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 overdispersion term and Gibbs sampler, the extended model can be re-written as the dynamic linear model so that both Kalman and sequential Kalman filters can be incorporated into the sampling scheme. Additionally, our meticulous prior settings can avoid the re-scaling step in each MCMC iteration, and allow model selection simultaneously conducted with estimation and prediction. The proposed method is applied to the mortality data of Chinese males during the period 1995-2016 to yield mortality rate forecasts for 2017-2039. The results are comparable to those based on the imputed data set, suggesting that our approach could handle incomplete data well.
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）
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…
Tracking and estimating Daily Fine Particulate Matter (PM2.5) is very important as it has been shown that PM2.5 is directly related to mortality related to lungs, cardiovascular system, and stroke. That is, high values of PM2.5 constitute a public health problem in the US, and it is important that we precisely estimate PM2.5 to aid in public policy decisions. Thus, we propose a Bayesian hierarchical model for high-dimensional "multi-type" responses. By "multi-type" responses we mean a collection of correlated responses that have different distributional assumptions (e.g., continuous skewed obs…
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…
A widely-used model for determining the long-term health impacts of public health interventions, often called a "multistate lifetable", requires estimates of incidence, case fatality, and sometimes also remission rates, for multiple diseases by age and gender. Generally, direct data on both incidence and case fatality are not available in every disease and setting. For example, we may know population mortality and prevalence rather than case fatality and incidence. This paper presents Bayesian continuous-time multistate models for estimating transition rates between disease states based on inc…
Estimating the true mortality burden of COVID-19 for every country in the world is a difficult, but crucial, public health endeavor. Attributing deaths, direct or indirect, to COVID-19 is problematic. A more attainable target is the "excess deaths", the number of deaths in a particular period, relative to that expected during "normal times", and we estimate this for all countries on a monthly time scale for 2020 and 2021. The excess mortality requires two numbers, the total deaths and the expected deaths, but the former is unavailable for many countries, and so modeling is required for these c…
Are continuous models better than areal models for spatial disease mapping with a large number of small areas?
Public University of Navarre（纳瓦拉公立大学）；Institute for Advanced Materials and Mathematics, InaMat 2 , Public University of Navarre（纳瓦拉公立大学高级材料与数学研究所 (InaMat 2)）；Norwegian University of Science and Technology (NTNU)（挪威科技大学）
Many of the data, particularly in medicine and disease mapping are count. Indeed, the under or overdispersion problem in count data distrusts the performance of the classical Poisson model. For taking into account this problem, in this paper, we introduce a new Bayesian structured additive regression model, called gamma count, with enough flexibility in modeling dispersion. Setting convenient prior distributions on the model parameters is a momentous issue in Bayesian statistics that characterize the nature of our uncertainty parameters. Relying on a recently proposed class of penalized comple…
The problem of estimating missing fragments of curves from a functional sample has been widely considered in the literature. However, a majority of the reconstruction methods rely on estimating the covariance matrix or the components of its eigendecomposition, a task that may be difficult. In particular, the accuracy of the estimation might be affected by the complexity of the covariance function and the poor availability of complete functional data. We introduce a non-parametric alternative based on a novel concept of depth for partially observed functional data. Our simulations point out tha…
The analysis of count data is commonly done using Poisson models. Negative binomial models are a straightforward and readily motivated generalization for the case of overdispersed data, i.e., when the observed variance is greater than expected under a Poissonian model. Rate and overdispersion parameters then need to be considered jointly, which in general is not trivial. Here we are concerned with evidence synthesis in the case where the reporting of data is rather heterogeneous, i.e., events are reported either in terms of mean event counts, the proportion of event-free patients, or rate esti…
Doubly Robust Machine Learning for Population Size Estimation with Missing Covariates: Application to Gaza Conflict Mortality
Center for Data Science New York University（纽约大学数据科学中心）；Department of Statistics & Data Science Carnegie Mellon University（卡内基梅隆大学统计与数据科学系）；Department of Medical Statistics London School of Hygiene and Tropical Medicine（伦敦卫生与热带医学院医学统计学系）
We focus on the problem of generalizing a causal effect estimated on a randomized controlled trial (RCT) to a target population described by a set of covariates from observational data. Available methods such as inverse propensity sampling weighting are not designed to handle missing values, which are however common in both data sources. In addition to coupling the assumptions for causal effect identifiability and for the missing values mechanism and to defining appropriate estimation strategies, one difficulty is to consider the specific structure of the data with two sources and treatment an…
Evidence supporting the current World Health Organization recommendations of early antiretroviral therapy (ART) initiation for adolescents is inconclusive. We leverage a large observational data and compare, in terms of mortality and CD4 cell count, the dynamic treatment initiation rules for HIV-infected adolescents. Our approaches extend the marginal structural model for estimating outcome distributions under dynamic treatment regimes (DTR), developed in Robins et al. (2008), to allow the causal comparisons of both specific regimes and regimes along a continuum. Furthermore, we propose strate…
Georgia Institute of Technology（佐治亚理工学院）；University of Michigan（密歇根大学）；University of Utah（犹他大学）
Panel count data describes aggregated counts of recurrent events observed at discrete time points. To understand dynamics of health behaviors, the field of quantitative behavioral research has evolved to increasingly rely upon panel count data collected via multiple self reports, for example, about frequencies of smoking using in-the-moment surveys on mobile devices. However, missing reports are common and present a major barrier to downstream statistical learning. As a first step, under a missing completely at random assumption (MCAR), we propose a simple yet widely applicable functional EM a…
Exposure to air pollution is associated with increased morbidity and mortality. Recent technological advancements permit the collection of time-resolved personal exposure data. Such data are often incomplete with missing observations and exposures below the limit of detection, which limit their use in health effects studies. In this paper we develop an infinite hidden Markov model for multiple asynchronous multivariate time series with missing data. Our model is designed to include covariates that can inform transitions among hidden states. We implement beam sampling, a combination of slice sa…
A new method for clustered survival data]{A new method for clustered survival data: Estimation of treatment effect heterogeneity and variable selection
