Illness-death model: statistical perspective and differential equations

Global Trend in Pancreatic Cancer Prevalence Rates Through 2040: An Illness-Death Modeling Study

BACKGROUND

Despite remarkable progress in contemporary medical technology and enhanced survival outcomes for various cancer types, pancreatic cancer (PC) continues to stand out as a particularly deadly gastrointestinal malignancy. Given a persistent rise in both incidence and the corresponding mortality rates of PC globally, evaluations of PC burden by sex are of great importance. Here, we used the illness-death multi-state model (IDM) to forecast the prevalence of PC through the year 2040.

METHODS

IDM was established based on obtainable data to predict the future prevalence of PC on global, regional, and national scales from 2019 to 2040. Analyses were also performed regarding sex and 95% confidence intervals (CIs) are presented for all estimates.

RESULTS

The projected prevalence rate for 2040 is anticipated to be 6.093 ([95% CI 5.47-6.786] per 100,000) worldwide, indicating a significant increase of 31.45% since 1990, and a 12.29% increase since 2019. The estimated average annual increase since 2020 was 0.5%. Considering sex differences, females are expected to have a steeper slope in prevalence rate than males. Intriguingly, when considering the percentage changes between the periods of 2019-2040 and 1990-2019 for both sexes, females exhibited 29% and 11% increase relative to males (2.6-fold greater increase).

CONCLUSIONS

By 2040, it is predicted that the prevalence of PC will increase globally, with women being at higher risk of developing the disease. Considering the percentage changes, regions with lower socioeconomic status are anticipated to face a greater risk of experiencing PC compared to other geographical areas.

Projected number of people with multiple sclerosis in Germany between 2015 and 2040

BACKGROUND

The global prevalence of multiple sclerosis has shown a marked rise in recent decades, with Germany reporting the highest prevalence among European countries. This study aims to project the future number of people with multiple sclerosis in Germany until 2040 which is necessary for effective resource allocation and health care planning.

METHODS

Based on data from the German statutory health insurance, the age- and sex-specific prevalence of multiple sclerosis was estimated applying mathematical relations between prevalence, incidence rate, and mortality rate. Subsequently, the projected prevalence was applied to the age structure of the German population between 2015 and 2040 to calculate the future number of people with multiple sclerosis. Several temporal trend scenarios pertaining to the incidence and mortality rate were compared.

RESULTS

Application of current age-specific prevalence estimates combined with the projected population structure in 2040, results in a decline of 8% in the number of people with multiple sclerosis. More realistic scenarios that reflect on trends in mortality and incidence rates, project between 453,000 (+75%) and 477,000 (+85%) multiple sclerosis cases in 2040. It is expected that females will be affected nearly 2.5 times more frequently than males in 2040.

CONCLUSION

The findings indicate a substantial rise in the prevalence of multiple sclerosis, ranging from 75% to 85% in 2040 compared to 2015. Assuming a constant age-specific prevalence between 2015 and 2040 without any temporal trends in mortality and incidence rates may underestimate the actual number of cases and consequently, future requirements for healthcare resources.

Multistate models of developmental toxicity: Application to valproic acid-induced malformations in the zebrafish embryo

For the determination of acute toxicity of chemicals in zebrafish (Danio rerio) embryos, the OECD test guideline 236, relative to the Fish Embryo Toxicity Test (FET), stipulates a dose-response analysis of four lethal core endpoints and a quantitative characterization of abnormalities including their time-dependency. Routinely, the data are analyzed at the different observation times separately. However, observations at a given time strongly depend on the previous effects and should be analyzed jointly with them. To solve this problem, we developed multistate models for occurrence of developmental malformations and live events in zebrafish embryos exposed to eight concentrations of valproic acid (VPA) the first five days of life. Observations were recorded daily per embryo. We statistically infer on model structure and parameters using a numerical Bayesian framework. Hatching probability rate changed with time and we compared five forms of its time-dependence; a constant rate, a piecewise constant rate with a fixed hatching time at 48 h post fertilization, a piecewise constant rate with a variable hatching time, as well as a Hill and Gaussian form. A piecewise constant function of time adequately described the hatching data. The other transition rates were conditioned on the embryo body concentration of VPA, obtained using a physiologically-based pharmacokinetic model. VPA impacted mostly the malformation probability rate in hatched and non-hatched embryos. Malformation reversion probability rates were lowered by VPA. Direct mortality was low at the concentrations tested, but increased linearly with internal concentration. The model makes full use of data and gives a finer grain analysis of the teratogenic effects of VPA in zebrafish than the OECD-prescribed approach. We discuss the use of the model for obtaining toxicological reference values suitable for inter-species extrapolation. A general result is that complex multistate models can be efficiently evaluated numerically.

Exact Traveling and Nano-Solitons Wave Solitons of the Ionic Waves Propagating along Microtubules in Living Cells

In this paper, the weakly nonlinear shallow-water wave model is mathematically investigated by applying the modified Riccati-expansion method and Adomian decomposition method. This model is used to describe the propagation of waves in weakly nonlinear and dispersive media. We obtain exact and solitary wave solutions of this model by using the modified Riccati-expansion method then using these solutions to determine the boundary and initial conditions. These conditions are employed to evaluate the semi-analytical wave solutions and calculate the absolute value of error. The values of absolute error show the accuracy of the obtained solutions. Some solutions are sketched to show the perspective view of the solution of this model. Moreover, the novelty of the obtained solutions is illustrated by showing the similarity and differences between our and previous solutions of the model.

Multistate analysis from cross-sectional and auxiliary samples

Epidemiological studies routinely involve cross-sectional sampling of a population comprised of individuals progressing through life history processes. We consider features of a cross-sectional sample in terms of the intensity functions of a progressive multistate disease process under stationarity assumptions. The limiting values of estimators for regression coefficients in naive logistic regression models are studied, and simulations confirm the key asymptotic results that are relevant in finite samples. We also consider the need for and the use of data from auxiliary samples, which enable one to fit the full multistate life history process. We conclude with an application to data from a national cross-sectional sample assessing marker effects on psoriatic arthritis among individuals with psoriasis.

Projected number of people with diagnosed Type 2 diabetes in Germany in 2040

AIMS

To project the number of people with Type 2 diabetes in Germany between 2015 and 2040.

METHODS

Based on data from 65 million insurees of the German statutory health insurance, we projected the age-specific prevalence of diabetes using mathematical relations between prevalence, incidence rate and mortality. We compared several scenarios regarding temporal trends in the incidence and mortality rate. The projected age-specific prevalence was applied to the projected age structure of the German population between 2015 and 2040 to calculate the number of people with Type 2 diabetes.

RESULTS

Application of current age-specific prevalence estimates to the projected age structure in 2040, although ignoring temporal trends in incidence and mortality, yielded an increase in the number of Type 2 diabetes cases from 6.9 million in 2015 to 8.3 million (+21%) in 2040. More realistic scenarios that account for decreasing mortality rates and different trends in the incidence rates project between 10.7 million (+54%) and 12.3 million (+77%) Type 2 diabetes cases in 2040.

CONCLUSIONS

For the first time, we projected the number of future Type 2 diabetes cases for the whole adult population in Germany. The results indicate a relative increase in the number of Type 2 diabetes cases of between 54% and 77% from 2015 to 2040. Temporal trends in the incidence rate are the main drivers of this increase. Simply applying current age-specific prevalence to the future age structure probably underestimates the future number of Type 2 diabetes cases.

New ways of estimating excess mortality of chronic diseases from aggregated data: insights from the illness-death model

Background

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). The transition rates are the incidence rate, the remission rate and mortality rates from the ‘Healthy’ and ‘Ill’ states. In case of a chronic disease, we now demonstrate that the PDE can be used to estimate the excess mortality from age-specific prevalence and incidence data. For the prevalence and incidence, aggregated data are sufficient - no individual subject data are needed, which allows application of the methods in contexts of strong data protection or where data from individual subjects is not accessible.

Methods

After developing novel estimators for the excess mortality derived from the PDE, we apply them to simulated data and compare the findings with the input values of the simulation aiming to evaluate the new approach. In a practical application to claims data from 35 million men insured by the German public health insurance funds, we estimate the population-wide excess mortality of men with diagnosed type 2 diabetes.

Results

In the simulation study, we find that the estimation of the excess mortality is feasible from prevalence and incidence data if the prevalence is given at two points in time. The accuracy of the method decreases as the temporal difference between these two points in time increases. In our setting, the relative error was 5% and below if the temporal difference was three years or less. Application of the new method to the claims data yields plausible findings for the excess mortality of type 2 diabetes in German men.

Conclusions

The described approach is useful to estimate the excess mortality of a chronic condition from aggregated age-specific incidence and prevalence data.

Trial registration

The article does not report the results of any health care intervention.

Electronic supplementary material

The online version of this article (10.1186/s12889-019-7201-7) contains supplementary material, which is available to authorized users.