A non-parametric method for the reconstruction of age- and time-dependent incidence from the prevalence data of irreversible diseases with differential mortality

Comorbidity risk and distribution characteristics of chronic diseases in the elderly population in China

BACKGROUND

The risk of comorbid chronic diseases in elderly people is an important problem affecting their health and quality of life. We analyzed the incidence of chronic diseases for combinations of chronic diseases analyzed.

METHODS

We used the original data to construct hypothetical cohorts of elderly individuals that evolved with age. The complex network was used to reduce the dimensionality of disease. The multistate transition model is used to calculate the incidence of each chronic disease, exploring comorbidity characteristics and rules.

RESULTS

(1) By using complex network, seven chronic diseases were screened out in men, including hypertension, diabetes, heart disease, stroke, chronic lung disease, arthritis and dyslipidemia; six chronic diseases in women showed significant comorbidity except chronic lung disease. (2) Incidence show differences in age and sex; incidence of chronic diseases generally increased with age. (3) The marginal risk increases with the number of basic chronic diseases associated with comorbidities. (4) When hypertension is present as a basic disease, its impact on the risk of other chronic diseases is much less than that of other chronic diseases. (5) When diseases occur as basic chronic diseases, hypertension-heart disease and diabetes-dyslipidemia are combinations that have the greatest impact on each other in men; hypertension-heart disease in women.

CONCLUSIONS

The incidence of chronic diseases in patients who have chronic diseases and will form comorbidities differs from that in healthy states, and the related effects of different chronic diseases also differ. Among these conditions, hypertension is caused by a special mechanism.

HIV incidence estimation among female sex workers in South Africa: a multiple methods analysis of cross-sectional survey data

BACKGROUND

Although numerous studies have investigated HIV risk factors and shown high HIV prevalence among female sex workers in South Africa, no national HIV incidence estimate exists for this potentially important group for HIV transmission. We aimed to estimate HIV incidence among female sex workers in South Africa who could be accessed through sex worker programmes, and to refine and describe the methods that enabled analysis.

METHODS

This study was embedded in a cross-sectional national survey of female sex workers who were linked to sex worker programmes. We aimed to enrol 3000 female sex workers aged at least 18 years who had sold or transacted in sex in the preceding 6 months in 12 randomly selected districts of the 22 districts with sex worker programmes, ensuring coverage of all provinces of South Africa. Women who self-reported as current victims of human trafficking were excluded from enrolment. We used a multistep process to sample districts and then hotspots, and a chain referral method to recruit participants. We collected cross-sectional data for self-reported HIV status, demographic characteristics, and exposure to violence. Two rapid tests were used to ascertain diagnostic markers, a viral load assay was used to ascertain clinical markers, and the Maxim Limiting Antigen Avidity EIA was used to ascertain infection-staging HIV markers. Given the challenges of estimating HIV incidence, especially cross-sectionally, multiple methods of estimation were adapted to our setting, leveraging the age structure of HIV prevalence, recency-of -infection biomarker results (ie, where recent infection is classified as ≤1·5 normalised optical density [ODn] on the avidity assay and viral load of ≥1000 copies per mL), and reported testing histories.

FINDINGS

Of 3005 female sex workers who were enrolled and interviewed between Feb 4 and June 26, 2019, 2999 who had HIV test results were included in this analysis. The median age of participants was 32 years (IQR 27-38). 1714 (57·2%) of 2999 participants self-reported as being HIV positive, and 1447 (48·3%) of 2993 participants reported client sexual violence in the past year. The measured HIV prevalence was 62·1% (95% CI 60·3-65·7) and peaked at approximately age 40 years. Using recency-of-infection biomarker results, we obtained a base case estimate of HIV incidence of 4·60 cases per 100 person-years (95% CI 1·53-8·45) for the population. Estimates were generally consistent by method, and outlying incidence estimates calculated by self-reported testing histories were considered unreliable. Various sensitivity analyses produced estimates up to 11 cases per 100 person-years, and we did not detect differences by age and region.

INTERPRETATION

We found that female sex workers have extraordinarily high HIV incidence of approximately 5 cases per 100 person-years, emphasising the need to sustain and strengthen efforts to mitigate risk and provide adequate care. The notable role that sex work has in HIV transmission demands substantial investment in ongoing epidemiological monitoring.

FUNDING

South African Medical Research Council, South African National Treasury, Global Fund, South African Department of Science and Innovation, Wellcome Trust.

Future projection of the health and functional status of older people in Japan: A multistate transition microsimulation model with repeated cross-sectional data

Accurate future projections of population health are imperative to plan for the future healthcare needs of a rapidly aging population. Multistate-transition microsimulation models, such as the U.S. Future Elderly Model, address this need but require high-quality panel data for calibration. We develop an alternative method that relaxes this data requirement, using repeated cross-sectional representative surveys to estimate multistate-transition contingency tables applied to Japan's population. We calculate the birth cohort sex-specific prevalence of comorbidities using five waves of the governmental health surveys. Combining estimated comorbidity prevalence with death record information, we determine the transition probabilities of health statuses. We then construct a virtual Japanese population aged 60 and older as of 2013 and perform a microsimulation to project disease distributions to 2046. Our estimates replicate governmental projections of population pyramids and match the actual prevalence trends of comorbidities and the disease incidence rates reported in epidemiological studies in the past decade. Our future projections of cardiovascular diseases indicate lower prevalence than expected from static models, reflecting recent declining trends in disease incidence and fatality.

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.

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.

Population-level HIV incidence estimates using a combination of synthetic cohort and recency biomarker approaches in KwaZulu-Natal, South Africa

Introduction

There is a notable absence of consensus on how to generate estimates of population-level incidence. Incidence is a considerably more sensitive indicator of epidemiological trends than prevalence, but is harder to estimate. We used a novel hybrid method to estimate HIV incidence by age and sex in a rural district of KwaZulu-Natal, South Africa.

Methods

Our novel method uses an ‘optimal weighting’ of estimates based on an implementation of a particular ‘synthetic cohort’ approach (interpreting the age/time structure of prevalence, in conjunction with estimates of excess mortality) and biomarkers of ‘recent infection’ (combining Lag-Avidity, Bio-Rad Avidity and viral load results to define recent infection, and adapting the method for age-specific incidence estimation). Data were obtained from a population-based cross-sectional HIV survey conducted in Mbongolwane and Eshowe health service areas in 2013.

Results

Using the combined method, we find that age-specific HIV incidence in females rose rapidly during adolescence, from 1.33 cases/100 person-years (95% CI: 0.98,1.67) at age 15 to a peak of 5.01/100PY (4.14,5.87) at age 23. In males, incidence was lower, 0.34/100PY (0.00-0.74) at age 15, and rose later, peaking at 3.86/100PY (2.52-5.20) at age 30. Susceptible population-weighted average incidence in females aged 15-29 was estimated at 3.84/100PY (3.36-4.40), in males aged 15-29 at 1.28/100PY (0.68-1.50) and in all individuals aged 15-29 at 2.55/100PY (2.09-2.76). Using the conventional recency biomarker approach, we estimated HIV incidence among females aged 15-29 at 2.99/100PY (1.79-4.36), among males aged 15-29 at 0.87/100PY (0.22-1.60) and among all individuals aged 15-59 at 1.66/100PY (1.13-2.27).

Discussion

HIV incidence was very high in women aged 15-30, peaking in the early 20s. Men had lower incidence, which peaked at age 30. The estimates obtained from the hybrid method are more informative than those produced by conventional analysis of biomarker data, and represents a more optimal use of available data than either the age-continuous biomarker or synthetic cohort methods alone. The method is mainly useful at younger ages, where excess mortality is low and uncertainty in the synthetic cohort estimates is reasonably small.

Conclusion

Application of this method to large-scale population-based HIV prevalence surveys is likely to result in improved incidence surveillance over methods currently in wide use. Reasonably accurate and precise age-specific estimates of incidence are important to target better prevention, diagnosis and care strategies.

Segmented polynomials for incidence rate estimation from prevalence data

The study considers the problem of estimating incidence of a non remissible infection (or disease) with possibly differential mortality using data from a(several) cross-sectional prevalence survey(s). Fitting segmented polynomial models is proposed to estimate the incidence as a function of age, using the maximum likelihood method. The approach allows automatic search for optimal position of knots, and model selection is performed using the Akaike information criterion. The method is applied to simulated data and to estimate HIV incidence among men in Zimbabwe using data from both the NIMH Project Accept (HPTN 043) and Zimbabwe Demographic Health Surveys (2005-2006). Copyright © 2016 John Wiley & Sons, Ltd.

Bayesian inference for age-structured population model of infectious disease with application to varicella in Poland

The dynamics of the infectious disease transmission are often best understood by taking into account the structure of population with respect to specific features, for example age or immunity level. The practical utility of such models depends on the appropriate calibration with the observed data. Here, we discuss the Bayesian approach to data assimilation in the case of a two-state age-structured model. Such models are frequently used to explore the disease dynamics (i.e. force of infection) based on prevalence data collected at several time points. We demonstrate that, in the case when the explicit solution to the model equation is known, accounting for the data collection process in the Bayesian framework allows us to obtain an unbiased posterior distribution for the parameters determining the force of infection. We further show analytically and through numerical tests that the posterior distribution of these parameters is stable with respect to a cohort approximation (Escalator Boxcar Train) of the solution. Finally, we apply the technique to calibrate the model based on observed sero-prevalence of varicella in Poland.

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.

Electronic supplementary material

The online version of this article (doi:10.1186/s12874-015-0094-y) contains supplementary material, which is available to authorized users.

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.

A general HIV incidence inference scheme based on likelihood of individual level data and a population renewal equation

We derive a new method to estimate the age specific incidence of an infection with a differential mortality, using individual level infection status data from successive surveys. The method consists of a) an SI-type model to express the incidence rate in terms of the prevalence and its derivatives as well as the difference in mortality rate, and b) a maximum likelihood approach to estimate the prevalence and its derivatives. Estimates can in principle be obtained for any chosen age and time, and no particular assumptions are made about the epidemiological or demographic context. This is in contrast with earlier methods for estimating incidence from prevalence data, which work with aggregated data, and the aggregated effect of demographic and epidemiological rates over the time interval between prevalence surveys. Numerical simulation of HIV epidemics, under the presumption of known excess mortality due to infection, shows improved control of bias and variance, compared to previous methods. Our analysis motivates for a) effort to be applied to obtain accurate estimates of excess mortality rates as a function of age and time among HIV infected individuals and b) use of individual level rather than aggregated data in order to estimate HIV incidence rates at times between two prevalence surveys.

CONVENIENT LINKS BETWEEN TIME VARYING INCIDENCE RATES AND CURRENT STATUS INFORMATION FOR EPIDEMIOLOGICAL MODELS WITH HETEROGENEITY

Many compartment based epidemiological models are written as differential equation systems for various status subpopulation sizes with per person-time transfer rates between compartments. However, field data obtained by sampling at chosen times is usually provided in terms of status proportions from the total observable population (e.g., relative prevalence). Relationships between per person-time transfer rates (incidence, mortality, intervention rates) and proportions are not obvious when heterogeneity is at work because the various subpopulation sizes undergo different attrition rates and are not evolving in synchrony with the corresponding proportions. Rules are proposed to write sets of differential equations for compartment models, directly in terms of the proportions of the total observable at any time. To facilitate the writing of relationships between per person-time transfer rates and proportions, the systems are cast in network equivalent forms satisfying rules analogous to those of electrical networks (Kirchhoff's law for currents). The method is also extended to variability in the rates within a status subpopulation, considering either a fixed set of compartmental subdivisions or an inner continuum of differences in rates.

Measures and models for causal inference in cross-sectional studies: arguments for the appropriateness of the prevalence odds ratio and related logistic regression

Background

Several papers have discussed which effect measures are appropriate to capture the contrast between exposure groups in cross-sectional studies, and which related multivariate models are suitable. Although some have favored the Prevalence Ratio over the Prevalence Odds Ratio -- thus suggesting the use of log-binomial or robust Poisson instead of the logistic regression models -- this debate is still far from settled and requires close scrutiny.

Discussion

In order to evaluate how accurately true causal parameters such as Incidence Density Ratio (IDR) or the Cumulative Incidence Ratio (CIR) are effectively estimated, this paper presents a series of scenarios in which a researcher happens to find a preset ratio of prevalences in a given cross-sectional study. Results show that, provided essential and non-waivable conditions for causal inference are met, the CIR is most often inestimable whether through the Prevalence Ratio or the Prevalence Odds Ratio, and that the latter is the measure that consistently yields an appropriate measure of the Incidence Density Ratio.

Summary

Multivariate regression models should be avoided when assumptions for causal inference from cross-sectional data do not hold. Nevertheless, if these assumptions are met, it is the logistic regression model that is best suited for this task as it provides a suitable estimate of the Incidence Density Ratio.

Do Tests Devised to Detect Recent HIV-1 Infection Provide Reliable Estimates of Incidence in Africa?

The objective of this study was to assess the performance of 4 biologic tests designed to detect recent HIV-1 infections in estimating incidence in West Africa (BED, Vironostika, Avidity, and IDE-V3). These tests were assessed on a panel of 135 samples from 79 HIV-1-positive regular blood donors from Abidjan, Côte d'Ivoire, whose date of seroconversion was known (Agence Nationale de Recherches sur le SIDA et les Hépatites Virales 1220 cohort). The 135 samples included 26 from recently infected patients (< or =180 days), 94 from AIDS-free subjects with long-standing infection (>180 days), and 15 from patients with clinical AIDS. The performance of each assay in estimating HIV incidence was assessed through simulations. The modified commercial assays gave the best results for sensitivity (100% for both), and the IDE-V3 technique gave the best result for specificity (96.3%). In a context like Abidjan, with a 10% HIV-1 prevalence associated with a 1% annual incidence, the estimated test-specific annual incidence rates would be 1.2% (IDE-V3), 5.5% (Vironostika), 6.2% (BED), and 11.2% (Avidity). Most of the specimens falsely classified as incident cases were from patients infected for >180 days but <1 year. The authors conclude that none of the 4 methods could currently be used to estimate HIV-1 incidence routinely in Côte d'Ivoire but that further adaptations might enhance their accuracy.

Randomization and baseline transmission in vaccine field trials

In randomized trials, the treatment assignment mechanism is independent of the outcome of interest and other covariates thought to be relevant in determining this outcome. It also allows, on average, for a balanced distribution of these covariates in the vaccine and placebo groups. Randomization, however, does not guarantee that the estimated effect is an unbiased estimate of the biological effect of interest. We show how exposure to infection can be a confounder even in randomized vaccine field trials. Based on a simple model of the biological efficacy of interest, we extend the arguments on comparability and collapsibility to examine the limits of randomization to control for unmeasured covariates. Estimates from randomized, placebo-controlled Phase III vaccine field trials that differ in baseline transmission are not comparable unless explicit control for baseline transmission is taken into account.

Estimating incidence of HIV infection in childbearing age African women using serial prevalence data from antenatal clinics

Ades and Medley provided the first flexible method for estimating age- and time-specific HIV incidence using HIV prevalence data collected among pregnant women and adjusting for the effect of differential selection between infected and uninfected women. This paper extends the approach proposed by these authors. We used a parametric model that allows the relative inclusion rate to depend on both age, calendar time, and duration of HIV infection. We developed a two dimensional penalized log-likelihood approach for estimating time- and age-specific incidence using a binomial likelihood function and a quadratic roughness penalty which allows smoothing over both age and time. Identifiability of the model parameters and effect of sample size are studied through simulations. The method is illustrated using prenatal HIV testing data recorded from 1995 to 2002 in Abidjan, Côte d'Ivoire, to estimate the HIV annual incidence rate among women aged 12-40 year old, from the beginning of the epidemic to 2002. We show that estimated incidence rates are highly dependent on hypotheses made to model the relative inclusion rate. Despite this dependency, the application of the method leads to new and accurate findings on HIV incidence qualitative features in Abidjan. We highlight the relevance of such a method in monitoring the dynamics of HIV epidemic in Africa which is essential for planning vaccine trials and future treatment needs, and for assessment of prevention policy.

Advances in medical statistics arising from the AIDS epidemic

Many statisticians have contributed to studies of the HIV epidemic and progression to AIDS. They have developed new statistical methodology, where needed, to address HIV-related issues. The transfer of methods from one area to another often involves a substantial delay. This paper points to methods that were developed in the HIV context and have either already found applications in other areas of medical research or have the potential for such applications, with the hope that this will promote a speedier transfer of the research methods. Among the new tools that HIV studies have placed firmly into the pool of statistical methods for medical research are the methods of back-calculation, methods for the analysis of retrospective ascertainment data and methods of analysis for the combined data from clinical trials and associated longitudinal studies. Notions that have been stimulated substantially are use of surrogate endpoints in clinical trials and screening blood products by the use of pooled serum samples. Research activity in many other areas has been boosted substantially through contributions motivated by HIV/AIDS studies. Noteworthy examples are analyses for doubly-censored lifetime data and methods for assessing vaccines for transmissible diseases.