Nowcasting Covid-19 statistics reported with delay. A case-study of Sweden and UK

A talk about a Nowcasting model we built for Covid-19 deaths.

Presenter

Jonas Wallin

Adam Altmejd

Joacim Rocklöv

Published

May 21, 2021

Publication

Statistical Learning Seminars, Online

Links

Abstract

Monitoring the progress of the Coronavirus is crucial for timely implementation of intervention. The availability of unbiased timely statistics of trends in disease events are a key to effective responses. But due to reporting delays, the most recently reported numbers are frequently underestimating the total number of infections, hospitalizations and deaths creating an illusion of a downward trend. Here we describe a statistical methodology for predicting true daily quantities and their uncertainty, estimated using historical reporting delays. The methodology takes into account the observed distribution pattern of the lag. It is derived from the “removal method”, a well-established estimation framework in the field of ecology. We show how the method works for both the Swedish and the UK death count.

</p> <div id="quarto-navigation-envelope" class="hidden"> <p><span class="hidden" data-render-id="quarto-int-sidebar-title">Jonas Wallin</span> <span class="hidden" data-render-id="quarto-int-navbar-title">Jonas Wallin</span> <span class="hidden" data-render-id="quarto-int-navbar:Publications">Publications</span> <span class="hidden" data-render-id="quarto-int-navbar:/publications/index.html">/publications/index.html</span> <span class="hidden" data-render-id="quarto-int-navbar:Online talks">Online talks</span> <span class="hidden" data-render-id="quarto-int-navbar:/talks/index.html">/talks/index.html</span></p> <div class="hidden" data-render-id="footer-left-Copyright 2023, Jonas Wallin"> <p>Copyright 2023, Jonas Wallin</p> </div> </div> <div id="quarto-meta-markdown" class="hidden"> <p><span class="hidden" data-render-id="quarto-metatitle">Jonas Wallin - Nowcasting Covid-19 statistics reported with delay. A case-study of Sweden and UK</span> <span class="hidden" data-render-id="quarto-twittercardtitle">Jonas Wallin - Nowcasting Covid-19 statistics reported with delay. A case-study of Sweden and UK</span> <span class="hidden" data-render-id="quarto-ogcardtitle">Jonas Wallin - Nowcasting Covid-19 statistics reported with delay. A case-study of Sweden and UK</span> <span class="hidden" data-render-id="quarto-metasitename">Jonas Wallin</span> <span class="hidden" data-render-id="quarto-twittercarddesc">A talk about a Nowcasting model we built for Covid-19 deaths.</span> <span class="hidden" data-render-id="quarto-ogcardddesc">A talk about a Nowcasting model we built for Covid-19 deaths.</span></p> </div> </main>  <script id = "quarto-html-after-body" type="application/javascript"> window.document.addEventListener("DOMContentLoaded", function (event) { const toggleBodyColorMode = (bsSheetEl) => { const mode = bsSheetEl.getAttribute("data-mode"); const bodyEl = window.document.querySelector("body"); if (mode === "dark") { bodyEl.classList.add("quarto-dark"); bodyEl.classList.remove("quarto-light"); } else { bodyEl.classList.add("quarto-light"); bodyEl.classList.remove("quarto-dark"); } } const toggleBodyColorPrimary = () => { const bsSheetEl = window.document.querySelector("link#quarto-bootstrap"); if (bsSheetEl) { toggleBodyColorMode(bsSheetEl); } } toggleBodyColorPrimary(); const icon = ""; const anchorJS = new window.AnchorJS(); anchorJS.options = { placement: 'right', icon: icon }; anchorJS.add('.anchored'); const isCodeAnnotation = (el) => { for (const clz of el.classList) { if (clz.startsWith('code-annotation-')) { return true; } } return false; } const clipboard = new window.ClipboardJS('.code-copy-button', { text: function(trigger) { const codeEl = trigger.previousElementSibling.cloneNode(true); for (const childEl of codeEl.children) { if (isCodeAnnotation(childEl)) { childEl.remove(); } } return codeEl.innerText; } }); clipboard.on('success', function(e) { // button target const button = e.trigger; // don't keep focus button.blur(); // flash "checked" button.classList.add('code-copy-button-checked'); var currentTitle = button.getAttribute("title"); button.setAttribute("title", "Copied!"); let tooltip; if (window.bootstrap) { button.setAttribute("data-bs-toggle", "tooltip"); button.setAttribute("data-bs-placement", "left"); button.setAttribute("data-bs-title", "Copied!"); tooltip = new bootstrap.Tooltip(button, { trigger: "manual", customClass: "code-copy-button-tooltip", offset: [0, -8]}); tooltip.show(); } setTimeout(function() { if (tooltip) { tooltip.hide(); button.removeAttribute("data-bs-title"); button.removeAttribute("data-bs-toggle"); button.removeAttribute("data-bs-placement"); } button.setAttribute("title", currentTitle); button.classList.remove('code-copy-button-checked'); }, 1000); // clear code selection e.clearSelection(); }); function tippyHover(el, contentFn, onTriggerFn, onUntriggerFn) { const config = { allowHTML: true, maxWidth: 500, delay: 100, arrow: false, appendTo: function(el) { return el.parentElement; }, interactive: true, interactiveBorder: 10, theme: 'quarto', placement: 'bottom-start', }; if (contentFn) { config.content = contentFn; } if (onTriggerFn) { config.onTrigger = onTriggerFn; } if (onUntriggerFn) { config.onUntrigger = onUntriggerFn; } window.tippy(el, config); } const noterefs = window.document.querySelectorAll('a[role="doc-noteref"]'); for (var i=0; i<noterefs.length; i++) { const ref = noterefs[i]; tippyHover(ref, function() { // use id or data attribute instead here let href = ref.getAttribute('data-footnote-href') || ref.getAttribute('href'); try { href = new URL(href).hash; } catch {} const id = href.replace(/^#\/?/, ""); const note = window.document.getElementById(id); return note.innerHTML; }); } const xrefs = window.document.querySelectorAll('a.quarto-xref'); const processXRef = (id, note) => { // Strip column container classes const stripColumnClz = (el) => { el.classList.remove("page-full", "page-columns"); if (el.children) { for (const child of el.children) { stripColumnClz(child); } } } stripColumnClz(note) if (id === null || id.startsWith('sec-')) { // Special case sections, only their first couple elements const container = document.createElement("div"); if (note.children && note.children.length > 2) { container.appendChild(note.children[0].cloneNode(true)); for (let i = 1; i < note.children.length; i++) { const child = note.children[i]; if (child.tagName === "P" && child.innerText === "") { continue; } else { container.appendChild(child.cloneNode(true)); break; } } if (window.Quarto?.typesetMath) { window.Quarto.typesetMath(container); } return container.innerHTML } else { if (window.Quarto?.typesetMath) { window.Quarto.typesetMath(note); } return note.innerHTML; } } else { // Remove any anchor links if they are present const anchorLink = note.querySelector('a.anchorjs-link'); if (anchorLink) { anchorLink.remove(); } if (window.Quarto?.typesetMath) { window.Quarto.typesetMath(note); } // TODO in 1.5, we should make sure this works without a callout special case if (note.classList.contains("callout")) { return note.outerHTML; } else { return note.innerHTML; } } } for (var i=0; i<xrefs.length; i++) { const xref = xrefs[i]; tippyHover(xref, undefined, function(instance) { instance.disable(); let url = xref.getAttribute('href'); let hash = undefined; if (url.startsWith('#')) { hash = url; } else { try { hash = new URL(url).hash; } catch {} } if (hash) { const id = hash.replace(/^#\/?/, ""); const note = window.document.getElementById(id); if (note !== null) { try { const html = processXRef(id, note.cloneNode(true)); instance.setContent(html); } finally { instance.enable(); instance.show(); } } else { // See if we can fetch this fetch(url.split('#')[0]) .then(res => res.text()) .then(html => { const parser = new DOMParser(); const htmlDoc = parser.parseFromString(html, "text/html"); const note = htmlDoc.getElementById(id); if (note !== null) { const html = processXRef(id, note); instance.setContent(html); } }).finally(() => { instance.enable(); instance.show(); }); } } else { // See if we can fetch a full url (with no hash to target) // This is a special case and we should probably do some content thinning / targeting fetch(url) .then(res => res.text()) .then(html => { const parser = new DOMParser(); const htmlDoc = parser.parseFromString(html, "text/html"); const note = htmlDoc.querySelector('main.content'); if (note !== null) { // This should only happen for chapter cross references // (since there is no id in the URL) // remove the first header if (note.children.length > 0 && note.children[0].tagName === "HEADER") { note.children[0].remove(); } const html = processXRef(null, note); instance.setContent(html); } }).finally(() => { instance.enable(); instance.show(); }); } }, function(instance) { }); } let selectedAnnoteEl; const selectorForAnnotation = ( cell, annotation) => { let cellAttr = 'data-code-cell="' + cell + '"'; let lineAttr = 'data-code-annotation="' + annotation + '"'; const selector = 'span[' + cellAttr + '][' + lineAttr + ']'; return selector; } const selectCodeLines = (annoteEl) => { const doc = window.document; const targetCell = annoteEl.getAttribute("data-target-cell"); const targetAnnotation = annoteEl.getAttribute("data-target-annotation"); const annoteSpan = window.document.querySelector(selectorForAnnotation(targetCell, targetAnnotation)); const lines = annoteSpan.getAttribute("data-code-lines").split(","); const lineIds = lines.map((line) => { return targetCell + "-" + line; }) let top = null; let height = null; let parent = null; if (lineIds.length > 0) { //compute the position of the single el (top and bottom and make a div) const el = window.document.getElementById(lineIds[0]); top = el.offsetTop; height = el.offsetHeight; parent = el.parentElement.parentElement; if (lineIds.length > 1) { const lastEl = window.document.getElementById(lineIds[lineIds.length - 1]); const bottom = lastEl.offsetTop + lastEl.offsetHeight; height = bottom - top; } if (top !== null && height !== null && parent !== null) { // cook up a div (if necessary) and position it let div = window.document.getElementById("code-annotation-line-highlight"); if (div === null) { div = window.document.createElement("div"); div.setAttribute("id", "code-annotation-line-highlight"); div.style.position = 'absolute'; parent.appendChild(div); } div.style.top = top - 2 + "px"; div.style.height = height + 4 + "px"; div.style.left = 0; let gutterDiv = window.document.getElementById("code-annotation-line-highlight-gutter"); if (gutterDiv === null) { gutterDiv = window.document.createElement("div"); gutterDiv.setAttribute("id", "code-annotation-line-highlight-gutter"); gutterDiv.style.position = 'absolute'; const codeCell = window.document.getElementById(targetCell); const gutter = codeCell.querySelector('.code-annotation-gutter'); gutter.appendChild(gutterDiv); } gutterDiv.style.top = top - 2 + "px"; gutterDiv.style.height = height + 4 + "px"; } selectedAnnoteEl = annoteEl; } }; const unselectCodeLines = () => { const elementsIds = ["code-annotation-line-highlight", "code-annotation-line-highlight-gutter"]; elementsIds.forEach((elId) => { const div = window.document.getElementById(elId); if (div) { div.remove(); } }); selectedAnnoteEl = undefined; }; // Handle positioning of the toggle window.addEventListener( "resize", throttle(() => { elRect = undefined; if (selectedAnnoteEl) { selectCodeLines(selectedAnnoteEl); } }, 10) ); function throttle(fn, ms) { let throttle = false; let timer; return (...args) => { if(!throttle) { // first call gets through fn.apply(this, args); throttle = true; } else { // all the others get throttled if(timer) clearTimeout(timer); // cancel #2 timer = setTimeout(() => { fn.apply(this, args); timer = throttle = false; }, ms); } }; } // Attach click handler to the DT const annoteDls = window.document.querySelectorAll('dt[data-target-cell]'); for (const annoteDlNode of annoteDls) { annoteDlNode.addEventListener('click', (event) => { const clickedEl = event.target; if (clickedEl !== selectedAnnoteEl) { unselectCodeLines(); const activeEl = window.document.querySelector('dt[data-target-cell].code-annotation-active'); if (activeEl) { activeEl.classList.remove('code-annotation-active'); } selectCodeLines(clickedEl); clickedEl.classList.add('code-annotation-active'); } else { // Unselect the line unselectCodeLines(); clickedEl.classList.remove('code-annotation-active'); } }); } const findCites = (el) => { const parentEl = el.parentElement; if (parentEl) { const cites = parentEl.dataset.cites; if (cites) { return { el, cites: cites.split(' ') }; } else { return findCites(el.parentElement) } } else { return undefined; } }; var bibliorefs = window.document.querySelectorAll('a[role="doc-biblioref"]'); for (var i=0; i<bibliorefs.length; i++) { const ref = bibliorefs[i]; const citeInfo = findCites(ref); if (citeInfo) { tippyHover(citeInfo.el, function() { var popup = window.document.createElement('div'); citeInfo.cites.forEach(function(cite) { var citeDiv = window.document.createElement('div'); citeDiv.classList.add('hanging-indent'); citeDiv.classList.add('csl-entry'); var biblioDiv = window.document.getElementById('ref-' + cite); if (biblioDiv) { citeDiv.innerHTML = biblioDiv.innerHTML; } popup.appendChild(citeDiv); }); return popup.innerHTML; }); } } }); </script> </div>  <footer class="footer"> <div class="nav-footer"> <div class="nav-footer-left"> <ul class="footer-items list-unstyled"> <li class="nav-item"> Copyright 2023, Jonas Wallin </li> </ul> </div> <div class="nav-footer-center">   </div> <div class="nav-footer-right"> <ul class="footer-items list-unstyled"> <li class="nav-item compact"> <a class="nav-link" href="https://github.com/JonasWallin"> <i class="bi bi-github" role="img" > </i> </a> </li> </ul> </div> </div> </footer> </body> </html>

Citation

BibTeX citation:

@unpublished{wallin2021,
  author = {Wallin, Jonas and Altmejd, Adam and Rocklöv, Joacim},
  title = {Nowcasting {Covid-19} Statistics Reported with Delay. {A}
    Case-Study of {Sweden} and {UK}},
  date = {2021-05-21},
  url = {https://www.youtube.com/embed/RHLPu389PNY},
  langid = {en},
  abstract = {Monitoring the progress of the Coronavirus is crucial for
    timely implementation of intervention. The availability of unbiased
    timely statistics of trends in disease events are a key to effective
    responses. But due to reporting delays, the most recently reported
    numbers are frequently underestimating the total number of
    infections, hospitalizations and deaths creating an illusion of a
    downward trend. Here we describe a statistical methodology for
    predicting true daily quantities and their uncertainty, estimated
    using historical reporting delays. The methodology takes into
    account the observed distribution pattern of the lag. It is derived
    from the “removal method”, a well-established estimation framework
    in the field of ecology. We show how the method works for both the
    Swedish and the UK death count.}
}

For attribution, please cite this work as:

Wallin, Jonas, Adam Altmejd, and Joacim Rocklöv. 2021. “Nowcasting Covid-19 Statistics Reported with Delay. A Case-Study of Sweden and UK.” Online, Online, May 21. https://www.youtube.com/embed/RHLPu389PNY.