{"id":2772,"date":"2020-06-15T19:33:03","date_gmt":"2020-06-15T18:33:03","guid":{"rendered":"https:\/\/marriott-stats.com\/nigels-blog\/?p=2772"},"modified":"2020-06-24T20:38:06","modified_gmt":"2020-06-24T19:38:06","slug":"estimating-excess-deaths-in-england-to-june-12th","status":"publish","type":"post","link":"https:\/\/marriott-stats.com\/nigels-blog\/estimating-excess-deaths-in-england-to-june-12th\/","title":{"rendered":"COVID19 Deaths #2F – Estimated Excess Deaths in England up to 12th June"},"content":{"rendered":"

In many countries across the world, the total effect of the Coronavirus pandemic is now being measured using the concept of Excess Deaths.<\/a>\u00a0 However, publication of such data by the Office of National Statistics for England is up to 2 weeks slower than the daily deaths published by Public Health England.\u00a0 In this post, I update my model which uses the PHE series to estimate what the ONS will publish for excess deaths in England on Tuesday 16th June.<\/p>\n

<\/p>\n

I intend to update this post every week and you can follow me on Twitter<\/a> to be told when I have made updates.\u00a0 Previous posts are listed below.<\/p>\n

    \n
  1. Estimates to 20th April<\/a><\/li>\n
  2. Estimates to 1st May<\/a><\/li>\n
  3. Estimates to 8th May<\/a><\/li>\n
  4. Estimates to 15th May<\/a><\/li>\n
  5. Estimates to 22nd May<\/a> – this is a tweet instead of a blog post since I did not have time to write a post that week.<\/li>\n
  6. Estimates to 29th May<\/a>\u00a0– this estimate was the first time I used the method described in this post.<\/li>\n
  7. Estimates to 5th June<\/a><\/li>\n<\/ol>\n

    The reader is advised to read these previous estimates so as to familiarise his or herself with the methods and terminology used throughout this post.<\/p>\n

    Time Series used in this post<\/span><\/strong><\/h4>\n

    I’ve used the following 4 time series, each denoted by a 4 letter code.\u00a0 Clicking on this will take you to the source data.<\/p>\n

      \n
    1. PHEr<\/span><\/a> – Public Health England COVID19 Registrations – <\/span><\/b>Daily number of deaths by date of registration with COVID19 on the death certificate and confirmed with a positive test in an NHS\/PHE laboratory<\/span><\/span>.\u00a0 Published everyday, this is the most common headline figure.\u00a0 The link given here contains a further link to a spreadsheet with the relevant data.<\/span><\/li>\n
    2. ONSr<\/a>\u00a0<\/span><\/strong>– ONS COVID19 Registrations<\/strong><\/span> – Daily number of deaths by date of registration with COVID19 on the death certificate from all locations.\u00a0 This is published weekly on a Tuesday but the daily data can be found on the COVID19-ENGLAND tab of the downloaded spreadsheet.<\/span><\/span><\/li>\n
    3. ONSx<\/a>\u00a0<\/strong>– ONS Excess Death Registrations<\/strong><\/span> – Daily number of deaths by date of registration with COVID19 on the death certificate from all locations.\u00a0 This is published weekly on a Tuesday and can be extracted from the WEEKLY DATA tab of the downloaded spreadsheet.\u00a0 I use the day of week pattern of the ONSr series to convert the ONSx weekly data into ONSx daily data.<\/span><\/span><\/li>\n
    4. CQCn<\/span><\/strong><\/a> – Care Quality Commission COVID19 Notifications<\/strong> <\/span>\u00a0– All care home are required to notify the CQC of any death in their home within a short period.\u00a0 Since the outbreak, care homes are now able to say if they suspect the death was COVID19 related without a test.\u00a0 The data is passed onto the ONS who published the data weekly.<\/li>\n<\/ol>\n

      I have only extracted data for England from these sources but some also cover Scotland, Wales & Northern Ireland.\u00a0 For more information about these and other COVID19 relates time series, please click here<\/a>.<\/p>\n

      My Weekly Estimates & Extrapolations for Excess Deaths in England<\/strong><\/span><\/h4>\n

      My estimates of excess deaths for the weeks ending 5th & 12th June are shown below along with extrapolations (not estimates) for ONSr which I explain in a separate post (see sections 1 & 4)<\/a>.\u00a0 Two estimates for ONSx are given, EST1 is based on my model described in links 1 to 4 above, EST2 is based on my new model described in links 6 & 7 above and also in this post.<\/p>\n

      \"\"<\/p>\n

      There were 1,630 excess deaths in England in the week ending 29th May.\u00a0 This was 300 lower than my estimate<\/a> which was based on my new method described in that post and again in this post.\u00a0 I have said before I would prefer to be overestimating than underestimating and the error is within the 95% confidence interval but I would like to be more accurate going forward.<\/p>\n

      Why write a series of posts on estimasting excess deaths?<\/strong><\/span><\/h4>\n

      I intend this weekly series of posts about estimating excess deaths to be a real time case study about the difference between Technical & Fundamental forecasting<\/strong>, a concept that I talk about in more depth in my 1-day training course “I<\/em><\/span><\/strong>de<\/strong>ntify trends & make forecasts<\/em><\/strong><\/span><\/a>“.\u00a0 These are the two avenues open to a forecaster when trying to forecast a quantity Q over a timeline T.<\/p>\n

        \n
      1. Predict Q(t+i) using the history of Q up to time period t only.\u00a0 This involves identifying the underlying pattern of Q over time and then extrapolating<\/strong> that pattern into the future.\u00a0 This is sometimes known as Technical forecasting<\/strong> in financial markets.<\/li>\n
      2. Predict Q(t+i) based on its relationship with an input variables X(t+j) (i not necessarily equal to j).\u00a0 This requires statistical modelling<\/strong> to quantify the relationship between Q & X.\u00a0 X can then used to predict Q in the future.\u00a0 This is sometimes known as Fundamental forecasting<\/strong> in financial markets.<\/li>\n<\/ol>\n

        There is never a right or wrong answer to this question.\u00a0 The advantage of extrapolation is that it only requires the history of Q itself and no other information.\u00a0 The disadvantage is that no insight is gained as to why Q is changing and you have to assume that the historical pattern observed will repeat itself in the future.\u00a0 Modelling on other hand will give you insight and can spot if the pattern of Q is going to change in the future.\u00a0 The difficulty is that you may need to forecast X in the future before you can use X in the future which has the effect of shifting uncertainty in Q to uncertainty in X rather than giving you greater accuracy.<\/p>\n

        Modelling ONSx as a function of PHEr<\/span><\/strong><\/h4>\n

        \"\"<\/p>\n

        In the case of excess deaths, our output time series Q(t) is ONSx(t) and our input time series is PHEr(t).\u00a0 Because the PHEr is published at least two weeks in advance of ONSx, we do not have a problem with not knowing what PHEr is going to be in the future since we already have the data as shown in the table above.\u00a0 Therefore modelling would appear to be the better option but how good is it?<\/p>\n

        Since both ONSx and PHEr are based on death registrations one would expect there to be some relationship in terms of timing.\u00a0 The big difference between the two time series is that PHEr only counts deaths with a positive test for COVID19 undertaken in a PHE\/NHS laboratory whereas ONSx counts all deaths over and above a baseline.\"\"<\/p>\n

        Until 3 weeks ago, my model was based on the ratio of ONSx to PHEr by day.\u00a0 I plotted these ratios by week as shown in the chart and then attempted to identify the appropriate average for each day of the week based initially on best guesses but then supplemented by published CQCn data (plotted below).\u00a0 The reason I initially did it this way was sample size.\u00a0 By taking daily data I could increase the sample size.\u00a0 \u00a0If I were to stick with this model, which is ratio is shown by the black line and happens to be the average of the last 4 weeks, this gives EST1 in the table at the beginning which shows 1989 deaths for week ending 5th June and 1543 deaths for week ending 12th June.\u00a0 I consider both of these to be overestimates but I am including them for completeness.<\/p>\n

        \"\"By now though, we have 9 weeks of data with significant excess deaths plus of couple weeks beforehand when the first COVID19 deaths were recorded.\u00a0 I think that is enough to start building a model with weekly data only.\u00a0 One change I made straightaway was to change the output variable.\u00a0 Currently it is<\/p>\n

        ONSx\u00a0 =\u00a0 ONSa\u00a0 –\u00a0 \u00a0ONSb<\/strong><\/span><\/p>\n

        where ONSa is total number of deaths from all causes and ONSb is the baseline number of deaths defined to be average of 2015 to 2019.\u00a0 Going forward my output variable will be<\/p>\n

        ONSm\u00a0 \u00a0=\u00a0 \u00a0ONSa\u00a0 \/\u00a0 ONSb<\/strong><\/span><\/p>\n

        I call ONSm the mortality ratio.\u00a0 The advantage of this is it makes is easier to predicted negative excess deaths which occurs when ONSm is less than 1.\u00a0 It also allows for log transformations of the output variable which couldn’t be done with ONSx but can be done with ONSm and is equal to log(ONSa) minus log(ONSb).<\/p>\n

        I then plotted ONSm against both PHEr and CQCn on the same scatter plot here since PHEr and CQCn are similar in scale.\u00a0 I have used ONS week numbers \"\"as the labels and the most recent week ending 29th May is week 22 and we are trying to predict ONSm for week 23.\u00a0 Since we already know what PHEr & CQCn are for week 23, we can show these values on the horizontal scale.\u00a0 The labels with white backgrounds (weeks 15 & 19) had Friday bank holidays (Good Friday & VE Day respectively).\u00a0 The reason I highlight this is because PHEr and ONSm are based on death registrations and bank holidays result in reduced staffing levels for compiling the data and thus artificially lower death counts.\u00a0 In contrast, I believe the effect of Monday bank holidays is more limited since staff have the rest of the week to catch up.<\/p>\n

        The relationship between ONSm and PHEr seems quite clear especially if a Friday bank holiday adjustment is taken into account.\u00a0 Using the purple line shown, I arrive at an estimated mortality ratio of 1.14 for week ending 29th May and 1.06 for week ending 5th June with 95% confidence intervals of +\/- 0.17.\u00a0 This converts into estimates for ONSx of 1301 for week ending 5th June and 498 for week ending 12th June with 95% confidence intervals of +\/-1587.\u00a0 These are the numbers appearing in the EST2 column in the table shown at the start of this post.<\/p>\n

        **IMPORTANT – PHE made a change in the way they record deaths in the week ending 29th May (week 22) as described in this link<\/a>.\u00a0 For the purposes of using the model shown in the chart here, I included an extra dummy variable for week 22 in my model hence why this week is highlighted in purple in the chart.\u00a0 My forecast for weeks 23 & 24 take this effect into account<\/em><\/span><\/p>\n

        CQCn data is only available from week 16 (week ending 17th April) and so cannot be incorporated directly into the model above.\u00a0 It was deaths in care homes that made my original model unreliable since it became clear that these deaths were on a different timeline as \"\"shown in the chart here.\u00a0 Over the 5 weeks to 29th May, deaths in care homes have been larger than in hospitals and is now the main driver of excess deaths.\u00a0 If I build a separate model for the blue labels on the scatter plot, I get an estimate for ONSm of 1.12 which converts to an estimate for ONSx of 1071.<\/p>\n

        Clearly a CQCn based forecast is very different from a PHEr based forecast.\u00a0 However the sample sizes are very different and I am not yet ready to publish a forecast based on CQCn.\u00a0 For now, I will stick with the PHEr based forecast.<\/p>\n

         <\/p>\n

        Comparing Estimated ONSx with Extrapolated ONSx<\/strong><\/span><\/h4>\n

        A few weeks ago, I pointed out the value<\/a> of comparing my modelled (or fundamental) estimate above with an extrapolated (or technical) estimate (see section 6 of this link)<\/a> as a sense check.\u00a0 My extrapolated estimate for week ending 29th May was 1696 deaths which turned out to be spot on and was a smaller margin of error than for EST2 & EST1.\u00a0 For week ending 5th June, my extrapolated estimate is 1,059 deaths which is closer to my CQCn (1071) estimate than my PHEr (1301) estimate.<\/p>\n

         <\/p>\n

        – More posts about COVID19 –<\/strong><\/span><\/h4>\n
          \n
        1. A very useful guidance to interpreting statistics of COVID19<\/a> published by the Royal Statistical Society.<\/li>\n
        2. My collection of links to all kinds of material<\/a> related to the statistics of COVID19, epidemiological modelling and testing.<\/li>\n
        3. How large a sample is needed<\/a> in order to decide whether COVID19 restrictions can be lifted?\u00a0 A lot, lot less than you think!<\/li>\n
        4. Latest trends and data for COVID19 deaths in England<\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

          In many countries across the world, the total effect of the Coronavirus pandemic is now being measured using the concept of Excess Deaths.\u00a0 However, publication of such data by the Office of National Statistics for England is up to 2 weeks slower than the daily deaths published by Public Health England.\u00a0 In this post, I […]<\/p>\n","protected":false},"author":3,"featured_media":2789,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[90],"tags":[164,163,25,180,179,169,182,168,183],"class_list":{"0":"post-2772","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-archive","8":"tag-coronavirus","9":"tag-covid19","10":"tag-forecasting-model","11":"tag-nhs","12":"tag-ons","13":"tag-pandemic","14":"tag-phe","15":"tag-sars-cov-2","16":"tag-trend-extrapolation","17":"entry","18":"override"},"_links":{"self":[{"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/posts\/2772","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/comments?post=2772"}],"version-history":[{"count":3,"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/posts\/2772\/revisions"}],"predecessor-version":[{"id":2791,"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/posts\/2772\/revisions\/2791"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/media\/2789"}],"wp:attachment":[{"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/media?parent=2772"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/categories?post=2772"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/tags?post=2772"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}