
    "corrs = rng.uniform(size=500)\n",
    "sim_res = []\n",
    "for cix, corr in enumerate(corrs):\n",
    "    vine = MixedVine(dim)\n",
    "    vine.set_marginal(0, norm(0,1))\n",
    "    vine.set_marginal(1, bernoulli(case_rate))\n",
    "    vine.set_copula(1, 0, GaussianCopula(corr))\n",
    "    population = vine.rvs(population_size)\n",
    "    pop_y_score = population[:, 0]\n",
    "    pop_y_true = population[:, 1]\n",
    "    pop_auc = roc_auc_score(pop_y_true, pop_y_score)\n",
    "    samples = rng.choice(population, size=sample_size, replace=False)\n",
    "    samp_y_score = samples[:,0]\n",
    "    samp_y_true = samples[:,1]\n",
    "    samp_auc = roc_auc_score(samp_y_true, samp_y_score)\n",
    "    boots = gen_auc_boots(samp_y_score, samp_y_true, nboots=1000, rng=rng)\n",
    "    boots = np.hstack([boots, np.array([samp_auc])])\n",
    "    p = (boots >= target_auc).mean()\n",
    "    row = {}\n",
    "    row['sim_ix'] = cix\n",
    "    row['corr'] = corr\n",
    "    row['pop_case_rate'] = pop_y_true.mean()\n",
    "    row['pop_auc'] = pop_auc\n",
    "    row['samp_case_rate'] = samp_y_true.mean()\n",
    "    row['samp_auc'] = samp_auc\n",
    "    row['samp_p'] = p\n",
    "    sim_res.append(row)\n",
    "sim_res = pd.DataFrame(sim_res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "a2e942d7-2181-4670-b341-ffbd0b8a0fe5",
   "metadata": {},
   "outputs": [],
   "source": [
    "while True:\n",
    "    try:\n",
    "        population_size = 100000\n",
    "        sample_size = 197\n",
    "        case_rate = 0.60\n",
    "        target_auc = 0.8\n",
    "        dim=2\n",
    "        corrs = rng.uniform(size=500)\n",
    "        sim_res = []\n",
    "        for cix, corr in enumerate(corrs):\n",
    "            vine = MixedVine(dim)\n",
    "            vine.set_marginal(0, norm(0,1))\n",
    "            vine.set_marginal(1, bernoulli(case_rate))\n",
    "            vine.set_copula(1, 0, GaussianCopula(corr))\n",
    "            population = vine.rvs(population_size)\n",
    "            pop_y_score = population[:, 0]\n",
    "            pop_y_true = population[:, 1]\n",
    "            pop_auc = roc_auc_score(pop_y_true, pop_y_score)\n",
    "            samples = rng.choice(population, size=sample_size, replace=False)\n",
    "            samp_y_score = samples[:,0]\n",
    "            samp_y_true = samples[:,1]\n",
    "            samp_auc = roc_auc_score(samp_y_true, samp_y_score)\n",
    "            boots = gen_auc_boots(samp_y_score, samp_y_true, nboots=1000, rng=rng)\n",
    "            boots = np.hstack([boots, np.array([samp_auc])])\n",
    "            p = (boots >= target_auc).mean()\n",
    "            row = {}\n",
    "            row['sim_ix'] = cix\n",
    "            row['corr'] = corr\n",
    "            row['pop_case_rate'] = pop_y_true.mean()\n",
    "            row['pop_auc'] = pop_auc\n",
    "            row['samp_case_rate'] = samp_y_true.mean()\n",
    "            row['samp_auc'] = samp_auc\n",
    "            row['samp_p'] = p\n",
    "            sim_res.append(row)\n",
    "        sim_res = pd.DataFrame(sim_res)\n",
    "    except:\n",
    "         continue\n",
    "    else:\n",
    "         break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "f45d1718",
   "metadata": {},
   "outputs": [],
   "source": [
    "# calculate cumulative power\n",
    "sim_res['sig'] = sim_res.samp_p < alpha\n",
    "sim_res['dummy'] = 1\n",
    "sim_res = sim_res.sort_values('pop_auc').reset_index(drop=True)\n",
    "sim_res['cumulative_power'] = sim_res.sig.cumsum()/sim_res.dummy.cumsum()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "05d3013d",
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sim_ix</th>\n",
       "      <th>corr</th>\n",
       "      <th>pop_case_rate</th>\n",
       "      <th>pop_auc</th>\n",
       "      <th>samp_case_rate</th>\n",
       "      <th>samp_auc</th>\n",
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       "      <th>cumulative_power</th>\n",
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       "      <td>1.000000</td>\n",
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       "      <td>306</td>\n",
       "      <td>0.007738</td>\n",
       "      <td>0.09967</td>\n",
       "      <td>0.503043</td>\n",
       "      <td>0.113541</td>\n",
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       "      <td>0.0</td>\n",
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       "      <td>0.09997</td>\n",
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>495</th>\n",
       "      <td>474</td>\n",
       "      <td>0.991252</td>\n",
       "      <td>0.09970</td>\n",
       "      <td>0.997083</td>\n",
       "      <td>0.111018</td>\n",
       "      <td>0.998352</td>\n",
       "      <td>1.0</td>\n",
       "      <td>False</td>\n",
       "      <td>1</td>\n",
       "      <td>0.477823</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>496</th>\n",
       "      <td>436</td>\n",
       "      <td>0.991960</td>\n",
       "      <td>0.10046</td>\n",
       "      <td>0.997134</td>\n",
       "      <td>0.104289</td>\n",
       "      <td>0.995722</td>\n",
       "      <td>1.0</td>\n",
       "      <td>False</td>\n",
       "      <td>1</td>\n",
       "      <td>0.476861</td>\n",
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       "    <tr>\n",
       "      <th>497</th>\n",
       "      <td>45</td>\n",
       "      <td>0.992274</td>\n",
       "      <td>0.09946</td>\n",
       "      <td>0.997196</td>\n",
       "      <td>0.091674</td>\n",
       "      <td>0.997256</td>\n",
       "      <td>1.0</td>\n",
       "      <td>False</td>\n",
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       "      <td>0.475904</td>\n",
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       "      <td>0.993486</td>\n",
       "      <td>0.10119</td>\n",
       "      <td>0.997714</td>\n",
       "      <td>0.097561</td>\n",
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       "      <td>1.0</td>\n",
       "      <td>False</td>\n",
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       "      <td>0.10058</td>\n",
       "      <td>0.997866</td>\n",
       "      <td>0.116064</td>\n",
       "      <td>0.997656</td>\n",
       "      <td>1.0</td>\n",
       "      <td>False</td>\n",
       "      <td>1</td>\n",
       "      <td>0.474000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>500 rows × 10 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     sim_ix      corr  pop_case_rate   pop_auc  samp_case_rate  samp_auc  \\\n",
       "0       311  0.008351        0.10006  0.496980        0.098402  0.516042   \n",
       "1         0  0.000475        0.10017  0.498178        0.106812  0.564579   \n",
       "2       306  0.007738        0.09967  0.503043        0.113541  0.477869   \n",
       "3       154  0.016403        0.09949  0.504426        0.109336  0.452597   \n",
       "4       399  0.001476        0.09997  0.504738        0.095038  0.504038   \n",
       "..      ...       ...            ...       ...             ...       ...   \n",
       "495     474  0.991252        0.09970  0.997083        0.111018  0.998352   \n",
       "496     436  0.991960        0.10046  0.997134        0.104289  0.995722   \n",
       "497      45  0.992274        0.09946  0.997196        0.091674  0.997256   \n",
       "498     113  0.993486        0.10119  0.997714        0.097561  0.998465   \n",
       "499     491  0.993892        0.10058  0.997866        0.116064  0.997656   \n",
       "\n",
       "     samp_p    sig  dummy  cumulative_power  \n",
       "0       0.0   True      1          1.000000  \n",
       "1       0.0   True      1          1.000000  \n",
       "2       0.0   True      1          1.000000  \n",
       "3       0.0   True      1          1.000000  \n",
       "4       0.0   True      1          1.000000  \n",
       "..      ...    ...    ...               ...  \n",
       "495     1.0  False      1          0.477823  \n",
       "496     1.0  False      1          0.476861  \n",
       "497     1.0  False      1          0.475904  \n",
       "498     1.0  False      1          0.474950  \n",
       "499     1.0  False      1          0.474000  \n",
       "\n",
       "[500 rows x 10 columns]"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sim_res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "4ffe45f5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots(1)\n",
    "plt.plot(sim_res.pop_auc, sim_res.cumulative_power, 'o')\n",
    "ax.set_xlabel('True AUC')\n",
    "ax.set_ylabel('Cumulative Power')\n",
    "fig.set_facecolor('white')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "8d2763d0",
   "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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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sim_ix</th>\n",
       "      <th>corr</th>\n",
       "      <th>pop_case_rate</th>\n",
       "      <th>pop_auc</th>\n",
       "      <th>samp_case_rate</th>\n",
       "      <th>samp_auc</th>\n",
       "      <th>samp_p</th>\n",
       "      <th>sig</th>\n",
       "      <th>dummy</th>\n",
       "      <th>cumulative_power</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>295</th>\n",
       "      <td>177</td>\n",
       "      <td>0.596154</td>\n",
       "      <td>0.09903</td>\n",
       "      <td>0.818834</td>\n",
       "      <td>0.082422</td>\n",
       "      <td>0.823276</td>\n",
       "      <td>0.879121</td>\n",
       "      <td>False</td>\n",
       "      <td>1</td>\n",
       "      <td>0.800676</td>\n",
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       "    <tr>\n",
       "      <th>294</th>\n",
       "      <td>111</td>\n",
       "      <td>0.591397</td>\n",
       "      <td>0.10034</td>\n",
       "      <td>0.818528</td>\n",
       "      <td>0.095038</td>\n",
       "      <td>0.836777</td>\n",
       "      <td>0.978022</td>\n",
       "      <td>False</td>\n",
       "      <td>1</td>\n",
       "      <td>0.803390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>293</th>\n",
       "      <td>287</td>\n",
       "      <td>0.594462</td>\n",
       "      <td>0.09939</td>\n",
       "      <td>0.817333</td>\n",
       "      <td>0.085786</td>\n",
       "      <td>0.826235</td>\n",
       "      <td>0.900100</td>\n",
       "      <td>False</td>\n",
       "      <td>1</td>\n",
       "      <td>0.806122</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>292</th>\n",
       "      <td>429</td>\n",
       "      <td>0.586070</td>\n",
       "      <td>0.10134</td>\n",
       "      <td>0.817298</td>\n",
       "      <td>0.110177</td>\n",
       "      <td>0.856463</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>False</td>\n",
       "      <td>1</td>\n",
       "      <td>0.808874</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>291</th>\n",
       "      <td>476</td>\n",
       "      <td>0.573988</td>\n",
       "      <td>0.09857</td>\n",
       "      <td>0.816322</td>\n",
       "      <td>0.081581</td>\n",
       "      <td>0.808117</td>\n",
       "      <td>0.655345</td>\n",
       "      <td>False</td>\n",
       "      <td>1</td>\n",
       "      <td>0.811644</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "      <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>95</th>\n",
       "      <td>224</td>\n",
       "      <td>0.173907</td>\n",
       "      <td>0.09960</td>\n",
       "      <td>0.600963</td>\n",
       "      <td>0.112700</td>\n",
       "      <td>0.573233</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>True</td>\n",
       "      <td>1</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>392</td>\n",
       "      <td>0.186834</td>\n",
       "      <td>0.10004</td>\n",
       "      <td>0.600961</td>\n",
       "      <td>0.111018</td>\n",
       "      <td>0.619098</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>True</td>\n",
       "      <td>1</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>93</th>\n",
       "      <td>198</td>\n",
       "      <td>0.165860</td>\n",
       "      <td>0.10041</td>\n",
       "      <td>0.593123</td>\n",
       "      <td>0.096720</td>\n",
       "      <td>0.576812</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>True</td>\n",
       "      <td>1</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>109</th>\n",
       "      <td>441</td>\n",
       "      <td>0.212177</td>\n",
       "      <td>0.10076</td>\n",
       "      <td>0.615979</td>\n",
       "      <td>0.102607</td>\n",
       "      <td>0.611628</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>True</td>\n",
       "      <td>1</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>147</th>\n",
       "      <td>202</td>\n",
       "      <td>0.279855</td>\n",
       "      <td>0.10074</td>\n",
       "      <td>0.651557</td>\n",
       "      <td>0.096720</td>\n",
       "      <td>0.657817</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>True</td>\n",
       "      <td>1</td>\n",
       "      <td>1.000000</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "<p>296 rows × 10 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     sim_ix      corr  pop_case_rate   pop_auc  samp_case_rate  samp_auc  \\\n",
       "295     177  0.596154        0.09903  0.818834        0.082422  0.823276   \n",
       "294     111  0.591397        0.10034  0.818528        0.095038  0.836777   \n",
       "293     287  0.594462        0.09939  0.817333        0.085786  0.826235   \n",
       "292     429  0.586070        0.10134  0.817298        0.110177  0.856463   \n",
       "291     476  0.573988        0.09857  0.816322        0.081581  0.808117   \n",
       "..      ...       ...            ...       ...             ...       ...   \n",
       "95      224  0.173907        0.09960  0.600963        0.112700  0.573233   \n",
       "94      392  0.186834        0.10004  0.600961        0.111018  0.619098   \n",
       "93      198  0.165860        0.10041  0.593123        0.096720  0.576812   \n",
       "109     441  0.212177        0.10076  0.615979        0.102607  0.611628   \n",
       "147     202  0.279855        0.10074  0.651557        0.096720  0.657817   \n",
       "\n",
       "       samp_p    sig  dummy  cumulative_power  \n",
       "295  0.879121  False      1          0.800676  \n",
       "294  0.978022  False      1          0.803390  \n",
       "293  0.900100  False      1          0.806122  \n",
       "292  1.000000  False      1          0.808874  \n",
       "291  0.655345  False      1          0.811644  \n",
       "..        ...    ...    ...               ...  \n",
       "95   0.000000   True      1          1.000000  \n",
       "94   0.000000   True      1          1.000000  \n",
       "93   0.000000   True      1          1.000000  \n",
       "109  0.000000   True      1          1.000000  \n",
       "147  0.000000   True      1          1.000000  \n",
       "\n",
       "[296 rows x 10 columns]"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sim_res.query('cumulative_power >= 0.8').sort_values('cumulative_power')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "f2b6475d",
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "     sim_ix      corr  pop_case_rate   pop_auc  samp_case_rate  samp_auc  \\\n",
       "499     491  0.993892        0.10058  0.997866        0.116064  0.997656   \n",
       "498     113  0.993486        0.10119  0.997714        0.097561  0.998465   \n",
       "497      45  0.992274        0.09946  0.997196        0.091674  0.997256   \n",
       "496     436  0.991960        0.10046  0.997134        0.104289  0.995722   \n",
       "495     474  0.991252        0.09970  0.997083        0.111018  0.998352   \n",
       "..      ...       ...            ...       ...             ...       ...   \n",
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       "274     377  0.561471        0.09818  0.804149        0.104289  0.769749   \n",
       "273     132  0.571204        0.09886  0.804019        0.103448  0.835682   \n",
       "272      50  0.562080        0.10039  0.802600        0.111859  0.787815   \n",
       "\n",
       "       samp_p    sig  dummy  cumulative_power  \n",
       "499  1.000000  False      1          0.474000  \n",
       "498  1.000000  False      1          0.474950  \n",
       "497  1.000000  False      1          0.475904  \n",
       "496  1.000000  False      1          0.476861  \n",
       "495  1.000000  False      1          0.477823  \n",
       "..        ...    ...    ...               ...  \n",
       "276  0.145854  False      1          0.855596  \n",
       "275  0.511489  False      1          0.858696  \n",
       "274  0.068931  False      1          0.861818  \n",
       "273  0.978022  False      1          0.864964  \n",
       "272  0.262737  False      1          0.868132  \n",
       "\n",
       "[228 rows x 10 columns]"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sim_res.query('pop_auc >= 0.7999').sort_values('cumulative_power')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "2334af1c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# make sure there's not a bias for sample AUC relative to population AUC\n",
    "fig, ax = plt.subplots(1)\n",
    "ax.plot(sim_res.pop_auc, sim_res.samp_auc)\n",
    "ax.plot([0.5,1], [0.5,1])\n",
    "ax.set_xlabel('Population AUC')\n",
    "ax.set_ylabel('Sample AUC')\n",
    "fig.set_facecolor('white')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bd1b1764",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}