Mortality Forecasts Research Articles

Bayesian Poisson common factor model with overdispersion for mortality forecasting in multiple populations

This article presents a Poisson common factor model with an overdispersion factor to predict some multiple populations’ mortality rates. We use Bayesian data analysis and an extension of the Hamiltonian Monte Carlo sampler to compute the estimation of the model parameters and mortality rates prediction. We apply the proposed model to the real mortality data of some European countries. Using some model selection measures, we compare the proposed model with a log-linear model and those introduced in Antonio, Bardoutsos, and Ouburg (2015, Bayesian Poisson log-bilinear models for mortality projections with multiple populations. European Actuarial Journal 5 (2): 245–281) and Wong, Forster, and Smith (2018, Bayesian mortality forecasting with overdispersion. Insurance: Mathematics and Economics 83: 206–221).

Bayesian model comparison for mortality forecasting

Abstract Stochastic models are appealing for mortality forecasting in their ability to generate intervals that quantify uncertainties underlying the forecasts. We present a fully Bayesian implementation of the age-period-cohort-improvement (APCI) model with overdispersion, which is compared with the Lee–Carter model with cohorts. We show that naive prior specification can yield misleading inferences, where we propose Laplace prior as an elegant solution. We also perform model averaging to incorporate model uncertainty. Our findings indicate that the APCI model offers better fit and forecast for England and Wales data spanning 1961–2002. Our approach also allows coherent inclusion of multiple sources of uncertainty, producing well-calibrated probabilistic intervals.

Managing Mortality and Aging Risks with a Time-Varying Lee-Carter Model.

Influential existing research has suggested that rather than being static, mortality declines decelerate at young ages and accelerate at old ages. Without accounting for this feature, the forecast mortality rates of the popular Lee-Carter (LC) model are less reliable in the long run. To provide more accurate mortality forecasting, we introduce a time-varying coefficients extension of the LC model by adopting the effective kernel methods. With two frequently used kernel functions, Epanechnikov (LC-E) and Gaussian (LC-G), we demonstrate that the proposed extension is easy to implement, incorporates the rotating patterns of mortality decline and is straightforwardly extensible to multi-population cases. Using a large sample of 15 countries over 1950-2019, we show that LC-E and LC-G, as well as their multi-population counterparts, can consistently improve the forecasting accuracy of the competing LC and Li-Lee models in both single- and multi-population scenarios.

Artificial intelligence in coronary computed tomography angiography: Demands and solutions from a clinical perspective.

Coronary computed tomography angiography (CCTA) is increasingly the cornerstone in the management of patients with chronic coronary syndromes. This fact is reflected by current guidelines, which show a fundamental shift towards non-invasive imaging - especially CCTA. The guidelines for acute and stable coronary artery disease (CAD) of the European Society of Cardiology from 2019 and 2020 emphasize this shift. However, to fulfill this new role, a broader availability in adjunct with increased robustness of data acquisition and speed of data reporting of CCTA is needed. Artificial intelligence (AI) has made enormous progress for all imaging methodologies concerning (semi)-automatic tools for data acquisition and data post-processing, with outreach toward decision support systems. Besides onco- and neuroimaging, cardiac imaging is one of the main areas of application. Most current AI developments in the scenario of cardiac imaging are related to data postprocessing. However, AI applications (including radiomics) for CCTA also should enclose data acquisition (especially the fact of dose reduction) and data interpretation (presence and extent of CAD). The main effort will be to integrate these AI-driven processes into the clinical workflow, and to combine imaging data/results with further clinical data, thus - beyond the diagnosis of CAD- enabling prediction and forecast of morbidity and mortality. Furthermore, data fusing for therapy planning (e.g., invasive angiography/TAVI planning) will be warranted. The aim of this review is to present a holistic overview of AI applications in CCTA (including radiomics) under the umbrella of clinical workflows and clinical decision-making. The review first summarizes and analyzes applications for the main role of CCTA, i.e., to non-invasively rule out stable coronary artery disease. In the second step, AI applications for additional diagnostic purposes, i.e., to improve diagnostic power (CAC = coronary artery classifications), improve differential diagnosis (CT-FFR and CT perfusion), and finally improve prognosis (again CAC plus epi- and pericardial fat analysis) are reviewed.

Small Area Forecasting of Opioid-Related Mortality: Bayesian Spatiotemporal Dynamic Modeling Approach

Opioid-related overdose mortality has remained at crisis levels across the United States, increasing 5-fold and worsened during the COVID-19 pandemic. The ability to provide forecasts of opioid-related mortality at granular geographical and temporal scales may help guide preemptive public health responses. Current forecasting models focus on prediction on a large geographical scale, such as states or counties, lacking the spatial granularity that local public health officials desire to guide policy decisions and resource allocation. The overarching objective of our study was to develop Bayesian spatiotemporal dynamic models to predict opioid-related mortality counts and rates at temporally and geographically granular scales (ie, ZIP Code Tabulation Areas [ZCTAs]) for Massachusetts. We obtained decedent data from the Massachusetts Registry of Vital Records and Statistics for 2005 through 2019. We developed Bayesian spatiotemporal dynamic models to predict opioid-related mortality across Massachusetts' 537 ZCTAs. We evaluated the prediction performance of our models using the one-year ahead approach. We investigated the potential improvement of prediction accuracy by incorporating ZCTA-level demographic and socioeconomic determinants. We identified ZCTAs with the highest predicted opioid-related mortality in terms of rates and counts and stratified them by rural and urban areas. Bayesian dynamic models with the full spatial and temporal dependency performed best. Inclusion of the ZCTA-level demographic and socioeconomic variables as predictors improved the prediction accuracy, but only in the model that did not account for the neighborhood-level spatial dependency of the ZCTAs. Predictions were better for urban areas than for rural areas, which were more sparsely populated. Using the best performing model and the Massachusetts opioid-related mortality data from 2005 through 2019, our models suggested a stabilizing pattern in opioid-related overdose mortality in 2020 and 2021 if there were no disruptive changes to the trends observed for 2005-2019. Our Bayesian spatiotemporal models focused on opioid-related overdose mortality data facilitated prediction approaches that can inform preemptive public health decision-making and resource allocation. While sparse data from rural and less populated locales typically pose special challenges in small area predictions, our dynamic Bayesian models, which maximized information borrowing across geographic areas and time points, were used to provide more accurate predictions for small areas. Such approaches can be replicated in other jurisdictions and at varying temporal and geographical levels. We encourage the formation of a modeling consortium for fatal opioid-related overdose predictions, where different modeling techniques could be ensembled to inform public health policy.

Evaluation of Lee-Carter model to breast cancer mortality prediction in China and Pakistan.

Precise breast cancer-related mortality forecasts are required for public health program and healthcare service planning. A number of stochastic model-based approaches for predicting mortality have been developed. The trends shown by mortality data from various diseases and countries are critical to the effectiveness of these models. This study illustrates the unconventional statistical method for estimating and predicting the mortality risk between the early-onset and screen-age/late-onset breast cancer population in China and Pakistan using the Lee-Carter model. Longitudinal death data for female breast cancer from 1990 to 2019 obtained from the Global Burden of Disease study database were used to compare statistical approach between early-onset (age group, 25-49 years) and screen-age/late-onset (age group, 50-84 years) population. We evaluated the model performance both within (training period, 1990-2010) and outside (test period, 2011-2019) data forecast accuracy using the different error measures and graphical analysis. Finally, using the Lee-Carter model, we predicted the general index for the time period (2011 to 2030) and derived corresponding life expectancy at birth for the female breast cancer population using life tables. Study findings revealed that the Lee-Carter approach to predict breast cancer mortality rate outperformed in the screen-age/late-onset compared with that in the early-onset population in terms of goodness of fit and within and outside forecast accuracy check. Moreover, the trend in forecast error was decreasing gradually in the screen-age/late-onset compared with that in the early-onset breast cancer population in China and Pakistan. Furthermore, we observed that this approach had provided almost comparable results between the early-onset and screen-age/late-onset population in forecast accuracy for more varying mortality behavior over time like in Pakistan. Both the early-onset and screen-age/late-onset populations in Pakistan were expected to have an increase in breast cancer mortality by 2030. whereas, for China, it was expected to decrease in the early-onset population. The Lee-Carter model can be used to estimate breast cancer mortality and so to project future life expectancy at birth, especially in the screen-age/late-onset population. As a result, it is suggested that this approach may be useful and convenient for predicting cancer-related mortality even when epidemiological and demographic disease data sets are limited. According to model predictions for breast cancer mortality, improved health facilities for disease diagnosis, control, and prevention are required to reduce the disease's future burden, particularly in less developed countries.

Enhancing Mortality Forecasting through Bivariate Model–Based Ensemble

We propose a bivariate model–based ensemble (BMBE) method to borrow information from the mortality data of a given pool of auxiliary populations to enhance the mortality forecasting of a target population. The BMBE method establishes a cascade of bivariate mortality models between the target population and each auxiliary population as the base learners. Then it aggregates prediction results from all of the base learners by means of an averaging strategy. Augmented common factor–type and CBD-type bivariate models are applied as the base learners as illustrative examples in the empirical studies with the Human Mortality Database. Empirical results presented in this article confirm the effectiveness of the proposed BMBE method in enhancing mortality prediction. For completeness, we also conduct a synthetic study to illustrate a particular setting for the superior performance of the BMBE method.

Rotation in age patterns of mortality decline: statistical evidence and modeling

In the context of mortality forecasting, “rotation” refers to the phenomenon that mortality decline accelerates at older ages but decelerates at younger ages. Since rotation is typically subtle, it is difficult to be confirmed and modeled in a statistical, data-driven manner. In this paper, we attempt to overcome this challenge by proposing an alternative modeling approach. The approach encompasses a new model structure, which includes a component that is devoted to measuring rotation. It also features a modeling technique known as ANCOVA, which allows us to statistically detect rotation and extrapolate the phenomenon into the future. Our proposed approach yields plausible mortality forecasts that are similar to those produced by Li et al. [Extending the Lee-Carter method to model the rotation of age patterns of mortality decline for long-term projections. Demography 50 (6), 2037–205, and may be considered more advantageous than the approach of Li et al. in the sense that it is able to generate not only static but also stochastic forecasts.

Machine Learning in Long-Term Mortality Forecasting

Machine Learning in Long-Term Mortality Forecasting

Forecasting mortality rates with a coherent ensemble averaging approach

AbstractModeling and forecasting of mortality rates are closely related to a wide range of actuarial practices, such as the designing of pension schemes. To improve the forecasting accuracy, age coherence is incorporated in many recent mortality models, which suggests that the long-term forecasts will not diverge infinitely among age groups. Despite their usefulness, misspecification is likely to occur for individual mortality models when applied in empirical studies. The reliableness and accuracy of forecast rates are therefore negatively affected. In this study, an ensemble averaging or model averaging (MA) approach is proposed, which adopts age-specific weights and asymptotically achieves age coherence in mortality forecasting. The ensemble space contains both newly developed age-coherent and classic age-incoherent models to achieve the diversity. To realize the asymptotic age coherence, consider parameter errors, and avoid overfitting, the proposed method minimizes the variance of out-of-sample forecasting errors, with a uniquely designed coherent penalty and smoothness penalty. Our empirical data set include ten European countries with mortality rates of 0–100 age groups and spanning 1950–2016. The outstanding performance of MA is presented using the empirical sample for mortality forecasting. This finding robustly holds in a range of sensitivity analyses. A case study based on the Italian population is finally conducted to demonstrate the improved forecasting efficiency of MA and the validity of the proposed estimation of weights, as well as its usefulness in actuarial applications such as the annuity pricing.

Forecasting Mortality Rates with a Two-Step LASSO Based Vector Autoregressive Model

This paper proposes a two-step LASSO based vector autoregressive (2-LVAR) model to forecast mortality rates. Within the VAR framework, recent studies have developed a spatial–temporal autoregressive (STAR) model, in which age-specific mortality rates are related to their own historical values (temporality) and the rates of the neighboring cohorts (spatiality). Despite its desirable age coherence property and the improved forecasting accuracy over the widely used Lee–Carter (LC) model, STAR employs a rather restrictive structure that only allows for non-zero cohort effects of the same cohorts and the neighboring cohorts. To address this limitation, the proposed 2-LVAR model adopts a data-driven principle, as in a sparse VAR (SVAR) model, to offer more flexibility in the parametric structure. A two-step estimation strategy is developed accordingly to resolve the challenging objective function of 2-LVAR, which consists of non-standard L2 and LASSO-type penalties with constraints. Using empirical data from Australia, the United Kingdom, France, and Switzerland, we show that the 2-LVAR model outperforms the LC, STAR, and SVAR models in most of our forecasting results. Further simulation studies confirm this outperformance, and analyses based on life expectancy at birth empirically support the existence of age coherence. The results of this paper will help researchers understand the mortality projections in the long run and improve the reserving/ratemaking accuracy for life insurers.

Stochastic mortality forecasts for Bangladesh.

Mortality forecasts are essential part for policymaking in any aging society. In recent years, methods to model and forecast mortality have improved considerably. Among them, Lee-Carter method is one of the most influential method. In this paper, Lee-Carter method is applied to forecast mortality and life expectancy of Bangladesh. A functional data analysis approach is used to decompose the smoothed log-mortality rates in Lee-Carter framework for higher goodness-of-fit of the models and for longer forecast horizons. Bangladesh has been experiencing a mortality transition and has gained life expectancy in last few decades. The fitted model here showed higher pace of mortality decline for women in Bangladesh than that of men. The forecasts showed continuation of mortality improvement in long run and by 2060 life expectancy at birth is expected to reach over 80 years for both sexes in Bangladesh. The study also predicts the effect of reduction in infant mortality on the life expectancy in Bangladesh.

Extensions of the Lee–Carter model to project the data‐driven rotation of age‐specific mortality decline and forecast coherent mortality rates

AbstractAccurate forecasts and analyses of mortality rates are essential to many operational practices, such as the designing of pension schemes. Recent studies have focused on the age coherent forecasts, such that long‐term predictions will not diverge infinitely among ages. Although intuitively and biologically reasonable, this age coherence property is lost when the seminal Lee–Carter (LC) model and almost all its existing extensions are employed. Those include the famous Li–Lee (LL) model, which is argued to produce coherent forecasts of mortality rates across populations, but not ages. In this paper, we progressively explore two effective frameworks with three extensions, by applying the LL specification to the single‐population model (LC‐S) and by introducing time‐dependent age patterns of mortality declines in the forecasting steps with fixed (LC‐VF) and variant (LC‐V) intercepts when modeling those patterns. In particular, the recommended LC‐V model is motivated from the intermediate LC‐S and LC‐VF and resolves all remaining issues of both models. Also, the final LC‐V model is easy to implement, incorporates the dynamic and rotating age‐specific patterns of mortality decline, provides age‐coherent forecasts of mortality rates in the long run, and is straightforwardly extensible to multi‐population cases. Using a large sample of 15 countries, we show that the LC‐V model and its multipopulation counterpart can consistently improve the forecasting accuracy of the competing LC, LL and other extensions in both single‐population and multipopulation scenarios. Long‐term analyses up to 2100 further demonstrate the existence of age coherence when forecasting with the proposed LC‐V model.

Якби не було війни: прогноз демографічних показників для громад Вишгородського району Київської області

Demographic processes have been disturbed on those Ukrainian territories which have undergone occupation as a result of Russian Federation’s war against Ukraine. However, in order to rebuild such territories, local authorities need information on the prospects of demographic situation. Therefore, determining possible information sources and choosing models to forecast demographic indicators for local communities is relevant. The purpose of this work is identifying possible information sources and choosing models to predict demographic indicators for local communities; forecasting of population numbers, birth rate and mortality via splines for Vyshgorodsky district, Kyiv oblast communities. Novelty: forecasting of demographic indicators for local communities via spline functions. It has been shown that retrospective demographic research at local communities level is possible, if the communities’ contemporary borders correspond to the past administrative and territorial division. However, there are certain limitations regarding the indicators set. The analysis of 1979-2020 data on population numbers, birth rate and mortality for Ivankivsky and Polisky local communities has shown that the 1986-1988 data cannot be used for forecasting, since it varies considerably. This has been caused by the evacuation of residents from Chornobyl Exclusion Zone and administrative and territorial changes. The usage of spline functions in forecasting has shown that splines which have 5-7 knots are optimal. The most adequate forecasts of population numbers can be obtained via cubic splines, whereas the most trustworthy forecasts of birth rate and mortality – via linear continuous splines. It has been determined that the last years’ trends in population numbers, birth rate and mortality would continue in Vyshgorodsky district, Kyiv oblast local communities during 2021-2024. Due to hostilities on the territory of the district, there is no true data on demographic situation, and actual data may turn out to be far from the forecasted because of families with children emigration and mortality growth. Further research to improve the methodology of demographic forecasting by taking into account accidents that cause unfavorable demographic consequences is necessary.

A Hermite spline approach for modelling population mortality

AbstractOne complication in mortality modelling is capturing the impact of risk factors that contribute to mortality differentials between different populations. Evidence has suggested that mortality differentials tend to diminish over age. Classical methods such as the Gompertz law attempt to capture mortality patterns over age using intercept and slope parameters, possibly causing an unjustified mortality crossover at advanced ages when applied independently to different populations. In recent research, Richards (Scandinavian Actuarial Journal2020(2), 110–127) proposed a Hermite spline (HS) model that describes the age pattern of mortality differentials using one parameter and circumvents an unreasonable crossover by default. The original HS model was applied to pension data at individual level in the age dimension only. This paper extends the method to model population mortality in both age and period dimensions. Our results indicate that in addition to possessing desirable fitting properties, the HS approach can produce accurate mortality forecasts, compared with the Gompertz and P-splines models.

A Bibliometric Analysis of Research on Stochastic Mortality Modelling and Forecasting

Mortality improvements and life expectancies have been increasing in recent decades, leading to growing interest in understanding mortality risk and longevity risk. Studies of mortality forecasting are of interest among actuaries and demographers because mortality forecasting can quantify mortality and longevity risks. There is an abundance of literature on the topic of modelling and forecasting mortality, which often leads to confusion in determining a particular model to be adopted as a reliable tool. In this study, we conducted a bibliometric analysis with a focus on citation and co-citation analyses and co-occurrences of keywords to determine the most widely used stochastic mortality model. We found that the Lee–Carter model has remained one of the most relevant mortality models since its development in the 1990s. Furthermore, we also aimed to identify emerging topics and trends relating to mortality modelling and forecasting based on an analysis of authors’ keywords. This study contributes to the literature by providing a comprehensive overview and evolution of publications in stochastic mortality modelling and forecasting. Researchers can benefit from the present work in determining and exploring emerging trends and topics for future studies.

A retrospective assessment of COVID-19 model performance in the USA.

Coronavirus disease 2019 (COVID-19) forecasts from over 100 models are readily available. However, little published information exists regarding the performance of their uncertainty estimates (i.e. probabilistic performance). To evaluate their probabilistic performance, we employ the classical model (CM), an established method typically used to validate expert opinion. In this analysis, we assess both the predictive and probabilistic performance of COVID-19 forecasting models during 2021. We also compare the performance of aggregated forecasts (i.e. ensembles) based on equal and CM performance-based weights to an established ensemble from the Centers for Disease Control and Prevention (CDC). Our analysis of forecasts of COVID-19 mortality from 22 individual models and three ensembles across 49 states indicates that—(i) good predictive performance does not imply good probabilistic performance, and vice versa; (ii) models often provide tight but inaccurate uncertainty estimates; (iii) most models perform worse than a naive baseline model; (iv) both the CDC and CM performance-weighted ensembles perform well; but (v) while the CDC ensemble was more informative, the CM ensemble was more statistically accurate across states. This study presents a worthwhile method for appropriately assessing the performance of probabilistic forecasts and can potentially improve both public health decision-making and COVID-19 modelling.

Evaluating the Comparative Accuracy of COVID-19 Mortality Forecasts: An Analysis of the First-Wave Mortality Forecasts in the United States

The sudden onset of the COVID-19 pandemic posed significant challenges for forecasting professionals worldwide. This article examines the early forecasts of COVID-19 transmission, using the context of the United States, one of the early epicenters of the crisis. The article compares the relative accuracy of selected models from two forecasters who informed government policy in the first three months of the pandemic, the Institute of Health Metrics and Evaluation (IHME) and Columbia University. Furthermore, we examine whether the forecasts improved as more data became available in the subsequent months of the pandemic, using the forecasts from Los Alamos National Laboratory and the University of Texas, Austin. The analysis focuses on mortality estimates and compares forecasts using epidemiological and curve-fitting models during the first wave of the pandemic from March 2020 to October 2020. As health agencies worldwide struggled with uncertainty in models and projections of COVID-19 caseload and mortality, this article provides important insights that can be useful for crafting policy responses to the ongoing pandemic and future outbreaks.

Hierarchical mortality forecasting with EVT tails: An application to solvency capital requirement

In this paper, we propose a new framework to coherently produce probabilistic mortality forecasts by exploiting techniques in seasonal time-series models, extreme value theory (EVT), and hierarchical forecast reconciliation. In a hierarchical setting, coherent forecasts are those forecasts that add up in a manner consistent with the aggregation structure of the collection of time series. We are amongst the first to model and analyze U.S. monthly death data during the period from 1968–2019 to explore the seasonality and the age–gender dependence structure of mortality. Our results indicate that incorporating EVT and hierarchical forecast reconciliation greatly improves the overall forecast accuracy, which has important implications for life insurers in terms of rate making, reserve setting, and capital adequacy compliance. Using the solvency capital requirement (SCR) under Solvency II as an example, we show that the SCR calculated by our approach is considerably higher than those calculated by alternative models, suggesting that failing to account for extreme mortality risk and mortality dependence in the hierarchy can result in significantly underfunded problems for life insurers. We also find that our model can yield death forecasts that are largely consistent with actual observations in most of months in 2021 when death tolls surged due to COVID-19. This provides additional evidence of the effectiveness of our model for practical uses.

A New Mortality Framework to Identify Trends and Structural Changes in Mortality Improvement and Its Application in Forecasting

We construct a new age-specific mortality framework and implement an exemplar (DLGC) that provides an excellent fit to data from various countries and across long time periods while also providing accurate mortality forecasts by projecting parameters with ARIMA models. The model parameters have clear and reasonable interpretations that, after fitting, show stable time trends that react to major world mortality events. These trends are similar for countries with similar life-expectancies and capture mortality improvement, mortality structural change, and mortality compression over time. The parameter time plots can also be used to improve forecasting accuracy by suggesting training data periods and appropriate stochastic assumptions for parameters over time. We also give a quantitative analysis on what factors contribute to increased life expectancy and gender mortality differences during different age periods.