Estimation of mortality rate ratios for chronic conditions with misclassification of disease status at death.

Estimation of mortality rates and mortality rate ratios (MRR) of diseased and non-diseased individuals is a core metric of disease impact used in chronic disease epidemiology. Estimation of mortality rates is often conducted through retrospective linkage of information from nationwide surveys such as the National Health Interview Survey (NHIS) and death registries. These surveys usually collect information on disease status during only one study visit. This infrequency leads to missing disease information (with right censored survival times) for deceased individuals who were disease-free at study participation, and a possibly biased estimation of the MRR because of possible undetected disease onset after study participation. This occurrence is called "misclassification of disease status at death (MicDaD)" and it is a potentially common source of bias in epidemiologic studies. In this study, we conducted a simulation analysis with a high and a low incidence setting to assess the extent of MicDaD-bias in the estimated mortality. For the simulated populations, MRR for diseased and non-diseased individuals with and without MicDaD were calculated and compared. Magnitude of MicDaD-bias depends on and is driven by the incidence of the chronic disease under consideration; our analysis revealed a noticeable shift towards underestimation for high incidences when MicDaD is present. Impact of MicDaD was smaller for lower incidence (but associated with greater uncertainty in the estimation of MRR in general). Further research can consider the amount of missing information and potential influencers such as duration and risk factors of the disease.

Five-year outcome in 18 010 patients from the German Aortic Valve Registry.

OBJECTIVES: To determine the 5-year outcome in patients treated by isolated transcatheter aortic valve implantation (TAVI) or surgical aortic valve replacement (sAVR)-a prospective observational cohort study. METHODS: A total of 18 010 patients were included (n = 8942 TAVI and n = 9068 sAVR) in the German Aortic Valve Registry (GARY) who were treated in 2011 and 2012 at 92 sites in central Germany. Eligible patients with TAVI and sAVR were matched using propensity scores in a nearest-neighbour approach. Patients with repeat procedures or unequivocal indication for one treatment option (e.g. frailty) were excluded (n = 4785 for TAVI and n = 2 for sAVR). This led to 13 223 patients (4157 TAVI and 9066 sAVR) as an unmatched subcohort. The main outcome measure was the 5-year all-cause mortality. RESULTS: TAVI patients were significantly older (80.9 ± 6.1 vs 68.5 ± 11.1 years, P < 0.001), had a higher Society of Thoracic Surgeons (STS) score (6.3 ± 4.9 vs 2.6 ± 3.0, P < 0.001) and a higher 5-year all-cause mortality (49.8% vs 16.5%, P < 0.0001). There was no major difference in in-hospital stroke, in-hospital myocardial infarction, or temporary and chronic dialysis. In the propensity score-matched group (n = 3640), there were 763 deaths (41.9%) among 1820 TAVI patients compared with 552 (30.3%) among 1820 treated with sAVR during the 5-year follow-up (hazard ratio 1.51, 95% confidence interval 1.35-1.68; P < 0.0001). New pacemaker implantation was performed in 448 patients (24.6%) after TAVI and in 201 (11.0%) after sAVR (P < 0.0001). CONCLUSIONS: The 5-year follow-up data show that TAVI patients were significantly older and had a higher STS score than sAVR patients. After propensity score matching, TAVI with early-generation prosthesis was associated with significantly higher 5-year all-cause mortality than sAVR.

Impact of new pacemaker implantation following surgical and transcatheter aortic valve replacement on 1-year outcome.

OBJECTIVES: The purpose of this study was to evaluate the incidence of new pacemaker implantation (NPMI) after surgical aortic valve replacement (SAVR) and transcatheter aortic valve replacement (TAVR), and investigate its influence on 1-year mortality. METHODS: Patients who were enrolled in 'The German Aortic Valve Registry' undergoing isolated TAVR or SAVR between 2011 and 2015 were analysed. The rate of NPMI was analysed for both groups and multivariable Cox regression analysis was performed to investigate the possible independent association between NPMI and 1-year mortality. RESULTS: Twenty thousand eight hundred and seventy-two patients who underwent TAVR and 17 750 patients who received SAVR were included in this study. The rate of NPMI was 16.6% after TAVR and 3.6% after SAVR. In the TAVR group, NPMI was associated with significantly increased 1-year mortality in univariable Cox regression analysis [hazard ratio (HR) 1.29, confidence interval (CI) 1.18-1.41; P < 0.001]. This association persisted after adjustment for confounding factors (HR 1.29, CI 1.16-1.43; P < 0.001). In the SAVR group, NPMI significantly increased 1-year mortality in univariable analysis as well (HR 1.55, CI 1.08-2.22; P = 0.02), whereas after multivariable adjustment, NPMI did not emerge as an independent risk factor (HR 1.29, 0.88-1.89; P = 0.19). NPMI was not associated with 30-day mortality in both procedure groups. CONCLUSIONS: The rate of NPMI was markedly higher after TAVR compared with SAVR and was independently associated with 1-year mortality after TAVR, whereas this was not significant after SAVR. As 30-day mortality was not different for TAVR and SAVR, the subsequent procedure of an NPMI itself seems not to increase the risk of mortality.

Patients at Intermediate Surgical Risk Undergoing Isolated Interventional or Surgical Aortic Valve Implantation for Severe Symptomatic Aortic Valve Stenosis.

BACKGROUND: Transcatheter aortic valve replacement (TAVR) is increasingly being used for treatment of severe aortic valve stenosis in patients at intermediate risk for surgical aortic valve replacement (SAVR). Currently, real-world data comparing indications and clinical outcomes of patients at intermediate surgical risk undergoing isolated TAVR with those undergoing SAVR are scarce. METHODS: We compared clinical characteristics and outcomes of patients with intermediate surgical risk (Society of Thoracic Surgeons score 4%-8%) who underwent isolated TAVR or conventional SAVR within the prospective, all-comers German Aortic Valve Registry. RESULTS: A total of 7613 patients at intermediate surgical risk underwent isolated TAVR (n=6469) or SAVR (n=1144) at 92 sites in Germany between 2012 and 2014. Patients treated by TAVR were significantly older (82.5±5.0 versus 76.6±6.7 years, P<0.001) and had higher risk scores (logistic EuroSCORE [European System for Cardiac Operative Risk Evaluation]: 21.2±12.3% versus 14.2±9.5%, P<0.001; Society of Thoracic Surgeons score: 5.6±1.1 versus 5.2±1.0, P<0.001). Multivariable analyses revealed that advanced age, coronary artery disease, New York Heart Association class III/IV, pulmonary hypertension, prior cardiac decompensation, elective procedure, arterial occlusive disease, no diabetes mellitus, and a smaller aortic valve area were associated with performing TAVR instead of SAVR (all P<0.001). Unadjusted in-hospital mortality rates were equal for TAVR and SAVR (3.6% versus 3.6%, P=0.976), whereas unadjusted 1-year mortality was significantly higher in patients after TAVR (17.5% versus 10.8%, P<0.001). After propensity score matching, the difference in 1-year mortality between patients with TAVR and SAVR was no longer significant (17.1% versus 15.7%, P=0.59). CONCLUSIONS: Patients at intermediate risk undergoing TAVR differ significantly from those treated with SAVR with regard to age and baseline characteristics. Isolated TAVR and SAVR were associated with an in-hospital mortality rate of 3.6%. In the propensity score analysis, there was no significant difference in 1-year mortality between patients with TAVR and SAVR.

Rapid Deployment Versus Conventional Bioprosthetic Valve Replacement for Aortic Stenosis.

BACKGROUND: Surgical aortic valve replacement using conventional biological valves (CBVs) is the standard of care for treatment of old patients with aortic valve disease. Recently, rapid deployment valves (RDVs) have been introduced. OBJECTIVES: The purpose of this study was to report the nationwide German experience concerning RDVs for treatment of aortic valve stenosis and provide a head-to-head comparison with CBVs. METHODS: A total of 22,062 patients who underwent isolated surgical aortic valve replacement using CBV or RDV between 2011 and 2015 were enrolled into the German Aortic Valve Registry. Baseline, procedural, and in-hospital outcome parameters were analyzed for CBVs and RDVs using 1:1 propensity score matching. Furthermore, 3 RDVs were compared with each other. RESULTS: A total of 20,937 patients received a CBV, whereas 1,125 patients were treated with an RDV. Patients treated with an RDV presented with significantly reduced procedure (160 min [25th to 75th percentile: 135 to 195 min] vs. 150 min [25th to 75th percentile: 127 to 179 min]; p < 0.001), cardiopulmonary bypass (83 min [25th to 75th percentile: 68 to 104 min] vs. 70 min [25th to 75th percentile: 56 to 87 min]; p < 0.001), and aortic cross clamp times (60 min [25th to 75th percentile: 48 to 75 min] vs. 44 min [25th to 75th percentile: 35 to 57 min]; p < 0.001), but showed significantly elevated rates of pacemaker implantation (3.7% vs. 8.8%; p < 0.001) and disabling stroke (0.9% vs. 2.2%; p < 0.001), whereas in-hospital mortality was similar (1.7% vs. 2.2%; p = 0.22). These findings persisted after 1:1 propensity score matching. Comparison of the 3 RDVs revealed statistically nonsignificant different pacemaker rates and significantly different post-operative transvalvular gradients. CONCLUSIONS: In this large, all-comers database, the incidence of pacemaker implantation and disabling stroke was higher with RDVs, whereas no beneficial effect on in-hospital mortality was seen. The 3 RDVs presented different complication profiles with regard to pacemaker implantation and transvalvular gradients. (German Aortic Valve Registry [GARY]; NCT01165827).

Impact of quality of life (QoL) on glycemic control (HbA1c) among adolescents and emerging adults with long-duration type 1 diabetes: A prospective cohort-study.

OBJECTIVE: To evaluate the impact of self-reported chronic-generic and condition-specific quality of life (QoL) on glycemic control among adolescents and emerging adults with long-duration type 1 diabetes (T1D) in a longitudinal design. METHODS: The database used was a nationwide cohort study of patients with ≥10 years T1D duration at baseline in Germany. The baseline questionnaire survey was conducted in 2009-2010, the follow-up survey in 2012-2013; additional clinical data of routine care procedures were linked. QoL was assessed by the DISABKIDS chronic generic module (DCGM-12) and diabetes module (DM) with treatment and impact scales. Regression analyses were conducted for the outcome hemoglobin A1c (HbA1c) at follow up with baseline DISABKIDS scores as predictors and sociodemographic and health-related covariates. RESULTS: At baseline, the included 560 patients had a mean age of 15.9 (SD 2.3) years, a diabetes duration of 13.0 (2.0) years, and an HbA1c of 67 (14.2) mmol/mol. Mean follow-up time was 3.0 (0.6) years. Univariate analyses indicated associations between baseline QoL scores and HbA1c at follow-up (ß[DCGM-12] = -0.174 (SE 0.038), ß[DM treatment] = -0.100 (0.022), ß[DM impact] = -0.177 (0.030), p < .001). The associations remained significant after adjustment for sociodemographic and illness-related factors, but dissolved (p > .60) when additionally adjusting for baseline HbA1c. In patients with poor baseline HbA1c (>75 mmol/mol), significant associations were observed between DCGM-12 and DM impact scores and follow-up HbA1c (ß[DCGM-12] = -0.144 (0.062), p = .021; ß[DM impact] = -0.139 (0.048), p = .004). CONCLUSIONS: QoL was inversely associated with HbA1c after 3 years in the course of T1D only in patients poorly controlled at baseline.

Quality of Life After Transcatheter Aortic Valve Replacement: Prospective Data From GARY (German Aortic Valve Registry).

OBJECTIVES: This study sought to analyze health-related quality-of-life (HrQoL) outcomes of patients undergoing transcatheter aortic valve replacement (TAVR) based on data from GARY (German Aortic Valve Registry). BACKGROUND: Typically, patients currently referred for and treated by TAVR are elderly with a concomitant variable spectrum of multiple comorbidities, disabilities, and limited life expectancy. Beyond mortality and morbidity, the assessment of HrQoL is of paramount importance not only to guide patient-centered clinical decision-making but also to judge this new treatment modality in this high-risk patient population. METHODS: In 2011, 3,875 patients undergoing TAVR were included in the GARY registry. HrQoL was prospectively measured using the EuroQol 5 dimensions questionnaire self-complete version on paper at baseline and 1 year. RESULTS: Complete follow-up EuroQol 5 dimensions questionnaire evaluation was available for 2,288 patients (transvascular transcatheter aortic valve replacement [TAVR-TV]: n = 1,626 and transapical TAVR [TAVR-TA]: n = 662). In-hospital mortality was 5.9% (n = 229) and the 1-year mortality was 23% (n = 893). The baseline visual analog scale score for general health status was 52.6% for TAVR-TV and 55.8% for TAVR-TA and, in parallel to an improvement in New York Heart Association functional class, improved to 59.6% and 58.5% at 1 year, respectively (p < 0.001). Between baseline and 1 year, the number of patients reporting no complaints increased by 7.8% (TAVR-TV) and by 3.5% within the mobility dimension, and by 14.1% (TAVR-TV) and 9.2% within the usual activity dimension, whereas only moderate changes were found for the self-care, pain or discomfort, and anxiety or depression dimensions. In a multiple linear regression analysis several pre- and post-operative factors were predictive for less pronounced HrQoL benefits. CONCLUSIONS: TAVR treatment led to improvements in HrQoL, especially in terms of mobility and usual activities. The magnitude of improvements was higher in the TAVR-TV group as compared to the TAVR-TA group. However, there was a sizable group of patients who did not derive any HrQoL benefits. Several independent pre- and post-operative factors were identified being predictive for less pronounced HrQoL benefits.

No adverse effect of outdoor air pollution on HbA1c in children and young adults with type 1 diabetes.

BACKGROUND: Evidence is growing that air pollutants deteriorate glucose metabolism and insulin sensitivity by oxidative stress and inflammation. This might affect HbA1c levels and insulin requirements in type 1 diabetes. There are no data available on this association. METHODS: Air pollution values of respirable particulate matter (PM10), nitrogen dioxides (NO2), and accumulated ozone (O3-AOT40) were obtained from the federal environmental agency (Umweltbundesamt II) and assigned to place of residence of 840 participants from a nation-wide population-based type 1 diabetes registry (German Diabetes Center, Düsseldorf, Germany). Information on HbA1c, social status, treatment and co-morbidities was collected by self-administered questionnaires. Complete information was available for 771 patients aged 11-21 years at the time of study. RESULTS: In linear regression models, no adverse effects of air pollutants (PM10, NO2 or O3-AOT40 on HbA1c level were found, but O3-AOT40 was inversely associated with HbA1c (mmol/mol) in the crude (estimate per IQR: -1.86; 95% CI: (-3.27; -0.44); p=0.01) and the best model adjusting for lifestyle, socioeconomic factors, clinical information, and season (-1.50; (-2.82; -0.17); 0.034). After adding area of residency as random effect to the crude and the best model, the association was no longer significant (-1.64; (-3.84; 0.56); 0.14); (-1.56; (-3.67; 0.55); 0.14). Adjustment for further possible confounders did not affect the estimates seriously. None of the pollutants was associated with insulin dose (IU/kg body weight). CONCLUSIONS: Investigated pollutants had no adverse effect on metabolic control in children and young adults with type 1 diabetes in this cross-sectional study. The weak inverse association of accumulated ozone with HbA1c might be due to confounding by regional characteristics or regional aspects of care.

Surveillance of the Incidence of Non-Communicable Diseases (NCDs) with Sparse Resources: A Simulation Study Using Data from a National Diabetes Registry, Denmark, 1995-2004.

We propose two new methods to estimate secular trends in the incidence of a chronic disease from a series of prevalence studies and mortality data. One method is a direct inversion formula, the second method is a least squares estimation. Both methods are validated in a simulation study based on data from a diabetes register. The results of the validation show that the proposed methods may be useful in epidemiological settings with sparse resources, where running a register or a series of follow-up studies is difficult or impossible.

A comparative study of prevalence-based incidence estimation techniques with application to dementia data in Germany.

Dementia is becoming a major health burden, which is mainly due to the increasing life expectancy in many developed countries. To describe the disease progression of individuals, multistate models are generally appropriate tools. These models allow the individuals to move along a path consisting of a finite number of disease states. We consider a simplifying illness-death model in which the subjects progress through the states healthy, diseased and dead. We use this model to study analytic relationships between the prevalence, incidence and mortality rates of irreversible diseases that have been applied in the past. One of these approaches is a rather recently proposed technique based on an ordinary differential equation (ODE). We conduct a simulation study to compare the performance of two suggested numerical approximations of this ODE with three alternative techniques, the common goal of which is to estimate age-specific incidence from cross-sectional information. The quality of the estimation methods is further explored using data on dementia in Germany. In the simulation scenarios as well as in the dementia data setting, the ODE method turns out to be the predominant technique with regard to the quality of the estimation of the known incidence regimes.

Development and demonstration of a state model for the estimation of incidence of partly undetected chronic diseases.

BACKGROUND: Estimation of incidence of the state of undiagnosed chronic disease provides a crucial missing link for the monitoring of chronic disease epidemics and determining the degree to which changes in prevalence are affected or biased by detection. METHODS: We developed a four-part compartment model for undiagnosed cases of irreversible chronic diseases with a preclinical state that precedes the diagnosis. Applicability of the model is tested in a simulation study of a hypothetical chronic disease and using diabetes data from the Health and Retirement Study (HRS). RESULTS: A two dimensional system of partial differential equations forms the basis for estimating incidence of the undiagnosed and diagnosed disease states from the prevalence of the associated states. In the simulation study we reach very good agreement between the estimates and the true values. Application to the HRS data demonstrates practical relevance of the methods. DISCUSSION: We have demonstrated the applicability of the modeling framework in a simulation study and in the analysis of the Health and Retirement Study. The model provides insight into the epidemiology of undiagnosed chronic diseases.

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

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, 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 limited the use of the model in epidemiology and public health. We develop a partial differential equation (PDE) that simplifies the use of the three-state model. To demonstrate the validity of the PDE, it is applied to two simulation studies, one about a hypothetical chronic disease and one about dementia in Germany. In two further applications, the PDE may provide insights into smoking behaviour of males in Germany and the knowledge about the ovulatory cycle in Egyptian women.

A new relation between prevalence and incidence of a chronic disease.

In 1991 Keiding published a relation between the age-specific prevalence and incidence of a chronic disease (in Age-specific incidence and prevalence: a statistical perspective. J. Roy. Stat. Soc. A, 154, 371-412). For special cases alternative formulations by differential equations were given recently in Brinks et al. (2013, Deriving age-specific incidence from prevalence with an ordinary differential equation. Statist. Med., 32, 2070-2078) and in Brinks & Landwehr (2014, Age- and time-dependent model of the prevalence of non-communicable diseases and application to dementia in Germany, Theor. Popul. Biol., 92, 62-68). From these works, we generalize formulations and discuss the advantages of the novel approach. As an implication, we obtain a new way of estimating the incidence rate of a chronic disease from prevalence data. This enables us to employ cross-sectional studies where otherwise expensive and lengthy follow-up studies are needed. This article illustrates and validates the novel method in a simulation study about dementia in Germany.

The intermediates take it all: asymptotics of higher criticism statistics and a powerful alternative based on equal local levels.

The higher criticism (HC) statistic, which can be seen as a normalized version of the famous Kolmogorov-Smirnov statistic, has a long history, dating back to the mid seventies. Originally, HC statistics were used in connection with goodness of fit (GOF) tests but they recently gained some attention in the context of testing the global null hypothesis in high dimensional data. The continuing interest for HC seems to be inspired by a series of nice asymptotic properties related to this statistic. For example, unlike Kolmogorov-Smirnov tests, GOF tests based on the HC statistic are known to be asymptotically sensitive in the moderate tails, hence it is favorably applied for detecting the presence of signals in sparse mixture models. However, some questions around the asymptotic behavior of the HC statistic are still open. We focus on two of them, namely, why a specific intermediate range is crucial for GOF tests based on the HC statistic and why the convergence of the HC distribution to the limiting one is extremely slow. Moreover, the inconsistency in the asymptotic and finite behavior of the HC statistic prompts us to provide a new HC test that has better finite properties than the original HC test while showing the same asymptotics. This test is motivated by the asymptotic behavior of the so-called local levels related to the original HC test. By means of numerical calculations and simulations we show that the new HC test is typically more powerful than the original HC test in normal mixture models.

Lexis diagram and illness-death model: simulating populations in chronic disease epidemiology.

Chronic diseases impose a tremendous global health problem of the 21st century. Epidemiological and public health models help to gain insight into the distribution and burden of chronic diseases. Moreover, the models may help to plan appropriate interventions against risk factors. To provide accurate results, models often need to take into account three different time-scales: calendar time, age, and duration since the onset of the disease. Incidence and mortality often change with age and calendar time. In many diseases such as, for example, diabetes and dementia, the mortality of the diseased persons additionally depends on the duration of the disease. The aim of this work is to describe an algorithm and a flexible software framework for the simulation of populations moving in an illness-death model that describes the epidemiology of a chronic disease in the face of the different times-scales. We set up a discrete event simulation in continuous time involving competing risks using the freely available statistical software R. Relevant events are birth, the onset (or diagnosis) of the disease and death with or without the disease. The Lexis diagram keeps track of the different time-scales. Input data are birth rates, incidence and mortality rates, which can be given as numerical values on a grid. The algorithm manages the complex interplay between the rates and the different time-scales. As a result, for each subject in the simulated population, the algorithm provides the calendar time of birth, the age of onset of the disease (if the subject contracts the disease) and the age at death. By this means, the impact of interventions may be estimated and compared.

Age- and time-dependent model of the prevalence of non-communicable diseases and application to dementia in Germany.

We derive a partial differential equation (PDE) that models the age-specific prevalence of a disease as a function of the incidence, remission and mortality rates. The main focus is on non-communicable diseases (NCDs), although the PDE is not restricted to NCDs. As an application of the PDE, the number of persons with dementia in Germany until the year 2050 is estimated based on German incidence data and official population projections. Uncertainty is treated by different scenarios about life expectancy, number of migrants, prevalence of the disease in migrants, and scenarios about the future incidence, and mortality of demented persons. Life expectancy and incidence of dementia have the strongest impact on the future number of persons with dementia. In nearly all scenarios, our estimated case numbers exceed former estimates. Furthermore, we use an example to show that the PDE method yields more accurate results than a common alternative approach.

Age of onset in chronic diseases: new method and application to dementia in Germany.

BACKGROUND: Age of onset is an important outcome to characterize a population with a chronic disease. With respect to social, cognitive, and physical aspects for patients and families, dementia is especially burdensome. In Germany, like in many other countries, it is highly prevalent in the older population and imposes enormous efforts for caregivers and society. METHODS: We develop an incidence-prevalence-mortality model to derive the mean and variance of the age of onset in chronic diseases. Age- and sex-specific incidence and prevalence of dementia is taken from published values based on health insurance data from 2002. Data about the age distribution in Germany in 2002 comes from the Federal Statistical Office. RESULTS: Mean age of onset of a chronic disease depends on a) the age-specific incidence of the disease, b) the prevalence of the disease, and c) the age distribution of the population. The resulting age of onset of dementia in Germany in 2002 is 78.8 ± 8.1 years (mean ± standard deviation) for men and 81.9 ± 7.6 years for women. CONCLUSIONS: Although incidence and prevalence of dementia in men are not greater than in women, men contract dementia approximately three years earlier than women. The reason lies in the different age distributions of the male and the female population in Germany.

Identification of a multistate continuous-time nonhomogeneous Markov chain model for patients with decreased renal function.

OBJECTIVES: Markov chain models are frequently used to study the clinical course of chronic diseases. The aim of this article is to adopt statistical methods to describe the time dynamics of chronically ill patients when 2 kinds of data sets--fully and partially observable data are available. MODEL: We propose a 6-state continuous-time Markov chain model for the progression of chronic kidney disease (CKD), where little is known about the transitions between the disease stages. States 1 to 3 of the model correspond to stages III to V of chronic kidney disease in the Kidney Disease Outcomes Quality Initiative (KDOQI) CKD classification. States 4 and 5 relate to dialysis and transplantation (renal replacement therapy), respectively. Death is the (absorbing) state 6. METHODS AND DATA: The model can be investigated and identified using Kolmogorov's forward equations and the methods of survival analysis. Age dependency, covariates in the form of the Cox regression, and unobservable risks of transition (frailties) can be included in the model. We applied our model to a data set consisting of all 2097 patients from all renal centers in a region in North Rhine-Westphalia (Germany) in 2005-2010. RESULTS: We compared transitions and relative risks to the few data published and found them to be reasonable. For example, patients with diabetes had a significantly higher risk for disease progression compared with patients without diabetes. CONCLUSIONS: In summary, modeling may help to quantify disease progression and its predictors when only partially observable prospective data are available.

Deriving age-specific incidence from prevalence with an ordinary differential equation.

This article describes new relationships between the age-specific incidence of, the prevalence of and mortality from a chronic disease. We express these relationships in terms of an ordinary differential equation and form the methodological basis for a novel approach to estimating incidences from age-specific prevalence data. We examine practical aspects of the relationships and a comparison with a known stochastic method in a simulation study. Finally, we apply the novel method to a data set of renal replacement therapy recorded from patients with chronic kidney failure in a region of Germany with approximately 310,000 inhabitants from 2002 to 2010.