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Calculation of Standardised Mortality Ratios (SMRs). This workbook contains examples of the methods of calculation used by ONS to produce Standardised Mortality Ratios for war where the age at death was under 85. Contents: SMR Template The method used to calculate an SMR for each ward. 95% confidence intervals were also calculated for each SMR using a method described by Goldblatt.1 The confidence intervals are derived from an assumption that the Poisson distribution of the observed number of deaths has a to the expected number. Where the number of deaths is less than 100 the calculation of the upper and lower limits are based on a table of exact confide which is also included in this workbook. For larger numbers of deaths little accuracy is lost by using a method which approximates the calculation of the exact limits. This method of calculation differs slightly if the observed number of deaths is greater than 900. Three examples are therefore included for the calculation of confidence intervals which vary depending on the observed numbe CIs - Example 1 Calculation of SMRs and 95% confidence intervals where observed number of deaths is less than 100. CIs - Example 2 Calculation of SMRs and 95% confidence intervals where observed number of deaths is 100 or greater but CIs - Example 3 Calculation of SMRs and 95% confidence intervals where observed number of deaths is 900 or greater. From these examples it can be noted that although the SMR is the same in each calculation, the width of the confidence interva as the number of deaths increase. The table of exact 95% confidence intervals used for the calculations in Example 1 is also included. 99% confidence intervals are also inlcuded in the table for reference: Exact CIs Exact 95 and 99 per cent confidence intervals when observed numbers are less than 100 1 Goldblatt P. Longitudinal Study, Mortality and social organisation. Series LS no 6, Chapter 3. HMSO London, 1990. dised Mortality Ratios for wards in England & Wales, ved number of deaths has a mean which is equal d on a table of exact confidence intervals ulation of the exact limits. ding on the observed numbers of deaths: deaths is less than 100. deaths is 100 or greater but less than 900. deaths is 900 or greater. idth of the confidence intervals decrease SO London, 1990. Template for the calculation of Standardised Mortality Ratios (SMRs). This spreadsheet illustrates the method used by ONS to calculate SMRs for ward in England and Wales where the age at death was less than 85 years. The figures highlighted in blue are the data needed to allow the SMR to be calculated. Figures highlighted in red are then calculated within the spreadsheet. Standard Population e.g. England & Wales Example Ward Deaths per Population Deaths 1000,000 Population population Age group 0 297,256 1,449 487 555 1-4 1,247,768 272 22 2,087 5-9 1,663,285 198 12 2,985 10-14 1,666,353 171 10 2,509 15-19 1,568,759 386 25 2,136 20-24 1,525,390 472 31 2,491 25-29 1,789,723 632 35 4,096 30-34 2,047,096 1,033 50 3,889 35-39 2,098,035 1,629 78 3,564 40-44 1,822,329 2,229 122 2,764 45-49 1,669,145 3,300 198 2,314 50-54 1,813,517 5,684 313 2,392 55-59 1,453,409 7,352 506 1,918 60-64 1,298,083 10,256 790 1,653 65-69 1,188,619 15,230 1,281 1,443 70-74 1,131,035 25,409 2,247 1,380 75-79 1,042,657 39,762 3,814 1,262 80-84 710,306 49,274 6,937 791 All ages 0-84 for ward in England and Wales Example Ward Observed deaths Expected deaths 3 0 0 0 1 1 1 2 3 3 5 7 10 13 18 31 48 55 300 202 SMR 149 1 Calculation of Standardised Mortality Ratios with 95% confidence intervals. Example 1 - where number of deaths is less than 100. This spreadsheet illustrates the method used by ONS to calculate SMRs for ward in England and Wales where the age at death was less than 85 years. The figures highlighted in blue are the data needed to allow the SMR to be calculated. Figures highlighted in red are then calculated within the spreadsheet. In this example, as there are fewer than 100 deaths, the 95% confidence intervals for the SMR are calculated using the exact method. The figures for the exact upper and lower limits are taken from the table of exact 95% confidence limits which is available on the following spreadsheet within this workbook -> Exact CIs Standard Population e.g. England & Wales Ward Example 1 Deaths per Population Deaths 1000,000 Population Observed deaths population Age group 0 297,256 1,449 487 55 1-4 1,247,768 272 22 208 5-9 1,663,285 198 12 298 10-14 1,666,353 171 10 250 15-19 1,568,759 386 25 213 20-24 1,525,390 472 31 249 25-29 1,789,723 632 35 409 30-34 2,047,096 1,033 50 388 35-39 2,098,035 1,629 78 356 40-44 1,822,329 2,229 122 276 45-49 1,669,145 3,300 198 231 50-54 1,813,517 5,684 313 239 55-59 1,453,409 7,352 506 191 60-64 1,298,083 10,256 790 165 65-69 1,188,619 15,230 1,281 144 70-74 1,131,035 25,409 2,247 138 75-79 1,042,657 39,762 3,814 126 80-84 710,306 49,274 6,937 79 All ages 0-84 30 SMR 95% Confidence intervals SMR EL EU Lower limit 149 20.2409 42.8269 100 1 The methods used for calculating the confidence intervals is described in more detail in: 1 Goldblatt P. Longitudinal Study, Mortality and social organisation. Series LS no 6, Chapter 3. HMSO London, 1990. alculated using Example 1 Expected deaths 0 0 0 0 0 0 0 0 0 0 0 1 1 1 2 3 5 5 20 149 ervals Upper limit 212 O London, 1990. Calculation of Standardised Mortality Ratios with 95% confidence intervals. 1 Example 2 - where number of deaths is 100 or greater but less than 900. This spreadsheet illustrates the method used by ONS to calculate SMRs for ward in England and Wales where the age at death was less than 85 years. The figures highlighted in blue are the data needed to allow the SMR to be calculated. Figures highlighted in red are then calculated within the spreadsheet. In this example as there are more than 100 deaths an approximation to the exact method illustrated in Example 1 is used. Standard Population e.g. England & Wales Ward Example 2 Deaths per Population Deaths 1000,000 Population population Age group 0 297,256 1,449 487 555 1-4 1,247,768 272 22 2,087 5-9 1,663,285 198 12 2,985 10-14 1,666,353 171 10 2,509 15-19 1,568,759 386 25 2,136 20-24 1,525,390 472 31 2,491 25-29 1,789,723 632 35 4,096 30-34 2,047,096 1,033 50 3,889 35-39 2,098,035 1,629 78 3,564 40-44 1,822,329 2,229 122 2,764 45-49 1,669,145 3,300 198 2,314 50-54 1,813,517 5,684 313 2,392 55-59 1,453,409 7,352 506 1,918 60-64 1,298,083 10,256 790 1,653 65-69 1,188,619 15,230 1,281 1,443 70-74 1,131,035 25,409 2,247 1,380 75-79 1,042,657 39,762 3,814 1,262 80-84 710,306 49,274 6,937 791 All ages 0-84 95% Confidence intervals SMR EL EL 149 267 336 1 The methods used for calculating the confidence intervals is described in more detail in: 1 Goldblatt P. Longitudinal Study, Mortality and social organisation. Series LS no 6, Chapter 3. HMSO London, 1990. d in England and Wales method illustrated in Example 1 is used. Ward Example 2 Observed deaths Expected deaths 3 0 0 0 1 1 1 2 3 3 5 7 10 13 18 31 48 55 300 202 SMR 149 95% Confidence intervals Lower limit Upper limit 132 166 6, Chapter 3. HMSO London, 1990. 1 Calculation of Standardised Mortality Ratios with 95% confidence intervals. Example 3 - where number of deaths is 900 or greater. This spreadsheet illustrates the method used by ONS to calculate SMRs for ward in England and Wales where the age at death was less than 85 years. The figures highlighted in blue are the data needed to allow the SMR to be calculated. Figures highlighted in red are then calculated within the spreadsheet. In this example an approximation to the exact method illustrated in Example 1 is used. As there are more than 900 deaths the method of approximation differs slightly from the calculation illustrated in Example 2. Standard Population e.g. England & Wales Ward Example 3 Deaths per Population Deaths 1000,000 Population Observed deaths population Age group 0 297,256 1,449 487 2,220 1-4 1,247,768 272 22 8,348 5-9 1,663,285 198 12 11,940 10-14 1,666,353 171 10 10,036 15-19 1,568,759 386 25 8,544 20-24 1,525,390 472 31 9,964 25-29 1,789,723 632 35 16,384 30-34 2,047,096 1,033 50 15,556 35-39 2,098,035 1,629 78 14,256 40-44 1,822,329 2,229 122 11,056 45-49 1,669,145 3,300 198 9,256 50-54 1,813,517 5,684 313 9,568 55-59 1,453,409 7,352 506 7,672 60-64 1,298,083 10,256 790 6,612 65-69 1,188,619 15,230 1,281 5,772 70-74 1,131,035 25,409 2,247 5,520 75-79 1,042,657 39,762 3,814 5,048 80-84 710,306 49,274 6,937 3,164 All ages 0-84 1200 SMR 95% Confidence intervals SMR EL EU Lower limit 149 1133 1270 140 1 The methods used for calculating the confidence intervals is described in more detail in: 1 Goldblatt P. Longitudinal Study, Mortality and social organisation. Series LS no 6, Chapter 3. HMSO London, 1990. ustrated in Example 2. Example 3 Expected deaths 11 2 1 1 2 3 6 8 11 14 18 30 39 52 74 124 193 219 808 149 ervals Upper limit 157 London, 1990. Exact 95 and 99 per cent confidence intervals when observed numbers are less than 100 95 per cent confidence interval Observed number Lower limit Upper limit Observed number 0 0.0000 3.6889 0 1 0.0253 5.5716 1 2 0.2422 7.2247 2 3 0.6187 8.7673 3 4 1.0899 10.2416 4 5 1.6235 11.6683 5 6 2.2019 13.0595 6 7 2.8144 14.4227 7 8 3.4538 15.7632 8 9 4.1154 17.0848 9 10 4.7954 18.3904 10 11 5.4912 19.6820 11 12 6.2006 20.9616 12 13 6.9220 22.2304 13 14 7.6539 23.4896 14 15 8.3954 24.7402 15 16 9.1454 25.9830 16 17 9.9031 27.2186 17 18 10.6679 28.4478 18 19 11.4392 29.6709 19 20 12.2165 30.8884 20 21 12.9993 32.1007 21 22 13.7873 33.3083 22 23 14.5800 34.5113 23 24 15.3773 35.7101 24 25 16.1787 36.9049 25 26 16.9841 38.0960 26 27 17.7932 39.2836 27 28 18.6058 40.4678 28 29 19.4218 41.6488 29 30 20.2409 42.8269 30 31 21.0630 44.0020 31 32 21.8880 45.1745 32 33 22.7157 46.3443 33 34 23.5460 47.5116 34 35 24.3788 48.6765 35 36 25.2140 49.8392 36 37 26.0514 50.9996 37 38 26.8911 52.1580 38 39 27.7328 53.3143 39 40 28.5766 54.4686 40 41 29.4223 55.6211 41 42 30.2699 56.7718 42 43 31.1193 57.9207 43 44 31.9705 59.0679 44 45 32.8233 60.2135 45 46 33.6778 61.3576 46 47 34.5338 62.5000 47 48 35.3914 63.6410 48 49 36.2505 64.7806 49 50 37.1110 65.9188 50 51 37.9728 67.0556 51 52 38.8361 68.1911 52 53 39.7006 69.3253 53 54 40.5665 70.4583 54 55 41.4335 71.5901 55 56 42.3018 72.7207 56 57 43.1712 73.8501 57 58 44.0418 74.9784 58 59 44.9135 76.1057 59 60 45.7863 77.2319 60 61 46.6602 78.3571 61 62 47.5350 79.4812 62 63 48.4109 80.6044 63 64 49.2878 81.7266 64 65 50.1656 82.8478 65 66 51.0444 83.9682 66 67 51.9241 85.0876 67 68 52.8047 86.2062 68 69 53.6861 87.3239 69 70 54.5684 88.4408 70 71 55.4516 89.5568 71 72 56.3356 90.6721 72 73 57.2203 91.7865 73 74 58.1059 92.9002 74 75 58.9923 94.0131 75 76 59.8794 95.1253 76 77 60.7672 96.2368 77 78 61.6558 97.3475 78 79 62.5450 98.4576 79 80 63.4350 99.5669 80 81 64.3257 100.6756 81 82 65.2170 101.7836 82 83 66.1090 102.8910 83 84 67.0017 103.9977 84 85 67.8950 105.1038 85 86 68.7889 106.2093 86 87 69.6834 107.3142 87 88 70.5786 108.4185 88 89 71.4743 109.5222 89 90 72.3706 110.6253 90 91 73.2675 111.7278 91 92 74.1650 112.8298 92 93 75.0630 113.9313 93 94 75.9616 115.0322 94 95 76.8607 116.1326 95 96 77.7603 117.2324 96 97 78.6605 118.3318 97 98 79.5611 119.4360 98 99 80.4623 120.5289 99 Goldblatt P. Longitudinal Study, Mortality and social organisation. Series LS no 6.HMSO London, 1990. Table 3.7, p58. umbers are less than 100 99 per cent confidence interval Lower limit Upper limit 0.0000 5.2983 0.0050 7.4301 0.1035 9.2738 0.3379 10.9775 0.6722 12.5941 1.0779 14.1498 1.5369 15.6597 2.0373 17.1336 2.5711 18.5782 3.1324 19.9984 3.7169 21.3978 4.3214 22.7793 4.9431 24.1449 5.5801 25.4967 6.2307 26.8360 6.8934 28.1641 7.5670 29.4820 8.2506 30.7906 8.9434 32.0907 9.6445 33.3830 10.3533 34.6680 11.0692 35.9463 11.7918 37.2183 12.5207 38.4844 13.2553 39.7450 13.9954 41.0004 14.7406 42.2510 15.4906 43.4969 16.2452 44.7384 17.0042 45.9758 11.7672 47.2093 18.5342 48.4391 19.3049 49.6652 20.0791 50.8880 20.8567 52.1074 21.6376 53.3238 22.4215 54.5372 23.2085 55.7477 23.9983 56.9554 24.7908 58.1605 25.5860 59.3631 26.3837 60.5631 27.1838 61.7609 27.9864 62.9563 28.7912 64.1495 29.5982 65.3405 30.4073 66.5295 31.2185 67.7165 32.0317 68.9016 32.8468 70.0847 33.6638 71.2661 34.4826 72.4457 35.3032 73.6235 36.1255 14.7997 36.9494 75.9742 37.7750 77.1472 38.6022 78.3186 39.4309 79.4886 40.2611 80.6570 41.0927 81.8241 41.9258 82.9898 42.7602 84.1541 43.5960 85.3170 44.4332 86.4787 45.2716 87.6392 46.1112 88.7984 46.9521 89.9564 47.7942 91.1132 48.6375 92.2689 49.4819 93.4234 50.3274 94.5769 51.1741 95.7292 52.0218 96.8806 52.8705 98.0308 53.7203 99.1801 54.5711 100.3284 55.4229 101.4757 56.2757 102.6220 57.1294 103.7674 57.9841 104.9119 58.8396 106.0555 59.6961 107.1982 60.5535 108.3401 61.4117 109.4811 62.2707 110.6212 63.1307 111.7605 63.9914 112.8991 64.8529 114.0368 65.7152 115.1737 66.5783 116.3099 67.4422 117.4453 68.3069 118.5800 69.1722 119.7139 70.0383 120.8472 70.9051 121.9797 71.7727 123.1115 72.6409 124.2427 73.5098 125.3731 74.3794 126.5029 75.2496 127.6321 S no 6.HMSO London, 1990. Table 3.7, p58.

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