Structure of the thesis
-Chapter 2 reviews the literature on spatial methods for mapping disease and mortality for small subnational regions, followed by the literature of separating total mortality into different causes of death. I will then explore inequalities in UK over the past few decades through to the present. Chapter 3 presents the data sources, and Chapter 4 the statistical modelling choices common to all objectives of this thesis. Chapter 5 concerns the first objective of the thesis - estimating trends in life expectancy for very small areas in England. Chapter 6 extends the first objective by focussing on London at a finer scale than the previous chapter as an attempt to gauge whether higher resolution analyses are possible. Chapter 7 addresses objective two of this thesis, breaking down total mortality in England into specific causes of deaths at a coarser scale, and looking at potential drivers of the observed trends in life expectancy. Chapter 8 follows the methods of Chapter 7, but focussing only on deaths from cancers. Chapter 9 concludes with a discussion on the public health implications of the findings and areas for future research building on the work in this thesis.
+Chapter 2 reviews the literature on spatial methods for mapping disease and mortality for small subnational regions, followed by the literature of separating total mortality into different causes of death. I will then explore inequalities in UK over the past few decades through to the present. Chapter 3 presents the data sources, and Chapter 4 the statistical modelling choices common to all objectives of this thesis. Chapter 5 concerns the first objective of the thesis - estimating trends in life expectancy for very small areas in England. Chapter 6 extends the first objective by focussing on London at a finer scale than the previous chapter as an attempt to gauge whether higher-resolution analyses are possible. Chapter 7 addresses objective two of this thesis, breaking down total mortality in England into specific causes of deaths at a coarser scale, and looking at potential drivers of the observed trends in life expectancy. Chapter 8 follows the methods of Chapter 7, but focussing only on deaths from cancers. Chapter 9 concludes with a discussion on the public health implications of the findings and areas for future research building on the work in this thesis.
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index fb2bc58..e095b63 100644
--- a/thesis/_thesis/search.json
+++ b/thesis/_thesis/search.json
@@ -25,7 +25,7 @@
"href": "index.html#structure-of-the-thesis",
"title": "Spatiotemporal mortality modelling",
"section": "1.3 Structure of the thesis",
- "text": "1.3 Structure of the thesis\nChapter 2 reviews the literature on spatial methods for mapping disease and mortality for small subnational regions, followed by the literature of separating total mortality into different causes of death. I will then explore inequalities in UK over the past few decades through to the present. Chapter 3 presents the data sources, and Chapter 4 the statistical modelling choices common to all objectives of this thesis. Chapter 5 concerns the first objective of the thesis - estimating trends in life expectancy for very small areas in England. Chapter 6 extends the first objective by focussing on London at a finer scale than the previous chapter as an attempt to gauge whether higher resolution analyses are possible. Chapter 7 addresses objective two of this thesis, breaking down total mortality in England into specific causes of deaths at a coarser scale, and looking at potential drivers of the observed trends in life expectancy. Chapter 8 follows the methods of Chapter 7, but focussing only on deaths from cancers. Chapter 9 concludes with a discussion on the public health implications of the findings and areas for future research building on the work in this thesis.\n\n\n\n\nBennett JE, Li G, Foreman K, Best N, Kontis V, Pearson C, Hambly P, Ezzati M. 2015. The future of life expectancy and life expectancy inequalities in England and Wales: Bayesian spatiotemporal forecasting. The Lancet 386:163–170. doi:10.1016/S0140-6736(15)60296-3\n\n\nBennett JE, Pearson-Stuttard J, Kontis V, Capewell S, Wolfe I, Ezzati M. 2018. Contributions of diseases and injuries to widening life expectancy inequalities in England from 2001 to 2016: A population-based analysis of vital registration data. The Lancet Public Health 3:e586–e597. doi:10.1016/S2468-2667(18)30214-7\n\n\nMarmot MG, Allen J, Boyce T, Goldblatt P, Morrison J. 2020. Marmot Review: 10 years on. Institute of Health Equity."
+ "text": "1.3 Structure of the thesis\nChapter 2 reviews the literature on spatial methods for mapping disease and mortality for small subnational regions, followed by the literature of separating total mortality into different causes of death. I will then explore inequalities in UK over the past few decades through to the present. Chapter 3 presents the data sources, and Chapter 4 the statistical modelling choices common to all objectives of this thesis. Chapter 5 concerns the first objective of the thesis - estimating trends in life expectancy for very small areas in England. Chapter 6 extends the first objective by focussing on London at a finer scale than the previous chapter as an attempt to gauge whether higher-resolution analyses are possible. Chapter 7 addresses objective two of this thesis, breaking down total mortality in England into specific causes of deaths at a coarser scale, and looking at potential drivers of the observed trends in life expectancy. Chapter 8 follows the methods of Chapter 7, but focussing only on deaths from cancers. Chapter 9 concludes with a discussion on the public health implications of the findings and areas for future research building on the work in this thesis.\n\n\n\n\nBennett JE, Li G, Foreman K, Best N, Kontis V, Pearson C, Hambly P, Ezzati M. 2015. The future of life expectancy and life expectancy inequalities in England and Wales: Bayesian spatiotemporal forecasting. The Lancet 386:163–170. doi:10.1016/S0140-6736(15)60296-3\n\n\nBennett JE, Pearson-Stuttard J, Kontis V, Capewell S, Wolfe I, Ezzati M. 2018. Contributions of diseases and injuries to widening life expectancy inequalities in England from 2001 to 2016: A population-based analysis of vital registration data. The Lancet Public Health 3:e586–e597. doi:10.1016/S2468-2667(18)30214-7\n\n\nMarmot MG, Allen J, Boyce T, Goldblatt P, Morrison J. 2020. Marmot Review: 10 years on. Institute of Health Equity."
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@@ -39,7 +39,7 @@
"href": "Chapters/Chapter2.html#mapping-mortality-and-disease-at-small-areas",
"title": "2 Background",
"section": "2.2 Mapping mortality and disease at small areas",
- "text": "2.2 Mapping mortality and disease at small areas\nMany studies compare the prevalence of diseases or mortality in different subgroups of the population by dividing the population geographically into small areas. The number of cases, or number of deaths, in an area are likely to be small numbers. This sparseness issue is even more pertinent when the population is further stratified by age group. When calculating rates of incidence from the observed data, there is an apparent variability between spatial units, which is often larger than the true differences in risk due to the noise in the data. To overcome these issues, we can use statistical smoothing techniques to obtain robust estimates of rates by sharing information between strata.\n\n2.2.1 Disease mapping methods\nIn small-area studies, it is common to smooth data using models with explicit spatial dependence, which are designed to give more weight to nearby areas than those further away. There are three main categories for modelling spatial effects. First, we can treat space as a continuous surface using Gaussian processes or splines. Second, we can use areal models, which make use of the spatial neighbourhood structure of the units. Thirdly, we can explicitly build effects based on a nested hierarchy of geographical units, for example between state, county and census tract in the US. Each of these methods rely on assumptions which may make them more or less appropriate in different applications.\n\nSpace as a continuous process\nIn the context of disease mapping, events are usually aggregated to areas rather than assigned specific geographical coordinates. Wakefield and Elliott (1999) model aggregated counts as realisations of a Poisson process, in which the expected number of cases is calculated by integrating a continuous surface that generates the cases over the area of the spatial unit. The surface was a function of spatially-referenced covariates. Kelsall and Wakefield (2002) describe an alternative model, where the log-transformed risk surface is modelled by a Gaussian process, whose correlation function depends on distance.\nBest et al. (2005) provide a review of the use of hierarchical models with spatial dependence for disease mapping. In particular, the authors focus on Bayesian estimation, and different classes of spatial prior distributions.\nThe first prior proposed for spatial effects \\(\\mathbf{S} = {S_1, ..., S_n}\\) is the multivariate normal \\[\n\\mathbf{S} \\sim \\mathcal{N}(\\pmb{\\mu}, \\pmb{\\Sigma}),\n\\tag{2.1}\\]\nwhere \\(\\pmb{\\mu}\\) is the mean effect vector, \\(\\pmb{\\Sigma} = \\sigma^2 \\pmb{\\Omega}\\) and \\(\\pmb{\\Omega}\\) is a symmetric, positive semi-definite matrix defining the correlation between spatial units. A common choice when specifying the structure of the correlation matrix is to assume a function that decays with the distance between the centroids of the areas, so that places nearby in space share similar disease profiles. Note, this is mathematically equivalent to the practical implementation of a Gaussian process, which uses a finite set of points. An example in Elliott et al. (2001b) chooses an exponential decay function to map cancer risk in northwest England.\n\n\nSpace as discrete units\nA more popular prior is the conditional autoregressive (CAR) prior, also known as a Gaussian Markov random field (GMRF), which was first introduced by Besag et al. (1991). These form a joint distribution as in Equation 2.1, but the covariance is usually defined instead in terms of the precision matrix \\[\n\\mathbf{P} = \\pmb{\\Sigma}^{-1} = \\tau(\\mathbf{D} - \\rho \\mathbf{A}),\n\\tag{2.2}\\] where \\(\\tau\\) controls the overall precision of the effects, \\(\\mathbf{A}\\) is the spatial adjacency matrix formed by the small areas, \\(\\mathbf{D}\\) is a diagonal matrix with entries equal to the number of neighbours for each spatial unit, and the autocorrelation parameter \\(\\rho\\) describes the amount of correlation. This can be seen as tuning the degree of spatial dependence, where \\(\\rho = 0\\) implies independence between areas, and \\(\\rho = 1\\) full dependence. The case with \\(\\rho = 1\\) is called the intrinsic conditional autoregressive (ICAR) model. There sometimes exists further over-dispersion in the residuals that cannot be modelled by purely spatially-structured random effects. Besag et al. (1991) proposed the model (hereafter called BYM) \\[\nS_i = U_i + V_i,\n\\tag{2.3}\\] where \\(U_i\\) follow an ICAR distribution, and \\(V_i\\) are independent and identically distributed random effects. The addition of the spatially-unstructured component \\(V\\) accounts for any non-spatial heterogeneity.\n\n\nSpace as a nested hierarchy of geographies\nThe relationships between different levels of a hierarchy of geographical units are often incorporated into models as a nested hierarchy of random effects. These models account for when spatial units lie within common administrative boundaries. This is often a desirable property of the model for certain geographies, like states in the US, which are administrative. Policy is decided at these geographies, so there is reason to believe these boundaries may have a greater effect on health outcomes than spatial structure. Finucane et al. (2014) demonstrate how country-level blood pressure can be modelled by exploiting the hierarchy global, super-region, region and country. Note, although these models group by geographical region, these models are not spatial as they do not contain any information on the relative position of the areas.\nOf the two specifications that are spatial, either as a continuous process or discrete units, the Markov random field priors are often preferred for computational reasons, as we can exploit the sparseness of the adjacency matrix in our inference algorithms rather than computing the covariance between each pair of spatial units as in the general case of Equation 2.1. There are concerns, however, that the GMRF representation of space as an adjacency matrix, which was originally proposed for a regular lattice of pixels in image analysis, is reductive for more complicated spatial problems. Despite this, in an epidemiological context, Duncan et al. (2017) found the standard ICAR model with binary, first-order neighbour weights outperformed models with a variety of different weighting schemes, including matrix weights based on higher-order degrees of neighbours, distance between neighbours, and distance between covariate values.\nIn applications to disease mapping, spatial models are the natural choice when the disease exhibits a spatial pattern. This is the case for mortality from infectious diseases, particularly on short timescales like Covid-19 (Konstantinoudis et al., 2022). Nested hierarchies are a more suitable choice when administrative areas are meaningful and have an effect on the health outcomes of the population. For example, state-specific abortion laws in the USA could affect maternal mortality, and so a model should include an effect for each state.\n\n\nModelling variation beyond space\nAs computational power has improved, it has become feasible to model patterns over other features of the population, such as time period and age group. Trends over time can be modelled as linear through slopes, or using nonlinear effects which allow neighbouring time points to be alike, the simplest of which is a first-order Gaussian random walk process. All-cause mortality varies smoothly over ages, following a characteristic J-shape with higher mortality in the infant and older age groups (Preston et al., 2001), and therefore can be modelled using a nonlinear process such as a random walk.\nDifficulties arise when considering interactions between the space, age, and time variables. One can imagine situations in which different spatial units will have different age patterns in disease rates, for example, if the certain age groups were vaccinated against disease in that spatial unit before others. After implementing a base model with the main effects, the question is how to model additional terms which account for the interactions between the variables. Space-time interactions could range from fully independent, to each spatial unit having independent temporal patterns, to inseparable space-time variation where interactions borrow strength across neighbouring spatial units and neighbouring time periods (Knorr-Held, 2000).\nHowever, it should be considered that by breaking the population down into smaller and smaller subgroups through space, age and time period, the counts of cases become more sparse and there is a need for stronger smoothing to produce robust estimates, particular for data that is already at the small-area level. Although interaction effects are plausible, modellers should consider whether there evidence for the interaction in the data or whether they can simplify the model if the interaction effect turns out to be negligible.\nIt should be noted that there are situations where statistical smoothing would not be appropriate. There might be true variability in the data which a smoothing model would conceal. For example, the Grenfell Tower fire in 2017 was a localised event that affected mortality. Without accounting for this event, the models described above would either attenuate its effect on mortality, or the spike in mortality would cause estimates of mortality in nearby spatial units or years to be erroneously high.\n\n\n\n2.2.2 Applications of disease mapping methods\n\nSmall-area analyses of mortality\nIn order to compare the health status between areas, health authorities require a measure of mortality that collapses age-specific information into a single number. Indirectly standardised measures such as the standardised mortality ratio – the ratio between total deaths and expected deaths in an area – are easy to calculate, but are not easily understood by laypeople. Directly standardised methods, in contrast, require knowledge of the full age structure of death rates rather than just the total number of deaths. Age-standardised death rates, however, suffer the same interpretability issue as the standardised mortality ratio, and are only comparable between studies if the same reference population is used. An alternative choice is life expectancy. Silcocks et al. (2001) explain that life expectancy is a “more intuitive and immediate measure of the mortality experience of a population, [and] is likely to have greater impact… than other measures that are incomprehensible to most people.”\nThe estimation of death rates requires two data sources: deaths counts and populations. Modern death registration systems are complete and accurate. On the other hand, although usually treated as a known quantity, the population denominator is often problematic. Populations for small geographies are only recorded during a decennial census, and estimates are generated for the years in-between using limited survey data on births, deaths and migration. And although the census is considered the “gold standard”, it is subject to enumeration errors, particularly for areas with special populations such as students or armed forces (Elliott et al., 2001b).\nBeyond the population issue, finer scale studies are restricted by data availability. Where data are available, there is still the need to overcome small number issues before feeding death rates through the life table to calculate life expectancy. Eayres and Williams (2004) recommend a minimum population size of 5000 when using traditional life table methods, below which the calculation of life expectancy is unstable1, or the error estimates become so large that any comparison between subgroups becomes meaningless. One approach, often taken by statistical agencies, is to build larger populations by either aggregating multiple years of data (Bahk et al., 2020; Office for National Statistics, 2015; Public Health England, 2021) or combining spatial units (Ezzati et al., 2008). Here, we focus on studies using Bayesian hierarchical models to generate robust estimates of age-specific death rates by recognising the correlations between spatial units and age groups, which produce more accurate estimates for small population studies of life expectancy (Congdon, 2009; Jonker et al., 2012).\nJonker et al. (2012) demonstrated the advantages of the Bayesian approach for 89 small areas in Rotterdam using a joint model for sex, space and age effects, finding a 8.2 year and 9.2 year gap between the neighbourhoods with the highest and lowest life expectancies for women and men. Stephens et al. (2013) employed the same model for 153 administrative areas in New South Wales, Australia.\nBayesian spatial models for mortality have been scaled to small areas for entire countries, and also consider trends in these regions over time. Bennett et al. (2015) forecasted life expectancy for 375 districts in England and Wales using a spatiotemporal model trained over a 31 year period, and Dwyer-Lindgren et al. (2017a) explored mortality trends 3110 US counties from 1980 to 2014.\nThere have also been studies on specific cities at a finer resolution. In order to improve estimates for disability-free life expectancy, Congdon (2014) considered both ill-health and mortality in a joint likelihood with spatial effects for 625 wards in London, finding more than a two-fold variation in the percent of life spent in disability for men. Bilal et al. (2019) looked at 266 subcity units for six large cities in Latin America. As there is no contiguous boundary in this case, a random effects model for each city was used instead of a spatial model. The largest difference between the top and bottom decile of life expectancy at birth was 17.7 years for women in Santiago, Chile.\nTwo studies in North America have looked below the county level, at census tracts, with wide-ranging population sizes as small as 40. Dwyer-Lindgren et al. (2017b), using a model that relied heavily on sociodemographic covariates, studied trends for life expectancy and many causes of death for 397 tracts in King County, Washington, uncovering an 18.3 year gap in life expectancy for men. Using the same model for Vancouver, Canada, Yu et al. (2021) found widening inequalities over time and a difference of 9.5 years for men.\n\n\nSmall Area Health Statistics Unit\nIn 1983, a documentary on the fallout from a fire at the Sellafield nuclear site in Cumbria claimed that there was a ten-fold increase in cases of childhood leukaemia in the surrounding community. This anomaly had gone undetected by public health authorities, raising concern that routinely collected data were not able to identify local clusters of disease. The subsequent enquiry confirmed the excess, and recommended that a research unit was set up to monitor small-area statistics and respond quickly to ad hoc queries on local health hazards. The Small Area Health Statistics Unit (SAHSU) was established in 1987 (Elliott et al., 1992).\nBeyond producing substantive research on environment and health, a core aim of SAHSU is to develop small-area statistical methodology (Wakefield and Elliott, 1999) for:\n\nPoint source type studies. Is there an increased risk close to an environmental hazard? SAHSU has investigated increased mortality from mesothelioma and asbestosis near Plymouth docks (Elliott et al., 1992); excess respiratory disease mortality near two factories in Barking and Havering (Aylin et al., 1999); kidney disease mortality near chemical plants in Runcorn (Hodgson et al., 2004); possible excess of several morbidities near landfill sites (Elliott et al., 2001a; Jarup et al., 2007, 2002b).\nGeographic correlation studies. Is there a correlation between disease risk and spatially-varying environmental variables? SAHSU have looked at several exposures, including a plume of mercury pollution (Hodgson et al., 2007); mobile phone base stations during pregnancy (Elliott et al., 2010); noise from aircraft near Heathrow (Hansell et al., 2013); road traffic noise in London (Halonen et al., 2015); particulate matter from incinerators during pregnancy (Parkes et al., 2020).\nClustering. Does a disease produce non-random spatial patterns of incidence? If the aetiology is unknown, this could suggest the disease is infectious.\nDisease mapping. Summarising the spatial variation in risk.\n\nSAHSU has been at the forefront of both methodology and applications in disease mapping. Aylin et al. (1999) mapped diseases for wards in Kensington, Chelsea and Westminster using a simple model that smoothed rates towards the mean risk across the region. Thereafter, SAHSU published a plethora of studies for disease mapping models with explicit spatial dependence, including using the BYM model (Equation 2.3) to map spatial variation in the relative risk of testicular (Toledano et al., 2001) and prostate (Jarup et al., 2002a) cancers for small areas in regions of England. In a landmark piece bringing together work on disease mapping and environmental exposures, SAHSU published an environment and health atlas for England and Wales, showing the spatial patterns of 14 health conditions at census ward level over an aggregated 25 year period alongside five environmental exposure surfaces (Hansell, Anna L. et al., 2014).\nFurther disease mapping studies at SAHSU using spatially structured effects have also extended the methodology to look at age patterns and trends over time. Asaria et al. (2012) analysed cardiovascular disease death rates by fitting a spatial model for all wards in England separately for each age group and time period. Bennett et al. (2015) designed a model to jointly forecast all-cause mortality for districts in England, age groups and years. The model used BYM spatial effects and random walk effects over age and time to capture nonlinear relationships."
+ "text": "2.2 Mapping mortality and disease at small areas\nMany studies compare the prevalence of diseases or mortality in different subgroups of the population by dividing the population geographically into small areas. The number of cases, or number of deaths, in an area are likely to be small numbers. This sparseness issue is even more pertinent when the population is further stratified by age group. When calculating rates of incidence from the observed data, there is an apparent variability between spatial units, which is often larger than the true differences in risk due to the noise in the data. To overcome these issues, we can use statistical smoothing techniques to obtain robust estimates of rates by sharing information between strata.\n\n2.2.1 Disease mapping methods\nIn small-area studies, it is common to smooth data using models with explicit spatial dependence, which are designed to give more weight to nearby areas than those further away. There are three main categories for modelling spatial effects. First, we can treat space as a continuous surface using Gaussian processes or splines. Second, we can use areal models, which make use of the spatial neighbourhood structure of the units. Thirdly, we can explicitly build effects based on a nested hierarchy of geographical units, for example between state, county and census tract in the US. Each of these methods rely on assumptions which may make them more or less appropriate in different applications.\n\nSpace as a continuous process\nIn the context of disease mapping, events are usually aggregated to areas rather than assigned specific geographical coordinates. Wakefield and Elliott (1999) model aggregated counts as realisations of a Poisson process, in which the expected number of cases is calculated by integrating a continuous surface that generates the cases over the area of the spatial unit. The surface was a function of spatially-referenced covariates. Kelsall and Wakefield (2002) describe an alternative model, where the log-transformed risk surface is modelled by a Gaussian process, whose correlation function depends on distance.\nBest et al. (2005) provide a review of the use of hierarchical models with spatial dependence for disease mapping. In particular, the authors focus on Bayesian estimation, and different classes of spatial prior distributions.\nThe first prior proposed for spatial effects \\(\\mathbf{S} = {S_1, ..., S_n}\\) is the multivariate normal \\[\n\\mathbf{S} \\sim \\mathcal{N}(\\pmb{\\mu}, \\pmb{\\Sigma}),\n\\tag{2.1}\\]\nwhere \\(\\pmb{\\mu}\\) is the mean effect vector, \\(\\pmb{\\Sigma} = \\sigma^2 \\pmb{\\Omega}\\) and \\(\\pmb{\\Omega}\\) is a symmetric, positive semi-definite matrix defining the correlation between spatial units. A common choice when specifying the structure of the correlation matrix is to assume a function that decays with the distance between the centroids of the areas, so that places nearby in space share similar disease profiles. Note, this is mathematically equivalent to the practical implementation of a Gaussian process, which uses a finite set of points. An example in Elliott et al. (2001b) chooses an exponential decay function to map cancer risk in northwest England.\n\n\nSpace as discrete units\nA more popular prior is the conditional autoregressive (CAR) prior, also known as a Gaussian Markov random field (GMRF), which was first introduced by Besag et al. (1991). These form a joint distribution as in Equation 2.1, but the covariance is usually defined instead in terms of the precision matrix \\[\n\\mathbf{P} = \\pmb{\\Sigma}^{-1} = \\tau(\\mathbf{D} - \\rho \\mathbf{A}),\n\\tag{2.2}\\] where \\(\\tau\\) controls the overall precision of the effects, \\(\\mathbf{A}\\) is the spatial adjacency matrix formed by the small areas, \\(\\mathbf{D}\\) is a diagonal matrix with entries equal to the number of neighbours for each spatial unit, and the autocorrelation parameter \\(\\rho\\) describes the amount of correlation. This can be seen as tuning the degree of spatial dependence, where \\(\\rho = 0\\) implies independence between areas, and \\(\\rho = 1\\) full dependence. The case with \\(\\rho = 1\\) is called the intrinsic conditional autoregressive (ICAR) model. There sometimes exists further overdispersion in the residuals that cannot be modelled by purely spatially-structured random effects. Besag et al. (1991) proposed the model (hereafter called BYM) \\[\nS_i = U_i + V_i,\n\\tag{2.3}\\] where \\(U_i\\) follow an ICAR distribution, and \\(V_i\\) are independent and identically distributed random effects. The addition of the spatially-unstructured component \\(V\\) accounts for any non-spatial heterogeneity.\n\n\nSpace as a nested hierarchy of geographies\nThe relationships between different levels of a hierarchy of geographical units are often incorporated into models as a nested hierarchy of random effects. These models account for when spatial units lie within common administrative boundaries. This is often a desirable property of the model for certain geographies, like states in the US, which are administrative. Policy is decided at these geographies, so there is reason to believe these boundaries may have a greater effect on health outcomes than spatial structure. Finucane et al. (2014) demonstrate how country-level blood pressure can be modelled by exploiting the hierarchy global, super-region, region and country. Note, although these models group by geographical region, these models are not spatial as they do not contain any information on the relative position of the areas.\nOf the two specifications that are spatial, either as a continuous process or discrete units, the Markov random field priors are often preferred for computational reasons, as we can exploit the sparseness of the adjacency matrix in our inference algorithms rather than computing the covariance between each pair of spatial units as in the general case of Equation 2.1. There are concerns, however, that the GMRF representation of space as an adjacency matrix, which was originally proposed for a regular lattice of pixels in image analysis (Besag et al., 1991), is reductive for more complicated spatial problems. Despite this, in an epidemiological context, Duncan et al. (2017) found the standard ICAR model with binary, first-order neighbour weights outperformed models with a variety of different weighting schemes, including matrix weights based on higher-order degrees of neighbours, distance between neighbours, and distance between covariate values.\nIn applications to disease mapping, spatial models are the natural choice when the disease exhibits a spatial pattern. This is the case for mortality from infectious diseases, particularly on short timescales like Covid-19 (Konstantinoudis et al., 2022). Nested hierarchies are a more suitable choice when administrative areas are meaningful and have an effect on the health outcomes of the population. For example, state-specific abortion laws in the USA could affect maternal mortality, and so a model should include an effect for each state.\n\n\nModelling variation beyond space\nAs computational power has improved, it has become feasible to model patterns over other features of the population, such as time period and age group. Trends over time can be modelled as linear through slopes, or using nonlinear effects which allow neighbouring time points to be alike, the simplest of which is a first-order Gaussian random walk process. All-cause mortality varies smoothly over ages, following a characteristic J-shape with higher mortality in the infant and older age groups (Preston et al., 2001), and therefore can be modelled using a nonlinear process such as a random walk.\nDifficulties arise when considering interactions between the space, age, and time variables. One can imagine situations in which different spatial units will have different age patterns in disease rates, for example, if the certain age groups were vaccinated against disease in that spatial unit before others. After implementing a base model with the main effects, the question is how to model additional terms which account for the interactions between the variables. Space-time interactions could range from fully independent, to each spatial unit having independent temporal patterns, to inseparable space-time variation where interactions borrow strength across neighbouring spatial units and neighbouring time periods (Knorr-Held, 2000).\nHowever, it should be considered that by breaking the population down into smaller and smaller subgroups through space, age and time period, the counts of cases become more sparse and there is a need for stronger smoothing to produce robust estimates, particular for data that are already at the small-area level. Although interaction effects are plausible, modellers should consider whether there evidence for the interaction in the data or whether they can simplify the model if the interaction effect turns out to be negligible.\nIt should be noted that there are situations where statistical smoothing would not be appropriate. There might be true variability in the data which a smoothing model would conceal. For example, the Grenfell Tower fire in 2017 was a localised event that affected mortality. Without accounting for this event, the models described above would either attenuate its effect on mortality, or the spike in mortality would cause estimates of mortality in nearby spatial units or years to be erroneously high.\n\n\n\n2.2.2 Applications of disease mapping methods\n\nSmall-area analyses of mortality\nIn order to compare the health status between areas, health authorities require a measure of mortality that collapses age-specific information into a single number. Indirectly standardised measures such as the standardised mortality ratio – the ratio between total deaths and expected deaths in an area – are easy to calculate, but are not easily understood by laypeople. Directly standardised methods, in contrast, require knowledge of the full age structure of death rates rather than just the total number of deaths. Age-standardised death rates, however, suffer the same interpretability issue as the standardised mortality ratio, and are only comparable between studies if the same reference population is used. An alternative choice is life expectancy. Silcocks et al. (2001) explain that life expectancy is a “more intuitive and immediate measure of the mortality experience of a population, [and] is likely to have greater impact… than other measures that are incomprehensible to most people.”\nThe estimation of death rates requires two data sources: deaths counts and populations. Modern death registration systems are complete and accurate. On the other hand, although usually treated as a known quantity, the population denominator is often problematic. Populations for small geographies are only recorded during a decennial census, and estimates are generated for the years in-between using limited survey data on births, deaths and migration. And although the census is considered the “gold standard”, it is subject to enumeration errors, particularly for areas with special populations such as students or armed forces (Elliott et al., 2001b).\nBeyond the population issue, finer scale studies are restricted by data availability. Where data are available, there is still the need to overcome small number issues before feeding death rates through the life table to calculate life expectancy. Eayres and Williams (2004) recommend a minimum population size of 5000 when using traditional life table methods, below which the calculation of life expectancy is unstable1, or the error estimates become so large that any comparison between subgroups becomes meaningless. One approach, often taken by statistical agencies, is to build larger populations by either aggregating multiple years of data (Bahk et al., 2020; Office for National Statistics, 2015; Public Health England, 2021) or combining spatial units (Ezzati et al., 2008). Here, we focus on studies using Bayesian hierarchical models to generate robust estimates of age-specific death rates by recognising the correlations between spatial units and age groups, which produce more accurate estimates for small population studies of life expectancy (Congdon, 2009; Jonker et al., 2012).\nJonker et al. (2012) demonstrated the advantages of the Bayesian approach for 89 small areas in Rotterdam using a joint model for sex, space and age effects, finding a 8.2 year and 9.2 year gap between the neighbourhoods with the highest and lowest life expectancies for women and men. Stephens et al. (2013) employed the same model for 153 administrative areas in New South Wales, Australia.\nBayesian spatial models for mortality have been scaled to small areas for entire countries, and also consider trends in these regions over time. Bennett et al. (2015) forecasted life expectancy for 375 districts in England and Wales using a spatiotemporal model trained over a 31 year period, and Dwyer-Lindgren et al. (2017a) explored mortality trends 3110 US counties from 1980 to 2014.\nThere have also been studies on specific cities at a finer resolution. In order to improve estimates for disability-free life expectancy, Congdon (2014) considered both ill-health and mortality in a joint likelihood with spatial effects for 625 wards in London, finding more than a two-fold variation in the percent of life spent in disability for men. Bilal et al. (2019) looked at 266 subcity units for six large cities in Latin America. As there is no contiguous boundary in this case, a random effects model for each city was used instead of a spatial model. The largest difference between the top and bottom decile of life expectancy at birth was 17.7 years for women in Santiago, Chile.\nTwo studies in North America have looked below the county level, at census tracts, with wide-ranging population sizes as small as 40. Dwyer-Lindgren et al. (2017b), using a model that relied heavily on sociodemographic covariates, studied trends for life expectancy and many causes of death for 397 tracts in King County, Washington, uncovering an 18.3 year gap in life expectancy for men. Using the same model for Vancouver, Canada, Yu et al. (2021) found widening inequalities over time and a difference of 9.5 years for men.\n\n\nSmall Area Health Statistics Unit\nIn 1983, a documentary on the fallout from a fire at the Sellafield nuclear site in Cumbria claimed that there was a ten-fold increase in cases of childhood leukaemia in the surrounding community. This anomaly had gone undetected by public health authorities, raising concern that routinely collected data were not able to identify local clusters of disease. The subsequent enquiry confirmed the excess, and recommended that a research unit was set up to monitor small-area statistics and respond quickly to ad hoc queries on local health hazards. The Small Area Health Statistics Unit (SAHSU) was established in 1987 (Elliott et al., 1992).\nBeyond producing substantive research on environment and health, a core aim of SAHSU is to develop small-area statistical methodology (Wakefield and Elliott, 1999) for:\n\nPoint source type studies. Is there an increased risk close to an environmental hazard? SAHSU has investigated increased mortality from mesothelioma and asbestosis near Plymouth docks (Elliott et al., 1992); excess respiratory disease mortality near two factories in Barking and Havering (Aylin et al., 1999); kidney disease mortality near chemical plants in Runcorn (Hodgson et al., 2004); possible excess of several morbidities near landfill sites (Elliott et al., 2001a; Jarup et al., 2007, 2002b).\nGeographic correlation studies. Is there a correlation between disease risk and spatially-varying environmental variables? SAHSU have looked at several exposures, including a plume of mercury pollution (Hodgson et al., 2007); mobile phone base stations during pregnancy (Elliott et al., 2010); noise from aircraft near Heathrow (Hansell et al., 2013); road traffic noise in London (Halonen et al., 2015); particulate matter from incinerators during pregnancy (Parkes et al., 2020).\nClustering. Does a disease produce non-random spatial patterns of incidence? If the aetiology is unknown, this could suggest the disease is infectious.\nDisease mapping. Summarising the spatial variation in risk.\n\nSAHSU has been at the forefront of both methodology and applications in disease mapping. Aylin et al. (1999) mapped diseases for wards in Kensington, Chelsea and Westminster using a simple model that smoothed rates towards the mean risk across the region. Thereafter, SAHSU published a plethora of studies for disease mapping models with explicit spatial dependence, including using the BYM model (Equation 2.3) to map spatial variation in the relative risk of testicular (Toledano et al., 2001) and prostate (Jarup et al., 2002a) cancers for small areas in regions of England. In a landmark piece bringing together work on disease mapping and environmental exposures, SAHSU published an environment and health atlas for England and Wales, showing the spatial patterns of 14 health conditions at census ward level over an aggregated 25 year period alongside five environmental exposure surfaces (Hansell, Anna L. et al., 2014).\nFurther disease mapping studies at SAHSU using spatially structured effects have also extended the methodology to look at age patterns and trends over time. Asaria et al. (2012) analysed cardiovascular disease death rates by fitting a spatial model for all wards in England separately for each age group and time period. Bennett et al. (2015) designed a model to jointly forecast all-cause mortality for districts in England, age groups and years. The model used BYM spatial effects and random walk effects over age and time to capture nonlinear relationships."
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- "text": "4.5 Clean code and open source\nI have paid a lot of attention to open sourcing code for all analyses during my PhD. The code is clean, version-controlled and follows best practices for scientific software engineering. As well as code contributed to open source projects along the way, the code for statistical models, plots and analysis, and the thesis itself can be found on GitHub.\n\n\n\n\nde Valpine P, Paciorek CJ, Turek D, Michaud N, Anderson-Bergman C, Obermayer F, Wehrhahn Cortes C, Rodrìguez A, Lang DT, Paganin S, Hug J. 2022. NIMBLE: MCMC, Particle Filtering, and Programmable Hierarchical Modeling.\n\n\nde Valpine P, Turek D, Paciorek CJ, Anderson-Bergman C, Lang DT, Bodik R. 2017. Programming With Models: Writing Statistical Algorithms for General Model Structures With NIMBLE. Journal of Computational and Graphical Statistics 26:403–413. doi:10.1080/10618600.2016.1172487\n\n\nHoffman MD, Gelman A. 2014. The No-U-Turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research 15:1593–1623. doi:10.48550/arXiv.1111.4246\n\n\nLao J, Suter C, Langmore I, Chimisov C, Saxena A, Sountsov P, Moore D, Saurous RA, Hoffman MD, Dillon JV. 2020. Tfp.mcmc: Modern Markov Chain Monte Carlo Tools Built for Modern Hardware. doi:10.48550/arXiv.2002.01184\n\n\nMcElreath R. 2020. Statistical Rethinking, 2nd ed. CRC Press.\n\n\nNumPyro documentation. 2023. CAR distribution. NumPyro.\n\n\nPhan D, Pradhan N, Jankowiak M. 2019. Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro. doi:10.48550/arXiv.1912.11554\n\n\nRashid T. 2022. Probabilistic-programming-packages. GitHub.\n\n\nRoberts GO, Rosenthal JS. 2004. General state space Markov chains and MCMC algorithms. Probability Surveys 1:20–71. doi:10.1214/154957804100000024"
+ "text": "4.5 Clean code and open source\nI have paid a lot of attention to open sourcing code for all analyses during my PhD. The code is clean, version-controlled, and follows best practices for scientific software engineering. As well as code contributed to open source projects along the way, the code for statistical models, plots and analysis, and the thesis itself can be found on GitHub.\n\n\n\n\nde Valpine P, Paciorek CJ, Turek D, Michaud N, Anderson-Bergman C, Obermayer F, Wehrhahn Cortes C, Rodrìguez A, Lang DT, Paganin S, Hug J. 2022. NIMBLE: MCMC, Particle Filtering, and Programmable Hierarchical Modeling.\n\n\nde Valpine P, Turek D, Paciorek CJ, Anderson-Bergman C, Lang DT, Bodik R. 2017. Programming With Models: Writing Statistical Algorithms for General Model Structures With NIMBLE. Journal of Computational and Graphical Statistics 26:403–413. doi:10.1080/10618600.2016.1172487\n\n\nHoffman MD, Gelman A. 2014. The No-U-Turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research 15:1593–1623. doi:10.48550/arXiv.1111.4246\n\n\nLao J, Suter C, Langmore I, Chimisov C, Saxena A, Sountsov P, Moore D, Saurous RA, Hoffman MD, Dillon JV. 2020. Tfp.mcmc: Modern Markov Chain Monte Carlo Tools Built for Modern Hardware. doi:10.48550/arXiv.2002.01184\n\n\nMcElreath R. 2020. Statistical Rethinking, 2nd ed. CRC Press.\n\n\nNumPyro documentation. 2023. CAR distribution. NumPyro.\n\n\nPhan D, Pradhan N, Jankowiak M. 2019. Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro. doi:10.48550/arXiv.1912.11554\n\n\nRashid T. 2022. Probabilistic-programming-packages. GitHub.\n\n\nRoberts GO, Rosenthal JS. 2004. General state space Markov chains and MCMC algorithms. Probability Surveys 1:20–71. doi:10.1214/154957804100000024"
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- "text": "9.1 Public health and policy implications of findings\nAlthough previous studies have observed a decline in female life expectancy in the bottom two deciles of deprivation in the past decade (Bennett et al., 2018; Marmot et al., 2020), this thesis has shown both for men and women where the declines have been happening for small areas. Not only have there been declines, but the declines have been accelerating in the latter half of the decade, such that in the period 2014-19, life expectancy fell 1 in 5 MSOAs for women and 1 in 9 for men. These trends happened in the years before the mortality-forcing event of the Covid-19 pandemic and are worse than comparable countries (Leon et al., 2019), and should be deemed a failure for public health policy. Although the complexity of policy means it cannot be proved causally, leaders within the NHS have pointed towards constrained funding for the healthcare body itself, as well as cuts to wider social determinants, such as housing and education, as the main reason for the country’s poor performance (Ham, 2023).\nThe declines in life expectancy were sustained over a long period of time, which serves as another example where death rates for some population subgroups run contrary to the persistent mortality decline of the third stage of the Epidemiologic Transition theory, as discussed in Gaylin and Kates (1997) with the HIV/AIDS pandemic. And even if England is in the hypothesised fourth stage of the transition, the Age of Delayed Degenerative diseases (Olshansky and Ault, 1986), there are subnational patterns where degenerative diseases are not killing at later and later ages. The difference in progress between districts in the last decade was largely driven by differences in these degenerative diseases. In particular, the rate of improvement for CVDs and all other NCDs, and the strength of the negative forcing effect of Alzheimer’s and other dementias. Furthermore, female mortality from infectious, maternal, perinatal and nutritional conditions (GBD group 1), which dominate the second stage of the transition, increased in many districts. There is also worrying shift towards injuries (GBD group 3) contributing negatively towards life expectancy progress, particularly for men. This is possibly driven by a rise in “deaths of despair” (Angus et al., 2023; Case and Deaton, 2015), although this would require further analysis by stratifying into intentional and unintentional injuries. It should be noted that IMPN and injuries do not play a major role in total mortality as they accounted for only 11.1% of all deaths from 2002 to 2019, but they are almost entirely preventable and should be addressed through appropriate policy.\nCancer survival outcomes in the UK are worse than those in Europe in general (OECD, 2016). In this thesis, I found mortality showed huge spatial variation for a number of preventable cancers. Worryingly, at the same level of poverty, London performed significantly better that the rest of the country for several cancers. This suggests either regional differences in the quality of care, or differences in the populations living in deprived areas, which should both be the subject for policy discussions.\nFinally, this thesis emphasises the value of small area work in informing policy. National trends in mortality are not spatially homogenous. Particular diseases have shown massive variation at the district level, such as COPD in women (6.0-fold in 2019), and by studying England at the MSOA level, I have uncovered the widest subnational gap in life expectancy of 27.0 years (men in 2019) in the literature. This rich source of data allows policy makers to work with local authorities to create targeted public health interventions. The population issues at the LSOA level in London and the coding of CVDs on the Isle of Wight show there are still limitations of the data. Nevertheless, the estimates from this thesis are already being used in the press to provide context for recent falls in US life expectancy (Burn-Murdoch, 2023), and I hope they are also being discussed by policymakers."
+ "text": "9.1 Public health and policy implications of findings\nAlthough previous studies have observed a decline in female life expectancy in the bottom two deciles of deprivation in the past decade (Bennett et al., 2018; Marmot et al., 2020), this thesis has shown both for men and women where the declines have been happening for small areas. Not only have there been declines, but the declines have been accelerating in the latter half of the decade, such that in the period 2014-19, life expectancy fell 1 in 5 MSOAs for women and 1 in 9 for men. These trends happened in the years before the mortality-forcing event of the Covid-19 pandemic and are worse than comparable countries (Leon et al., 2019), and should be deemed a failure for public health policy. Although the complexity of policy means it cannot be proved causally, leaders within the NHS have pointed towards constrained funding for the healthcare body itself, as well as cuts to wider social determinants, such as housing and education, as the main reason for the country’s poor performance (Ham, 2023).\nThe declines in life expectancy were sustained over a long period of time, which serves as another example where death rates for some population subgroups run contrary to the persistent mortality decline of the third stage of the Epidemiologic Transition theory, as discussed in Gaylin and Kates (1997) with the HIV/AIDS pandemic. And even if England is in the hypothesised fourth stage of the transition, the Age of Delayed Degenerative diseases (Olshansky and Ault, 1986), there are subnational patterns where degenerative diseases are not killing at later and later ages. The difference in progress between districts in the last decade was largely driven by differences in these degenerative diseases. In particular, the rate of improvement for CVDs and all other NCDs, and the strength of the negative forcing effect of Alzheimer’s and other dementias. Furthermore, female mortality from infectious, maternal, perinatal and nutritional conditions (GBD group 1), which dominate the second stage of the transition, increased in many districts. There is also worrying shift towards injuries (GBD group 3) contributing negatively towards life expectancy progress, particularly for men. This is possibly driven by a rise in “deaths of despair” (Angus et al., 2023; Case and Deaton, 2015), although this would require further analysis by separating intentional and unintentional injuries. It should be noted that IMPN and injuries do not play a major role in total mortality as they accounted for only 11.1% of all deaths from 2002 to 2019, but they are almost entirely preventable and should be addressed through appropriate policy.\nCancer survival outcomes in the UK are worse than those in Europe in general (OECD, 2016). In this thesis, I found mortality showed huge spatial variation for a number of preventable cancers. Worryingly, at the same level of poverty, London performed significantly better that the rest of the country for several cancers. This suggests either regional differences in the quality of care, or differences in the populations living in deprived areas, which should both be the subject for policy discussions.\nFinally, this thesis emphasises the value of small area work in informing policy. National trends in mortality are not spatially homogenous. Particular diseases have shown massive variation at the district level, such as COPD in women (6.0-fold in 2019), and by studying England at the MSOA level, I have uncovered the widest subnational gap in life expectancy of 27.0 years (men in 2019) in the literature. This rich source of data allows policymakers to work with local authorities to create targeted public health interventions. The population issues at the LSOA level in London and the coding of CVDs on the Isle of Wight show there are still limitations of the data. Nevertheless, the estimates from this thesis are already being used in the press to provide context for recent falls in US life expectancy (Burn-Murdoch, 2023), and I hope they are also being used in policy discussions."
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- "text": "9.2 Future work\nThere are many possible substantive and methodological extensions to the work presented in this thesis. Firstly, on the substantive side, there is a reason the final year of study period was restricted at 2019 that has nothing to do with the availability of vital registration data for the proceeding years: the Covid-19 pandemic. It would be naïve to fit the same model to an extended time period that includes the pandemic years because the pandemic had such a major influence on mortality patterns. The model relies heavily on linear trends, which would be affected by the final years. Further, pandemics are fat-tailed events, so the Gaussian random walk effects would struggle to capture the shock without increasing the overall variance of the effect.\nRather than extending the study to include the pandemic years and look at the trends between 2002 and 2023, a more interesting question is “had the pandemic not happened, how would mortality patterns be different?” This would be done using a counterfactual analysis: train a model to estimate annual mortality from 2002 to 2019 and produce a forecast for the years from 2020. A team, including myself, has already done this analysis at the national level at a weekly temporal resolution (Kontis et al., 2022, 2020). Here, the task would instead involve forecasts for each sex-age-space-time-cause stratum on annual timescales. The group has been involved in a number of mortality forecasting projects (Bennett et al., 2015; Foreman et al., 2017; Kontis et al., 2017). The models are similar to those in this thesis, but would need to be adapted and trained specifically for forecasting purposes, with the possibility of averaging multiple models to reduce bias. The results would allow us to see how the cause-composition of mortality has changed compared to the business as usual scenario. We would obviously expect and increase in deaths infectious disease, but were injuries reduced as the country was locked down in their homes? Did cancer outcomes worsen due to missed surgeries as hospitals were flooded with Covid-19 patients? Is there a longer term effect due to strain on emergency services, which has manifested in longer waiting lists and waiting times for appointments (Dorling, 2023)? And, how have these effects varied for different age groups and different areas of the country?\nIn theory, with improvements both to hardware and the rise of approximate inference algorithms to replace computationally costly sampling methods, the models can be scaled to higher and higher spatial resolutions and we could potentially estimate mortality for the entire country for LSOAs, OAs, or even postcodes. However, given the data issues in Chapter 5, perhaps bigger is not better when the quality of the data is lacking.\nOne of the major strengths of the thesis was the use of Bayesian methods, at one of the highest spatial resolutions in the literature for a model estimating mortality. This was largely thanks to recent developments in probabilistic programming, which allow sampling algorithms to run on GPUs rather than CPUs, and is generally faster for models with over 10,000 parameters (Lao et al., 2020). The models themselves, which were based on previous work in the group (Bennett et al., 2018, 2015), followed traditional statistical approaches using intercepts and linear slopes and adding in random walk effects for nonlinearities. However, with models such as Equation 4.4, we are actually only interested in the left-hand side of the equation – the death rate – and not at all in the values of the parameters on the right-hand side. There are a vast array of flexible models which can describe complex data without needing to design heavily parametrised structures. These range from Gaussian processes (Flaxman et al., 2015; Rasmussen and Williams, 2006), where the user can use inductive biases and their own knowledge to influence how the model fits the data, to wilder options like neural networks, which completely sacrifice any remaining interpretability of the effects.\nDuring my PhD, I became very familiar with the literature on Gaussian processes, and was involved with a paper aimed at speeding up inference in spatial settings (Semenova et al., 2022). One of the most promising avenues for the task of mortality estimation in this thesis, outlined in Flaxman et al. (2015), is the use of Kronecker-structured covariance matrices to create hierarchical Gaussian processes. In the context of this thesis, the covariance matrix would be defined as the Kronecker product of three smaller matrices: one for age effects, one for spatial effects, and one for temporal effects. We can exploit the Kronecker structure for faster inference, as we no longer need to invert the full matrix (an operation that scales cubically with the number of data points), but rather the smaller constituent matrices of each effect. Ultimately, nothing came to fruition as the working environment due to the sensitivity of the data1 was not conducive to developing novel statistical methods. Also, there was no guarantee the Gaussian process methods would be quicker, as it still requires the inversion of a large spatial matrix, nor would it produce a result much different from the original model. Instead, I allocated time to scaling existing models and testing new hardware. I believe the hierarchical Gaussian process model should be the starting point for future research because it is much more flexible and requires less testing of each effect than the models in this thesis.\nAnother methodological extension would be to model causes of death jointly, thereby borrowing strength across causes. Studies have built spatial models which use shared components between diseases, either modelling spatial patterns of any number of diseases using a weighted sum of shared components (Best et al., 2005; Held et al., 2005; Knorr-Held and Best, 2001) or pre-assigning the spatial components to the diseases based on knowledge of common risk factors (Downing et al., 2008; Mahaki et al., 2018). However, as the number of diseases in the study increases, more spatial components must be fitted, which is computationally prohibitive. Furthermore, unless the spatial components are defined a priori, there is a question of how many spatial components are required to parsimoniously describe the variance in the data. Alternatively, the correlations between the causes can be modelled using a multivariate normal distribution of the same dimensions as the number of cause groups, as in Foreman et al. (2017). Extending this idea, there is also the option to extend the hierarchical Gaussian process described above with another component covariance matrix describing the correlations between each of the cause groups. Ultimately, the goal would be to run a single joint model that flexibly describes interactions between sexes, age groups, spatial units, time, and causes of death.\n\n\n\n\n\nAngus C, Buckley C, Tilstra AM, Dowd JB. 2023. Increases in “deaths of despair” during the COVID-19 pandemic in the United States and the United Kingdom. Public Health 218:92–96. doi:10.1016/j.puhe.2023.02.019\n\n\nBennett JE, Li G, Foreman K, Best N, Kontis V, Pearson C, Hambly P, Ezzati M. 2015. The future of life expectancy and life expectancy inequalities in England and Wales: Bayesian spatiotemporal forecasting. The Lancet 386:163–170. doi:10.1016/S0140-6736(15)60296-3\n\n\nBennett JE, Pearson-Stuttard J, Kontis V, Capewell S, Wolfe I, Ezzati M. 2018. Contributions of diseases and injuries to widening life expectancy inequalities in England from 2001 to 2016: A population-based analysis of vital registration data. The Lancet Public Health 3:e586–e597. doi:10.1016/S2468-2667(18)30214-7\n\n\nBest N, Richardson S, Thomson A. 2005. A comparison of Bayesian spatial models for disease mapping. Statistical Methods in Medical Research 14:35–59. doi:10.1191/0962280205sm388oa\n\n\nBurn-Murdoch J. 2023. Why are Americans dying so young? Financial Times.\n\n\nCase A, Deaton A. 2015. Rising morbidity and mortality in midlife among white non-Hispanic Americans in the 21st century. Proceedings of the National Academy of Sciences 112:15078–15083. doi:10.1073/pnas.1518393112\n\n\nDorling D. 2023. How austerity caused the NHS crisis. openDemocracy.\n\n\nDowning A, Forman D, Gilthorpe MS, Edwards KL, Manda SO. 2008. Joint disease mapping using six cancers in the Yorkshire region of England. International Journal of Health Geographics 7:41. doi:10.1186/1476-072X-7-41\n\n\nFlaxman S, Gelman A, Neill D, Smola A, Vehtari A, Wilson AG. 2015. Fast hierarchical Gaussian processes.\n\n\nForeman KJ, Li G, Best N, Ezzati M. 2017. Small area forecasts of cause-specific mortality: Application of a Bayesian hierarchical model to US vital registration data. Journal of the Royal Statistical Society Series C (Applied Statistics) 66:121–139. doi:10.1111/rssc.12157\n\n\nGaylin DS, Kates J. 1997. Refocusing the lens: Epidemiologic transition theory, mortality differentials, and the AIDS pandemic. Social Science & Medicine 44:609–621. doi:10.1016/S0277-9536(96)00212-2\n\n\nHam C. 2023. The Rise and Decline of the NHS in England 2000-20. The King’s Fund.\n\n\nHeld L, Natário I, Fenton SE, Rue H, Becker N. 2005. Towards joint disease mapping. Statistical Methods in Medical Research 14:61–82. doi:10.1191/0962280205sm389oa\n\n\nKnorr-Held L, Best NG. 2001. A Shared Component Model for Detecting Joint and Selective Clustering of Two Diseases. Journal of the Royal Statistical Society Series A (Statistics in Society) 164:73–85.\n\n\nKontis V, Bennett JE, Mathers CD, Li G, Foreman K, Ezzati M. 2017. Future life expectancy in 35 industrialised countries: Projections with a Bayesian model ensemble. The Lancet 389:1323–1335. doi:10.1016/S0140-6736(16)32381-9\n\n\nKontis V, Bennett JE, Parks RM, Rashid T, Pearson-Stuttard J, Asaria P, Zhou B, Guillot M, Mathers CD, Khang Y-H, McKee M, Ezzati M. 2022. Lessons learned and lessons missed: Impact of the coronavirus disease 2019 (COVID-19) pandemic on all-cause mortality in 40 industrialised countries and US states prior to mass vaccination. Wellcome Open Research 6:279. doi:10.12688/wellcomeopenres.17253.2\n\n\nKontis V, Bennett JE, Rashid T, Parks RM, Pearson-Stuttard J, Guillot M, Asaria P, Zhou B, Battaglini M, Corsetti G, McKee M, Di Cesare M, Mathers CD, Ezzati M. 2020. Magnitude, demographics and dynamics of the effect of the first wave of the COVID-19 pandemic on all-cause mortality in 21 industrialized countries. Nature Medicine 26:1919–1928. doi:10.1038/s41591-020-1112-0\n\n\nLao J, Suter C, Langmore I, Chimisov C, Saxena A, Sountsov P, Moore D, Saurous RA, Hoffman MD, Dillon JV. 2020. Tfp.mcmc: Modern Markov Chain Monte Carlo Tools Built for Modern Hardware. doi:10.48550/arXiv.2002.01184\n\n\nLeon DA, Jdanov DA, Shkolnikov VM. 2019. Trends in life expectancy and age-specific mortality in England and Wales, 1970, in comparison with a set of 22 high-income countries: An analysis of vital statistics data. The Lancet Public Health 4:e575–e582. doi:10.1016/S2468-2667(19)30177-X\n\n\nMahaki B, Mehrabi Y, Kavousi A, Schmid VJ. 2018. Joint Spatio-temporal Shared Component Model with an Application in Iran Cancer Data. Asian Pacific Journal of Cancer Prevention 19:1553–1560. doi:10.22034/APJCP.2018.19.6.1553\n\n\nMarmot MG, Allen J, Boyce T, Goldblatt P, Morrison J. 2020. Marmot Review: 10 years on. Institute of Health Equity.\n\n\nOECD. 2016. OECD Reviews of Health Care Quality: United Kingdom 2016: Raising Standards. Paris: Organisation for Economic Co-operation and Development.\n\n\nOlshansky SJ, Ault AB. 1986. The Fourth Stage of the Epidemiologic Transition: The Age of Delayed Degenerative Diseases. The Milbank Quarterly 64:355–391. doi:10.2307/3350025\n\n\nRasmussen CE, Williams CKI. 2006. Gaussian Processes for Machine Learning. MIT Press.\n\n\nSemenova E, Xu Y, Howes A, Rashid T, Bhatt S, Mishra S, Flaxman S. 2022. PriorVAE: Encoding spatial priors with variational autoencoders for small-area estimation. Journal of The Royal Society Interface 19:20220094. doi:10.1098/rsif.2022.0094"
+ "text": "9.2 Future work\nThere are many possible substantive and methodological extensions to the work presented in this thesis. Firstly, on the substantive side, there is a reason the final year of study period was restricted at 2019 that has nothing to do with the availability of vital registration data for the proceeding years: the Covid-19 pandemic. It would be naïve to fit the same model to an extended time period that includes the pandemic years because the pandemic had such a major influence on mortality patterns. The model relies heavily on linear trends, which would be affected by the final years. Further, pandemics are fat-tailed events, so the Gaussian random walk effects would struggle to capture the shock without increasing the overall variance of the effect.\nRather than extending the study to include the pandemic years and look at the trends between 2002 and 2023, a more interesting question is “had the pandemic not happened, how would mortality patterns be different?” This would be done using a counterfactual analysis: train a model to estimate annual mortality from 2002 to 2019 and produce a forecast for the years from 2020. A team, including myself, has already done this analysis at the national level at a weekly temporal resolution (Kontis et al., 2022, 2020). Here, the task would instead involve forecasts for each sex-age-space-time-cause stratum on annual timescales. The group has been involved in a number of mortality forecasting projects (Bennett et al., 2015; Foreman et al., 2017; Kontis et al., 2017). The models are similar to those in this thesis, but would need to be adapted and trained specifically for forecasting purposes, with the possibility of averaging multiple models to reduce bias. The results would allow us to see how the cause-composition of mortality has changed compared to the business as usual scenario. We would obviously expect and increase in deaths infectious disease, but were injuries reduced as the country was locked down in their homes? Did cancer outcomes worsen due to missed surgeries as hospitals were flooded with Covid-19 patients? Is there a longer term effect due to strain on emergency services, which has manifested in longer waiting lists and waiting times for appointments (Dorling, 2023)? And, how have these effects varied for different age groups and different areas of the country?\nIn theory, with improvements both to hardware and the rise of approximate inference algorithms to replace computationally costly sampling methods, the models can be scaled to higher and higher spatial resolutions and we could potentially estimate mortality for the entire country for LSOAs, OAs, or even postcodes. However, given the data issues in Chapter 5, perhaps smaller is not better when the quality of the data is lacking.\nOne of the major strengths of the thesis was the use of Bayesian methods, at one of the highest spatial resolutions in the literature for a model estimating mortality. This was largely thanks to recent developments in probabilistic programming, which allow sampling algorithms to run on GPUs rather than CPUs, and is generally faster for models with over 10,000 parameters (Lao et al., 2020). The models themselves, which were based on previous work in the group (Bennett et al., 2018, 2015), followed traditional statistical approaches using intercepts and linear slopes and adding in random walk effects for nonlinearities. However, with models such as Equation 4.4, we are actually only interested in the left-hand side of the equation – the death rate – and not at all in the values of the parameters on the right-hand side. There are a vast array of flexible models which can describe complex data without needing to design heavily parametrised structures. These range from Gaussian processes (Flaxman et al., 2015; Rasmussen and Williams, 2006), where the user can use inductive biases and their own knowledge to influence how the model fits the data, to wilder options like neural networks, which completely sacrifice any remaining interpretability of the effects.\nDuring my PhD, I became very familiar with the literature on Gaussian processes, and was involved with a paper aimed at speeding up inference in spatial settings (Semenova et al., 2022). One of the most promising avenues for the task of mortality estimation in this thesis, outlined in Flaxman et al. (2015), is the use of Kronecker-structured covariance matrices to create hierarchical Gaussian processes. In the context of this thesis, the covariance matrix would be defined as the Kronecker product of three smaller matrices: one for age effects, one for spatial effects, and one for temporal effects. We can exploit the Kronecker structure for faster inference, as we no longer need to invert the full matrix (an operation that scales cubically with the number of data points), but rather the smaller constituent matrices of each effect. Ultimately, nothing came to fruition as the working environment due to the sensitivity of the data1 was not conducive to developing novel statistical methods. Also, there was no guarantee the Gaussian process methods would be quicker, as it still requires the inversion of a large spatial matrix, nor would it produce a result much different from the original model. Instead, I allocated time to scaling existing models and testing new hardware. I believe the hierarchical Gaussian process model should be the starting point for future research because it is much more flexible and requires less testing of each effect than the models in this thesis.\nAnother methodological extension would be to model causes of death jointly, thereby borrowing strength across causes. Studies have built spatial models which use shared components between diseases, either modelling spatial patterns of any number of diseases using a weighted sum of shared components (Best et al., 2005; Held et al., 2005; Knorr-Held and Best, 2001) or pre-assigning the spatial components to the diseases based on knowledge of common risk factors (Downing et al., 2008; Mahaki et al., 2018). However, as the number of diseases in the study increases, more spatial components must be fitted, which is computationally prohibitive. Furthermore, unless the spatial components are defined a priori, there is a question of how many spatial components are required to parsimoniously describe the variance in the data. Alternatively, the correlations between the causes can be modelled using a multivariate normal distribution of the same dimensions as the number of cause groups, as in Foreman et al. (2017). Extending this idea, there is also the option to extend the hierarchical Gaussian process described above with another component covariance matrix describing the correlations between each of the cause groups. Ultimately, the goal would be to run a single joint model that flexibly describes interactions between sexes, age groups, spatial units, time, and causes of death.\n\n\n\n\n\nAngus C, Buckley C, Tilstra AM, Dowd JB. 2023. Increases in “deaths of despair” during the COVID-19 pandemic in the United States and the United Kingdom. Public Health 218:92–96. doi:10.1016/j.puhe.2023.02.019\n\n\nBennett JE, Li G, Foreman K, Best N, Kontis V, Pearson C, Hambly P, Ezzati M. 2015. The future of life expectancy and life expectancy inequalities in England and Wales: Bayesian spatiotemporal forecasting. The Lancet 386:163–170. doi:10.1016/S0140-6736(15)60296-3\n\n\nBennett JE, Pearson-Stuttard J, Kontis V, Capewell S, Wolfe I, Ezzati M. 2018. Contributions of diseases and injuries to widening life expectancy inequalities in England from 2001 to 2016: A population-based analysis of vital registration data. The Lancet Public Health 3:e586–e597. doi:10.1016/S2468-2667(18)30214-7\n\n\nBest N, Richardson S, Thomson A. 2005. A comparison of Bayesian spatial models for disease mapping. Statistical Methods in Medical Research 14:35–59. doi:10.1191/0962280205sm388oa\n\n\nBurn-Murdoch J. 2023. Why are Americans dying so young? Financial Times.\n\n\nCase A, Deaton A. 2015. Rising morbidity and mortality in midlife among white non-Hispanic Americans in the 21st century. Proceedings of the National Academy of Sciences 112:15078–15083. doi:10.1073/pnas.1518393112\n\n\nDorling D. 2023. How austerity caused the NHS crisis. openDemocracy.\n\n\nDowning A, Forman D, Gilthorpe MS, Edwards KL, Manda SO. 2008. Joint disease mapping using six cancers in the Yorkshire region of England. International Journal of Health Geographics 7:41. doi:10.1186/1476-072X-7-41\n\n\nFlaxman S, Gelman A, Neill D, Smola A, Vehtari A, Wilson AG. 2015. Fast hierarchical Gaussian processes.\n\n\nForeman KJ, Li G, Best N, Ezzati M. 2017. Small area forecasts of cause-specific mortality: Application of a Bayesian hierarchical model to US vital registration data. Journal of the Royal Statistical Society Series C (Applied Statistics) 66:121–139. doi:10.1111/rssc.12157\n\n\nGaylin DS, Kates J. 1997. Refocusing the lens: Epidemiologic transition theory, mortality differentials, and the AIDS pandemic. Social Science & Medicine 44:609–621. doi:10.1016/S0277-9536(96)00212-2\n\n\nHam C. 2023. The Rise and Decline of the NHS in England 2000-20. The King’s Fund.\n\n\nHeld L, Natário I, Fenton SE, Rue H, Becker N. 2005. Towards joint disease mapping. Statistical Methods in Medical Research 14:61–82. doi:10.1191/0962280205sm389oa\n\n\nKnorr-Held L, Best NG. 2001. A Shared Component Model for Detecting Joint and Selective Clustering of Two Diseases. Journal of the Royal Statistical Society Series A (Statistics in Society) 164:73–85.\n\n\nKontis V, Bennett JE, Mathers CD, Li G, Foreman K, Ezzati M. 2017. Future life expectancy in 35 industrialised countries: Projections with a Bayesian model ensemble. The Lancet 389:1323–1335. doi:10.1016/S0140-6736(16)32381-9\n\n\nKontis V, Bennett JE, Parks RM, Rashid T, Pearson-Stuttard J, Asaria P, Zhou B, Guillot M, Mathers CD, Khang Y-H, McKee M, Ezzati M. 2022. Lessons learned and lessons missed: Impact of the coronavirus disease 2019 (COVID-19) pandemic on all-cause mortality in 40 industrialised countries and US states prior to mass vaccination. Wellcome Open Research 6:279. doi:10.12688/wellcomeopenres.17253.2\n\n\nKontis V, Bennett JE, Rashid T, Parks RM, Pearson-Stuttard J, Guillot M, Asaria P, Zhou B, Battaglini M, Corsetti G, McKee M, Di Cesare M, Mathers CD, Ezzati M. 2020. Magnitude, demographics and dynamics of the effect of the first wave of the COVID-19 pandemic on all-cause mortality in 21 industrialized countries. Nature Medicine 26:1919–1928. doi:10.1038/s41591-020-1112-0\n\n\nLao J, Suter C, Langmore I, Chimisov C, Saxena A, Sountsov P, Moore D, Saurous RA, Hoffman MD, Dillon JV. 2020. Tfp.mcmc: Modern Markov Chain Monte Carlo Tools Built for Modern Hardware. doi:10.48550/arXiv.2002.01184\n\n\nLeon DA, Jdanov DA, Shkolnikov VM. 2019. Trends in life expectancy and age-specific mortality in England and Wales, 1970, in comparison with a set of 22 high-income countries: An analysis of vital statistics data. The Lancet Public Health 4:e575–e582. doi:10.1016/S2468-2667(19)30177-X\n\n\nMahaki B, Mehrabi Y, Kavousi A, Schmid VJ. 2018. Joint Spatio-temporal Shared Component Model with an Application in Iran Cancer Data. Asian Pacific Journal of Cancer Prevention 19:1553–1560. doi:10.22034/APJCP.2018.19.6.1553\n\n\nMarmot MG, Allen J, Boyce T, Goldblatt P, Morrison J. 2020. Marmot Review: 10 years on. Institute of Health Equity.\n\n\nOECD. 2016. OECD Reviews of Health Care Quality: United Kingdom 2016: Raising Standards. Paris: Organisation for Economic Co-operation and Development.\n\n\nOlshansky SJ, Ault AB. 1986. The Fourth Stage of the Epidemiologic Transition: The Age of Delayed Degenerative Diseases. The Milbank Quarterly 64:355–391. doi:10.2307/3350025\n\n\nRasmussen CE, Williams CKI. 2006. Gaussian Processes for Machine Learning. MIT Press.\n\n\nSemenova E, Xu Y, Howes A, Rashid T, Bhatt S, Mishra S, Flaxman S. 2022. PriorVAE: Encoding spatial priors with variational autoencoders for small-area estimation. Journal of The Royal Society Interface 19:20220094. doi:10.1098/rsif.2022.0094"
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- "text": "Table D.1: Groups of causes of death used in the district-level cause-specific analysis in Chapter 7 with ICD-10 codes.\n\n\n\n\n\n\nCause\nICD-10 codes\n\n\n\n\nTrachea, bronchus and lung cancers\nC33-C34\n\n\nBreast cancer\nC50\n\n\nProstate cancer\nC61\n\n\nColorectal cancers\nC18-C21\n\n\nPancreatic cancer\nC25\n\n\nOvarian cancer\nC56\n\n\nLymphomas, multiple myeloma\nC81-C90, C96\n\n\nOesophageal cancer\nC15\n\n\nAll other cancers\nC00-C14, C16-C17, C22-C24, C26-C32, C37-C41, C43-C49, C51-C55, C57-C60, C62-C67, C68-C80, C91-C95, C97, D00-D48\n\n\nIschaemic heart disease\nI20-I25\n\n\nStroke\nI60-I69\n\n\nAll other CVDs\nI00-I19, I26-I59, I70-I99\n\n\nAlzheimer’s and other dementias\nF00-F03, G30\n\n\nCOPD\nJ40-44\n\n\nDiabetes mellitus, nephritis and nephrosis\nE10-14, N00-19\n\n\nLiver cirrhosis\nK70, K74\n\n\nAll other NCDs\nD55-D648, D65-D89, E03-E07, E15-E16, E20-E34, E65-E88, F01-F99, G06-G13, G15-G98, H00-H61, H68-H93, J30-J39, J45-J98, K00-K14, K20-K69, K71-K73, K75-K92, L00-L98, M00-M99, N20-64, N75-N99, Q00-Q99, R95, X41-X42, X45\n\n\nLower respiratory infections\nJ09-18, J20-J22\n\n\nAll other IMPN\nA00-99, B00-99, D50-53, D649, E00-E02, E40-46, E50-54, G00, G03-G04, G14, H65-H66, N70-N73, J00-J06, O00-O99, P00-P96, Z353\n\n\nInjuries\nU00-U01, U509, V00-V99, W00-W99, X00-X40, X43-X44, X46-X99, Y00-Y01, Y10-Y36, Y381, Y40-Y86, Y870-Y872, Y88-Y89\n\n\n\n\nOvarian cancer (women) and prostate cancer (men) are sex specific. The all other cancers group also includes breast cancer for men. Liver cirrhosis was not in the top 12 leading causes of death for women, so it was included within all other NCDs.\nThe residual groups (all other cancers, all other CVDs, all other NCDs, all other IMPN) also contained deaths from the “ill-defined diseases” GHE group (R00-R94, R96-R99, U07, U99). There were 196,055 deaths from ill-defined diseases. These were proportionately assigned between the residual groups.\nCauses of death with the ICD-10 code S00-S99 or T00-T99 are not valid underlying causes of death. These were all neonatal deaths, which are not assigned an underlying cause of death, and were imputing using the code in the first position on the death record. These deaths were classified as injuries.\n\n\nTable D.2: Groups of causes of death used in the district-level cancer analysis in Chapter 8 with ICD-10 codes.\n\n\n\n\n\n\nCancer\nICD-10 codes\n\n\n\n\nTrachea, bronchus and lung cancers\nC33-C34\n\n\nBreast cancer\nC50\n\n\nProstate cancer\nC61\n\n\nColorectal cancer\nC18-C21\n\n\nPancreatic cancer\nC25\n\n\nOvarian cancer\nC56\n\n\nLymphomas, multiple myeloma\nC81-C90, C96\n\n\nOesophageal cancer\nC15\n\n\nBladder cancer\nC67\n\n\nLeukaemia\nC91-C95\n\n\nCorpus uteri cancer\nC54-C55\n\n\nStomach cancer\nC16\n\n\nLiver cancer\nC22\n\n\nAll other cancers\nC00-C14, C17, C23-24, C26-C32, C37-C41, C43-C49, C51-C53, C57-C60, C62-C66, C68-C80, C97 D00-D48\n\n\n\n\nThe residual group also contained deaths from the “ill-defined diseases”, which were proportionately assigned as above. The residual group also includes breast cancer for men. Ovarian cancer, corpus uteri cancer (women) and prostate cancer (men) are sex specific. Bladder cancer and liver cancer were not leading cancers for women, so they were included in the residual group.\nThe next leading cancers in the residual group of all other cancers were bladder cancer, brain and nervous system cancers, and liver cancer for women, and brain and nervous system cancers, mesothelioma, and melanoma and other skin cancers for men."
+ "text": "Table D.1: Groups of causes of death used in the district-level cause-specific mortality analysis in Chapter 7 with ICD-10 codes.\n\n\n\n\n\n\nCause\nICD-10 codes\n\n\n\n\nTrachea, bronchus and lung cancers\nC33-C34\n\n\nBreast cancer\nC50\n\n\nProstate cancer\nC61\n\n\nColorectal cancers\nC18-C21\n\n\nPancreatic cancer\nC25\n\n\nOvarian cancer\nC56\n\n\nLymphomas, multiple myeloma\nC81-C90, C96\n\n\nOesophageal cancer\nC15\n\n\nAll other cancers\nC00-C14, C16-C17, C22-C24, C26-C32, C37-C41, C43-C49, C51-C55, C57-C60, C62-C67, C68-C80, C91-C95, C97, D00-D48\n\n\nIschaemic heart disease\nI20-I25\n\n\nStroke\nI60-I69\n\n\nAll other CVDs\nI00-I19, I26-I59, I70-I99\n\n\nAlzheimer’s and other dementias\nF00-F03, G30\n\n\nCOPD\nJ40-44\n\n\nDiabetes mellitus, nephritis and nephrosis\nE10-14, N00-19\n\n\nLiver cirrhosis\nK70, K74\n\n\nAll other NCDs\nD55-D648, D65-D89, E03-E07, E15-E16, E20-E34, E65-E88, F01-F99, G06-G13, G15-G98, H00-H61, H68-H93, J30-J39, J45-J98, K00-K14, K20-K69, K71-K73, K75-K92, L00-L98, M00-M99, N20-64, N75-N99, Q00-Q99, R95, X41-X42, X45\n\n\nLower respiratory infections\nJ09-18, J20-J22\n\n\nAll other IMPN\nA00-99, B00-99, D50-53, D649, E00-E02, E40-46, E50-54, G00, G03-G04, G14, H65-H66, N70-N73, J00-J06, O00-O99, P00-P96, Z353\n\n\nInjuries\nU00-U01, U509, V00-V99, W00-W99, X00-X40, X43-X44, X46-X99, Y00-Y01, Y10-Y36, Y381, Y40-Y86, Y870-Y872, Y88-Y89\n\n\n\n\nOvarian cancer (women) and prostate cancer (men) are sex specific. The all other cancers group also includes breast cancer for men. Liver cirrhosis was not in the top 12 leading causes of death for women, so it was included within all other NCDs.\nThe residual groups (all other cancers, all other CVDs, all other NCDs, all other IMPN) also contained deaths from the “ill-defined diseases” GHE group (R00-R94, R96-R99, U07, U99). There were 196,055 deaths from ill-defined diseases. These were proportionately assigned between the residual groups.\nCauses of death with the ICD-10 code S00-S99 or T00-T99 are not valid underlying causes of death. These were all neonatal deaths, which are not assigned an underlying cause of death, and were imputing using the code in the first position on the death record. These deaths were classified as injuries.\n\n\nTable D.2: Groups of causes of death used in the district-level cancer mortality analysis in Chapter 8 with ICD-10 codes.\n\n\n\n\n\n\nCancer\nICD-10 codes\n\n\n\n\nTrachea, bronchus and lung cancers\nC33-C34\n\n\nBreast cancer\nC50\n\n\nProstate cancer\nC61\n\n\nColorectal cancer\nC18-C21\n\n\nPancreatic cancer\nC25\n\n\nOvarian cancer\nC56\n\n\nLymphomas, multiple myeloma\nC81-C90, C96\n\n\nOesophageal cancer\nC15\n\n\nBladder cancer\nC67\n\n\nLeukaemia\nC91-C95\n\n\nCorpus uteri cancer\nC54-C55\n\n\nStomach cancer\nC16\n\n\nLiver cancer\nC22\n\n\nAll other cancers\nC00-C14, C17, C23-24, C26-C32, C37-C41, C43-C49, C51-C53, C57-C60, C62-C66, C68-C80, C97 D00-D48\n\n\n\n\nThe residual group also contained deaths from the “ill-defined diseases”, which were proportionately assigned as above. The residual group also includes breast cancer for men. Ovarian cancer, corpus uteri cancer (women) and prostate cancer (men) are sex specific. Bladder cancer and liver cancer were not leading cancers for women, so they were included in the residual group.\nThe next leading cancers in the residual group of all other cancers were bladder cancer, brain and nervous system cancers, and liver cancer for women, and brain and nervous system cancers, mesothelioma, and melanoma and other skin cancers for men."
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