{"text_format":"1","workbook":"xlsx","n_sheets":3,"sheets":["Introduction and Method","Interactive Tool","Chart"],"not_rendered":{"charts":1,"images":1,"macros":1,"external_links":0,"defined_names":1,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Introduction and Method","index":0,"n_rows":27,"n_cols":9,"rows_kept":27,"cut":false,"hidden":false,"merged":[[12,1,12,8],[20,1,20,8],[17,1,17,8],[0,6,0,7],[1,6,1,7],[2,6,2,7],[3,6,3,7],[7,1,7,8],[10,1,10,8],[14,1,14,8],[13,1,13,8]]}
[null,"Department of Health & Social Care"]
[null,"Interactive tool for calculating the Slope Index"]
[null,"of Inequality (SII) and Relative Index of Inequality (RII)",null,null,null,null,null,null,"Dec 25"]
[]
[]
[]
[null,"Introduction"]
[null,"The Slope Index of Inequality (SII) and Relative Index of Inequality (RII) are summary measures of inequality in health outcomes by deprivation.\n\nThe SII and RII are measures of how much an indicator varies with deprivation. They takes account of variation across the whole range of deprivation within a population and summarise this in a single number representing the range in indicator values across the social gradient from most to least deprived.\n\nThis workbook provides an interactive tool to facilitate calculation of the SII and RII. \n"]
[]
[null,"Method"]
[null,"This section sets out essential information on the SII/RII calculation method. The method of calculating and interpreting the SII and RII is set out comprehensively in the Public Health Technical Guidance book and this should be referred to for full details of the method."]
[null,"https://fingertips.phe.org.uk/static-reports/public-health-technical-guidance/inequality/SII.html"]
[null,"The SII is calculated using a linear regression formula which takes into account the indicator values for each deprivation decile, and the population denominator for each deprivation decile. Figure 1 provides an example of the calculation of the slope index of inequality where there is a linear relationship between the indicator and deprivation.\n\nThe chart shows indicator values for 10 deprivation deciles. These have been plotted to take account of their population size. The orange line on the chart is a linear regression line of best fit for the data, calculated by the ordinary least squares method. The SII is the gradient of the regression line. Since the x axis is plotted on a scale from 0 to 1, the SII is also equal to the difference between the top of the line (at x=1 on the horizontal axis) and the bottom (at x=0 on the horizontal axis).\n\nThe RII is is the proportional difference between the top of the line and the bottom of the line.\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nTransformation\nThe standard approach for calculating the SII and RII described above has the assumption that there is a linear relationship between the indicator and deprivation. In health indicators, this is not always the case, and the relationship is not linear. In these cases, it is possible to log or logit transform the data prior to calculation to improve linearity of the data prior to calculation of the SII/RII. OHID’s approach is that all indicators, except for life expectancy and healthy life expectancy, are log or logit transformed prior to calculation of the SII/RII to account for the non-linearity.\n\nIn this tool, the user can opt to transform data for an indicator or not. If transformation is selected, a log transformation is used for rate indicators and logit transformation is used for proportions. Data are transformed back to the original units of the indicator for presentation.\n\nConfidence intervals\nConfidence intervals for the SII and RII are calculated using a simulation approach. Simulation is a method used to estimate the degree of uncertainty for measures where the statistical distributions underpinning the measure are too complex to analyse mathematically.\n\nFor each decile value, the confidence intervals give information about the degree of uncertainty around each of the indicator values: essentially it describes a statistical distribution for each decile. Using a random number generating algorithm, a random value is taken from each decile indicator value distribution and the SII recalculated. This is repeated many times to build up a distribution of SII values based on random sampling from the decile indicator value distributions. These distributions are then used to provide values for the confidence intervals around the SII and RII.\n\nThe tool allows the user to choose the number of repetitions that are used in the calculation, although at least 100,000 is recommended."]
[null,"Figure 1: An example SII chart\nSlope index of inequality = 6.9\nRelative index of inequality = 1.1"]
[null,"Transformation\nThe standard approach for calculating the SII and RII described above has the assumption that there is a linear relationship between the indicator and deprivation. In health indicators, this is not always the case, and the relationship is not linear. In these cases, it is possible to log or logit transform the data prior to calculation to improve linearity of the data prior to calculation of the SII/RII. OHID’s approach is that rates are log-transformed and proportions logit-transformed prior to calculation of the SII/RII to account for the assumption of non-linearity with these statistics.\n\nIn this tool, the user can opt to transform data for an indicator or not. If transformation is selected, a log transformation is used for rate indicators and logit transformation is used for proportions. Data are transformed back to the original units of the indicator for presentation.\n\nConfidence intervals\nConfidence intervals for the SII and RII are calculated using a simulation approach. Simulation is a method used to estimate the degree of uncertainty for measures where the statistical distributions underpinning the measure are too complex to analyse mathematically.\n\nFor each decile value, the confidence intervals give information about the degree of uncertainty around each of the indicator values: essentially it describes a statistical distribution for each decile. Using a random number generating algorithm, a random value is taken from each decile indicator value distribution and the SII recalculated. This is repeated many times to build up a distribution of SII values based on random sampling from the decile indicator value distributions. These distributions are then used to provide values for the confidence intervals around the SII and RII.\n\nThe tool allows the user to choose the number of repetitions that are used in the calculation, although at least 100,000 is recommended."]
[]
[null,"Interpretation of results"]
[null,"The SII is presented in the same units of the indicator values, and represents the hypothetical absolute difference between the extremes of deprivation within the area as a whole.\n\nThe RII is presented with no units, and represents the hypothetical relative difference between the extremes of deprivation within an area."]
[]
[null,"Using this tool"]
[null,"Use the 'Interactive Tool' tab to enter data and view SII and RII figures. Guidance on the data required and how to enter it in the tool is provided on the right hand side of the page. A chart to visualise the results can be viewed on the 'Chart' tab.\n\nThe tool allows calculation and visualisation of a single SII and RII at a time. The time taken to calculate results will be longer the higher the number of repetitions selected to be used in the calculation. If 1,000,000 repetitions is selected, it can take several minutes to return results. \n\nBecause of the limitations of Excel, it is recommended that R is used if SII/RII figures are required for multiple time periods, geographies or indicators. A function has been included in the PHEindicatormethods R package linked to below which can be used for this, and offers additional flexibility to this Excel calculator. "]
[]
[null,"Additional resources"]
[null,"More detailed guidance on the calculation and use of the slope index of inequality and relative index of inequality can be found at the link below:"]
[null,"https://fingertips.phe.org.uk/static-reports/public-health-technical-guidance/inequality/SII.html"]
[null,"The PHEindicatormethods R package includes the function phe_sii(), which can be used to calculate the SII and can be installed from the link below:"]
[null,"https://github.com/ukhsa-collaboration/PHEindicatormethods"]

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[null,"Department of Health & Social Care"]
[null,"Interactive tool for calculating the Slope Index"]
[null,"of Inequality (SII) and Relative Index of Inequality (RII)",null,null,null,null,null,null,null,null,null,"Dec 25"]
[]
[]
[]
[null,null,"Step 1: Enter data by deprivation decile",null,null,null,null,null,null,null,"Guidance on using this tool"]
[null,null,null,null,null,null,null,null,null,null,"\nData\n\nIn order to calculate an SII or RII value using this tool, data are required for the indicator of interest broken down by deprivation decile. These indicator values should be entered in cells D10 to D19. If the indicator is a proportion, all values should be between 0 and 1.\n\n95% confidence intervals for the decile values should be entered into cells E10 to E19. If confidence intervals are not available, these cells should be left blank. If this is done, only the SII, RII, and Intercept will be output by the tool.\n\nDenominator values for each deprivation decile should be entered into cells G10 to G19.\n\nAdditional calculation parameters\n\nAll the additional calculation parameters should be completed before viewing results.\n\nIndicator type: This field should be completed with 1 if the indicator is a rate, 2 if the indicator is a proportion, and 0 for other indicator types (for example life expectancy). This argument determines how the standard error is calculated from the confidence interval values, and, if transformation is selected, how the indicator is transformed.\n\nTransformation: This field should be completed with TRUE if the indicator is to be log or logit transformed, or FALSE if no transformation is to be applied. See the method tab for details on when to apply a transformation when calculating an SII. This tool only allows transformation for rate or proportion indicators.\n\nRepetitions: Enter the number of repetitions required to calculate confidence intervals for the SII and RII. See the method tab for more details on the method used. This field can contain any number between 1,000 and 1,000,000. A small number of repetitions is suggested for testing, but a large number (at least 100,000) is recommended for final results.\n\nConfidence level of results: Enter the confidence levels that you require for the confidence intervals of the SII and RII results. This field can contain any number between 50% and 99%.\n\nResults\n\nResults are presented, with confidence intervals, for both the SII and RII. The units of the SII are the same as those of the input indicator data, and the RII does not have any units. See the methods tab for more details on interpretation of the results. A chart visualising the SII is displayed on the Chart tab."]
[null,null,"Decile","Indicator value","Lower 95% confidence interval","Upper 95% confidence interval","Denominator"]
[null,null,"1 (most deprived)",152.37975459053649,149.95892735642423,154.829527053493,14915653]
[null,null,2,125.5188429326689,123.34321781333354,127.7228624143729,15086655]
[null,null,3,107.671703273642,105.71946709542779,109.65067238337075,15119203]
[null,null,4,90.981348926933791,89.268634504881419,92.718501100163309,14986094]
[null,null,5,78.703037926063303,77.173608821443935,80.255046827745389,14670691]
[null,null,6,71.298439586520999,69.879126395504954,72.739231515014609,14647622]
[null,null,7,64.265350664003705,62.936769547088467,65.614822310259925,14464673]
[null,null,8,59.041336854033176,57.767626142115368,60.335956330377954,14422469]
[null,null,9,53.023974311092097,51.824667484815976,54.243928006387989,14389398]
[null,null,"10 (least deprived)",45.084745866101258,43.978484953176817,46.211677510652727,14118227]
[null,null,{"$f":"IF( OR(AND(G26=0, G29=TRUE), OR(G32<1000, G32>1000000), OR(G35<0.5, G35>0.99) ), \"\",IF(ISNUMBER(C100)=FALSE,C100,\"\"))","v":""}]
[]
[]
[]
[null,null,"Step 2: Enter additional calculation parameters"]
[]
[null,null,"Enter indicator type:",null,null,null,1]
[null,null,"1 = Rate, 2 = Proportion, 0 = Other"]
[]
[null,null,"Is indicator transformation required?",null,null,null,true]
[null,null,"TRUE = Yes, FALSE = No"]
[null,null,{"$f":"IF(AND(G26=0, G29=TRUE), \"ERROR: transformation can only be set to TRUE with rate or proportion indicator types\", \"\")","v":""}]
[null,null,"Enter the number of repetitions required to calculate confidence intervals:",null,null,null,1000]
[null,null,"Minimum = 1,000, Maximum = 1,000,000"]
[null,null,{"$f":"IF(OR(G32<1000, G32>1000000), \"ERROR - value must be between 1,000 and 1,000,000\", \"\")","v":""}]
[null,null,"Enter confidence level required for SII/RII results:",null,null,null,0.95]
[null,null,"Minimum = 50%, Maximum = 99%"]
[null,null,{"$f":"IF(OR(G35<0.5, G35>0.99), \"ERROR - value must be between 50 and 99\", \"\")","v":""}]
[]
[]
[]
[null,null,"Step 3: View results"]
[]
[null,null,"Measure","Indicator value",{"$f":" \"Lower \" & G35 *100 & \"% confidence interval\"","v":"Lower 95% confidence interval"},{"$f":" \"Upper \" & G35 *100 & \"% confidence interval\"","v":"Upper 95% confidence interval"}]
[null,null,"Slope index of inequality (SII)",{"$f":"IF(ISNUMBER(C100)=FALSE,0,C100)","v":-109.17195479039037},{"$f":"D100","v":-111.51481255304353},{"$f":"E100","v":-106.75610978604965}]
[null,null,"Relative index of inequality (RII)",{"$f":"F100","v":0.2776575119365346},{"$f":"G100","v":0.27102359630619005},{"$f":"H100","v":0.28471780596417245}]
[null,null,"Intercept",{"$f":"I100","v":151.13600071216976}]
[]
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[null,null,"OUTPUTS:"]
[null,null,"SII","SII LCI","SII UCI","RII","RII LCI","RII UCI","Intercept x=0"]
[null,null,{"$f":"SIITR($D$10:$D$19,$E$10:$E$19,$F$10:$F$19,$G$10:$G$19,$G$32,$G$35,$G$26,$G$29)","v":-109.17195479039037},-111.51481255304353,-106.75610978604965,0.2776575119365346,0.27102359630619005,0.28471780596417245,151.13600071216976]

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[null,"Department of Health & Social Care"]
[null,"Interactive tool for calculating the Slope Index"]
[null,"of Inequality (SII) and Relative Index of Inequality (RII)",null,null,null,null,null,null,"Dec 25"]
[]
[null,"Copy Chart",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Figures used to calculate the chart (to be hidden or incorporated into VBA code)"]
[null,"  Slope index of inequality chart",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Grey values come from interactive tool sheet"]
[null,{"$f":"IF('Interactive Tool'!E44=\"\",\"   Slope index of inequality: \"&ROUND('Interactive Tool'!D44,1),\"   Slope index of inequality: \"&ROUND('Interactive Tool'!D44,1)&\" (\"&'Interactive Tool'!G35*100&\"% confidence interval: \"&ROUND('Interactive Tool'!E44,1)&\" to \"&ROUND('Interactive Tool'!F44,1)&\")\")","v":"   Slope index of inequality: -109.2 (95% confidence interval: -111.5 to -106.8)"}]
[null,{"$f":"IF('Interactive Tool'!E44=\"\", \"   Relative index of inequality: \"& ROUND('Interactive Tool'!D45,1),  \"   Relative index of inequality: \"& ROUND('Interactive Tool'!D45,1) &\" (\"&'Interactive Tool'!G35*100&\"% confidence interval: \" & ROUND('Interactive Tool'!E45,1) & \" to \" & ROUND('Interactive Tool'!F45,1) & \")\")","v":"   Relative index of inequality: 0.3 (95% confidence interval: 0.3 to 0.3)"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Table for plotting decile values on chart"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Decile","Indicator value","Denominator","Proportion of pop in decile","Chart x value"]
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[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Table for plotting SII line on chart"]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"sii",{"$f":"'Interactive Tool'!D44","v":-109.17195479039037}]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Chart x value","Intercept and x=1 indicator value","transformed values (if required)","Antitransformed values to plot"]
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