diff --git a/thesis/Appendices/AppendixD.qmd b/thesis/Appendices/AppendixD.qmd index 4efc119..0db0fc1 100755 --- a/thesis/Appendices/AppendixD.qmd +++ b/thesis/Appendices/AppendixD.qmd @@ -23,7 +23,7 @@ | All other IMPN | A00-99, 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 | | Injuries | U00-U01, U509, V00-V99, W00-W99, X00-X40, X43-X44, X46-X99, Y00-Y01, Y10-Y36, Y381, Y40-Y86, Y870-Y872, Y88-Y89 | -: Groups of causes of death used in the district-level cause-specific analysis in @sec-Chapter7 with ICD-10 codes. {#tbl-ap-ch7-causes} +: Groups of causes of death used in the district-level cause-specific mortality analysis in @sec-Chapter7 with ICD-10 codes. {#tbl-ap-ch7-causes} Ovarian cancer (women) and prostate cancer (men) are sex specific. The all other cancers group also includes breast cancer for men. @@ -54,7 +54,7 @@ These deaths were classified as injuries. | Liver cancer | C22 | | All other cancers | C00-C14, C17, C23-24, C26-C32, C37-C41, C43-C49, C51-C53, C57-C60, C62-C66, C68-C80, C97 D00-D48 | -: Groups of causes of death used in the district-level cancer analysis in @sec-Chapter8 with ICD-10 codes. {#tbl-ap-ch8-cancers} +: Groups of causes of death used in the district-level cancer mortality analysis in @sec-Chapter8 with ICD-10 codes. {#tbl-ap-ch8-cancers} The 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. diff --git a/thesis/Chapters/Chapter1.qmd b/thesis/Chapters/Chapter1.qmd index 7403f0b..986dd46 100755 --- a/thesis/Chapters/Chapter1.qmd +++ b/thesis/Chapters/Chapter1.qmd @@ -25,7 +25,7 @@ There are two specific objectives which will help achieve this aim: I will then explore inequalities in UK over the past few decades through to the present. @sec-Chapter3 presents the data sources, and @sec-Chapter4 the statistical modelling choices common to all objectives of this thesis. @sec-Chapter5 concerns the first objective of the thesis - estimating trends in life expectancy for very small areas in England. -@sec-Chapter6 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. +@sec-Chapter6 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. @sec-Chapter7 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. @sec-Chapter8 follows the methods of @sec-Chapter7, but focussing only on deaths from cancers. @sec-Chapter9 concludes with a discussion on the public health implications of the findings and areas for future research building on the work in this thesis. diff --git a/thesis/Chapters/Chapter2.qmd b/thesis/Chapters/Chapter2.qmd index e12a10e..52cdda0 100644 --- a/thesis/Chapters/Chapter2.qmd +++ b/thesis/Chapters/Chapter2.qmd @@ -56,7 +56,7 @@ $$ {#eq-CAR-prec} where $\tau$ controls the overall precision of the effects, $\mathbf{A}$ is the spatial adjacency matrix formed by the small areas, $\mathbf{D}$ is a diagonal matrix with entries equal to the number of neighbours for each spatial unit, and the autocorrelation parameter $\rho$ describes the amount of correlation. This can be seen as tuning the degree of spatial dependence, where $\rho = 0$ implies independence between areas, and $\rho = 1$ full dependence. The case with $\rho = 1$ is called the intrinsic conditional autoregressive (ICAR) model. -There sometimes exists further over-dispersion in the residuals that cannot be modelled by purely spatially-structured random effects. +There sometimes exists further overdispersion in the residuals that cannot be modelled by purely spatially-structured random effects. @besagBayesianImageRestoration1991 proposed the model (hereafter called BYM) $$ S_i = U_i + V_i, @@ -74,7 +74,7 @@ Policy is decided at these geographies, so there is reason to believe these boun 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. Of 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 @eq-MVN. -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. +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 [@besagBayesianImageRestoration1991], is reductive for more complicated spatial problems. Despite this, in an epidemiological context, @duncanSpatialSmoothingBayesian2017 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. In applications to disease mapping, spatial models are the natural choice when the disease exhibits a spatial pattern. @@ -93,7 +93,7 @@ One can imagine situations in which different spatial units will have different 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-heldBayesianModellingInseparable2000]. -However, 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. +However, 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. It should be noted that there are situations where statistical smoothing would not be appropriate. diff --git a/thesis/Chapters/Chapter4.qmd b/thesis/Chapters/Chapter4.qmd index cbfc207..6cb809b 100644 --- a/thesis/Chapters/Chapter4.qmd +++ b/thesis/Chapters/Chapter4.qmd @@ -114,5 +114,5 @@ Rewriting the model in `NumPyro` and sampling on a GPU cut the runtime down to a ## Clean code and open source I 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. +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](https://github.com/theorashid/mortality-statsmodel), [plots and analysis](https://github.com/theorashid/thesis-analysis), and the [thesis itself](https://github.com/theorashid/thesis) can be found on GitHub. diff --git a/thesis/Chapters/Chapter7.qmd b/thesis/Chapters/Chapter7.qmd index a307c6f..eff9cd9 100644 --- a/thesis/Chapters/Chapter7.qmd +++ b/thesis/Chapters/Chapter7.qmd @@ -25,7 +25,7 @@ Together, these form a mutually exclusive, collectively exhaustive list of cause The full list of ICD-10 codes for each cause group can be found in @tbl-ap-ch7-causes. -![Total number of deaths for the twelve leading causes of death in England from 2002 to 2019, and the residual groups all other cancers, all other NCDs, all other CVDs, all other infections, maternal, perinatal and nutritional conditions (IMPN), and injuries. The boxes are coloured by the wider groups of CVDs; NCDs; cancers; maternal, perinatal, nutritional and infectious causes; injuries. See @tbl-ap-ch7-causes for ICD-10 codes for each category.](../thesis-analysis/thesis_analysis/causes/figures/treemap.pdf){#fig-ch-7-treemap fig-scap="Total number of deaths for the twelve leading causes of death in England from 2002 to 2019, and the residual groups all other cancers, all other NCDs, all other CVDs, all other infections, maternal, perinatal and nutritional conditions, and injuries."} +![Total number of deaths for the twelve leading causes of death in England from 2002 to 2019, and the residual groups all other cancers, all other NCDs, all other CVDs, all other infections, maternal, perinatal and nutritional conditions (IMPN), and injuries. The boxes are coloured by the wider groups of CVDs; NCDs; cancers; maternal, perinatal, nutritional and infectious causes; injuries. See @tbl-ap-ch7-causes for ICD-10 codes for each category.](../thesis-analysis/thesis_analysis/causes/figures/treemap.pdf){#fig-ch-7-treemap fig-scap="Total number of deaths for the twelve leading causes of death in England from 2002 to 2019 and residual groups."} There were 4,465,948 (51.6%) deaths in women and 4,182,108 (48.4%) in men in England from 2002 to 2019. 3,972,286 (45.9%) of these deaths occurred in people aged younger than 80 years of age. diff --git a/thesis/Chapters/Chapter9.qmd b/thesis/Chapters/Chapter9.qmd index b4af660..7749745 100644 --- a/thesis/Chapters/Chapter9.qmd +++ b/thesis/Chapters/Chapter9.qmd @@ -13,7 +13,7 @@ The difference in progress between districts in the last decade was largely driv 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" [@angusIncreasesDeathsDespair2023; @caseRisingMorbidityMortality2015], although this would require further analysis by stratifying into intentional and unintentional injuries. +This is possibly driven by a rise in "deaths of despair" [@angusIncreasesDeathsDespair2023; @caseRisingMorbidityMortality2015], 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. Cancer survival outcomes in the UK are worse than those in Europe in general [@oecdOECDReviewsHealth2016]. @@ -24,9 +24,9 @@ This suggests either regional differences in the quality of care, or differences Finally, 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. +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-murdochWhyAreAmericans2023], and I hope they are also being discussed by policymakers. +Nevertheless, the estimates from this thesis are already being used in the press to provide context for recent falls in US life expectancy [@burn-murdochWhyAreAmericans2023], and I hope they are also being used in policy discussions. ## Future work @@ -49,7 +49,7 @@ Is there a longer term effect due to strain on emergency services, which has man And, how have these effects varied for different age groups and different areas of the country? In 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 @sec-Chapter5, perhaps bigger is not better when the quality of the data is lacking. +However, given the data issues in @sec-Chapter5, perhaps smaller is not better when the quality of the data is lacking. One 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 [@laoTfpMcmcModern2020]. diff --git a/thesis/Frontmatter/abbreviations.tex b/thesis/Frontmatter/abbreviations.tex index 3b1deef..efbd922 100644 --- a/thesis/Frontmatter/abbreviations.tex +++ b/thesis/Frontmatter/abbreviations.tex @@ -10,7 +10,7 @@ \textbf{ICAR} & \textbf{I}ntrinsic \textbf{C}onditional \textbf{a}uto\textbf{r}egressive\\ \textbf{ICD} & \textbf{I}nternational \textbf{C}lassification of \textbf{D}iseases\\ \textbf{IMD} & \textbf{I}ndex of \textbf{M}ultiple \textbf{D}eprivation\\ - \textbf{IMPN} & \textbf{I}nfections, \textbf{M}aternal \textbf{P}erinatal and \textbf{N}utritional\\ + \textbf{IMPN} & \textbf{I}nfections, \textbf{M}aternal, \textbf{P}erinatal and \textbf{N}utritional\\ \textbf{LSOA} & \textbf{L}ower Layer \textbf{S}uper \textbf{O}utput \textbf{A}rea\\ \textbf{MCMC} & \textbf{M}arkov \textbf{c}hain \textbf{M}onte \textbf{C}arlo\\ \textbf{MSOA} & \textbf{M}iddle Layer \textbf{S}uper \textbf{O}utput \textbf{A}rea\\ diff --git a/thesis/_thesis/Appendices/AppendixD.html b/thesis/_thesis/Appendices/AppendixD.html index a77cf3a..4c9670e 100644 --- a/thesis/_thesis/Appendices/AppendixD.html +++ b/thesis/_thesis/Appendices/AppendixD.html @@ -217,7 +217,7 @@

Appendix
- +@@ -317,7 +317,7 @@

Appendix

Causes 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.

Table D.1: Groups of causes of death used in the district-level cause-specific analysis in Chapter 7 with ICD-10 codes.Table D.1: Groups of causes of death used in the district-level cause-specific mortality analysis in Chapter 7 with ICD-10 codes.
- +diff --git a/thesis/_thesis/Chapters/Chapter2.html b/thesis/_thesis/Chapters/Chapter2.html index 2e4c697..d55d8bf 100644 --- a/thesis/_thesis/Chapters/Chapter2.html +++ b/thesis/_thesis/Chapters/Chapter2.html @@ -278,21 +278,21 @@

S

Space as discrete units

A 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 \[ \mathbf{P} = \pmb{\Sigma}^{-1} = \tau(\mathbf{D} - \rho \mathbf{A}), -\tag{2.2}\] 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) \[ +\tag{2.2}\] 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) \[ S_i = U_i + V_i, \tag{2.3}\] 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.

Space as a nested hierarchy of geographies

The 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.

-

Of 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.

+

Of 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.

In 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.

Modelling variation beyond space

As 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.

Difficulties 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).

-

However, 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.

+

However, 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.

It 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.

diff --git a/thesis/_thesis/Chapters/Chapter4.html b/thesis/_thesis/Chapters/Chapter4.html index 2a40e54..76d0475 100644 --- a/thesis/_thesis/Chapters/Chapter4.html +++ b/thesis/_thesis/Chapters/Chapter4.html @@ -291,7 +291,7 @@

4.5 Clean code and open source

-

I 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.

+

I 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.

Table D.2: Groups of causes of death used in the district-level cancer analysis in Chapter 8 with ICD-10 codes.Table D.2: Groups of causes of death used in the district-level cancer mortality analysis in Chapter 8 with ICD-10 codes.