A Bayesian hierarchical model with novel prior specifications for estimating HIV testing rates

Human immunodeficiency virus (HIV) infection is a severe infectious disease actively spreading globally, and acquired immunodeficiency syndrome (AIDS) is an advanced stage of HIV infection. The HIV testing rate, that is, the probability that an AIDS‐free HIV infected person seeks a test for HIV during a particular time interval, given no previous positive test has been obtained prior to the start of the time, is an important parameter for public health. In this paper, we propose a Bayesian hierarchical model with two levels of hierarchy to estimate the HIV testing rate using annual AIDS and AIDS‐free HIV diagnoses data. At level one, we model the latent number of HIV infections for each year using a Poisson distribution with the intensity parameter representing the HIV incidence rate. At level two, the annual numbers of AIDS and AIDS‐free HIV diagnosed cases and all undiagnosed cases stratified by the HIV infections at different years are modeled using a multinomial distribution with parameters including the HIV testing rate. We propose a new class of priors for the HIV incidence rate and HIV testing rate taking into account the temporal dependence of these parameters to improve the estimation accuracy. We develop an efficient posterior computation algorithm based on the adaptive rejection metropolis sampling technique. We demonstrate our model using simulation studies and the analysis of the national HIV surveillance data in the USA. Copyright © 2015 John Wiley & Sons, Ltd.     

Computing back-calculation estimates of aids epidemic

The method of back-calculation estimates the number of HIV infections from AIDS incidence data and projects future AIDS incidence. We explore a conditional likelihood approach for computing estimates of the number of HIV infections and the parameters in the epidemic density. This method is asymptotically equivalent to the usual likelihood method. The asymptotic normal distribution of the estimates facilitates the computation of confidence intervals. We compute standard deviations for the estimates of HIV incidence and project AIDS incidence from the underlying multinomial distributions. We illustrate the methods with applications to AIDS data in the United States.     

Estimating HIV prevalence and projecting AIDS incidence in the United States: a model that accounts for therapy and changes in the surveillance definition of AIDS.

The AIDS incubation distribution is changing in calendar time because of treatment and changes in the surveillance definition of AIDS. To obtain reliable estimates of HIV prevalence and projections of AIDS incidence in the 1990s using the method of backcalculation, we constructed an appropriate incubation distribution for each calendar date of infection. We parameterized the impact of treatment on the incubation distribution by specifying the relative hazard for AIDS in treated versus untreated people as a function of duration of HIV infection. To account for trends in the incubation distribution, we modelled the prevalence of treatment, the distribution of treatment onset times, and the impact of the revision of the AIDS surveillance definition in 1987. We selected and evaluated backcalculation models based on consistency with external information. We defined a 'plausible range' of estimates that took into account uncertainty about the natural incubation distribution and treatment efficacy, as well as bootstrap assessment of stochastic error. Using these methods, we projected that national United States AIDS incidence will plateau during 1991-1994 at over 50,000 cases per year. Projections exhibited substantial systematic uncertainty, and we calculated a plausible range for AIDS incidence in 1994 of 42,300 to 70,700 cases. An estimated 628,000 to 988,000 cumulative HIV infections occurred as of 1 January 1991. After accounting for AIDS mortality, we estimated that 484,000 to 844,000 people were living with HIV infection on 1 January 1991. Favourable trends in HIV incidence appeared in gay men and intravenous drug users. Plausible ranges for our estimates overlapped with those from a 'stage model' approach to incorporating treatment effects in backcalculations. Our approach, however, tended to yield smaller estimates of epidemic size, mainly because the parameters used with the stage model implied that more treatment was in use and that treatment was more effective than in our model.     

COMPARISON OF TRENDS IN HIV INFECTION FOR TWO RISK CATEGORIES

Sensible plans for health-care needs and determination of priorities for expenditure require regular assessment of trends in HIV incidences. In particular, trends in the relative HIV incidences of different risk categories are useful when assessing whether current control strategies are working equally well for all risk categories. Here five tests for such trends are proposed for the analysis of AIDS incidence data and their performances are compared by a simulation study, assuming a log-linear trend in the HIV incidences for two risk categories. A convenient test based on a log-linear model for AIDS incidences is found both effective and robust to the nature of the underlying trend. The maximum likelihood estimate of the trend parameter is found stable even though estimates of other HIV incidence parameters are unstable. Smoothing of estimates of the other HIV incidence parameters is recommended because this dramatically reduces the rate of convergence of the iterative methods used to obtain the estimates.     

An age- and sex-structured HIV epidemiological model: features and applications.

An important challenge in modelling the human immunodeficiency virus (HIV)/acquired immunodeficiency syndrome (AIDS) epidemic is to use the increasing quantity of disease surveillance data to validate estimates and forecasts. Presented is a novel model for forecasting HIV incidence by age and sex and among sentinel groups for which data are available. This approach permits a closer relationship between forecasting and surveillance activities, and more accurate estimates validated to data. As inputs the model uses an estimate of the HIV prevalence, country demographic data, and a profile of the sexual risk of HIV infection by age, to project HIV incidence, prevalence, number of AIDS cases and population. The following examples of the use of the model are given: forecasting HIV incidence in East Africa, by age, sex, and among pregnant women; 3-5-year forecasts of HIV incidence; modelling mixed risk behaviour HIV epidemics in South-east Asia; demographic indicators; and targeting a preventive vaccine by age group.     

Joint analysis of HIV and AIDS surveillance data in back-calculation

AIDS surveillance data are the main source of information to perform back-calculation of HIV incidence. We propose a method to incorporate additional information gained by linkage with an HIV surveillance system, containing data on the time of first positive HIV test. In this paper we generalize an earlier method that was developed to use HIV testing data available only for AIDS cases. The new method also makes use of cases with an HIV positive test who have not yet developed AIDS, typically a substantial proportion of the HIV-infected population. Furthermore, we use a more realistic model for the HIV testing rate, incorporating dependence on both time since infection and calendar time. The method makes use of an EM algorithm with generalized additive model smoothing, and is applied to data from Veneto, a region of northern Italy. Our results show that HIV incidence in Veneto peaked in the late 1980s, and decreased thereafter. Importantly, the HIV incidence estimates based on joint analysis of HIV and AIDS surveillance data are more efficient than estimates based on AIDS surveillance data alone. Our estimates also show a decreasing trend in the HIV testing rate over time, which leads to the conclusion that the interval between HIV infection and first positive test has lengthened over time. Furthermore, it is found that for infected individuals, the probability of seeking on HIV test is highest soon after infection.     

A method to test for a recent increase in HIV-1 seroconversion incidence: Results from the multicenter AIDS cohort study (MACS)

We have formulated the problem of determining whether there has been an upturn in HIV-1 seroconversion incidence over the first five years of follow-up in the Multicenter AIDS Cohort Study (MACS) as that of locating the minimum of a quadratic regression or examination of two-knot piecewise spline models. Under a quadratic model, we propose a method to obtain a direct estimate and a bootstrap estimate for the location of the temporal turning point (local minimum) for HIV-1 seroconversion incidence and three methods to estimate confidence intervals for the location of the turning point for HIV seroconversion incidence: (1) Wald confidence interval estimate with or without log transformation assuming the asymptotic normality and applying the Delta method; (2) asymmetric confidence intervals using Fieller's Theorem and its modification; and (3) bootstrapping confidence intervals. Inferences for the temporal turning point based on Wald tests for a single regression term in a non-linear regression model were not reliable compared to inferences based on confidence intervals placed on calendar time. We present results using these different method applied to the MACS data and we obtain power estimates to illustrate the performance of different methods.     

Acquired immunodeficiency syndrome (AIDS)-free time after human immunodeficiency virus type 1 (HIV-1) seroconversion in homosexual men. Multicenter AIDS Cohort Study Group

To estimate the time interval between human immunodeficiency virus type 1 (HIV-1) seroconversion and acquired immunodeficiency syndrome (AIDS) diagnosis in homosexual men, prospective incident cohorts are difficult to obtain and, if assembled, provide few events owing to the long incubation time. Although seroprevalent cohorts are numerous in size and events, the information is limited due to the unknown times since seroconversion. To combine the information provided by 1,628 seroprevalent men (304 AIDS cases) and 233 seroconverters (12 AIDS cases) being followed in a multicenter study since 1984, the postseroconversion changes in hematologic variables occurring in the incident cohort were used to develop a model that allowed for the imputation of the unknown times since seroconversion for the seroprevalent cohort. Nonparametric life table methods incorporating truncation and censoring were applied for the estimation of the probability distribution of the AIDS-free time after seroconversion. The precision of the estimates was evaluated using bootstrap methods. The analysis suggested that AIDS is unlikely (less than 0.5%) in the first year; 78% of seropositive homosexual men remain AIDS-free 60 months after seroconversion; and the AIDS incidence increases for months 12-36 and levels off at 38 per 1,000 person-semesters for months 42-60. The nonparametric estimate of the incidence rate suggests a median AIDS-free time of 11 years, which is longer than previous estimates based on parametric models.     

Projections of HIV infections and AIDS cases to the year 2000

After the recognition of AIDS (acquired immunodeficiency syndrome) in the early 1980s, uncertainty about the present and future dimensions of HIV (human immunodeficiency virus) infection led to the development of many models to estimate current and future numbers of HIV infections and AIDS cases. The Global Programme on AIDS (GPA) of the World Health Organization (WHO) has developed an AIDS projection model which relies on available HIV seroprevalence data and on the annual rate of progression from HIV infection to AIDS for use in areas where reporting of AIDS cases is incomplete, and where scant data are available to quantify biological and human behavioural variables. Virtually all models, including the WHO model, have projected large increases in the number of AIDS cases by the early 1990s. Such short-term projections are considered relatively reliable since most of the new AIDS cases will develop in persons already infected with HIV. Longer-term prediction (10 years or longer) is less reliable because HIV prevalence and future trends are determined by many variables, most of which are still not well understood. WHO has now applied the Delphi method to project HIV prevalence from the year 1988 to mid-2000. This method attempts to improve the quality of the judgements and estimates for relatively uncertain issues by the systematic use of knowledgeable "experts". The mean value of the Delphi projections for HIV prevalence in the year 2000 is between 3 and 4 times the 1988 base estimate of 5.1 million; these projections have been used to obtain annual estimates of adult AIDS cases up to the year 2000. Coordinated HIV/AIDS prevention and control programmes are considered by the Delphi participants to be potentially capable of preventing almost half of the new HIV infections that would otherwise occur between 1988 and the year 2000. However, more than half of the approximately 5 million AIDS cases which are projected for the next decade will occur despite the most rigorous and effective HIV/AIDS prevention efforts since these AIDS cases will develop in persons whose HIV infection was acquired prior to 1989. The Delphi projections of HIV infection and AIDS cases derived from the WHO projection model need to be periodically reviewed and modified as additional data become available. These projections should be viewed as the first of many attempts to develop estimates for planning strategies to combat the HIV/AIDS pandemic in the 1990s.     

Uncertainty in estimates of HIV prevalence derived by backcalculation.

The incidence of consistently defined acquired immunodeficiency syndrome (AIDS) among adults in the United States was used to "backcalculate" the prevalence of human immunodeficiency virus (HIV) as of January 1, 1985, and July 1, 1987. The sensitivity of estimates to random and systematic sources of uncertainty was assessed. Using a "standard" incubation distribution with a 10-year median time-to-AIDS, we estimated that 544,000 persons were infected as of January 1, 1985, and that 992,000 persons were infected as of July 1, 1987. Variation from model selection and fitting was only 2% and 5%, respectively. Perturbations of the AIDS incidence counts to reflect plausible reporting biases reduced prevalence estimates by as much as 9.6% and 16.0%, respectively. Uncertainty about the incubation distribution had an even greater impact. A "plausible range" of prevalence estimates was calculated using alternative "Fast" and "Slow" incubation distributions. The plausible range varied from 415,000 to 760,000 persons in 1985 and from 737,000 to 1.4 million persons in July 1987. Inclusion of AIDS incidence counts beyond mid-1987 can lead to serious underestimates of prevalence, because use of zidovudine and other therapies beginning in mid-1987 has lengthened the incubation distribution in many severely immunodepressed persons without AIDS.     

Using AIDS mortality data to reconstruct HIV/AIDS epidemics

The back-calculation methods used to reconstruct HIV epidemics and to predict future AIDS cases use data on the number of AIDS reported cases and information about the time from HIV infection to AIDS diagnosis. In this paper we modify a back-calculation method, presented in Verdecchia and Mariotto, to estimate HIV incidence from AIDS mortality data rather than the AIDS registered cases. In this application the AIDS incubation time is replaced by the time from HIV infection to AIDS death. Since AIDS is an irreversible condition leading to death within a few years, mortality data is expected to be approximately as informative as AIDS data. The main application of this method would be in countries where an AIDS registry is not available or where the registration of AIDS cases is not consistent, for example, due to changes in the definition of AIDS. Application to the Italian AIDS mortality data shows that the number of AIDS cases reconstructed from this method is very close to the registered number of cases. Also, the two estimates of HIV incidence and prevalence obtained from back-calculation on both AIDS mortality data and the number of AIDS reported cases were very similar, although there was more variability in the estimates obtained from mortality data.     

Projections of the HIV/AIDS epidemic for homosexual/bisexual men in France,the Federal Republic of Germany and the United Kingdom

Projections of the spread of the acquired immunodeficiency syndrome (AIDS) and of its etiologic agent, the human immunodeficiency virus (HIV), are presented for homosexual/bisexual men in the three European countries with the largest caseloads. The results suggest that the HIV epidemic for French, German, and British homosexual/bisexual men has peaked around 1985 and declined rapidly thereafter. By the end of the century, and for a median incubation period of AIDS equal to 8 years, the total numbers infected in these groups are predicted to be about 31,200, 10,400 and 9,800, respectively. (These estimates more than double if the median incubation period is 12 years). In all cases the annual incidence of AIDS will reach its maximum in the early to mid-1990s. However, the AIDS epidemic will be protracted because of the long incubation period.     

A method of non-parametric back-projection and its application to AIDS data

The method of back-projection has been used to estimate the unobserved past incidence of infection with the human immunodeficiency virus (HIV) and to obtain projections of future AIDS incidence. Here a new approach to back-projection, which avoids parametric assumptions about the form of the HIV infection intensity, is described. This approach gives the data greater opportunity to determine the shape of the estimated intensity function. The method is based on a modification of an EM algorithm for maximum likelihood estimation that incorporates smoothing of the estimated parameters. It is easy to implement on a computer because the computations are based on explicit formulae. The method is illustrated with applications to AIDS data from Australia, U.S.A. and Japanese haemophiliacs.     

Age and human immunodeficiency virus infection in persons with hemophilia in California.

Thirteen hemophilia centers provide comprehensive care to approximately 90 percent of persons with hemophilia in California. For 1987, these centers reported patient human immunodeficiency virus (HIV) antibody status, age group, level of clotting factor deficiency, and hemophilia type on 1,438 persons with hemophilia A and B; HIV serologic status was known for 860 persons (59.8 percent) of whom 537 (62.4 percent) were HIV-antibody-positive. The HIV positivity rate increased with age after taking into account hemophilia type, clotting factor level and treatment center type. The three-year cumulative incidence of reported AIDS (acquired immunodeficiency syndrome) cases based on the number of HIV positive patients, was 11.6 percent. The cumulative incidence rate was 14.6 percent (54 of 370) for those patients over 20 years of age and 4.8 percent (8 of 167) for those under 21 years of age. Although a comparable distribution of the date of diagnoses of AIDS was seen by age group, there appeared to be a bimodal distribution in the rate of AIDS among the age groups, with the 6-12-year-olds and the 21 and older age groups showing higher incidence rates.     

A Markov model for HIV disease progression including the effect of HIV diagnosis and treatment: Application to AIDS prediction in England and Wales

Back-calculation is a widely used method to estimate HIV incidence rates, and is commonly based on times of AIDS diagnosis. Following up earlier work, we extend this method to also incorporate knowledge of times of HIV diagnosis (first positive test). This is achieved through the use of a Markov model which describes the progress of an HIV infected person through various stages, and which allows causal connections between events to be explicitly modelled. Estimation is based on maximum likelihood, the likelihood being calculated within a discretized version of the Markov model. The effect of sampling uncertainty and model uncertainty (sensitivity) is evaluated simultaneously by means of a combined bootstrap and simulation procedure. At each replication we resample both the data and the model (from a set of possible models described by randomizing one or more parameters). For instance, uncertain knowledge about the incubation distribution affects the estimates of some parameters, but not others. The Markov approach is applied to the prediction of AIDS incidence for homosexuals in England and Wales up to the year 2000. © 1997 John Wiley & Sons, Ltd.     

Mean square error of estimates of HIV prevalence and short-term AIDS projections derived by backcalculation

We simulated multinomial AIDS incidence counts from 27 'representative' AIDS epidemics that spanned a period corresponding to previous applications of backcalculation (1 January 1977 to 1 July 1987) and assessed mean square error for several back-calculated estimators of HIV prevalence and short-term AIDS projections. Estimators were based on flexible model selection procedures that chose the best-fitting non-negatively constrained model of the infection curve from a family of possible step-function models. Selection of the best-fitting model from a family of four-step models each with a long last step of width of 4 or 4.5 years offered a favourable tradeoff between bias and variance when compared with selection from families of models with three steps or from families with a short last step. Five-step models performed as well as four-step models. Three-step models had substantially larger mean square error in some epidemic situations. Percentage root mean square error (PRMSE) for estimates of cumulative HIV prevalence as of 1 January 1985 was less than 14 per cent over a range of hypothetical epidemics of N = 50,000 infected individuals. PRMSE for short-term projections was less than 18 per cent. Estimates of cumulative HIV prevalence as of 1 July 1987 were substantially more uncertain and had a PRMSE of 33 per cent in the unfavourable case of a rapidly rising HIV epidemic. Estimates of cumulative HIV prevalence as of 1 July 1987 were positively biased in HIV epidemics with a rapidly decreasing recent HIV incidence rate and negatively biased in rapidly increasing HIV epidemics. Despite these uncertainties, we obtained useful estimates even for HIV epidemics with as few as 5000 infected individuals.     

The value of AIDS incidence data in assessing the spread of HIV infection

Changes over time in the cumulative number of cases of AIDS depend in a complex way on several features of the epidemic, including the distribution of the induction time between infection with the human immunodeficiency virus (HIV) and onset of symptoms of AIDS, heterogeneity in such behaviours as sexual practices, selection of partners, and IV drug use, and changes over time in these behaviours. Consequently, the observed increase in the doubling time in cumulative AIDS incidence from 5 to 13 months, since AIDS was first recognized in 1982, demonstrates neither that the epidemic has begun to 'run its course' nor that behavioural changes have had a major impact in reducing incidence. Even in a homogeneous population with known induction distribution, AIDS incidence data currently are of little value in determining the number of persons infected with HIV unless additional information is available about the shape of cumulative incidence curve of HIV infection.     

Knowledge about AIDS and HIV in the US adult population: influence of the local incidence of AIDS.

BACKGROUND. Accurate information about acquired immunodeficiency syndrome (AIDS) and human immunodeficiency virus (HIV) is important for prevention. This study determined whether AIDS knowledge varied among populations residing in areas with a low, medium, or high incidence of AIDS. METHODS. Respondents to the 1988 National Health Interview Survey of AIDS Knowledge and Attitudes, which is based on a nationally representative sample of 29,659 adults, were rated on their knowledge about modes of HIV transmission, general knowledge about AIDS, and misperceptions about HIV transmission through casual contact. RESULTS. Persons 50 years of age or older, Blacks, Hispanics, and persons with less than a high school education had lower knowledge scores and higher misperception scores. Residents of the high-incidence area had more misperceptions than those who lived in the medium- or low-incidence areas. Sociodemographic determinants of scores were important factors overall and within each AIDS incidence area. CONCLUSIONS. These data suggest that the ability of educational messages to reach and be absorbed by individuals nationwide is less dependent on whether they live in an area with a high incidence of AIDS and more dependent on other demographic variables. New and continued efforts are needed to improve knowledge in older persons, minorities, and the less educated in all parts of the country.     

HISTORICAL HIV INCIDENCE MODELLING IN REGIONAL SUBGROUPS: USE OF FLEXIBLE DISCRETE MODELS WITH PENALIZED SPLINES BASED ON PRIOR CURVES

This paper presents an approach to back-projection (back-calculation) of human immunodeficiency virus (HIV) person-year infection rates in regional subgroups based on combining a log-linear model for subgroup differences with a penalized spline model for trends. The penalized spline approach allows flexible trend estimation but requires far fewer parameters than fully non-parametric smoothers, thus saving parameters that can be used in estimating subgroup effects. Use of a reasonable prior curve to construct the penalty function minimizes the degree of smoothing needed beyond model specification. The approach is illustrated in application to acquired immunodeficiency syndrome (AIDS) surveillance data from Los Angeles County.