Recently, we have shown that the age-specific prevalence of a disease can be related to the transition rates in the illness-death model via a partial differential equation (PDE). In case of a chronic disease, we show that the PDE can be used to estimate excess mortality from prevalence and incidence. Applicability of the new method is demonstrated in a simulation and claims data about diabetes in German men.
Aggregated health data such as claims data from health insurances become more and more available for research purposes. Estimates of excess mortality from prevalence and incidence of a chronic condition have only been possible for ages 50 years and older and have shown to be unstable in younger ages. The aim of this article is to explore the reasons why estimates of excess mortality for younger ages are prone to bias and what can be done to extend the age range to ages below 50 years.
This article describes a method to estimate the mortality rate ratio R from current status data with duration in a chronic condition in case the general mortality of the overall population is known. Apart from the general mortality, the method requires four pieces of information from the study participants: age and time at the survey/interview, whether the chronic condition is present (current status) and if so, for how long the condition is present (duration). The method uses a differential equation that relates prevalence, incidence and mortality to estimate R of the people with the chronic …
In this article, we use the illness-death model to present a mathematical framework for studying the compression of morbidity (COM) hypothesis. It turns out that questions about COM are completely determined by the transition rates in the illness-death model and a closely related partial differential equation. By this, the COM hypothesis is analytically tractable. To demonstrate the usefulness of the mathematical framework, an example is given, which has been motivated by empirical findings from Germany.
We study the relation between the age-specific prevalence, incidence and mortality in an illness-death model consisting of the three states Healthy, Ill, Dead. The dependency on three different time scales (age, calendar time, disease duration) is considered. It is shown that Keiding's equation published in 1991 is a generalisation of the solution of Brunet and Struchiner's partial differential equation from 1999. In a special case, we propose a particularly simple estimate of the incidence from prevalence data.
Relevant events in a three state illness-death model (IDM) of a chronic disease are the diagnosis of the disease and death with or without the disease. In this article a simulation framework for populations moving in the IDM is presented. The simulation is closely related to the concept of Lexis diagrams in event history analysis. Details of the implementation and an example of a hypothetical disease are described.
The illness-death model of a chronic disease consists of the states 'Normal', 'Disease' and 'Death'. In general, the transition rates between the states depend on three time scales: calendar time, age and duration of the chronic disease. Previous works have shown that the age-specific prevalence of the chronic disease can be described by differential equations if the duration is negligible. This article derives a partial differential equation (PDE) in the presence of duration dependency. As an important application, the PDE allows the calculation of the age-specific incidence from cross-sectio…
This paper descibes a new method of calculating the mean duration and mean age of onset of a chronic disease from incidence and mortality rates. It is based on an ordinary differential equation resulting from a simple compartment model. Applicability of the method is demonstrated in data about dementia in Germany.
Recently, we have proposed a new illness-death model that comprises a state of undiagnosed chronic disease preceding the diagnosed disease. Based on this model, the question arises how case-finding can be assessed in the presence of mortality from all these states. We simulate two scenarios of different performance of case-finding and apply several indices to assess case-finding in both scenarios. One of the prevalence based indices leads to wrong conclusions. Some indices are partly insensitive to distinguish the quality of case-finding. The incidence based indices perform well. If possible, …
Recently, we proposed an state model (compartment model) to describe the progression of a chronic disease with an pre-clinical (undiagnosed) state before clinical diagnosis. It is an open question, if a sequence of cross-sectional studies with mortality follow-up is sufficient to estimate the true incidence rate of the disease, i.e. the incidence of the undiagnosed and diagnosed disease. In this note, we construct a counterexample and show that this cannot be achieved in general.
This paper generalizes a previously published differential equation that describes the relation between the age-specific incidence, remission, and mortality of a disease with its prevalence. The underlying model is a simple compartment model with three states (illness-death model). In contrast to the former work, migration- and calendar time-effects are included. As an application of the theoretical findings, a hypothetical example of an irreversible disease is treated.
University of Virginia（弗吉尼亚大学）；University of California Los Angeles（加州大学洛杉矶分校）
Chronic kidney disease (CKD) is a gradual loss of renal function over time, and it increases the risk of mortality, decreased quality of life, as well as serious complications. The prevalence of CKD has been increasing in the last couple of decades, which is partly due to the increased prevalence of diabetes and hypertension. To accurately detect CKD in diabetic patients, we propose a novel framework to learn sparse longitudinal representations of patients' medical records. The proposed method is also compared with widely used baselines such as Aggregated Frequency Vector and Bag-of-Pattern in…
This paper descibes a new method for deriving incidence rates of a chronic disease from prevalence data. It is based on a new ordinary differential equation, which relates the change in the age-specific prevalence to the agespecific incidence and mortality rates. The method allows the extraction of longtudinal information from cross-sectional studies. Applicability of the method is tested in the prevalence of dementia in Germany. The derived age-specific incidence is in good agreement with published values.
The risk for severe illness and mortality from COVID-19 significantly increases with age. As a result, age-stratified modeling for COVID-19 dynamics is the key to study how to reduce hospitalizations and mortality from COVID-19. By taking advantage of network theory, we develop an age-stratified epidemic model for COVID-19 in complex contact networks. Specifically, we present an extension of standard SEIR (susceptible-exposed-infectious-removed) compartmental model, called age-stratified SEAHIR (susceptible-exposedasymptomatic-hospitalized-infectious-removed) model, to capture the spread of CO…
Co-infecting parasites and pathogens remain a leading challenge for global public health due to their consequences for individual-level infection risk and disease progression. However, a clear understanding of the population-level consequences of co-infection is lacking. Here, we constructed a model that includes three individual-level effects of co-infection: mortality, fecundity, and transmission. We used the model to investigate how these individual-level consequences of co-infection scale up to produce population-level infection patterns. To parameterize this model, we conducted a four-yea…
The demographic factors have a substantial impact on the overall casualties caused by the COVID-19. In this study, the spatial association between the key demographic variables and COVID-19 cases and deaths were analyzed using the spatial regression models. Total 13 (for COVID-19 case factor) and 8 (for COVID-19 death factor) key variables were considered for the modelling. Total five spatial regression models such as Geographically weighted regression (GWR), Spatial Error Model (SEM), Spatial Lag Model (SLM), Spatial Error_Lag model (SEM_SLM), and Ordinary Least Square (OLS) were performed fo…
Although accumulation of molecular damage is suggested to be an important molecular mechanism of aging, a quantitative link between the dynamics of damage accumulation and mortality of species has so far remained elusive. To address this question, we examine stability properties of a generic gene regulatory network (GRN) and demonstrate that many characteristics of aging and the associated population mortality rate emerge as inherent properties of the critical dynamics of gene regulation and metabolic levels. Based on the analysis of age-dependent changes in gene-expression and metabolic profi…
Global, Regional, and National Burden of Chronic Kidney Disease Attributable to High Body Mass Index (BMI) among Individuals Aged 20-54 Years from 1990 to 2021: An Analysis of the Global Burden of Disease Study
