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.
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.
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 …
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.
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 introduces new methods to study the changing dynamics of COVID-19 cases and deaths among the 50 worst-affected countries throughout 2020. First, we analyse the trajectories and turning points of rolling mortality rates to understand at which times the disease was most lethal. We demonstrate five characteristic classes of mortality rate trajectories and determine structural similarity in mortality trends over time. Next, we introduce a class of \emph{virulence matrices} to study the evolution of COVID-19 cases and deaths on a global scale. Finally, we introduce \emph{three-way incons…
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.
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.
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.
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, …
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…
Background: A common modelling approach in public health and epidemiology divides the population under study into compartments containing persons that share the same status. Here we consider a three-state model with the compartments: A, B and Dead. States A and B may be the states of any dichotomous variable, for example, Healthy and Ill, respectively. The transitions between the states are described by change rates (or synonymously: densities), which depend on calendar time and on age. So far, a rigorous mathematical calculation of the prevalence of property B has been difficult, which has li…
In this work we examine the properties of a recently described ordinary differential equation that relates the age-specific prevalence of a chronic disease with the incidence and mortalities of the diseased and healthy persons. The equation has been used to estimate the incidence from prevalence data, which is an inverse problem. The ill-posedness of this problem is proven, too.
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…
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
The severe acute respiratory syndrome COVID-19 has been in the center of the ongoing global health crisis in 2020. The high prevalence of mild cases facilitates sub-notification outside hospital environments and the number of those who are or have been infected remains largely unknown, leading to poor estimates of the crude mortality rate of the disease. Here we use a simple model to describe the number of accumulated deaths caused by COVID-19. The close connection between the proposed model and an approximate solution of the SIR model provides a system of equations whose solutions are robust …
We recently described a dynamic causal model of a COVID-19 outbreak within a single region. Here, we combine several of these (epidemic) models to create a (pandemic) model of viral spread among regions. Our focus is on a second wave of new cases that may result from loss of immunity--and the exchange of people between regions--and how mortality rates can be ameliorated under different strategic responses. In particular, we consider hard or soft social distancing strategies predicated on national (Federal) or regional (State) estimates of the prevalence of infection in the population. The mode…
Complex diseases are multifactorial traits caused by both genetic and environmental factors. They represent the most part of human diseases and include those with largest prevalence and mortality (cancer, heart disease, obesity, etc.). Despite of a large amount of information that have been collected about both genetic and environmental risk factors, there are relatively few examples of studies on their interactions in epidemiological literature. One reason can be the incomplete knowledge of the power of statistical methods designed to search for risk factors and their interactions in this dat…
