{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "078900c6-d71d-44f0-9e76-cc5ce66f0ca9",
   "metadata": {},
   "source": [
    "# Logistic regression with uncertainties"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0de7f02-942b-42ff-874c-3c0e2ac1e0dc",
   "metadata": {},
   "source": [
    "## Data & common "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "be75450c",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "\n",
    "from fitter import Fitter, get_common_distributions, get_distributions\n",
    "from scipy import io\n",
    "\n",
    "import scipy.stats as ss\n",
    "\n",
    "from sklearn import linear_model\n",
    "import os"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3373f87f",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "#data_path = \"/home/marija/maki/\"\n",
    "data_path = \"../data/\"\n",
    "suv_filename = data_path + \"suv_percentilesSLOthenUWM.mat\"\n",
    "flags_filename=  data_path + \"flags_combined.mat\"\n",
    "normal_range_filename =  data_path + \"normal_range.mat\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "811d990d",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Loading all data\n",
    "\"\"\"\n",
    "suv_dict = io.loadmat(suv_filename)\n",
    "flags_dict = io.loadmat(flags_filename)\n",
    "normal_range_dict = io.loadmat(normal_range_filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b47b0289-1378-40a8-88e2-acfed4c4cd69",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "## Testing"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35e9bb7b-5a50-4cae-9af4-261c11453dd4",
   "metadata": {},
   "source": [
    "### General ideas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ae5d1e06-5122-400d-a9ab-7f04867f8cdb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(58, 17, 100)\n",
      "(58,)\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "Extracting only data associated to organ of interest, you need to choose data and column of flags that shoud be taken depended on data \n",
    "\"\"\"\n",
    "# in suv values can be (choose one of them): 'lung_SUVperc_COMBINED' , 'bowel_SUVperc_COMBINED' or 'thyroid_SUVperc_COMBINED'\n",
    "# in flags choose the column depended on the data of interest (1 for bowel, 3 for lung, 5 for thyroid)\n",
    "\n",
    "suv = suv_dict['lung_SUVperc_COMBINED'][0:58,:,:]\n",
    "flags = flags_dict['flags'][0:58,3]\n",
    "\n",
    "print(suv.shape)\n",
    "print(flags.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a70c64a3",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
      " 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      "[1 1 1 1 1]\n"
     ]
    }
   ],
   "source": [
    "print(flags[flags==0])\n",
    "print(flags[flags==1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9b894e29",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(58, 1)\n"
     ]
    }
   ],
   "source": [
    "p = 94  # choose percentile of interest (for lung and bowel 95, for thyroid 75), numerating here is from 0 so take the one less\n",
    "X = np.nanmax(suv[:,:,p], axis=1).reshape(-1,1)\n",
    "\n",
    "print(X.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6deba69b-9c9c-47b6-b02d-f40998729aa1",
   "metadata": {},
   "source": [
    "Logistic regression documentation:\n",
    "* https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
    "* https://stats.stackexchange.com/questions/186830/what-is-scikit-learns-logisticregression-minimizing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "239ae789",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "ename": "InvalidParameterError",
     "evalue": "The 'penalty' parameter of LogisticRegression must be a str among {'elasticnet', 'l1', 'l2'} or None. Got 'none' instead.",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mInvalidParameterError\u001b[0m                     Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[7], line 2\u001b[0m\n\u001b[0;32m      1\u001b[0m logr \u001b[38;5;241m=\u001b[39m linear_model\u001b[38;5;241m.\u001b[39mLogisticRegression(penalty\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mnone\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m----> 2\u001b[0m clf \u001b[38;5;241m=\u001b[39m logr\u001b[38;5;241m.\u001b[39mfit(X, flags)\n\u001b[0;32m      4\u001b[0m \u001b[38;5;66;03m# underlaying linear model coefficients\u001b[39;00m\n\u001b[0;32m      5\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mw0:\u001b[39m\u001b[38;5;124m\"\u001b[39m, logr\u001b[38;5;241m.\u001b[39mintercept_)\n",
      "File \u001b[1;32mc:\\Users\\zahra\\anaconda3\\Lib\\site-packages\\sklearn\\base.py:1466\u001b[0m, in \u001b[0;36m_fit_context.<locals>.decorator.<locals>.wrapper\u001b[1;34m(estimator, *args, **kwargs)\u001b[0m\n\u001b[0;32m   1461\u001b[0m partial_fit_and_fitted \u001b[38;5;241m=\u001b[39m (\n\u001b[0;32m   1462\u001b[0m     fit_method\u001b[38;5;241m.\u001b[39m\u001b[38;5;18m__name__\u001b[39m \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mpartial_fit\u001b[39m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;129;01mand\u001b[39;00m _is_fitted(estimator)\n\u001b[0;32m   1463\u001b[0m )\n\u001b[0;32m   1465\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m global_skip_validation \u001b[38;5;129;01mand\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m partial_fit_and_fitted:\n\u001b[1;32m-> 1466\u001b[0m     estimator\u001b[38;5;241m.\u001b[39m_validate_params()\n\u001b[0;32m   1468\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m config_context(\n\u001b[0;32m   1469\u001b[0m     skip_parameter_validation\u001b[38;5;241m=\u001b[39m(\n\u001b[0;32m   1470\u001b[0m         prefer_skip_nested_validation \u001b[38;5;129;01mor\u001b[39;00m global_skip_validation\n\u001b[0;32m   1471\u001b[0m     )\n\u001b[0;32m   1472\u001b[0m ):\n\u001b[0;32m   1473\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m fit_method(estimator, \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n",
      "File \u001b[1;32mc:\\Users\\zahra\\anaconda3\\Lib\\site-packages\\sklearn\\base.py:666\u001b[0m, in \u001b[0;36mBaseEstimator._validate_params\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m    658\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m_validate_params\u001b[39m(\u001b[38;5;28mself\u001b[39m):\n\u001b[0;32m    659\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"Validate types and values of constructor parameters\u001b[39;00m\n\u001b[0;32m    660\u001b[0m \n\u001b[0;32m    661\u001b[0m \u001b[38;5;124;03m    The expected type and values must be defined in the `_parameter_constraints`\u001b[39;00m\n\u001b[1;32m   (...)\u001b[0m\n\u001b[0;32m    664\u001b[0m \u001b[38;5;124;03m    accepted constraints.\u001b[39;00m\n\u001b[0;32m    665\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[1;32m--> 666\u001b[0m     validate_parameter_constraints(\n\u001b[0;32m    667\u001b[0m         \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_parameter_constraints,\n\u001b[0;32m    668\u001b[0m         \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_params(deep\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mFalse\u001b[39;00m),\n\u001b[0;32m    669\u001b[0m         caller_name\u001b[38;5;241m=\u001b[39m\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m\u001b[38;5;18m__class__\u001b[39m\u001b[38;5;241m.\u001b[39m\u001b[38;5;18m__name__\u001b[39m,\n\u001b[0;32m    670\u001b[0m     )\n",
      "File \u001b[1;32mc:\\Users\\zahra\\anaconda3\\Lib\\site-packages\\sklearn\\utils\\_param_validation.py:95\u001b[0m, in \u001b[0;36mvalidate_parameter_constraints\u001b[1;34m(parameter_constraints, params, caller_name)\u001b[0m\n\u001b[0;32m     89\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m     90\u001b[0m     constraints_str \u001b[38;5;241m=\u001b[39m (\n\u001b[0;32m     91\u001b[0m         \u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;132;01m{\u001b[39;00m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m, \u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;241m.\u001b[39mjoin([\u001b[38;5;28mstr\u001b[39m(c)\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mfor\u001b[39;00m\u001b[38;5;250m \u001b[39mc\u001b[38;5;250m \u001b[39m\u001b[38;5;129;01min\u001b[39;00m\u001b[38;5;250m \u001b[39mconstraints[:\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m]])\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m or\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[0;32m     92\u001b[0m         \u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mconstraints[\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m]\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m\n\u001b[0;32m     93\u001b[0m     )\n\u001b[1;32m---> 95\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m InvalidParameterError(\n\u001b[0;32m     96\u001b[0m     \u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mThe \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mparam_name\u001b[38;5;132;01m!r}\u001b[39;00m\u001b[38;5;124m parameter of \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mcaller_name\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m must be\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[0;32m     97\u001b[0m     \u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mconstraints_str\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m. Got \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mparam_val\u001b[38;5;132;01m!r}\u001b[39;00m\u001b[38;5;124m instead.\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[0;32m     98\u001b[0m )\n",
      "\u001b[1;31mInvalidParameterError\u001b[0m: The 'penalty' parameter of LogisticRegression must be a str among {'elasticnet', 'l1', 'l2'} or None. Got 'none' instead."
     ]
    }
   ],
   "source": [
    "logr = linear_model.LogisticRegression(penalty='none')\n",
    "clf = logr.fit(X, flags)\n",
    "\n",
    "# underlaying linear model coefficients\n",
    "print(\"w0:\", logr.intercept_)\n",
    "print(\"w1:\", logr.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "54f463d0",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fb6b21c2560>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0, 6, 100)\n",
    "y = logr.predict_proba(x.reshape(-1,1))\n",
    "\n",
    "plt.title(\"Prediction probability of AE depending on maxSUV value\")\n",
    "plt.xlabel(r\"$x = max_{visit} SUV(visit, p)$\")\n",
    "plt.ylabel(\"P(AE|X=x)\")\n",
    "\n",
    "plt.scatter(X[flags==0], flags[flags==0],label=\"NC\")  \n",
    "plt.scatter(X[flags==1], flags[flags==1],label=\"AE\")\n",
    "\n",
    "plt.plot(x, 1/(1 + np.exp(-logr.intercept_[0] - logr.coef_[0,0]*x)), label=\"logistic reg\")\n",
    "plt.legend(loc='center right')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2c16aad9",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Covariance matrix: \n",
      " [[12.32329923 -6.71305958]\n",
      " [-6.71305958  3.81886093]]\n",
      "Standard errors:  [3.5104557  1.95419061]\n",
      "logitParams: [-11.68397793   5.68702693]\n"
     ]
    }
   ],
   "source": [
    "#Ref: \n",
    "# https://stats.stackexchange.com/questions/89484/how-to-compute-the-standard-errors-of-a-logistic-regressions-coefficients\n",
    "\n",
    "# Calculate matrix of predicted class probabilities.\n",
    "predProbs = logr.predict_proba(X) #has two col. p, (1-p)\n",
    "\n",
    "# Design matrix -- add column of 1's at the beginning of your X_train matrix\n",
    "X_design = np.hstack([np.ones((X.shape[0], 1)), X]) \n",
    "\n",
    "# Initiate matrix of 0's, fill diagonal with each predicted observation's variance\n",
    "V = np.diagflat(np.product(predProbs, axis=1)) #dig.matrix where each element is p*(1-p)\n",
    "\n",
    "# Covariance matrix C_params = (X^T V X)^-1, params = (b0,b1) \n",
    "covLogit = np.linalg.inv(np.dot(np.dot(X_design.T, V), X_design))\n",
    "print(\"Covariance matrix: \\n\", covLogit)\n",
    "\n",
    "# Standard errors\n",
    "print(\"Standard errors: \", np.sqrt(np.diag(covLogit)))\n",
    "\n",
    "# Wald statistic (coefficient / s.e.) ^ 2\n",
    "logitParams = np.insert(logr.coef_, 0, logr.intercept_)\n",
    "print(\"logitParams:\", logitParams)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2f0ac198",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Logistic regresion modeling with estimated uncertainties')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Direct approach to variance in logit regression:\n",
    "#\n",
    "#   f(x|p*)    p ~ N(p*,C_p)\n",
    "#\n",
    "\n",
    "f = lambda x,p: 1/(1 + np.exp(-p[0] - p[1]*x))\n",
    "fopt = lambda x: 1/(1 + np.exp(-logitParams[0] - logitParams[1]*x))\n",
    "\n",
    "#generate parameters and points in x axis\n",
    "ps = np.random.multivariate_normal(logitParams, covLogit, 1000)\n",
    "xs = np.linspace(0, 6, 100)\n",
    "\n",
    "# generate values in y axis\n",
    "yopts = fopt(xs)\n",
    "ys = np.array([np.fromiter(map(lambda p: f(x,p), ps),float) for x in xs])\n",
    "\n",
    "# doing statistics on values\n",
    "mys = np.median(ys,axis=1)\n",
    "alpha=0.05\n",
    "yerr_min = np.quantile(ys, alpha/2, axis=1)\n",
    "yerr_max = np.quantile(ys, 1-alpha/2, axis=1)\n",
    "\n",
    "plt.xlabel(\"x = maxSUV\")\n",
    "plt.ylabel(\"P(AE|X=x)\")\n",
    "plt.scatter(X[flags==0], flags[flags==0],label=\"NC\")  \n",
    "plt.scatter(X[flags==1], flags[flags==1],label=\"AE\")\n",
    "plt.plot(xs, yopts, label=\"fit logit model\",color=\"red\")\n",
    "#plt.errorbar(xs, mys, yerr = [mys-yerr_min, yerr_max-mys], label=\"direct variance\",fmt=' ')\n",
    "plt.fill_between(xs, yerr_min, yerr_max, alpha=0.5, label=\"confidence interval\")\n",
    "\n",
    "plt.legend(loc='center right')\n",
    "plt.title(\"Logistic regresion modeling with estimated uncertainties\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a1a899c-ac8a-44e8-bad6-04262e429913",
   "metadata": {},
   "source": [
    "### Distribution of parameters via BS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "712f33c6-b772-4c90-b2e0-ad9336fc8d83",
   "metadata": {},
   "outputs": [],
   "source": [
    "# loading data for lungs\n",
    "suv = suv_dict['lung_SUVperc_COMBINED'][0:58,:,:]\n",
    "flags = flags_dict['flags'][0:58,3]\n",
    "\n",
    "per = 94  # choose percentile of interest (for lung and bowel 95, for thyroid 75), numerating here is from 0 so take the one less\n",
    "X = np.nanmax(suv[:,:,per], axis=1).reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8d8c5f8a-f065-4980-a313-786e0df9b2c2",
   "metadata": {},
   "outputs": [],
   "source": [
    "gauss = lambda x, mu, var: np.exp(-(x - mu)**2/(2*var))/np.sqrt(2*np.pi*var)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d2ff06ca-e6f3-4442-9bce-29ee929c0071",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "rng = np.random.default_rng()\n",
    "\n",
    "def get_params(idx = None):\n",
    "    if idx is None:\n",
    "        idx = rng.choice(n, n)\n",
    "        while (flags[idx] == 0).all() or (flags[idx] == 1).all():\n",
    "            idx = rng.choice(n, n)\n",
    "            \n",
    "    clf = linear_model.LogisticRegression(penalty='none').fit(X[idx], flags[idx])\n",
    "    return np.insert(clf.coef_, 0, clf.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "69792c6a-18d5-43c1-b1f9-a0744beb1ebb",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# original p0\n",
    "n = len(X)\n",
    "p0 = get_params(np.arange(n))\n",
    "\n",
    "# bootstrapping\n",
    "ps = np.array([get_params() for _ in range(10**7)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a97debd2-00cf-4ebc-9b50-da847daf6d63",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting distribution of parameters\n",
    "sns.set(rc={\"figure.figsize\":(6, 4), \"font.size\": 14})\n",
    "\n",
    "ax = sns.jointplot(x = ps[:,0], y = ps[:,1], kind ='kde', fill=True)\n",
    "ax.set_axis_labels(xlabel= f\"$\\\\beta_0$\", ylabel=f\"$\\\\beta_1$\")\n",
    "\n",
    "plt.text(0.04, 0.9, \"(a)\", fontsize=16, horizontalalignment='center', verticalalignment='center', transform=ax.figure.transFigure)\n",
    "plt.savefig(\"./figs/logit_boots.pdf\", bbox_inches='tight')\n",
    "plt.show()\n",
    "sns.reset_orig()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4f08a287-fdcb-47cc-a2fd-55ddba066ce8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "size_selectd: 6298713\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# select main peak and check distribution\n",
    "ps_sel = ps[(ps[:,0] > -25) & ( ps[:,0] < 0) & (ps[:,1]> 0) & ( ps[:,1] < 10)];\n",
    "print(\"size_selectd:\", len(ps_sel))\n",
    "\n",
    "# plotting distribution of parameters\n",
    "sns.set(rc={\"figure.figsize\":(6, 4), \"font.size\":14})\n",
    "\n",
    "ax = sns.jointplot(x = ps_sel[:,0], y = ps_sel[:,1], kind ='kde', fill=True)\n",
    "ax.set_axis_labels(xlabel= f\"$\\\\beta_0$\", ylabel=f\"$\\\\beta_1$\")\n",
    "\n",
    "plt.text(0.04, 0.9, \"(b)\", fontsize=16, horizontalalignment='center', verticalalignment='center', transform=ax.figure.transFigure)\n",
    "plt.plot([p0[0]], [p0[1]], marker=\"o\", markersize=10, markeredgecolor=\"red\", markerfacecolor=\"red\")\n",
    "\n",
    "x = np.linspace(-25,0,100)\n",
    "ax.ax_marg_x.plot(x, gauss(x, logitParams[0], covLogit[0][0]), \"r\" )\n",
    "\n",
    "y = np.linspace(0, 10,100)\n",
    "ax.ax_marg_y.plot(gauss(y, logitParams[1], covLogit[1][1]), y, \"r\" )\n",
    "\n",
    "plt.savefig(\"./figs/logit_boots_sel.pdf\", bbox_inches='tight')\n",
    "plt.show()\n",
    "sns.reset_orig()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "668f5b02-e351-4dde-9697-af36b49588f2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MLE: beta:\n",
      " [-11.68397793   5.68702693]\n",
      "MLE: cov(beta):\n",
      " [[12.32329923 -6.71305958]\n",
      " [-6.71305958  3.81886093]]\n"
     ]
    }
   ],
   "source": [
    "# MLE: optimal beta and covariance\n",
    "print(\"MLE: beta:\\n\", logitParams)\n",
    "print(\"MLE: cov(beta):\\n\", covLogit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "308b94a4-7a95-47c8-b0c5-4a80bc05b3df",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sample_mean(beta):\n",
      " [-10.82981446   5.00156176]\n",
      "sample_cov(beta):\n",
      " [[ 4.5526891  -2.65783521]\n",
      " [-2.65783521  1.70060809]]\n"
     ]
    }
   ],
   "source": [
    "# sample mean and covariance of selected main peak\n",
    "smean = np.mean(ps_sel, axis=0)\n",
    "print(\"sample_mean(beta):\\n\", smean)\n",
    "db = ps_sel - smean\n",
    "scov = np.dot(db.T, db)/(len(db)-1)\n",
    "print(\"sample_cov(beta):\\n\", scov)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cc3d41a7-518f-4804-832a-090cd1501d35",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# zooming specific area and marking MLE solution:\n",
    "sns.set(rc={\"figure.figsize\":(6, 4), \"font.size\":14})\n",
    "\n",
    "ax = sns.jointplot(x = ps[:,0], y = ps[:,1], kind ='kde', fill=True)\n",
    "ax.set_axis_labels(xlabel= f\"$\\\\beta_0$\", ylabel=f\"$\\\\beta_1$\")\n",
    "\n",
    "x = np.linspace(-25,10,100)\n",
    "ax.ax_marg_x.plot(x, gauss(x, logitParams[0], covLogit[0][0]), \"r\" )\n",
    "\n",
    "y = np.linspace(-20,40,100)\n",
    "ax.ax_marg_y.plot(gauss(y, logitParams[1], covLogit[1][1]), y, \"r\" )\n",
    "\n",
    "plt.text(0.04, 0.9, \"(b)\", fontsize=16, horizontalalignment='center', verticalalignment='center', transform=ax.figure.transFigure)\n",
    "plt.plot([p0[0]], [p0[1]], marker=\"o\", markersize=10, markeredgecolor=\"red\", markerfacecolor=\"red\")\n",
    "\n",
    "plt.xlim(-80,30)\n",
    "plt.ylim(-20,40)\n",
    "plt.savefig(\"./figs/logit_boots_zoom.pdf\", bbox_inches='tight')\n",
    "plt.show()\n",
    "sns.reset_orig()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4c2f7492-6caa-4f05-8a2f-a5a1eac28d30",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "exact: opt(p)= [-11.68397793   5.68702693]\n",
      "exact: covlogit= [[12.32329923 -6.71305958]\n",
      " [-6.71305958  3.81886093]]\n",
      "mean(p)= [-45.79078382  25.75168304]\n",
      "cov(p)= [[ 5276.30572959 -3232.9241108 ]\n",
      " [-3232.9241108   1991.14599825]]\n"
     ]
    }
   ],
   "source": [
    "# calculate empirical average and variance-covariance matrix\n",
    "pmean = np.mean(ps, axis=0)\n",
    "dp = ps - pmean\n",
    "pcov = np.dot(dp.T, dp)/(len(dp)-1)\n",
    "\n",
    "print(\"exact: opt(p)=\", p0)\n",
    "print(\"exact: covlogit=\",covLogit)\n",
    "\n",
    "print(\"mean(p)=\", pmean)\n",
    "print(\"cov(p)=\", pcov)\n",
    "\n",
    "# Conclusion: due to multiple peaks the empirical values are very far from MLE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9bd0c944-1793-42f5-8a78-8a38e339e8f4",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Install:\n",
    "#!pip install pingouin\n",
    "#\n",
    "# Ref: \n",
    "#  * https://www.statology.org/multivariate-normality-test-python/\n",
    "#  * https://pingouin-stats.org/build/html/generated/pingouin.multivariate_normality.html\n",
    "# https://www.sfu.ca/sasdoc/sashtml/ets/chap14/sect38.htm\n",
    "\n",
    "from pingouin import multivariate_normality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5160ac22-29e7-4c06-8b60-1214231fbc43",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "HZResults(hz=0.6501826885176032, pval=0.6851557047523155, normal=True)\n",
      "HZResults(hz=10.665573669445136, pval=7.185502334798263e-24, normal=False)\n"
     ]
    }
   ],
   "source": [
    "# testing multivariate_normality\n",
    "want_to_test = False\n",
    "\n",
    "if want_to_test:\n",
    "    # test cases\n",
    "    test1 = multivariate_normality(rng.multivariate_normal([1,2],[[2,0.5],[0.5,1]], size = 1000), alpha=.05)\n",
    "    \n",
    "    data = rng.multivariate_normal([3,5],[[1,0.5],[0.5,1]], size = 1000)\n",
    "    test2 = multivariate_normality(np.log(np.abs(data)), alpha=.05)\n",
    "    \n",
    "    print(test1)\n",
    "    print(test2)\n",
    "\n",
    "if want_to_test:\n",
    "    # testing our paramaters\n",
    "    our_case = multivariate_normality(ps, alpha=.05)\n",
    "    print(our_case)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98ad2d95-d89b-4f18-a2f7-c7fc17473135",
   "metadata": {},
   "source": [
    "Conclusion: Statistically looking, the distribution of parameters is far from multivariate Gaussian for these sizes of samples, but is captures essential properties."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e065c5d1-7dd5-4098-a095-5a283a8d408c",
   "metadata": {},
   "source": [
    "## Final results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8305144d",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "figsdir = \"./figs/\"\n",
    "\n",
    "def gen_plots(pert, organ, prefix, alpha, title, bootstrapping = False):\n",
    "    \n",
    "    suv = suv_dict[organ + '_SUVperc_COMBINED'][0:58,:,:]\n",
    "  \n",
    "    if organ == \"lung\":\n",
    "        idx = 3\n",
    "    elif organ == \"bowel\":\n",
    "        idx = 1\n",
    "    elif organ == \"thyroid\":\n",
    "        idx = 5\n",
    "        \n",
    "    flags = flags_dict['flags'][0:58, idx]\n",
    "    \n",
    "    # choose percentile of interest (for lung and bowel 95, for thyroid 75), \n",
    "    # numerating here is from 0 so take the one less\n",
    "    X = np.nanmax(suv[:, :, pert - 1], axis=1).reshape(-1,1)\n",
    "    \n",
    "    # fitting\n",
    "    clf = linear_model.LogisticRegression(penalty='none').fit(X, flags)\n",
    "\n",
    "    # Store fitted parameters in array\n",
    "    logitParams = np.insert(clf.coef_, 0, clf.intercept_)\n",
    "    \n",
    "    # logit function\n",
    "    f = lambda x, p: 1/(1 + np.exp(-p[0] - p[1]*x))\n",
    "\n",
    "    Nsamples = 10**5\n",
    "    \n",
    "    if bootstrapping:\n",
    "        # obtaining parameters via bootstrapping method\n",
    "        rng = np.random.default_rng()\n",
    "\n",
    "        def BS_sample():\n",
    "            idx = rng.integers(len(X), size=len(X))\n",
    "            st = (flags[idx] == 0)\n",
    "            \n",
    "            while st.all() or (~st).all(): \n",
    "                idx = rng.integers(len(X), size=len(X))\n",
    "                st = (flags[idx] == 0)\n",
    "                \n",
    "            tmp = linear_model.LogisticRegression(penalty='none').fit(X[idx], flags[idx])\n",
    "            \n",
    "            return np.insert(tmp.coef_, 0, tmp.intercept_)\n",
    "        \n",
    "        ps = np.array([BS_sample() for _ in range(Nsamples)])\n",
    "\n",
    "    else:\n",
    "        # Calculate matrix of predicted class probabilities.\n",
    "        predProbs = clf.predict_proba(X) #has two col. p, (1-p)\n",
    "        \n",
    "        # Design matrix -- add column of 1's at the beginning of your X_train matrix\n",
    "        X_design = np.hstack([np.ones((X.shape[0], 1)), X]) \n",
    "    \n",
    "        # Initiate matrix of 0's, fill diagonal with each predicted observation's variance\n",
    "        V = np.diagflat(np.prod(predProbs, axis=1)) #dig.matrix where each element is p*(1-p)\n",
    "    \n",
    "        # Covariance matrix C_params = (X^T V X)^-1, params = (b0,b1) \n",
    "        covLogit = np.linalg.inv(np.dot(np.dot(X_design.T, V), X_design))\n",
    "        \n",
    "        #generate parameters and points in x axis\n",
    "        ps = np.random.multivariate_normal(logitParams, covLogit, Nsamples)\n",
    "        \n",
    "    # get for plotting purpose meaningful xmax\n",
    "    # f = 1- eps, np.exp(-p[0] - p[1]*x) ~ eps => -log(eps) = p[0] + p[1]*x\n",
    "    xmax = max(X.max(), (-np.log(1e-3)-logitParams[0])/logitParams[1])\n",
    "    \n",
    "    xs = np.linspace(0, xmax, 200)\n",
    "    \n",
    "    # generate values in y axis\n",
    "    yopts = f(xs, logitParams)\n",
    "    ys = np.array([np.fromiter(map(lambda p: f(x,p), ps),float) for x in xs])\n",
    "\n",
    "    # calculate median and quantiles\n",
    "    mys = np.median(ys, axis=1)\n",
    "    yerr_min = np.quantile(ys, alpha/2, axis=1)\n",
    "    yerr_max = np.quantile(ys, 1-alpha/2, axis=1)\n",
    "\n",
    "    # generate plots\n",
    "    plt.clf()\n",
    "    fs=14\n",
    "    params = {'font.size': fs, 'axes.labelsize': fs, 'axes.titlesize':fs, 'legend.fontsize': fs, 'xtick.labelsize': fs, 'ytick.labelsize': fs}\n",
    "    plt.rcParams.update(params)\n",
    "\n",
    "    fig = plt.figure(figsize = (7, 5))\n",
    "    \n",
    "    #plt.xlabel(r\"$x = max_{visit} SUV(visit, p)$\")\n",
    "    #plt.ylabel(\"P(YAE|X=x)\")\n",
    "    \n",
    "    plt.xlabel(r\"$x$\")\n",
    "    plt.ylabel(r\"$P(Y = AE|x)$\")\n",
    "   \n",
    "    plt.scatter(X[flags==0], flags[flags==0], label=\"NC\")  \n",
    "    plt.scatter(X[flags==1], flags[flags==1], label=\"AE\")\n",
    "    \n",
    "    plt.plot(xs, yopts, label=\"optimal\", color=\"red\")\n",
    "    plt.plot(xs, mys, label=\"median\", color=\"blue\")\n",
    "    \n",
    "    plt.fill_between(xs, yerr_min, yerr_max, alpha=0.5, label=\"confidence band\")\n",
    "\n",
    "    #plt.title(title+\":\" + organ)\n",
    "    #plt.text()\n",
    "    plt.text(0.1, 0.93, \"(\"+organ+\")\", fontsize=16, horizontalalignment='center', verticalalignment='center', transform=fig.transFigure)\n",
    "    \n",
    "    plt.legend(loc = 'lower right', fancybox=True, fontsize=fs, framealpha=0.5)\n",
    "    plt.tight_layout()\n",
    "\n",
    "    if not os.path.exists(figsdir): os.makedirs(figsdir)\n",
    "        \n",
    "    plt.savefig(figsdir + prefix + \"_\" + organ + \".pdf\")\n",
    "    plt.show()\n",
    "\n",
    "\n",
    "def gen_allplots(perts, organs, prefix, alpha, bootstrapping = False):\n",
    "\n",
    "    fs = 14\n",
    "    params = {'font.size': fs, 'axes.labelsize': fs, 'axes.titlesize':fs, 'legend.fontsize': fs, 'xtick.labelsize': fs, 'ytick.labelsize': fs}\n",
    "    plt.rcParams.update(params)\n",
    "    \n",
    "    fig, axs = plt.subplots(nrows=1, ncols=len(organs), sharey = True, figsize=(6*len(organs), 4))\n",
    "    \n",
    "    res_fit_pars = []\n",
    "    \n",
    "    for i, organ in enumerate(organs):\n",
    "        suv = suv_dict[organ + '_SUVperc_COMBINED'][0:58,:,:]\n",
    "      \n",
    "        if organ == \"lung\":\n",
    "            idx = 3\n",
    "        elif organ == \"bowel\":\n",
    "            idx = 1\n",
    "        elif organ == \"thyroid\":\n",
    "            idx = 5\n",
    "            \n",
    "        flags = flags_dict['flags'][0:58, idx]\n",
    "        pert = perts[i]\n",
    "        \n",
    "        # choose percentile of interest (for lung and bowel 95, for thyroid 75), \n",
    "        # numerating here is from 0 so take the one less\n",
    "        X = np.nanmax(suv[:, :, pert - 1], axis=1).reshape(-1,1)\n",
    "        \n",
    "        # fitting\n",
    "        clf = linear_model.LogisticRegression(penalty='none').fit(X, flags)\n",
    "    \n",
    "        # Store fitted parameters in array\n",
    "        logitParams = np.insert(clf.coef_, 0, clf.intercept_)\n",
    "\n",
    "        # store fit result in res\n",
    "        res_fit_pars.append((organ, logitParams[0],  logitParams[1]))\n",
    "        \n",
    "        # logit function\n",
    "        f = lambda x, p: 1/(1 + np.exp(-p[0] - p[1]*x))\n",
    "    \n",
    "        Nsamples = 10**5\n",
    "        \n",
    "        if bootstrapping:\n",
    "            # obtaining parameters via bootstrapping method\n",
    "            rng = np.random.default_rng()\n",
    "    \n",
    "            def BS_sample():\n",
    "                idx = rng.integers(len(X), size=len(X))\n",
    "                st = (flags[idx] == 0)\n",
    "                \n",
    "                while st.all() or (~st).all(): \n",
    "                    idx = rng.integers(len(X), size=len(X))\n",
    "                    st = (flags[idx] == 0)\n",
    "                    \n",
    "                tmp = linear_model.LogisticRegression(penalty='none').fit(X[idx], flags[idx])\n",
    "                \n",
    "                return np.insert(tmp.coef_, 0, tmp.intercept_)\n",
    "            \n",
    "            ps = np.array([BS_sample() for _ in range(Nsamples)])\n",
    "    \n",
    "        else:\n",
    "            # Calculate matrix of predicted class probabilities.\n",
    "            predProbs = clf.predict_proba(X) #has two col. p, (1-p)\n",
    "            \n",
    "            # Design matrix -- add column of 1's at the beginning of your X_train matrix\n",
    "            X_design = np.hstack([np.ones((X.shape[0], 1)), X]) \n",
    "        \n",
    "            # Initiate matrix of 0's, fill diagonal with each predicted observation's variance\n",
    "            V = np.diagflat(np.prod(predProbs, axis=1)) #dig.matrix where each element is p*(1-p)\n",
    "        \n",
    "            # Covariance matrix C_params = (X^T V X)^-1, params = (b0,b1) \n",
    "            covLogit = np.linalg.inv(np.dot(np.dot(X_design.T, V), X_design))\n",
    "            \n",
    "            #generate parameters and points in x axis\n",
    "            ps = np.random.multivariate_normal(logitParams, covLogit, Nsamples)\n",
    "            \n",
    "        # get for plotting purpose meaningful xmax\n",
    "        # f = 1- eps, np.exp(-p[0] - p[1]*x) ~ eps => -log(eps) = p[0] + p[1]*x\n",
    "        xmax = max(X.max(), (-np.log(1e-3)-logitParams[0])/logitParams[1])\n",
    "        \n",
    "        xs = np.linspace(0, xmax, 200)\n",
    "        \n",
    "        # generate values in y axis\n",
    "        yopts = f(xs, logitParams)\n",
    "        ys = np.array([np.fromiter(map(lambda p: f(x,p), ps),float) for x in xs])\n",
    "    \n",
    "        # calculate median and quantiles\n",
    "        mys = np.median(ys, axis=1)\n",
    "        yerr_min = np.quantile(ys, alpha/2, axis=1)\n",
    "        yerr_max = np.quantile(ys, 1-alpha/2, axis=1)\n",
    "\n",
    "        axs[i].set_xlabel(r\"$x$\")\n",
    "        if i == 0: axs[i].set_ylabel(r\"$P(Y = AE|x)$\")\n",
    "    \n",
    "        axs[i].scatter(X[flags==0], flags[flags==0], label=\"NC\")  \n",
    "        axs[i].scatter(X[flags==1], flags[flags==1], label=\"AE\")\n",
    "        \n",
    "        axs[i].plot(xs, yopts, label=\"optimal\", color=\"red\")\n",
    "        axs[i].plot(xs, mys, label=\"median\", color=\"blue\")\n",
    "        \n",
    "        axs[i].fill_between(xs, yerr_min, yerr_max, alpha=0.5, label=\"confidence band\")\n",
    "        axs[i].text(0.1, 0.90, \"(\"+organ+\")\", fontsize=16, horizontalalignment='center', verticalalignment='center', transform=axs[i].transAxes)\n",
    "\n",
    "    #plt.title(title+\":\" + organ)\n",
    "    #plt.text()\n",
    "    #plt.text(0.1, 0.93, \"(\"+organ+\")\", fontsize=16, horizontalalignment='center', verticalalignment='center', transform=fig.transFigure)\n",
    "\n",
    "    if not os.path.exists(figsdir): os.makedirs(figsdir)\n",
    "    \n",
    "    loc = 'lower center'\n",
    "    ncol = 5\n",
    "    handles, labels = axs[-1].get_legend_handles_labels()\n",
    "    fig.legend(handles=handles, labels=labels, loc=loc, ncol=ncol, bbox_to_anchor=(0.5, -0.1))    \n",
    "    \n",
    "    plt.subplots_adjust(wspace=0, hspace=0)\n",
    "    plt.tight_layout()\n",
    "    plt.savefig(figsdir + prefix + \".pdf\", bbox_inches='tight')\n",
    "    plt.show()\n",
    "\n",
    "    # print results\n",
    "    print(pd.DataFrame(res_fit_pars, columns=[\"organ\", \"beta0\", \"beta1\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb7dda9a-2deb-44ac-823d-66773165be59",
   "metadata": {},
   "source": [
    "### Multivaiate normal approx of parameter pdf -- \"parametric BS\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3b3a0f89-bad4-4a39-81b9-1b9ac8ca3f75",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "title=\"Logistic regresion with estimated uncertainties\"\n",
    "gen_plots(95, \"lung\", \"logit_mvn\", 0.05, title)\n",
    "gen_plots(95, \"bowel\", \"logit_mvn\", 0.05, title)\n",
    "gen_plots(75, \"thyroid\", \"logit_mvn\", 0.05, title)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "37d5a1c0-6b4f-40c1-b866-4cd0baa05159",
   "metadata": {},
   "outputs": [],
   "source": [
    "#plt.rcParams.keys() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f116b595-6fc5-47cb-80be-21b50b3422e3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1296x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     organ      beta0     beta1\n",
      "0     lung -11.683978  5.687027\n",
      "1    bowel  -3.474206  0.337083\n",
      "2  thyroid  -4.387076  1.163232\n"
     ]
    }
   ],
   "source": [
    "gen_allplots([95, 95, 75], [\"lung\", \"bowel\", \"thyroid\"], \"logit_mvn\", 0.05)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1e9c470-9a7d-4490-9912-be9d24a31bab",
   "metadata": {},
   "source": [
    "### Non-parametric Bootstrapping (BS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2c461077-18cd-4200-88fb-f10976449eb6",
   "metadata": {},
   "outputs": [],
   "source": [
    "title=\"Logistic regresion with estimated uncertainties\"\n",
    "gen_plots(95, \"lung\", \"logit_bs\", 0.05, title, bootstrapping = True)\n",
    "gen_plots(95, \"bowel\", \"logit_bs\", 0.05, title, bootstrapping = True)\n",
    "gen_plots(75, \"thyroid\", \"logit_bs\", 0.05, title, bootstrapping = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "20503b2a-51c4-4ad1-8cff-d222d734e198",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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