Back-projection of German AIDS data using information on dates of tests

Modeling methods for estimating HIV incidence: a mathematical review

Estimating HIV incidence is crucial for monitoring the epidemiology of this infection, planning screening and intervention campaigns, and evaluating the effectiveness of control measures. However, owing to the long and variable period from HIV infection to the development of AIDS and the introduction of highly active antiretroviral therapy, accurate incidence estimation remains a major challenge. Numerous estimation methods have been proposed in epidemiological modeling studies, and here we review commonly-used methods for estimation of HIV incidence. We review the essential data required for estimation along with the advantages and disadvantages, mathematical structures and likelihood derivations of these methods. The methods include the classical back-calculation method, the method based on CD4+ T-cell depletion, the use of HIV case reporting data, the use of cohort study data, the use of serial or cross-sectional prevalence data, and biomarker approach. By outlining the mechanistic features of each method, we provide guidance for planning incidence estimation efforts, which may depend on national or regional factors as well as the availability of epidemiological or laboratory datasets.

Extending Bayesian back-calculation to estimate age and time specific HIV incidence

CD4-based multi-state back-calculation methods are key for monitoring the HIV epidemic, providing estimates of HIV incidence and diagnosis rates by disentangling their inter-related contribution to the observed surveillance data. This paper, extends existing approaches to age-specific settings, permitting the joint estimation of age- and time-specific incidence and diagnosis rates and the derivation of other epidemiological quantities of interest. This allows the identification of specific age-groups at higher risk of infection, which is crucial in directing public health interventions. We investigate, through simulation studies, the suitability of various bivariate splines for the non-parametric modelling of the latent age- and time-specific incidence and illustrate our method on routinely collected data from the HIV epidemic among gay and bisexual men in England and Wales.

Verlauf der HIV-Epidemie in Deutschland

The course of the HIV epidemic in Germany can be modelled by back calculation until the beginning of the nineties. The recent course of the epidemic can only be derived from surveillance data of newly diagnosed HIV infections in conjunction with other data sources. Based on these surveillance data HIV incidence in Germany can be estimated to have been stable with 2000 to 2500 new infections per year since the early nineties, after having peaked in the early eighties. The most affected group are men who have sex with men followed by persons infected by heterosexual contact and migrants from high prevalence countries. The number of intravenous drug users has declined over the years and is now in fourth place. There are indications that increased risk behaviour and rising numbers of other sexually transmitted infections together with a change towards later initiation of antiretroviral therapy has led to an increase in new HIV infections in Germany in recent years. An improvement of the epidemiological surveillance for "indicator" STIs in combination with the assessment of risk behaviours in high risk groups would be desirable steps towards a second generation surveillance in Germany.

Estimating HIV Incidence and Detection Rates From Surveillance Data

BACKGROUND

Markov models that incorporate HIV test information can increase precision in estimates of new infections and permit the estimation of detection rates. The purpose of this study was to assess the functioning of a Markov model for estimating new HIV infections and HIV detection rates in Louisiana using surveillance data.

METHODS

We expanded a discrete-time Markov model by accounting for the change in AIDS case definition made by the Centers for Disease Control and Prevention in 1993. The model was applied to quarterly HIV/AIDS surveillance data reported in Louisiana from 1981 to 1996 for various exposure and demographic subgroups. When modeling subgroups defined by exposure categories, we adjusted for the high proportion of missing exposure information among recent cases. We ascertained sensitivity to changes in various model assumptions.

RESULTS

The model was able to produce results consistent with other sources of information in the state. Estimates of new infections indicated a transition of the HIV epidemic in Louisiana from (1) predominantly white men and men who have sex with men to (2) women, blacks, and high-risk heterosexuals. The model estimated that 61% of all HIV/AIDS cases were detected and reported by 1996, yet half of all HIV/non-AIDS cases were yet to be detected. Sensitivity analyses demonstrated that the model was robust to several uncertainties.

CONCLUSIONS

In general, the methodology provided a useful and flexible alternative for estimating infection and detection trends using data from a U.S. surveillance program. Its use for estimating current infection will need further exploration to address assumptions related to newer treatments.

Age-specific back-projection of HIV diagnosis data

A method for reconstructing the HIV infection curve from data on both HIV and AIDS diagnoses is enhanced by using age as a covariate and by using the diagnosis data to estimate parameters that were previously assumed known. Maximum likelihood estimation is used for parameters of the induction distribution. Each of the set of parameters that specify the baseline rate of infection over time and the set of parameters giving the relative susceptibility over age are estimated by maximizing the likelihood subject to a smoothness requirement. We find that estimating the extra parameters is feasible, producing estimates with good precision. Including age as a covariate gives 90 per cent confidence intervals for the HIV incidence curve that are about 20 per cent narrower than those obtained when age data are not used.

Estimating HIV incidence using dates of both HIV and AIDS diagnoses

Knowledge of HIV incidence is important to formulate sensible strategies aimed at controlling the HIV/AIDS epidemic. Back-projection is one of the methods for reconstructing the HIV incidence curve from AIDS incidence data. However, because of the low risk of developing AIDS during the first few years after infection, precise estimates of HIV incidence for the recent past are unlikely if we use AIDS incidence data only. As a result there have been recent attempts to use, not only the date of AIDS diagnosis, but also to use the date of their first positive HIV test. The objective of this paper is to incorporate into back-projection the additional information provided by those individuals who have tested HIV positive but have not yet developed AIDS. This adds information on a very large number of other individuals, and provides the hope that the precision of back-projection is improved considerably. The date of a positive HIV test or an AIDS diagnosis of an individual, whichever comes first, is used in a generalized convolution equation for the purpose of back-projection. The method is illustrated by an application to Australian HIV and AIDS data. Study results show that dramatic improvement in precision is gained for estimates of HIV incidence in recent years when both HIV and AIDS diagnosis dates are used on all individuals.

Reconstruction and prediction of the HIV/AIDS epidemic among adults in the European Union and in the low prevalence countries of central and eastern Europe

OBJECTIVES

To reconstruct the HIV epidemic and to provide forecasts of AIDS incidence among adults in the European Union (EU) and in a group of low prevalence (LP) countries of central and eastern Europe (including the Asian republics of the former Soviet Union).

METHODS

An empirical Bayesian back-calculation method was applied to AIDS incidence data reported by 31 March 1994. The HIV-infection curve was modelled as a yearly step function and a seven-stage Markov model of disease progression, incorporating effects of pre-AIDS treatment, was used. Estimation was by penalized maximum likelihood with empirical Bayesian smoothing. Data were analysed by transmission group and, within the EU, by country. Predictions of AIDS cases to 1998 were made assuming constant annual HIV incidence from 1993 onwards.

RESULTS

Estimated HIV prevalences per 100,000 population aged 15-59 years were, at 31 December 1993, 198 (n = 447,800) in the EU and 2.7 (n = 6840) in the 22 LP countries, with increases of 41% (EU) and 71% (LP) between 1989 and 1993. Among homo/bisexual men in the EU, prevalence appears to have stabilized since 1989 and AIDS incidence appears to be reaching a peak. Among all prevalent HIV infections in the EU, 42% were estimated to be among injecting drug users, 25% among homo-/bisexual men and 18% among persons infected heterosexually, compared with 29%, 35% and 19%, respectively, in the LP countries. Without allowing for the 1993 revision of the case definition, annual AIDS incidence is predicted to increase, between 1994 and 1998, by 24% in the EU and by 48% in the LP countries, with the largest percentage increases among heterosexually-infected persons.

CONCLUSION

The overall HIV prevalence rate is estimated to have been about 70-fold lower in the LP countries than in the EU in the early 1990s, but to be increasing much more rapidly in the former. Moreover, recent reports of rapidly increasing HIV infection rates suggest that back-calculation may seriously underestimate the size of the epidemic in the LP countries. Implementation of effective preventive measures is urgent if large-scale epidemics are to be avoided in the presently LP countries of the European region.

Uses of the EM algorithm in the analysis of data on HIV/AIDS and other infectious diseases

The analysis of data on infectious diseases is a natural setting for applications of the EM algorithm, because the infection process is only partially observable. Difficulties in determining the expectation at the E step have been side-stepped by adopting pragmatic models which reflect only part of the mechanism that generates the data. In the HIV/AIDS context the EM algorithm has helped in the reconstruction of the unobserved HIV infection curve, the so-called backprojection problem, as well as in the estimation of the distribution for the incubation period until AIDS, in estimating the infectivity of HIV in partnerships and in estimating parameters describing the decline in the immune system. There is a need for smooth estimates of functions in these applications, suggesting the use of the EMS algorithm or use of the EM algorithm to maximize a penalized likelihood. For data on other infectious diseases the application of the EM algorithm has so far been restricted to analyses of data on the size of outbreaks in a sample of households.

Incorporating HIV test data into forecasts of the AIDS epidemic in Scotland

For AIDS cases in Scotland the date of HIV antibody positive diagnosis (HIV test date) is recorded on the AIDS case reports. Data are also available on the total numbers of individuals with HIV positive test reports in Scottish laboratories in each year since testing became available. These data are incorporated into a model of the HIV epidemic described in terms of testing rates by calendar year. The HIV infection curve is modelled as a step function, and the testing rates are allowed to differ between steps. Results are presented for intravenous drug users (IDUs) and for homosexual/bisexual men. The estimated rates of testing for the IDUs (estimates from 19 per cent to 44 per cent per year) are considerably higher than those for homosexual/bisexual men (estimates of 10 per cent to 17 per cent per year). Data on the year of testing for AIDS diagnoses gave relatively little improvement in estimates of the HIV infection curve. However, when this information is combined with data on the total number of HIV positive diagnoses per year, there is a dramatic improvement in the estimate of the HIV infection curve. This is particularly marked for infections in the most recent period and for the estimates of cumulative infections up to the present. However, these improvements are gained at the cost of assumptions of similar testing rates applying to all sections of the HIV infected populations, which will be difficult to check in practice. This suggests that these methods should not be used in isolation but in combination with other evidence about the spread of HIV infection in a population.