Change rates and prevalence of a dichotomous variable: simulations and applications

Estimating incidence of type 1 and type 2 diabetes using prevalence data: the SEARCH for Diabetes in Youth study

BACKGROUND

Incidence is one of the most important epidemiologic indices in surveillance. However, determining incidence is complex and requires time-consuming cohort studies or registries with date of diagnosis. Estimating incidence from prevalence using mathematical relationships may facilitate surveillance efforts. The aim of this study was to examine whether a partial differential equation (PDE) can be used to estimate diabetes incidence from prevalence in youth.

METHODS

We used age-, sex-, and race/ethnicity-specific estimates of prevalence in 2001 and 2009 as reported in the SEARCH for Diabetes in Youth study. Using these data, a PDE was applied to estimate the average incidence rates of type 1 and type 2 diabetes for the period between 2001 and 2009. Estimates were compared to annual incidence rates observed in SEARCH. Precision of the estimates was evaluated using 95% bootstrap confidence intervals.

RESULTS

Despite the long period between prevalence measures, the estimated average incidence rates mirror the average of the observed annual incidence rates. Absolute values of the age-standardized sex- and type-specific mean relative errors are below 8%.

CONCLUSIONS

Incidence of diabetes can be accurately estimated from prevalence. Since only cross-sectional prevalence data is required, employing this methodology in future studies may result in considerable cost savings.

Age-specific incidence of need for long-term care for men and women in Germany 2015: Cross-sectional study comprising 82 million people

Background: With the growing number of older people, the number of people in need of long-term care is increasing, too. Official statistics only report on the age-specific prevalence of long-term care. Therefore, there is no data on the age- and sex-specific incidence of the need for care at the population level for Germany available. Methods: Analytical relationships between age-specific prevalence, incidence rate, remission rate, all-cause mortality, and mortality rate ratio are used to estimate the age-specific incidence of long-term care among men and women in 2015. The data is based on the official prevalence data from the nursing care statistics for the years 2011 to 2019 and official mortality rates from the Federal Statistical Office. For Germany, there is no data on the mortality rate ratio of people with and without a need for care, which is why we use two extreme scenarios that were obtained in a systematic literature search to estimate the incidence. Results: The age-specific incidence is about 1 per 1000 person-years (PY) in men and women at the age of 50 and increases exponentially up to the age of 90. Up to about the age of 60, men have a higher incidence rate than women. Thereafter, women have a higher incidence. At the age of 90, women and men have an incidence rate of 145 to 200 and 94 to 153 per 1000 PY, respectively, depending on the scenario. Conclusion: We estimated the age-specific incidence of the need for long-term care for women and men in Germany for the first time. We observed a strong increase, leading to a huge number of people in need of long-term care in higher age groups. It is to be expected that this will result in an increased economic burden and a further increased need for nursing and medical staff.

Diabetes free life expectancy and years of life lost associated with type 2 diabetes: projected trends in Germany between 2015 and 2040

BACKGROUND

Type 2 diabetes (T2D) causes substantial disease burden and is projected to affect an increasing number of people in coming decades. This study provides projected estimates of life years free of type 2 diabetes (T2D) and years of life lost ([Formula: see text]) associated with T2D for Germany in the years 2015 and 2040.

METHODS

Based on an illness-death model and the associated mathematical relation between prevalence, incidence and mortality, we projected the prevalence of diagnosed T2D using currently available data on the incidence rate of diagnosed T2D and mortality rates of people with and without diagnosed T2D. Projection of prevalence was achieved by integration of a partial differential equation, which governs the illness-death model. These projected parameters were used as input values to calculate life years free of T2D and [Formula: see text] associated with T2D for the German population aged 40 to 100 years in the years 2015 and 2040, while accounting for different assumptions on future trends in T2D incidence and mortality.

RESULTS

Assuming a constant incidence rate, women and men at age 40 years in 2015 will live approximately 38 years and 33 years free of T2D, respectively. Up to the year 2040, these numbers are projected to increase by 1.0 years and 1.3 years. Assuming a decrease in T2D-associated excess mortality of 2% per year, women and men aged 40 years with T2D in 2015 will be expected to lose 1.6 and 2.7 years of life, respectively, compared to a same aged person without T2D. In 2040, these numbers would reduce by approximately 0.9 years and 1.6 years. This translates to 10.8 million and 6.4 million [Formula: see text] in the German population aged 40-100 years with prevalent T2D in 2015 and 2040, respectively.

CONCLUSIONS

Given expected trends in mortality and no increase in T2D incidence, the burden due to premature mortality associated with T2D will decrease on the individual as well as on the population level. In addition, the expected lifetime without T2D is likely to increase. However, these trends strongly depend on future improvements of excess mortality associated with T2D and future incidence of T2D, which should motivate increased efforts of primary and tertiary prevention.

Estimating the impact of tax policy interventions on the projected number and prevalence of adults with type 2 diabetes in Germany between 2020 and 2040

INTRODUCTION

As a population-wide intervention, it has been proposed to raise taxes on unhealthy products to prevent diseases such as type 2 diabetes. In this study, we aimed to estimate the effect of tax policy interventions in 2020 on the projected prevalence and number of people with type 2 diabetes in the German adult population in 2040.

RESEARCH DESIGN AND METHODS

We applied an illness-death model and the German Diabetes Risk Score (GDRS) to project the prevalence and number of adults with type 2 diabetes in Germany under a base case scenario and under a tax policy intervention scenario. For the base case scenario, we assumed constant age-specific incidence rates between 2020 and 2040. For the intervention scenario, we assumed a 50% price increase for sugar-sweetened beverages, tobacco and red meat products in the year 2020. Based on price elasticities, we estimated the impact on these risk factors alone and in combination, and calculated subsequent reductions in the age-specific and sex-specific GDRS. These reductions were used to determine reductions in the incidence rate and prevalence using a partial differential equation.

RESULTS

Compared with the base case scenario, combined tax interventions in 2020 resulted in a 0.95 percentage point decrease in the prevalence of type 2 diabetes (16.2% vs 17.1%), which corresponds to 640 000 fewer prevalent cases of type 2 diabetes and a relative reduction by 6%.

CONCLUSIONS

Taxation of sugar-sweetened beverages, tobacco products and red meat by 50% modestly lowered the projected number and prevalence of adults with type 2 diabetes in Germany in 2040. Raising taxes on unhealthy products as a stand-alone measure may not be enough to attenuate the future rise of type 2 diabetes.

Risk factors in the illness-death model: Simulation study and the partial differential equation about incidence and prevalence

Recently, we developed a partial differential equation (PDE) that relates the age-specific prevalence of a chronic disease with the age-specific incidence and mortality rates in the illness-death model (IDM). With a view to planning population-wide interventions, the question arises how prevalence can be calculated if the distribution of a risk-factor in the population shifts. To study the impact of such possible interventions, it is important to deal with the resulting changes of risk-factors that affect the rates in the IDM. The aim of this work is to show how the PDE can be used to study such effects on the age-specific prevalence of a chronic disease, to demonstrate its applicability and to compare the results to a discrete event simulation (DES), a frequently used simulation technique. This is done for the first time based on the PDE which only needs data on population-wide epidemiological indices and is related to the von Foerster equation. In a simulation study, we analyse the effect of a hypothetical intervention against type 2 diabetes. We compare the age-specific prevalence obtained from a DES with the results predicted from modifying the rates in the PDE. The DES is based on 10000 subjects and estimates the effect of changes in the distributions of risk-factors. With respect to the PDE, the change of the distribution of risk factors is synthesized to an effective rate that can be used directly in the PDE. Both methods, DES and effective rate method (ERM) are capable of predicting the impact of the hypothetical intervention. The age-specific prevalences resulting from the DES and the ERM are consistent. Although DES is common in simulating effects of hypothetical interventions, the ERM is a suitable alternative. ERM fits well into the analytical theory of the IDM and the related PDE and comes with less computational effort.

Estimating prevalence of type I and type II diabetes using incidence rates: the SEARCH for diabetes in youth study

PURPOSE

Most surveillance efforts in childhood diabetes have focused on incidence, whereas prevalence is rarely reported. This study aimed to assess whether a mathematical illness-death model accurately estimated future prevalence from baseline prevalence and incidence rates in children.

METHODS

SEARCH for Diabetes in Youth is an ongoing population-based surveillance study of prevalence and incidence of diabetes and its complications among youth in the United States. We used age-, sex-, and race/ethnicity-specific SEARCH estimates of the prevalence of type I and type II diabetes in 2001 and incidence from 2002 to 2008. These data were used in a partial differential equation to estimate prevalence in 2009 with 95% bootstrap confidence intervals. Model-based prevalence was compared with the observed prevalence in 2009.

RESULTS

Most confidence intervals for the difference between estimated and observed prevalence included zero, indicating no evidence for a difference between the two methods. The width of confidence intervals indicated high precision for the estimated prevalence when considering all races/ethnicities. In strata with few cases, precision was reduced.

CONCLUSIONS

Future prevalence of type I and type II diabetes in youth may be accurately estimated from baseline prevalence and incidence. Diabetes surveillance could benefit from potential cost savings of this method.

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.

Second Order Segmented Polynomials for Syphilis and Gonorrhea Prevalence and Incidence Trends Estimation: Application to Spectrum's Guinea-Bissau and South Africa Data

This paper presents two approaches to smoothing time trends in prevalence and estimating the underlying incidence of remissible infections. In the first approach, we use second order segmented polynomials to smooth a curve in a bounded domain. In the second, incidence is modeled instead and the prevalence is reconstructed using the recovery rate which is assumed to be known. In both approaches, the number of knots and their positions are estimated, resulting in non-linear regressions. Akaike Information Criterion is used for model selection. The method is illustrated with Syphilis and Gonorrhea prevalence smoothing and incidence trend estimation in Guinea-Bissau and South Africa, respectively.

Illness-death model: statistical perspective and differential equations

The aim of this work is to relate the theory of stochastic processes with the differential equations associated with multistate (compartment) models. We show that the Kolmogorov Forward Differential Equations can be used to derive a relation between the prevalence and the transition rates in the illness-death model. Then, we prove mathematical well-definedness and epidemiological meaningfulness of the prevalence of the disease. As an application, we derive the incidence of diabetes from a series of cross-sections.

Illness-Death Model in Chronic Disease Epidemiology: Characteristics of a Related, Differential Equation and an Inverse Problem

Chronic diseases impose a huge burden for mankind. Recently, a mathematical relation between the incidence and prevalence of a chronic disease in terms of a differential equation has been described. In this article, we study the characteristics of this differential equation. Furthermore, we prove the ill-posedness of a related inverse problem arising in chronic disease epidemiology. An example application for the inverse problem about type 1 diabetes in German women aged up to 35 years is given.

Excess mortality for people diagnosed with type 2 diabetes in 2012 - Estimates based on claims data from 70 million Germans

BACKGROUND AND AIMS

The hazard ratio (HR) is a meaningful concept for comparing the mortality of people with and without type 2 diabetes (T2D). Nevertheless, there is only one German study estimating age-specific HRs. Thus, this study aimed to provide population-wide age-specific HRs for Germany using a novel method based on aggregated population data.

METHODS AND RESULTS

We used an illness-death model and published data on T2D prevalence and incidence as well as mortality in the German general population to estimate age-specific HRs in the year 2012 for the population aged 65-90 years. For men, the overall HR was 2.3, which decreased from 2.8 between 65 and 69 years old to 1.6 between 85 and 90 years old. For women, the overall HR was 3.0, which decreased from 4.2 to 1.7 in the same age groups, respectively.

CONCLUSION

In Germany, men and women in 2012 with T2D aged 65-90 years experienced a three-to four-fold higher mortality compared to people without T2D, which might indicate that the excess mortality could be higher than in countries with comparable health care systems. Female sex and younger age were associated with higher excess mortality.

Estimation of chronic kidney disease incidence from prevalence and mortality data in American Indians with type 2 diabetes

The objective was to estimate chronic kidney disease (CKD) incidence rates from prevalence and mortality data, and compare the estimates with observed (true) incidence rates in a well-characterized population with diabetes. Pima Indians aged 20 years and older with type 2 diabetes were followed from 1982 through 2007. CKD was defined by estimated GFR (eGFR) <60 ml/min/1.72 m2 or albumin-to-creatinine ratio (ACR) ≥30 mg/g. True CKD incidence and mortality rates were computed for the whole study period, and prevalence for the intervals 1982-1994 and 1995-2007. Estimated age-sex stratified CKD incidence rates were computed using illness-death models of the observed prevalences, and of the whole-period mortality rate ratio of CKD to non-CKD persons. Among 1201 participants, 616 incident events of CKD occurred during a median follow-up of 5.6 years. Observed CKD prevalence was 56.9% (95%CI 53.7-60.0) and 48.0% (95%CI 45.2-50.8) in women; 54.0% (95%CI 49.9-58.1) and 49.6% (95%CI 46.0-53.3) in men, across the two periods. Mortality rate was 2.5 (95%CI 1.9-3.3) times as high in women with CKD and 1.6 (95%CI 1.3-2.1) times as high in men with CKD, compared to women or men without CKD. In women, estimated CKD incidence increased linearly from 25.6 (95%CI 4.2-53.0) to 128.6 (95%CI 77.1-196.6) with each 5-year age group up to 69 years, and to 99.8 (95%CI 38.7-204.7) at age ≥70. In men, estimated CKD incidence increased form 28.5 (95%CI 3.8-71.2) at age 20-24 years to 118.7 (95%CI 23.6-336.7) at age ≥70. Age-sex-stratified estimated incidence reflected the magnitude and directional trend of the true incidence and were similar to the true incidence rates (p>0.05 for difference) except for age 20-24 in women (p = 0.008) and age 25-29 in men (p = 0.002). In conclusion, the estimated and observed incidence rates of CKD agree well over 25 years of observation in this well characterized population with type 2 diabetes.