2b:null 2c:["$","title",null,{"children":"Covid-19 — Case Fatality and Growth Rates | polarblau | Observable"}] 31:T438,md`# Covid-19 — Case Fatality and Growth Rates The case fatality rate (CFR) in context of the Corona crisis represents the proportion of COVID-19 cases who eventually die from the disease. Once an epidemic has ended, it is calculated with the formula: ${tex`CFR = \frac {deaths}{cases}`} But while an epidemic is still ongoing this formula is, at the very least, “naïve” and can be “misleading if, at the time of analysis, the outcome is unknown for a non negligible proportion of patients.” In other words, current deaths belong to a total case figure of the past, not to the current case figure in which the outcome (recovery or death) of a proportion (the most recent cases) hasn't yet been determined. The correct formula, therefore, would appear to be: ${tex`CFR = \frac {deaths_i}{cases_{i-T}}`} Below you can explore the CFR calculated for a ${tex`T = 7`} for all countries as well as the linear regression model applied to each data set. [Coronavirus (COVID-19) Mortality Rate](https://www.worldometers.info/coronavirus/coronavirus-death-rate/) `32:T4f7,html``33:T437,html``34:[] 2f:{"id":"35157983a3ae7469","slug":"covid-19-case-fatality-and-growth-rates","title":"Covid-19 — Case Fatality and Growth Rates","thumbnail":"02af391c28bc8a32708c649cf534b6cca36a037d47ed109183a656ad07b99fc1","access_level":"public","create_time":"$D2020-05-08T22:09:42.033Z","update_time":"$D2021-10-23T19:14:34.957Z","view_time":null,"first_public_time":"$D2020-05-09T01:08:48.042Z","fork":true,"stars":0,"starred":false,"owner":{"type":"team","id":"e347a51db6a48600","login":"polarblau","name":"","avatar_url":"https://avatars-next.observableusercontent.com/005b3e88f291bc1ad01758e9b8ed4730c6d3b82647e3174fedbe039d14d2e06d","tier":"starter_2024"},"version":592,"publish_version":592,"role":null,"authored":false,"authors":[{"type":"individual","id":"79fc1cacb22f9941","login":"polarblau","name":"","avatar_url":"https://avatars-next.observableusercontent.com/005b3e88f291bc1ad01758e9b8ed4730c6d3b82647e3174fedbe039d14d2e06d","tier":null}],"members":[{"type":"individual","id":"79fc1cacb22f9941","login":"polarblau","name":"","avatar_url":"https://avatars-next.observableusercontent.com/005b3e88f291bc1ad01758e9b8ed4730c6d3b82647e3174fedbe039d14d2e06d","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"Covid-19 — Case Fatality and Growth Rates","cells":[{"id":0,"value":"$31","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":57,"value":"viewof region = select({ title: 'Region', options: allCountries, value: 'Global' })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":327,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":44,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":446,"value":"chart = {\n const height = 150;\n const svg = d3.create(\"svg\")\n .attr(\"viewBox\", [0, 0, width, height]);\n\n let x = d3.scaleBand()\n .domain(statsData['confirmed']['Global'].map(d => d.date))\n .range([margin.left, width - margin.right])\n .padding(0.1);\n \n let y = getY(growthFactorData[region], height, margin)\n \n let xAxis = getXAxis(xDate, width, height, margin);\n let yAxis = getYAxis(y, height, margin);\n \n svg.append(\"g\")\n .attr(\"fill\", \"steelblue\")\n .selectAll(\"rect\")\n .data(growthFactorData[region])\n .join(\"rect\")\n .attr(\"x\", (d, i) => x(d.date))\n .attr(\"y\", d => y(d.value))\n .attr(\"height\", d => y(0) - y(d.value))\n .attr(\"width\", x.bandwidth());\n \n svg.append(\"g\")\n .call(xAxis);\n\n svg.append(\"g\")\n .call(yAxis);\n \n svg.append(\"line\")\n .attr(\"x1\", margin.left)\n .attr(\"y1\", y(1)+0.5)\n .attr(\"x2\", width-margin.right)\n .attr(\"y2\", y(1)+0.5)\n .attr(\"stroke\", \"#DC3900\")\n .attr(\"stroke-width\", 1)\n\n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":422,"value":"md`## Growth Factor\n\nThe growth factor determines how fast the population of infected is growing for a given region.\n\nDuring exponential growth the factor stays consistently above 1. As you reach the inflection point of a logistic curve (which describes growth in a biological population) the growth factor will become closer to 1 and eventually fall below it. \n\nThe growth factor is calculated using the following formula:\n\n${tex`Growth factor = \\frac {\\Delta N_d}{\\Delta N_{d-1}}`}\n\nNew cases of one day divided by the new cases of the previous day.\n\n[Exponential growth and epidemics (3Blue1Brown on Youtube)](https://www.youtube.com/watch?v=Kas0tIxDvrg)\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":170,"value":"md`## Data\n\nAll data has been loaded from the [Github repository of the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University](https://github.com/CSSEGISandData/COVID-19) and processed. \n\nThe processing has been done in Python with Pandas, Numpy, Scikit, and visualized using Matplotlib in a [Jupyter Notebook](https://github.com/polarblau/covid19-notebooks/blob/master/Case%20Fatality%20Rate.ipynb).\n\nThe resulting data sets are as well hosted in the same repository.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":113,"value":"dataBaseUrl = 'https://raw.githubusercontent.com/polarblau/covid19-notebooks/master/'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":570,"value":"timestamp = '20201022'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":10,"value":"statsData = loadStats(timestamp + '_stats.json');","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":99,"value":"cfrData = loadTimeSeriesData(timestamp + '_cfr.json');","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":156,"value":"cfrLinRegData = loadTimeSeriesData(timestamp + '_cfr_lin_reg.json');","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":152,"value":"growthFactorData = loadTimeSeriesData(timestamp + '_growth_factor.json');","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":104,"value":"allCountries = Object.keys(statsData['confirmed']).sort((x,y) => x == 'Global' ? -1 : y == 'Global' ? 1 : 0 )","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":12,"value":"md`## Appendix`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":14,"value":"d3 = require(\"d3@5\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":60,"value":"import {select, checkbox} from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":39,"value":"height = 300","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":36,"value":"margin = ({top: 5, right: 60, bottom: 20, left: 60})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":33,"value":"xDate = getX(statsData['confirmed']['Global'], width, margin)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":525,"value":"getX = (data, width, margin) => {\n return d3.scaleUtc()\n .domain(d3.extent(data, d => d.date))\n .range([margin.left, width - margin.right]) \n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":42,"value":"yCFR = getY(cfrData[region], height, margin)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":250,"value":"yGrowthFactor = getY(growthFactorData[region], height, margin)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":475,"value":"getY = (data, height, margin) => {\n return d3.scaleLinear()\n .domain([0, d3.max(data, d => d.value)])\n .range([height - margin.bottom, margin.top])\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":356,"value":"yStats = getY(statsData['confirmed'][region], height, margin)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":491,"value":"getXAxis = (x, width, height, margin) => {\n return g => g\n .attr(\"transform\", `translate(0,${height - margin.bottom})`)\n .call(d3.axisBottom(x).ticks(width / 80).tickSizeOuter(0))\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":45,"value":"xAxis = getXAxis(xDate, width, height, margin)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":499,"value":"getYAxis = (y, height, margin, format=\",\") => {\n return g => g\n .attr(\"transform\", `translate(${margin.left},0)`)\n .call(d3.axisLeft(y).ticks(height / 30).tickFormat(d3.format(format)))\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":48,"value":"yAxisCFR = getYAxis(yCFR, height, margin, '.0%')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":229,"value":"yAxisGrowthFactor = getYAxis(yGrowthFactor, height, margin)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":361,"value":"yAxisStats = getYAxis(yStats, height, margin)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":510,"value":"getLine = (y, x) => d3.line().x(d => x(d.date)).y(d => y(d.value))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":256,"value":"cfrLine = getLine(yCFR, xDate)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":365,"value":"growFactorLine = getLine(yGrowthFactor, xDate)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":371,"value":"statsLine = getLine(yStats, xDate)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":121,"value":"convertRegionTimeSeries = function(data) {\n let convertedData = {};\n for (let [region, series] of Object.entries(data)) {\n if (series) {\n convertedData[region] = Object.keys(series).map((ts) => ({ date: new Date(+ts), value: series[ts] }));\n } else {\n convertedData[region] = null;\n }\n }\n return convertedData;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":81,"value":"loadTimeSeriesData = async function(url) {\n let data = await d3.json(dataBaseUrl + url);\n return convertRegionTimeSeries(data);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":112,"value":"loadStats = async function(url) {\n let dataByType = await d3.json(dataBaseUrl + url);\n \n let convertedDataByType = {};\n for (let [type, data] of Object.entries(dataByType)) {\n convertedDataByType[type] = convertRegionTimeSeries(data);\n }\n return convertedDataByType;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W34","stdlib":"1","titling":"auto"}} 30:"$2f:body"