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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Predicting rare things is hard\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Incidence of schizophrenia 0.000163\n"
     ]
    }
   ],
   "source": [
    "schiz_incidence = 16.3 / 100000\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Incidence of schizophrenia 0.000163\n",
      "Specificity: 0.999\n",
      "Sensitivity: 0.999\n",
      "True positives: 163\n",
      "False positives: 1000\n",
      "True negatives: 998837\n",
      "False negatives: 0\n",
      "Positive predictive value: 0.1401\n"
     ]
    }
   ],
   "source": [
    "specificity = .999\n",
    "sensitivity = .999\n",
    "n_screened = 1000000\n",
    "print(f\"Incidence of schizophrenia {schiz_incidence:.04}\")\n",
    "print(f\"Specificity: {specificity:.04}\")\n",
    "print(f\"Sensitivity: {sensitivity:.04}\")\n",
    "\n",
    "# True positives\n",
    "tp = n_screened * schiz_incidence * sensitivity\n",
    "\n",
    "# False negatives\n",
    "fn = n_screened * schiz_incidence - tp\n",
    "\n",
    "# True negatives\n",
    "tn = n_screened * (1 - schiz_incidence) * specificity\n",
    "\n",
    "# False positives\n",
    "fp = n_screened * (1 - schiz_incidence) - tn\n",
    "\n",
    "\n",
    "print(f\"True positives: {tp:.0f}\")\n",
    "print(f\"False positives: {fp:.0f}\")\n",
    "print(f\"True negatives: {tn:.0f}\")\n",
    "print(f\"False negatives: {fn:.0f}\")\n",
    "\n",
    "# Positive predictive value\n",
    "ppv = tp / (tp + fp)\n",
    "print(f\"Positive predictive value: {ppv:.04}\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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