A Bayesian Spatial Modeling Approach to Mortality Forecasting
Zhen Liu, Xiaoqian Sun, Yu-Bo Wang
备注：
The corresponding author considers there is a huge drawback at the main methodology to revise in a long time and is not willing to be the duty of corresponding author. Hence, I request the publisher to withdraw this paper. Thanks
This paper extends Bayesian mortality projection models for multiple populations considering the stochastic structure and the effect of spatial autocorrelation among the observations. We explain high levels of overdispersion according to adjacent locations based on the conditional autoregressive model. In an empirical study, we compare different hierarchical projection models for the analysis of geographical diversity in mortality between the Japanese counties in multiple years, according to age. By a Markov chain Monte Carlo (MCMC) computation, results have demonstrated the flexibility and predictive performance of our proposed model.
The determination of the shapes of mortality curves, the estimation and projection of mortality patterns over time, and the investigation of differences in mortality patterns across different small underdeveloped populations have received special attention in recent years. The challenges involved in this type of problems are the common sparsity and the unstable behavior of observed death counts in small areas (populations). These features impose many dificulties in the estimation of reasonable mortality schedules. In this chapter, we present a discussion about this problem and we introduce the…
Bayesian mortality forecasting with a Conway--Maxwell--Poisson specification
School of Mathematics, Statistics, and Actuarial Science, University of Essex（埃塞克斯大学数学、统计与精算学院）；Department of Mathematics, University of Connecticut（康涅狄格大学数学系）
We propose a probabilistic mortality forecasting model that can be applied to derive forecasts for populations with regular and irregular mortality developments. Our model (1) uses rates of mortality improvement to model dynamic age patterns of mortality change and it can (2) optionally complement the mortality trend of a country of interest with that of at least one reference country. Retrospective mortality forecasts for British and Danish women from 1991 to 2011 suggest that our model can generate smaller forecast errors than other widely accepted approaches like, for instance, the Lee-Cart…
The missing data problem pervasively exists in statistical applications. Even as simple as the count data in mortality projections, it may not be available for certain age-and-year groups due to the budget limitations or difficulties in tracing research units, resulting in the follow-up estimation and prediction inaccuracies. To circumvent this data-driven challenge, we extend the Poisson log-normal Lee-Carter model to accommodate a more flexible time structure, and develop the new sampling algorithm that improves the MCMC convergence when dealing with incomplete mortality data. Via the overdi…
Allocating patients to treatment arms during a trial based on the observed responses accumulated prior to the decision point, and sequential adaptation of this allocation,, could minimize the expected number of failures or maximize total benefit to patients. In this study, we developed a Bayesian response adaptive randomization (RAR) design targeting the endpoint of organ support-free days (OSFD) for patients admitted to the intensive care units (ICU). The OSFD is a mixture of mortality and morbidity assessed by the number of days of free of organ support within a predetermined time-window pos…
We provide forecasts for mortality rates by using two different approaches. First we employ dynamic non-linear logistic models based on Heligman-Pollard formula. Second, we assume that the dynamics of the mortality rates can be modelled through a Gaussian Markov random field. We use efficient Bayesian methods to estimate the parameters and the latent states of the proposed models. Both methodologies are tested with past data and are used to forecast mortality rates both for large (UK and Wales) and small (New Zealand) populations up to 21 years ahead. We demonstrate that predictions for indivi…
We investigate the decline of infant mortality in 42 low and middle income countries (LMIC) using detailed micro data from 84 Demographic and Health Surveys. We estimate infant mortality risk for each infant in our data and develop a novel extension of Oaxaca decomposition to understand the sources of these changes. We find that the decline in infant mortality is due to a declining propensity for parents with given characteristics to experience the death of an infant rather than due to changes in the distributions of these characteristics over time. Our results suggest that technical progress …
Smoking is one of the main risk factors that has affected human mortality and life expectancy over the past century. Smoking accounts for a large part of the nonlinearities in the growth of life expectancy and of the geographic and sex differences in mortality. As Bongaarts (2006) and Janssen (2018) suggested, accounting for smoking could improve the quality of mortality forecasts due to the predictable nature of the smoking epidemic. We propose a new Bayesian hierarchical model to forecast life expectancy at birth for both sexes and for 69 countries with good data on smoking-related mortality…
Functional data are often extremely high-dimensional and exhibit strong dependence structures but can often prove valuable for both prediction and inference. The literature on functional data analysis is well developed; however, there has been very little work involving functional data in complex survey settings. Motivated by physical activity monitor data from the National Health and Nutrition Examination Survey (NHANES), we develop a Bayesian model for functional covariates that can properly account for the survey design. Our approach is intended for non-Gaussian data and can be applied in m…
Smoking is one of the preventable threats to human health and is a major risk factor for lung cancer, upper aero-digestive cancer, and chronic obstructive pulmonary disease. Estimating and forecasting the smoking attributable fraction (SAF) of mortality can yield insights into smoking epidemics and also provide a basis for more accurate mortality and life expectancy projection. Peto et al. (1992) proposed a method to estimate the SAF using the lung cancer mortality rate as an indicator of exposure to smoking in the population of interest. Here we use the same method to estimate the all-age SAF…
There has been growing interest on forecasting mortality. In this article, we propose a novel dynamic Bayesian approach for modeling and forecasting the age-at-death distribution, focusing on a three-components mixture of a Dirac mass, a Gaussian distribution and a Skew-Normal distribution. According to the specified model, the age-at-death distribution is characterized via seven parameters corresponding to the main aspects of infant, adult and old-age mortality. The proposed approach focuses on coherent modeling of multiple countries, and following a Bayesian approach to inference we allow to…
Predicting the evolution of mortality rates plays a central role for life insurance and pension funds.Various stochastic frameworks have been developed to model mortality patterns taking into account the main stylized facts driving these patterns. However, relying on the prediction of one specific model can be too restrictive and lead to some well documented drawbacks including model misspecification, parameter uncertainty and overfitting. To address these issues we first consider mortality modelling in a Bayesian Negative-Binomial framework to account for overdispersion and the uncertainty ab…
Age-disaggregated health data is crucial for effective public health planning and monitoring. Monitoring under-five mortality, for example, requires highly detailed age data since the distribution of potential causes of death varies substantially within the first few years of life. Comparative researchers often have to rely on multiple data sources yet, these sources often have ages aggregated at different levels, making it difficult to combine the data into a single, coherent picture. To address this challenge in the context of under-five cause-specific mortality, we propose a Bayesian approa…
Reliable mortality estimates at the subnational level are essential in the study of health inequalities within a country. One of the difficulties in producing such estimates is the presence of small populations, where the stochastic variation in death counts is relatively high, and so the underlying mortality levels are unclear. We present a Bayesian hierarchical model to estimate mortality at the subnational level. The model builds on characteristic age patterns in mortality curves, which are constructed using principal components from a set of reference mortality curves. Information on morta…
The improvement of mortality projection is a pivotal topic in the diverse branches related to insurance, demography, and public policy. Motivated by the thread of Lee-Carter related models, we propose a Bayesian model to estimate and predict mortality rates for multi-population. This new model features in information borrowing among populations and properly reflecting variations of data. It also provides a solution to a long-time overlooked problem: model selection for dependence structures of population-specific time parameters. By introducing a Dirac spike function, simultaneous model select…
Moderation effects and elasticities in compositional regression with a total. Application to Bayesian spatiotemporal modelling of all-cause mortality from environmental stressors
University of Girona（赫罗纳大学）；Centro de Investigación Biomédica en Red de Epidemiología y Salud Pública, Instituto de Salud Carlos III（公共卫生与流行病学生物医学研究中心，卡洛斯三世健康研究所）
Forecasting enterprise-wide revenue is critical to many companies and presents several challenges and opportunities for significant business impact. This case study is based on model developments to address these challenges for forecasting in a large-scale retail company. Focused on multivariate revenue forecasting across collections of supermarkets and product Categories, hierarchical dynamic models are natural: these are able to couple revenue streams in an integrated forecasting model, while allowing conditional decoupling to enable relevant and sensitive analysis together with scalable com…
Most studies on inequality in infant and child mortality compare average mortality rates between large groups of births, for example, comparing births from different countries, income groups, ethnicities, or different times. These studies do not measure within-group disparities. The few studies that have measured within-group variability in infant and child mortality have used tools from the income inequality literature, such as Gini indices. We show that the latter are inappropriate for infant and child mortality. We develop novel tools that are appropriate for analyzing infant and child mort…
A common goal in modeling demographic rates is to compare two or more groups. For ex- ample comparing mortality rates between men and women or between geographic regions may reveal health inequalities. A popular class of models for all-cause mortality as well as incidence of specific diseases like cancer is the age-period-cohort (APC) model. Extending this model to the multivariate setting is not straightforward because the univariate APC model suffers from well-known identifiability problems. Often APC models are fit separately for each strata, and then comparisons are made post hoc. This pap…
Bayesian ACCESS for Understanding Latent Epidemic Trajectories from Publicly Released Suppressed Data: Application to U.S. Opioid-related Overdose Mortality
The University of Texas Health Science Center at Houston（休斯顿德克萨斯大学健康科学中心）
We develop the methodology and a detailed case study in use of a class of Bayesian predictive synthesis (BPS) models for multivariate time series forecasting. This extends the recently introduced foundational framework of BPS to the multivariate setting, with detailed application in the topical and challenging context of multi-step macroeconomic forecasting in a monetary policy setting. BPS evaluates-- sequentially and adaptively over time-- varying forecast biases and facets of miscalibration of individual forecast densities, and-- critically-- of time-varying inter-dependencies among them ov…
In this work we present a spatial approach to model and investigate mortality data referenced over a Lexis structure. We decompose the force of mortality into two interpretable components: a Markov random field, smooth with respect to time, age and cohort which explains the main pattern of mortality; and a secondary component of independent shocks, accounting for additional non-smooth mortality. Inference is based on a hierarchical Bayesian approach with Markov chain Monte Carlo computations. We present an extensive application to data from the Human Mortality Database about 37 countries. For …
We present a case study and methodological developments in large-scale hierarchical dynamic modeling for personalized prediction in commerce. The context is supermarket sales, where improved forecasting of customer/household-specific purchasing behavior informs decisions about personalized pricing and promotions on a continuing basis. This is a big data, big modeling and forecasting setting involving many thousands of customers and items on sale, requiring sequential analysis, addressing information flows at multiple levels over time, and with heterogeneity of customer profiles and item catego…
In order to implement disease-specific interventions in young age groups, policy makers in low- and middle-income countries require timely and accurate estimates of age- and cause-specific child mortality. High quality data is not available in settings where these interventions are most needed, but there is a push to create sample registration systems that collect detailed mortality information. Current methods that estimate mortality from this data employ multistage frameworks without rigorous statistical justification that separately estimate all-cause and cause-specific mortality and are no…
Approximate Bayesian Computation (ABC) has become increasingly prominent as a method for conducting parameter inference in a range of challenging statistical problems, most notably those characterized by an intractable likelihood function. In this paper, we focus on the use of ABC not as a tool for parametric inference, but as a means of generating probabilistic forecasts; or for conducting what we refer to as `approximate Bayesian forecasting'. The four key issues explored are: i) the link between the theoretical behavior of the ABC posterior and that of the ABC-based predictive; ii) the use …
Civil registration vital statistics (CRVS) data are used to produce national estimates of maternal mortality, but are often subject to substantial reporting errors due to misclassification of maternal deaths. The accuracy of CRVS systems can be assessed by comparing CRVS-based counts of maternal and non-maternal deaths to those obtained from specialized studies, which are rigorous assessments of maternal mortality for a given country-period. We developed a Bayesian bivariate random walk model to estimate sensitivity and specificity of the reporting on maternal mortality in CRVS data, and assoc…
Forecasts of mortality provide vital information about future populations, with implications for pension and health-care policy as well as for decisions made by private companies about life insurance and annuity pricing. Stochastic mortality forecasts allow the uncertainty in mortality predictions to be taken into consideration when making policy decisions and setting product prices. Longer lifespans imply that forecasts of mortality at ages 90 and above will become more important in such calculations. This paper presents a Bayesian approach to the forecasting of mortality that jointly estimat…
In recent years, much of the focus in monitoring child mortality has been on assessing changes in the under-five mortality rate (U5MR). However, as the U5MR decreases, the share of neonatal deaths (within the first month) tends to increase, warranting increased efforts in monitoring this indicator in addition to the U5MR. A Bayesian splines regression model is presented for estimating neonatal mortality rates (NMR) for all countries. In the model, the relationship between NMR and U5MR is assessed and used to inform estimates, and spline regression models are used to capture country-specific tr…
We develop a Gaussian process ("GP") framework for modeling mortality rates and mortality improvement factors. GP regression is a nonparametric, data-driven approach for determining the spatial dependence in mortality rates and jointly smoothing raw rates across dimensions, such as calendar year and age. The GP model quantifies uncertainty associated with smoothed historical experience and generates full stochastic trajectories for out-of-sample forecasts. Our framework is well suited for updating projections when newly available data arrives, and for dealing with "edge" issues where credibili…
Human mortality is in part a function of multiple socioeconomic factors that differ both spatially and temporally. Adjusting for other covariates, the human lifespan is positively associated with household wealth. However, the extent to which mortality in a geographical region is a function of socioeconomic factors in both that region and its neighbors is unclear. There is also little information on the temporal components of this relationship. Using the districts of Hong Kong over multiple census years as a case study, we demonstrate that there are differences in how wealth indicator variable…
Racialized economic segregation, a key metric that simultaneously accounts for spatial, social and income polarization, has been linked to adverse health outcomes, including morbidity and mortality; however, statistical methods for measuring the association between racialized economic segregation and health outcomes are not well-developed and are usually studied at the individual level. In this paper we propose a two-stage Bayesian statistical framework that provides a broad, flexible approach to studying the spatially varying association between premature mortality and racialized economic seg…
In the initial wave of the COVID-19 pandemic we observed great discrepancies in both infection and mortality rates between countries. Besides the biological and epidemiological factors, a multitude of social and economic criteria also influence the extent to which these discrepancies appear. Consequently, there is an active debate regarding the critical socio-economic and health factors that correlate with the infection and mortality rates outcome of the pandemic. Here, we leverage Bayesian model averaging techniques and country level data to investigate the potential of 28 variables, describi…
Estimates of the under-five mortality rate (U5MR) are used to track progress in reducing child mortality and to evaluate countries' performance related to Millennium Development Goal 4. However, for the great majority of developing countries without well-functioning vital registration systems, estimating the U5MR is challenging due to limited data availability and data quality issues. We describe a Bayesian penalized B-spline regression model for assessing levels and trends in the U5MR for all countries in the world, whereby biases in data series are estimated through the inclusion of a multil…
The recently introduced class of simultaneous graphical dynamic linear models (SGDLMs) defines an ability to scale on-line Bayesian analysis and forecasting to higher-dimensional time series. This paper advances the methodology of SGDLMs, developing and embedding a novel, adaptive method of simultaneous predictor selection in forward filtering for on-line learning and forecasting. The advances include developments in Bayesian computation for scalability, and a case study in exploring the resulting potential for improved short-term forecasting of large-scale volatility matrices. A case study co…
Decision-making often involves ranking and selection. For example, to assemble a team of political forecasters, we might begin by narrowing our choice set to the candidates we are confident rank among the top 10% in forecasting ability. Unfortunately, we do not know each candidate's true ability but observe a noisy estimate of it. This paper develops new Bayesian algorithms to rank and select candidates based on noisy estimates. Using simulations based on empirical data, we show that our algorithms often outperform frequentist ranking and selection algorithms. Our Bayesian ranking algorithms y…
The maternal mortality ratio (MMR) is defined as the number of maternal deaths in a population per 100,000 live births. Country-specific MMR estimates are published on a regular basis by the United Nations Maternal Mortality Estimation Inter-agency Group (UN MMEIG) to track progress in reducing maternal deaths and to evaluate regional and national performance related to Millennium Development Goal (MDG) 5, which calls for a 75% reduction in the MMR between 1990 and 2015. Until 2014, the UN MMEIG used a multilevel regression model for producing estimates for countries without sufficient data fr…
In many countries life expectancy gains have been substantially higher than predicted by even recent forecasts. This is primarily due to increasing rates of improvement in old-age mortality not captured by existing models. In this paper we show how the concept of frailty can be used to model both changing rates of improvement and the deceleration of mortality at old ages, also seen in data. We present a "fragilization" method by which frailty can be added to standard mortality models. The aim is to improve the modeling and forecasting of old-age mortality while preserving the structure of the …
IMEDACS；Vivace Health Solutions Inc（Vivace健康解决方案公司）；Johns Hopkins University（约翰斯·霍普金斯大学）；Scripps Memorial Hospital - Encinitas（斯克里普斯恩西尼塔斯纪念医院）
Although timely sepsis diagnosis and prompt interventions in Intensive Care Unit (ICU) patients are associated with reduced mortality, early clinical recognition is frequently impeded by non-specific signs of infection and failure to detect signs of sepsis-induced organ dysfunction in a constellation of dynamically changing physiological data. The goal of this work is to identify patient at risk of life-threatening sepsis utilizing a data-centered and machine learning-driven approach. We derive a mortality risk predictive dynamic Bayesian network (DBN) guided by a customized sepsis knowledgeba…
Acute infection, if not rapidly and accurately detected, can lead to sepsis, organ failure and even death. Current detection of acute infection as well as assessment of a patient's severity of illness are imperfect. Characterization of a patient's immune response by quantifying expression levels of specific genes from blood represents a potentially more timely and precise means of accomplishing both tasks. Machine learning methods provide a platform to leverage this 'host response' for development of deployment-ready classification models. Prioritization of promising classifiers is dependent, …
The original version of Bayesian reconstruction, a method for estimating age-specific fertility, mortality, migration and population counts of the recent past with uncertainty, produced estimates for female-only populations. Here we show how two-sex populations can be similarly reconstructed and probabilistic estimates of various sex ratio quantities obtained. We demonstrate the method by reconstructing the populations of India from 1971 to 2001, Thailand from 1960 to 2000, and Laos from 1985 to 2005. We found evidence that in India, sex ratio at birth exceeded its conventional upper limit of …
