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Comparison of Bayesian Spatiotemporal Models for Small-Area Life Expectancy: A Simulation Study
Abstract
The purpose of this study was to assess the precision, uncertainty, and normality of small-area life expectancy estimates calculated using Bayesian spatio-temporal models. We hypothesized six scenarios in which all 247 districts of Korea had the same year-specific female population of 500, 1,000, 2,000, 5,000, 10,000, and 25,000 individuals during the study period (2013–2017). We generated 1,000 hypothetical datasets for each scenario and calculated district-year life expectancies. The precision and uncertainty of life expectancy estimates were compared between the two Bayesian spatio-temporal models and the traditional method and Bayesian spatial models. We examined the normality of the life expectancy distributions generated by each method and investigated an optimal cut-off value for the comparisons. The Bayesian spatio-temporal models produced precise life expectancy estimates. However, the 95% uncertainty interval contained the true value with a probability of less than 95%. The Bayesian spatio-temporal models violated the normality assumption in scenarios with small population sizes. Therefore, life expectancy comparisons should be conducted using a cut-off value that minimizes false-positive and false-negative rates. We proposed 0.8 as a cut-off value to determine the statistical significance of the difference in life expectancy.
... Consistent with previous cross-national studies have also described the spatiotemporal trends of life expectancy, and revealed African countries experienced the lowest life expectancies [19]. Additionally, spatial dependence has also been explained in both developed countries [20][21][22][23] (such as the UK, South Korea, and the US) and developing countries (such as China) [12,24]. Although development of economy maintained homologous in West Africa, it is argued that existed disparities in HLE among countries, highlighting the enormous challenge of addressing health inequality in the region. ...
Background
Health financing produce a broad range of healthy life expectancy (HLE) disparities. In West Africa, limited research exists on the association between health financing and HLE at ecological level during a consecutive period of time from the spatial perspectives. This study aimed to determine the existence, quantify the magnitude, and interpret the association between health financing and HLE.
Methods
A Dynamic Spatial Durbin model was used to explain the association between HLE and health financing level and structure during 1995-2019 in West Africa. Spatial spillover effects were introduced to interpret the direct and indirect effects caused by health financing level and structure on HLE during the long and short terms.
Results
Spatial dependence and clustering on HLE were observed in West Africa. Although the overall level of total health spending, government health spending, out-of-pocket health spending, and development assistance for health (DAH) increased from 1995 to 2019, government health spending per person experienced a declining trend. Out-of-pocket health spending per total health spending was the highest among other sources of health financing, decreasing from 57% during 1995-1999 to 42% during 2015-2019. Total health spending and out-of-pocket health spending affected HLE positively and negatively in the long term, respectively. Government health spending and prepaid private health spending per person had positive effects on local and adjacent country HLE in the short-term, while DAH had negative effects on the same. The short-term spatial spillover effects of government health spending, DAH, and prepaid private health spending per person were more pronounced than the long-term effects.
Conclusions
Spatial variations of HLE existed at country-level in West Africa. Health financing regarding government, non-government, as well as external assistance not only affected HLE disparities at local scale but also among nearby countries. Policymakers should optimise supportive health financing transition policies and narrow the national gap to reduce health disparities and increase HLE. Externalities of policy of those health financing proxies should be took into consideration to promote health equity to improve global health governance.
Background
High-resolution data for how mortality and longevity have changed in England, UK are scarce. We aimed to estimate trends from 2002 to 2019 in life expectancy and probabilities of death at different ages for all 6791 middle-layer super output areas (MSOAs) in England.
Methods
We performed a high-resolution spatiotemporal analysis of civil registration data from the UK Small Area Health Statistics Unit research database using de-identified data for all deaths in England from 2002 to 2019, with information on age, sex, and MSOA of residence, and population counts by age, sex, and MSOA. We used a Bayesian hierarchical model to obtain estimates of age-specific death rates by sharing information across age groups, MSOAs, and years. We used life table methods to calculate life expectancy at birth and probabilities of death in different ages by sex and MSOA.
Findings
In 2002–06 and 2006–10, all but a few (0–1%) MSOAs had a life expectancy increase for female and male sexes. In 2010–14, female life expectancy decreased in 351 (5·2%) of 6791 MSOAs. By 2014–19, the number of MSOAs with declining life expectancy was 1270 (18·7%) for women and 784 (11·5%) for men. The life expectancy increase from 2002 to 2019 was smaller in MSOAs where life expectancy had been lower in 2002 (mostly northern urban MSOAs), and larger in MSOAs where life expectancy had been higher in 2002 (mostly MSOAs in and around London). As a result of these trends, the gap between the first and 99th percentiles of MSOA life expectancy for women increased from 10·7 years (95% credible interval 10·4–10·9) in 2002 to reach 14·2 years (13·9–14·5) in 2019, and for men increased from 11·5 years (11·3–11·7) in 2002 to 13·6 years (13·4–13·9) in 2019.
Interpretation
In the decade before the COVID-19 pandemic, life expectancy declined in increasing numbers of communities in England. To ensure that this trend does not continue or worsen, there is a need for pro-equity economic and social policies, and greater investment in public health and health care throughout the entire country.
Funding
Wellcome Trust, Imperial College London, Medical Research Council, Health Data Research UK, and National Institutes of Health Research.
Objectives
To estimate life expectancy at the local authority level and detect those areas that have a substantially low life expectancy after accounting for deprivation.
Design
We used registration data from the Office for National Statistics on mortality and population in England, by local authority, age group and socioeconomic deprivation decile, for both men and women over the period 2001–2018. We used a statistical model within the Bayesian framework to produce robust mortality rates, which were then transformed to life expectancy estimates. A rule based on exceedance probabilities was used to detect local authorities characterised by a low life expectancy among areas with a similar deprivation level from 2012 onwards.
Results
We confirmed previous findings showing differences in the life expectancy gap between the most and least deprived areas from 2012 to 2018. We found variations in life expectancy trends across local authorities, and we detected a number of those with a low life expectancy when compared with others of a similar deprivation level.
Conclusions
There are factors other than deprivation that are responsible for low life expectancy in certain local authorities. Further investigation on the detected areas can help understand better the stalling of life expectancy which was observed from 2012 onwards and plan efficient public health policies.
Small-area studies offer a powerful epidemiological approach to study disease patterns at the population level and assess health risks posed by environmental pollutants. They involve a public health investigation on a geographical scale (e.g. neighbourhood) with overlay of health, environmental, demographic and potential confounder data. Recent methodological advances, including Bayesian approaches, combined with fast-growing computational capabilities, permit more informative analyses than previously possible, including the incorporation of data at different scales, from satellites to individual-level survey information. Better data availability has widened the scope and utility of small-area studies, but has also led to greater complexity, including choice of optimal study area size and extent, duration of study periods, range of covariates and confounders to be considered and dealing with uncertainty. The availability of data from large, well-phenotyped cohorts such as UK Biobank enables the use of mixed-level study designs and the triangulation of evidence on environmental risks from small-area and individual-level studies, therefore improving causal inference, including use of linked biomarker and -omics data. As a result, there are now improved opportunities to investigate the impacts of environmental risk factors on human health, particularly for the surveillance and prevention of non-communicable diseases.
Background:
Health outcomes are known to vary at both the country and local levels, but trends in mortality across a detailed and comprehensive set of causes have not been previously described at a very local level. Life expectancy in King County, WA, USA, is in the 95th percentile among all counties in the USA. However, little is known about how life expectancy and mortality from different causes of death vary at a local, neighbourhood level within this county. In this analysis, we estimated life expectancy and cause-specific mortality within King County to describe spatial trends, quantify disparities in mortality, and assess the contribution of each cause of death to overall disparities in all-cause mortality.
Methods:
We applied established so-called garbage code redistribution algorithms and small area estimation methods to death registration data for King County to estimate life expectancy, cause-specific mortality rates, and years of life lost (YLL) rates from 152 causes of death for 397 census tracts from Jan 1, 1990, to Dec 31, 2014. We used the cause list developed for the Global Burden of Disease 2015 study for this analysis. Deaths were tabulated by age group, sex, census tract, and cause of death. We used Bayesian mixed-effects regression models to estimate mortality overall and from each cause.
Findings:
Between 1990 and 2014, life expectancy in King County increased by 5·4 years (95% uncertainty interval [UI] 5·0-5·7) among men (from 74·0 years [73·7-74·3] to 79·3 years [79·1-79·6]) and by 3·4 years (3·0-3·7) among women (from 80·0 years [79·7-80·2] to 83·3 years [83·1-83·5]). In 2014, life expectancy ranged from 68·4 years (95% UI 66·9-70·1) to 86·7 years (85·0-88·2) for men and from 73·6 years (71·6-75·5) to 88·4 years (86·9-89·9) for women among census tracts within King County. Rates of YLL by cause also varied substantially among census tracts for each cause of death. Geographical areas with relatively high and relatively low YLL rates differed by cause. In general, causes of death responsible for more YLLs overall also contributed more significantly to geographical inequality within King County. However, certain causes contributed more to inequality than to overall YLLs.
Interpretation:
This census tract-level analysis of life expectancy and cause-specific YLL rates highlights important differences in health among neighbourhoods in King County that are masked by county-level estimates. Efforts to improve population health in King County should focus on reducing geographical inequality, by targeting those health conditions that contribute the most to overall YLLs and to inequality. This analysis should be replicated in other locations to more fully describe fine-grained local-level variation in population health and contribute to efforts to improve health while reducing inequalities.
Funding:
John W Stanton and Theresa E Gillespie.
Background:
To plan for pensions and health and social services, future mortality and life expectancy need to be forecast. Consistent forecasts for all subnational units within a country are very rare. Our aim was to forecast mortality and life expectancy for England and Wales' districts.
Methods:
We developed Bayesian spatiotemporal models for forecasting of age-specific mortality and life expectancy at a local, small-area level. The models included components that accounted for mortality in relation to age, birth cohort, time, and space. We used geocoded mortality and population data between 1981 and 2012 from the Office for National Statistics together with the model with the smallest error to forecast age-specific death rates and life expectancy to 2030 for 375 of England and Wales' 376 districts. We measured model performance by withholding recent data and comparing forecasts with this withheld data.
Findings:
Life expectancy at birth in England and Wales was 79·5 years (95% credible interval 79·5-79·6) for men and 83·3 years (83·3-83·4) for women in 2012. District life expectancies ranged between 75·2 years (74·9-75·6) and 83·4 years (82·1-84·8) for men and between 80·2 years (79·8-80·5) and 87·3 years (86·0-88·8) for women. Between 1981 and 2012, life expectancy increased by 8·2 years for men and 6·0 years for women, closing the female-male gap from 6·0 to 3·8 years. National life expectancy in 2030 is expected to reach 85·7 (84·2-87·4) years for men and 87·6 (86·7-88·9) years for women, further reducing the female advantage to 1·9 years. Life expectancy will reach or surpass 81·4 years for men and reach or surpass 84·5 years for women in every district by 2030. Longevity inequality across districts, measured as the difference between the 1st and 99th percentiles of district life expectancies, has risen since 1981, and is forecast to rise steadily to 8·3 years (6·8-9·7) for men and 8·3 years (7·1-9·4) for women by 2030.
Interpretation:
Present forecasts underestimate the expected rise in life expectancy, especially for men, and hence the need to provide improved health and social services and pensions for elderly people in England and Wales. Health and social policies are needed to curb widening life expectancy inequalities, help deprived districts catch up in longevity gains, and avoid a so-called grand divergence in health and longevity.
Funding:
UK Medical Research Council and Public Health England.
The issue of setting prior distributions on model parameters, or to attribute
uncertainty for model parameters, is a difficult issue in applied Bayesian
statistics. Although the prior distribution should ideally encode the users'
prior knowledge about the parameters, this level of knowledge transfer seems to
be unattainable in practice and applied statisticians are forced to search for
a "default" prior. Despite the development of objective priors, which are only
available explicitly for a small number of highly restricted model classes, the
applied statistician has few practical guidelines to follow when choosing the
priors. An easy way out of this dilemma is to re-use prior choices of others,
with an appropriate reference.
In this paper, we introduce a new concept for constructing prior
distributions. We exploit the natural nested structure inherent to many model
components, which defines the model component to be a flexible extension of a
base model. Proper priors are defined to penalise the complexity induced by
deviating from the simpler base model and are formulated after the input of a
user-defined scaling parameter for that model component. These priors are
invariant to reparameterisations, have a natural connection to Jeffreys'
priors, are designed to support Occam's razor and seem to have excellent
robustness properties, all which are highly desirable and allow us to use this
approach to define default prior distributions.
The United States spends more than any other country on health care. The poor relative performance of the US compared to other high-income countries has attracted attention and raised questions about the performance of the US health system. An important dimension to poor national performance is the large disparities in life expectancy.
We applied a mixed effects Poisson statistical model and Gaussian Process Regression to estimate age-specific mortality rates for US counties from 1985 to 2010. We generated uncertainty distributions for life expectancy at each age using standard simulation methods.
Female life expectancy in the United States increased from 78.0 years in 1985 to 80.9 years in 2010, while male life expectancy increased from 71.0 years in 1985 to 76.3 years in 2010. The gap between female and male life expectancy in the United States was 7.0 years in 1985, narrowing to 4.6 years in 2010. For males at the county level, the highest life expectancy steadily increased from 75.5 in 1985 to 81.7 in 2010, while the lowest life expectancy remained under 65. For females at the county level, the highest life expectancy increased from 81.1 to 85.0, and the lowest life expectancy remained around 73. For male life expectancy at the county level, there have been three phases in the evolution of inequality: a period of rising inequality from 1985 to 1993, a period of stable inequality from 1993 to 2002, and rising inequality from 2002 to 2010. For females, in contrast, inequality has steadily increased during the 25-year period. Compared to only 154 counties where male life expectancy remained stagnant or declined, 1,405 out of 3,143 counties (45%) have seen no significant change or a significant decline in female life expectancy from 1985 to 2010. In all time periods, the lowest county-level life expectancies are seen in the South, the Mississippi basin, West Virginia, Kentucky, and selected counties with large Native American populations.
The reduction in the number of counties where female life expectancy at birth is declining in the most recent period is welcome news. However, the widening disparities between counties and the slow rate of increase compared to other countries should be viewed as a call for action. An increased focus on factors affecting health outcomes, morbidity, and mortality such as socioeconomic factors, difficulty of access to and poor quality of health care, and behavioral, environmental, and metabolic risk factors is urgently required.
There are several measures that summarize the mortality experience of a population. Of these measures, life expectancies are
generally preferred based on their simpler interpretation and direct age standardization, which makes them directly comparable
between different populations. However, traditional life expectancy estimations are highly inaccurate for smaller populations
and consequently are seldom used in small-area applications. In this paper, the authors compare the relative performance of
traditional life expectancy estimation with a Bayesian random-effects approach that uses correlations (i.e., borrows strength)
between different age groups, geographic areas, and sexes to improve the small-area life expectancy estimations. In the presented
Monte Carlo simulations, the Bayesian random-effects approach outperforms the traditional approach in terms of bias, root
mean square error, and coverage of the 95% confidence intervals. Moreover, the Bayesian random-effects approach is found to
be usable for populations as small as 2,000 person-years at risk, which is considerably smaller than the minimum of 5,000
person-years at risk recommended for the traditional approach. As such, the proposed Bayesian random-effects approach is well-suited
for estimation of life expectancies in small areas.
We study bias, standard errors, and distributions of characteristics of life tables for small populations. Theoretical considerations and simulations show that statistical efficiency of different methods is, above all, affected by the population size. Yet it is also significantly affected by the life table construction method and by a population's age composition. Study results are presented in the form of ready-to-use tables and relations, which may be useful in assessing the significance of estimates and differences in life expectancy across time and space for the territories with a small population size, when standard errors of life expectancy estimates may be high.
Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. We consider approximate Bayesian inference in a popular subset of structured additive regression models, "latent Gaussian models", where the latent field is Gaussian, controlled by a few hyperparameters and with non-Gaussian response variables. The posterior marginals are not available in closed form owing to the non-Gaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, in terms of both convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo sampling is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations is computational: where Markov chain Monte Carlo algorithms need hours or days to run, our approximations provide more precise estimates in seconds or minutes. Another advantage with our approach is its generality, which makes it possible to perform Bayesian analysis in an automatic, streamlined way, and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged. Copyright (c) 2009 Royal Statistical Society.
The use of Bayesian hierarchical spatial models has become widespread in disease mapping and ecologic studies of health-environment associations. In this type of study, the data are typically aggregated over an extensive time period, thus neglecting the time dimension. The output of purely spatial disease mapping studies is therefore the average spatial pattern of risk over the period analyzed, but the results do not inform about, for example, whether a high average risk was sustained over time or changed over time.
We investigated how including the time dimension in disease-mapping models strengthens the epidemiologic interpretation of the overall pattern of risk.
We discuss a class of Bayesian hierarchical models that simultaneously characterize and estimate the stable spatial and temporal patterns as well as departures from these stable components. We show how useful rules for classifying areas as stable can be constructed based on the posterior distribution of the space-time interactions. We carry out a simulation study to investigate the sensitivity and specificity of the decision rules we propose, and we illustrate our approach in a case study of congenital anomalies in England.
Our results confirm that extending hierarchical disease-mapping models to models that simultaneously consider space and time leads to a number of benefits in terms of interpretation and potential for detection of localized excesses.
To investigate the sampling distribution and usefulness of expectation of life in comparisons of mortality at health district level or below.
Derivation of a formula for the variance of the expectation of life, confirmation of the result and generation of the sampling distribution by Monte Carlo simulation; comparison of expectation of life with standardised mortality ratio (SMR) and other summary indices of mortality.
A health district in Trent Region, England.
Routinely available mortality statistics at electoral ward level and above.
Given reasonable and simple assumptions the sampling distribution of the expectation of life is approximately normal. Expectation of life shows a high negative correlation with SMR even if the oldest age band for the SMR is open ended.
Where sampling error is an issue, inference concerning differences in mortality rates between populations can be based on expectation of life, which is better for illustrative purposes than SMR. The formula for the variance of the expectation of life is more complex however. If the final age band is open ended, its lower bound should be as high as possible to avoid misleading results caused by hidden differences in age structure.
A risk ratio or difference from a meta-analysis is as many as ten steps away from the unobservable causal risk ratios and differences in target populations. The steps are like lenses, filters, or other fallible components of the epidemiologist's "telescope" for observing populations. Each step is another domain where different biases can be caused. How biases combine across domains in the production of epidemiologic evidence can be quickly explained to nonepidemiologists by using a sequence of causal arrow diagrams with easy notation: (a) agent of interest, (b) background risk factors, (c) correlated causes, (d) diagnosis, (e) exposure measurement, (f) filing of data, (g) grouping of cohorts, (h) harvesting of cases and controls, (i) interpretations of investigators, (j) judgments of journals, and (k) knowledge of meta-analysts. For epidemiologists, this article serves as a review of ideas about confounding, information bias, and selection bias and underscores the need for routinely analyzing the sensitivity of study findings to multiple hypothesized biases.
There is currently much interest in conducting spatial analyses of health outcomes at the small-area scale. This requires sophisticated statistical techniques, usually involving Bayesian models, to smooth the underlying risk estimates because the data are typically sparse. However, questions have been raised about the performance of these models for recovering the "true" risk surface, about the influence of the prior structure specified, and about the amount of smoothing of the risks that is actually performed. We describe a comprehensive simulation study designed to address these questions. Our results show that Bayesian disease-mapping models are essentially conservative, with high specificity even in situations with very sparse data but low sensitivity if the raised-risk areas have only a moderate (less than 2-fold) excess or are not based on substantial expected counts (> 50 per area). Semiparametric spatial mixture models typically produce less smoothing than their conditional autoregressive counterpart when there is sufficient information in the data (moderate-size expected count and/or high true excess risk). Sensitivity may be improved by exploiting the whole posterior distribution to try to detect true raised-risk areas rather than just reporting and mapping the mean posterior relative risk. For the widely used conditional autoregressive model, we show that a decision rule based on computing the probability that the relative risk is above 1 with a cutoff between 70 and 80% gives a specific rule with reasonable sensitivity for a range of scenarios having moderate expected counts (approximately 20) and excess risks (approximately 1.5- to 2-fold). Larger (3-fold) excess risks are detected almost certainly using this rule, even when based on small expected counts, although the mean of the posterior distribution is typically smoothed to about half the true value.
Objectives
This study aimed to review the types and applications of fully Bayesian (FB) spatial–temporal models and covariates used to study cancer incidence and mortality.Methods
This systematic review searched articles published within Medline, Embase, Web-of-Science and Google Scholar between 2014 and 2018.ResultsA total of 38 studies were included in our study. All studies applied Bayesian spatial–temporal models to explore spatial patterns over time, and over half assessed the association with risk factors. Studies used different modelling approaches and prior distributions for spatial, temporal and spatial–temporal interaction effects depending on the nature of data, outcomes and applications. The most common Bayesian spatial–temporal model was a generalized linear mixed model. These models adjusted for covariates at the patient, area or temporal level, and through standardization.Conclusions
Few studies (4) modelled patient-level clinical characteristics (11%), and the applications of an FB approach in the forecasting of spatial–temporally aligned cancer data were limited. This review highlighted the need for Bayesian spatial-temporal models to incorporate patient-level prognostic characteristics through the multi-level framework and forecast future cancer incidence and outcomes for cancer prevention and control strategies.
Life expectancy inequalities are an established indicator of health inequalities. More recent attention has been given to lifespan variation, which measures the amount of heterogeneity in age at death across all individuals in a population. International studies have documented diverging socioeconomic trends in lifespan variation using individual level measures of income, education and occupation. Despite using different socioeconomic indicators and different indices of lifespan variation, studies reached the same conclusion: the most deprived experience the lowest life expectancy and highest lifespan variation, a double burden of mortality inequality. A finding of even greater concern is that relative differences in lifespan variation between socioeconomic group were growing at a faster rate than life expectancy differences. The magnitude of lifespan variation inequalities by area-level deprivation has received limited attention. Area-level measures of deprivation are actively used by governments for allocating resources to tackle health inequalities. Establishing if the same lifespan variation inequalities emerge for area-level deprivation will help to better inform governments about which dimension of mortality inequality should be targeted. We measure lifespan variation trends (1981–2011) stratified by an area-level measure of socioeconomic deprivation that is applicable to the entire population of Scotland, the country with the highest level of variation and one of the longest, sustained stagnating trends in Western Europe. We measure the gradient in variation using the slope and relative indices of inequality. The deprivation, age and cause specific components driving the increasing gradient are identified by decomposing the change in the slope index between 1981 and 2011. Our results support the finding that the most advantaged are dying within an ever narrower age range while the most deprived are facing greater and increasing uncertainty. The least deprived group show an increasing advantage, over the national average, in terms of deaths from circulatory disease and external causes.
Importance
In the United States, regional variation in cardiovascular mortality is well-known but county-level estimates for all major cardiovascular conditions have not been produced.
Objective
To estimate age-standardized mortality rates from cardiovascular diseases by county.
Design and Setting
Deidentified death records from the National Center for Health Statistics and population counts from the US Census Bureau, the National Center for Health Statistics, and the Human Mortality Database from 1980 through 2014 were used. Validated small area estimation models were used to estimate county-level mortality rates from all cardiovascular diseases, including ischemic heart disease, cerebrovascular disease, ischemic stroke, hemorrhagic stroke, hypertensive heart disease, cardiomyopathy, atrial fibrillation and flutter, rheumatic heart disease, aortic aneurysm, peripheral arterial disease, endocarditis, and all other cardiovascular diseases combined.
Exposures
The 3110 counties of residence.
Main Outcomes and Measures
Age-standardized cardiovascular disease mortality rates by county, year, sex, and cause.
Results
From 1980 to 2014, cardiovascular diseases were the leading cause of death in the United States, although the mortality rate declined from 507.4 deaths per 100 000 persons in 1980 to 252.7 deaths per 100 000 persons in 2014, a relative decline of 50.2% (95% uncertainty interval [UI], 49.5%-50.8%). In 2014, cardiovascular diseases accounted for more than 846 000 deaths (95% UI, 827-865 thousand deaths) and 11.7 million years of life lost (95% UI, 11.6-11.9 million years of life lost). The gap in age-standardized cardiovascular disease mortality rates between counties at the 10th and 90th percentile declined 14.6% from 172.1 deaths per 100 000 persons in 1980 to 147.0 deaths per 100 000 persons in 2014 (posterior probability of decline >99.9%). In 2014, the ratio between counties at the 90th and 10th percentile was 2.0 for ischemic heart disease (119.1 vs 235.7 deaths per 100 000 persons) and 1.7 for cerebrovascular disease (40.3 vs 68.1 deaths per 100 000 persons). For other cardiovascular disease causes, the ratio ranged from 1.4 (aortic aneurysm: 3.5 vs 5.1 deaths per 100 000 persons) to 4.2 (hypertensive heart disease: 4.3 vs 17.9 deaths per 100 000 persons). The largest concentration of counties with high cardiovascular disease mortality extended from southeastern Oklahoma along the Mississippi River Valley to eastern Kentucky. Several cardiovascular disease conditions were clustered substantially outside the South, including atrial fibrillation (Northwest), aortic aneurysm (Midwest), and endocarditis (Mountain West and Alaska). The lowest cardiovascular mortality rates were found in the counties surrounding San Francisco, California, central Colorado, northern Nebraska, central Minnesota, northeastern Virginia, and southern Florida.
Conclusions and Relevance
Substantial differences exist between county ischemic heart disease and stroke mortality rates. Smaller differences exist for diseases of the myocardium, atrial fibrillation, aortic and peripheral arterial disease, rheumatic heart disease, and endocarditis.
Importance:
County-level patterns in mortality rates by cause have not been systematically described but are potentially useful for public health officials, clinicians, and researchers seeking to improve health and reduce geographic disparities.
Objectives:
To demonstrate the use of a novel method for county-level estimation and to estimate annual mortality rates by US county for 21 mutually exclusive causes of death from 1980 through 2014.
Design, setting, and participants:
Redistribution methods for garbage codes (implausible or insufficiently specific cause of death codes) and small area estimation methods (statistical methods for estimating rates in small subpopulations) were applied to death registration data from the National Vital Statistics System to estimate annual county-level mortality rates for 21 causes of death. These estimates were raked (scaled along multiple dimensions) to ensure consistency between causes and with existing national-level estimates. Geographic patterns in the age-standardized mortality rates in 2014 and in the change in the age-standardized mortality rates between 1980 and 2014 for the 10 highest-burden causes were determined.
Exposure:
County of residence.
Main outcomes and measures:
Cause-specific age-standardized mortality rates.
Results:
A total of 80 412 524 deaths were recorded from January 1, 1980, through December 31, 2014, in the United States. Of these, 19.4 million deaths were assigned garbage codes. Mortality rates were analyzed for 3110 counties or groups of counties. Large between-county disparities were evident for every cause, with the gap in age-standardized mortality rates between counties in the 90th and 10th percentiles varying from 14.0 deaths per 100 000 population (cirrhosis and chronic liver diseases) to 147.0 deaths per 100 000 population (cardiovascular diseases). Geographic regions with elevated mortality rates differed among causes: for example, cardiovascular disease mortality tended to be highest along the southern half of the Mississippi River, while mortality rates from self-harm and interpersonal violence were elevated in southwestern counties, and mortality rates from chronic respiratory disease were highest in counties in eastern Kentucky and western West Virginia. Counties also varied widely in terms of the change in cause-specific mortality rates between 1980 and 2014. For most causes (eg, neoplasms, neurological disorders, and self-harm and interpersonal violence), both increases and decreases in county-level mortality rates were observed.
Conclusions and relevance:
In this analysis of US cause-specific county-level mortality rates from 1980 through 2014, there were large between-county differences for every cause of death, although geographic patterns varied substantially by cause of death. The approach to county-level analyses with small area models used in this study has the potential to provide novel insights into US disease-specific mortality time trends and their differences across geographic regions.
The recently developed R package INLA (Integrated Nested Laplace Approximation) is becoming a more widely used package for Bayesian inference. The INLA software has been promoted as a fast alternative to MCMC for disease mapping applications. Here, we compare the INLA package to the MCMC approach by way of the BRugs package in R, which calls OpenBUGS. We focus on the Poisson data model commonly used for disease mapping. Ultimately, INLA is a computationally efficient way of implementing Bayesian methods and returns nearly identical estimates for fixed parameters in comparison to OpenBUGS, but falls short in recovering the true estimates for the random effects, their precisions, and model goodness of fit measures under the default settings. We assumed default settings for ground truth parameters, and through altering these default settings in our simulation study, we were able to recover estimates comparable to those produced in OpenBUGS under the same assumptions.
Since the early 1980s, a bewildering array of methods for constructing bootstrap confidence intervals have been proposed. In this article, we address the following questions. First, when should bootstrap confidence intervals be used. Secondly, which method should be chosen, and thirdly, how should it be implemented. In order to do this, we review the common algorithms for resampling and methods for constructing bootstrap confidence intervals, together with some less well known ones, highlighting their strengths and weaknesses. We then present a simulation study, a flow chart for choosing an appropriate method and a survival analysis example. Copyright © 2000 John Wiley & Sons, Ltd.
We investigate two options for performing Bayesian inference on spatial
log-Gaussian Cox processes assuming a spatially continuous latent field: Markov
chain Monte Carlo (MCMC) and the integrated nested Laplace approximation
(INLA). We first describe the device of approximating a spatially continuous
Gaussian field by a Gaussian Markov random field on a discrete lattice, and
present a simulation study showing that, with careful choice of parameter
values, small neighbourhood sizes can give excellent approximations. We then
introduce the spatial log-Gaussian Cox process and describe MCMC and INLA
methods for spatial prediction within this model class. We report the results
of a simulation study in which we compare MALA and the technique of
approximating the continuous latent field by a discrete one, followed by
approximate Bayesian inference via INLA over a selection of 18 simulated
scenarios. The results question the notion that the latter technique is both
significantly faster and more robust than MCMC in this setting; 100,000
iterations of the MALA algorithm running in 20 minutes on a desktop PC
delivered greater predictive accuracy than the default \verb=INLA= strategy,
which ran in 4 minutes and gave comparative performance to the full Laplace
approximation which ran in 39 minutes.
Monitoring small area contrasts in life expectancy is important for health policy purposes but subject to difficulties under conventional life table analysis. Additionally, the implicit model underlying conventional life table analysis involves a highly parametrized fixed effect approach. An alternative strategy proposed here involves an explicit model based on random effects for both small areas and age groups. The area effects are assumed to be spatially correlated, reflecting unknown mortality risk factors that are themselves typically spatially correlated. Often mortality observations are disaggregated by demographic category as well as by age and area, e.g. by gender or ethnic group, and multivariate area and age random effects will be used to pool over such groups. A case study considers variations in life expectancy in 1 118 small areas (known as wards) in Eastern England over a five-year period 1999-2003. The case study deaths data are classified by gender, age, and area, and a bivariate model for area and age effects is therefore applied. The interrelationship between the random area effects and two major influences on small area life expectancy is demonstrated in the study, these being area socio-economic status (or deprivation) and the location of nursing and residential homes for frail elderly. Copyright (c) 2009 The Author. Journal compilation (c) 2009 International Statistical Institute.
There has been much recent interest in Bayesian image analysis, including such topics as removal of blur and noise, detection of object boundaries, classification of textures, and reconstruction of two- or three-dimensional scenes from noisy lower-dimensional views. Perhaps the most straightforward task is that of image restoration, though it is often suggested that this is an area of relatively minor practical importance. The present paper argues the contrary, since many problems in the analysis of spatial data can be interpreted as problems of image restoration. Furthermore, the amounts of data involved allow routine use of computer intensive methods, such as the Gibbs sampler, that are not yet practicable for conventional images. Two examples are given, one in archeology, the other in epidemiology. These are preceded by a partial review of pixel-based Bayesian image analysis.
Optimal use of epidemiologic findings in decision making requires more information than standard analyses provide. It requires calculating and reporting the total uncertainty in the results, which in turn requires methods for quantifying the uncertainty introduced by systematic error. Quantified uncertainty can improve policy and clinical decisions, better direct further research, and aid public understanding, and thus enhance the contributions of epidemiology. The error quantification approach proposed here is based on estimating a probability distribution for a bias-corrected effect measure based on externally-derived distributions of bias levels. Using Monte Carlo simulation, corrections for multiple biases are combined by identifying the steps through which true causal effects become data, and (in reverse order) correcting for the errors introduced by each step. The bias-correction calculations are the same as those used in sensitivity analysis, but the resulting distribution of possible true values is more than a sensitivity analysis; it is a more complete reporting of the actual study results. The approach is illustrated with an application to a recent study that resulted in the drug, phenylpropanolamine, being removed from the market.
The drive to tackle health inequalities at the local level has increased interest in mortality data for small populations. There is some concern that nursing homes may affect measures of mortality for small populations, but there has been little in depth analysis of this.
Deaths between 1997 and 2001 and population figures from the GP register (Exeter) database and census 2001 were used to produce life expectancy (LE) figures for all electoral wards in West Sussex. The proportion of those dying within each ward that had been residents of nursing homes was calculated and the relation between these variables and deprivation investigated.
There was a significant linear relation between nursing home deaths and LE (p<0.0001), which explained 36% of variation in LE between wards. Deprivation accounted for around 35% of the variation in LE (p<0.0001) but was not correlated with nursing home deaths (p> or =0.0982). Multiple linear regression shows that over 60% of the variation in LE at ward level can be explained by both nursing home deaths and deprivation (p<0.0001) and that the two variables explain similar proportions of this variation. The relation between LE and nursing home deaths within wards grouped by deprivation suggests that the impact of nursing homes is strongest in deprived wards.
This finding has important implications for LE calculations in small populations. Further investigation is now needed to examine the impact of nursing homes in other areas, on other mortality measures, and in larger populations.
To evaluate methods for calculating life expectancy in small areas, for example, English electoral wards.
The Monte Carlo method was used to simulate the distribution of life expectancy (and its standard error) estimates for 10 alternative life table models. The models were combinations of Chiang or Silcocks methodology, 5 or 10 year age intervals, and a final age interval of 85+, 90+, or 95+.
A hypothetical small area experiencing the population age structure and age specific mortality rates of English men 1998-2000.
Routine mortality and population statistics for England.
Silcocks and Chiang based models gave similar estimates of life expectancy and its standard error. For all models, life expectancy was increasingly overestimated as the simulated population size decreased. The degree of overestimation depended largely on the final age interval chosen. Life expectancy estimates of small populations are normally distributed. The standard error estimates are normally distributed for large populations but become increasingly skewed as the population size decreases. Substitution methods to compensate for the effect of zero death counts on the standard error estimate did not improve the estimate.
It is recommended that a population years at risk of 5000 is a reasonable point above which life expectancy calculations can be performed with reasonable confidence. Implications are discussed. Within the UK, the Chiang methodology and a five year life table to 85+ is recommended, with no adjustments to age specific death counts of zero.
Conventional analytic results do not reflect any source of uncertainty other than random error, and as a result readers must rely on informal judgments regarding the effect of possible biases. When standard errors are small these judgments often fail to capture sources of uncertainty and their interactions adequately. Multiple-bias models provide alternatives that allow one systematically to integrate major sources of uncertainty, and thus to provide better input to research planning and policy analysis. Typically, the bias parameters in the model are not identified by the analysis data and so the results depend completely on priors for those parameters. A Bayesian analysis is then natural, but several alternatives based on sensitivity analysis have appeared in the risk assessment and epidemiologic literature. Under some circumstances these methods approximate a Bayesian analysis and can be modified to do so even better. These points are illustrated with a pooled analysis of case-control studies of residential magnetic field exposure and childhood leukaemia, which highlights the diminishing value of conventional studies conducted after the early 1990s. It is argued that multiple-bias modelling should become part of the core training of anyone who will be entrusted with the analysis of observational data, and should become standard procedure when random error is not the only important source of uncertainty (as in meta-analysis and pooled analysis). Copyright 2005 Royal Statistical Society.
This paper proposes a unified framework for the analysis of incidence or mortality data in space and time. The problem with such analysis is that the number of cases and the corresponding population at risk in any single unit of space Theta time are too small to produce a reliable estimate of the underlying disease risk without "borrowing strength" from neighbouring cells. The goal here could be described as one of smoothing, in which both spatial and non--spatial considerations may arise, and spatio--temporal interactions may become an important feature. Based on an extended version of the main effects model proposed in KnorrHeld and Besag (1998), four generic types of space Theta time interactions are introduced. Each type implies a certain degree of prior (in)dependence for interaction parameters, and corresponds to the product of one of the two spatial main effects with one of the two temporal main effects. Data analysis is implemented via Markov chain Monte Carlo methods. The methodology is illustrated by an analysis of Ohio lung cancer data 1968-88. We compare the fit and the complexity of each model by the DIC criterion, recently proposed in Spiegelhalter et al. (1998).
Number of deaths by district/sex/age (5 years old)
- Korean Statistical Information Service
Resident registration population by district/sex/age (5 years old)
- Korean Statistical Information Service