Improved methods and assumptions for estimation of the HIV/AIDS epidemic and its impact: Recommendations of the UNAIDS Reference Group on Estimates, Modelling and Projections: The UNAIDS Reference Group on Estimates, Modelling and Projections

UNAIDS and WHO produce biannual country-specific estimates of HIV/AIDS and its impact. These estimates are based on methods and assumptions that reflect the best understanding of HIV epidemiology and demography at the time. Where significant advances are made in epidemiological and demographic research, the methods and assumptions must evolve to match these advances. UNAIDS established an Epidemiology Reference Group in 1999 to advise them and other organisations on HIV epidemiology and methods for making estimates and projections of HIV/AIDS. During the meeting of the reference group in 2001, four priority areas were identified where methods and assumptions should be reviewed and perhaps modified: a) models of the HIV epidemic, b) survival of adults with HIV-1 in low and middle income countries, c) survival of children with HIV-1 in low and middle income countries, and d) methods to estimate numbers of AIDS orphans. Research and literature reviews were carried out by Reference Group members and invited specialists, prior to meetings held during 2001-2. Recommendations reflecting the consensus of the meeting participants on the four priority areas were determined at each meeting. These recommendations were followed in UNAIDS and WHO development of country-specific estimates of HIV/AIDS and its impact for end of 2001.

Introduction

Country-specific estimates of HIV prevalence, AIDS mortality and AIDS orphan are a biannual product of the Joint WHO/UNAIDS Working Group on Global Surveillance of HIV/AIDS and STIs. Building on available HIV surveillance data, country-specific estimates have been produced and compiled for 1997 and 1999, in collaboration with countries. Estimates for the end of 2001 will be released prior to the XIV International Conference on HIV/AIDS in July 2002 in Barcelona.

In 1999 the Joint United Nations Programme of HIV/AIDS (UNAIDS) formally established the Epidemiology Reference Group. This Reference Group followed a series of consultations that were jointly sponsored by The United Nations Population Division, The World Health Organization, and UNAIDS. The Reference Group is composed of epidemiologists, demographers, and other researchers in areas related to HIV/AIDS and modelling. It has a secretariat at Imperial College, London, and serves to advise the UNAIDS/WHO Working Group on Global HIV/AIDS and STI Surveillance and other relevant organizations on methods and assumptions for making estimates and projections of HIV prevalence and its demographic impact.

The Reference Group has provided reviews of current knowledge, helped develop methods for estimates and projections, and has identified areas for future research that are relevant for improving estimates and projections of HIV/AIDS. In a meeting held in October 2000, the Reference Group identified four areas in which the assumptions and methods for making estimates could be improved.

1. Modelling the epidemic

2. Survival distributions of adults living with HIV-1 in low and middle income countries

3. Survival distributions of children living with HIV-1 in low and middle income countries

4. Methods to estimate numbers of AIDS orphans

During 2001, several working meetings were convened, where Reference Group members and other researchers were invited to review data and develop new methodologies to address these research priorities. This report presents the findings and recommendations of these working meetings, which underlie the end-2001 estimates and projections of HIV/AIDS.

Modelling the epidemic

Background

The country-specific estimates of HIV-1 prevalence and AIDS mortality produced by the UNAIDS and WHO are widely used for both planning and advocacy purposes [¹]. In interpreting the progress of the epidemic a suitably generic, yet appropriate model is required to represent the course of a country's HIV epidemic and to make short-term projections. To date, UNAIDS has used a simple curve fitting procedure, based on a gamma distribution of HIV incidence [²]. However, this method is not designed to make projections, and does not describe the mechanisms underlying the spread of infection.

Many models of HIV spread have been developed that incorporate complex patterns of risk behaviour and mixing [³]. These provide a useful tool for understanding the spread and control of HIV, but require a large number of biological and behavioural parameters. Such models are inappropriate for the country-specific estimates made by UNAIDS, where the relevant behavioural data are rarely available. A simpler model is therefore required, but one which captures the dynamics of HIV transmission, and which can be used for all countries.

Process

The questions and framework for this work were discussed at the Reference Group meeting in Autumn 2000. Subsequently, members of the Reference Group and independent researchers with experience in modelling HIV dynamics (listed in the Cited Here...), were invited to present approaches to estimating and projecting HIV prevalence appropriate for all countries of the world. Six modelling approaches were presented, and classified according to their key features: compartmental models or parametric curves, timescale, stratification by age and/or sex, description of HIV positive adult survival, inclusion of 'not at-risk' population, dynamic or fixed parameters, demographic specifications, data fitted and method of obtaining best fit, and production of prediction intervals. A discussion of the features necessary to maintain epidemiologic realism and interpretation, but which allowed the practical application of the approach to many countries with different epidemics, led to the current UNAIDS/WHO model. This model represents a hybrid of those models presented at the Reference Group meeting. Software implementing this model, termed the Epidemic Projection Package, is now available (www.tfgi.com; www.who.int; www.unaids.org).

Recommendations

In the majority of countries, the HIV epidemic has been monitored through sentinel populations of women attending antenatal clinics, and vulnerable populations such as patients with sexually transmitted infections, intravenous drug users, men who have sex with men or sex workers. Observed epidemics amongst these populations typically follow one of three possible patterns: peaked epidemic, stable endemic or slowly rising (Figure 1). These patterns can be captured by an intuitive epidemiological model with a very restricted number of parameters. In this model the initial rate of spread of HIV is determined by the reproductive potential, r, the peak prevalence primarily by the fraction of the population considered to be at-risk of infection f, and the final endemic prevalence by a parameter φ, which specifies the behavioural response of the population to the epidemic (see the Cited Here... for details). Including the start date of the epidemic, four parameters must be estimated from sentinel site prevalence data.

Figure 1

A positive value of the behavioural response parameter φ, indicates that the decline in size of the at-risk population due to AIDS mortality is balanced by an increase in recruitment to the at-risk population. This may, for example, reflect the influence of demand for risky sex maintaining the at-risk population. Alternatively, it may reflect the gradual exposure of at-risk populations previously isolated from the virus by geography or culture. A negative value of φ indicates that people become less likely to adopt risky behaviour in response to observed AIDS mortality or prevention programmes. Different values for φ allow the model to produces both sharply peaked epidemics (negative φ), and a constant endemic prevalence following the initial peak (positive φ). In the absence of behavioural change (φ = 0), the epidemic is still slightly peaked, due to the lag between infection and death from AIDS. Interventions to prevent the transmission of HIV may also be reflected by changes in the reproductive potential r, due to changes in condom use or improved STI treatment for example, and by changes in the fraction 'at-risk'f, if, for example, a vaccine were to become available.

Figure 1 illustrates the fit of the model to prevalence data from sentinel sites. The Ugandan HIV epidemic has peaked (Figure 1a), and the decline requires a negative φ, indicating that risky behaviour has declined. In contrast, in Benin (Figure 1e), and other West African countries (data not shown), there has been a trend over the last few years of increasing adult HIV-1 prevalence. When prevalence first begins to increase, the future trends in prevalence and expected peak prevalence cannot be estimated solely from prevalence data. Behavioural surveys may be useful in such situations to assess the potential of an HIV epidemic. As an epidemic progresses, it becomes possible to use prevalence data to estimate confidence limits about the size of the at-risk population and the behavioural response parameters, therefore evaluating the epidemic potential. These limits tend to become progressively narrower as more data becomes available, provided that the data paint a consistent picture of trends in prevalence (Figure 2).

Figure 2

The demography of the model is described by the rates of entry and exit of individuals. For the general adult population, the rate of entry is the rate of becoming 15 years old, which is defined by the birth rate and population size 15 years earlier, and the probability of survival to age 15. The rate of exit is determined by the crude adult death rate, and for populations with an upper age-limit, the rate of exceeding that age. For specific risk groups such as IDUs or sex workers, the demography is less well defined. Estimates and projections of HIV prevalence based on fitting prevalence data are relatively insensitive to the specification of demographic rates, but absolute numbers are more dependent on these rates. For risk groups where the demography is poorly specified, estimates of the numbers of AIDS deaths or HIV cases must therefore be interpreted with caution.

To generate a widely applicable model of the HIV epidemic much complexity has been ignored. The priority for improving estimates is to improve the coverage of sentinel sites, to understand the biases in sentinel data, and to include behavioural data in surveillance. As the quality of data improves, so too can the models that inform policy.

Survival distribution of adults living with HIV-1 in low and middle income countries

Background

The primary data available for making estimates of the extent of HIV/AIDS spread and its impact are HIV prevalence data. Although incident data are becoming available for some countries, estimates of the incidence of HIV, AIDS and mortality mainly have to be derived from data on prevalence over time and an assumption about survival from infection to death. As estimates of HIV incidence and associated mortality are important in tracking the course of the epidemic and its impact, improved assumptions about the survival time from infection until death are crucial.

In previous estimates of HIV/AIDS by UNAIDS/WHO [^1,2], two different survival functions have been used: a median survival time of nine years for countries with less well developed health care systems, and one of 11 years for countries with better systems. As a proxy indicator, countries with under-five mortality greater than 50 per 1,000 were assumed to have less well developed systems [³]. The purpose of the reference group meeting was to develop an improved set of assumptions on survival for developing countries based on the best available data.

Researchers involved in studies in various countries on factors related to survival with HIV/AIDS were invited for this meeting of the reference group. The group also included representatives from three major incident cohort studies that had investigated survival from infection to death in low and middle income countries (Thailand, Uganda, Haiti). The list of participants is provided in the Cited Here....

Process

A review paper was prepared in advance of the reference group meeting and sent to the attendees for comments and additions. In this paper, research on factors that possibly related to survival of those infected with HIV was summarized. The review paper covered three broad areas of research. First, it reviewed studies of non-treatment factors proposed to affect survival time for people living with HIV/AIDS. Second, it reviewed studies that focused on the treatment and prophylaxis of specific opportunistic infections (e.g., tuberculosis) as well as studies that investigated overall case management of people living with HIV/AIDS. Finally it reviewed cohort studies. While cohort studies from industrialized countries were reviewed, the primary focus was on studies from low and middle income countries. An annotated bibliography was sent to the meeting participants before the review paper was written to help ensure the completeness of the articles reviewed.

During the meeting, each of the non-treatment and treatment related factor were discussed, and by reviewing the evidence a decision was reached on whether or not the factor influenced survival. If the factor influenced survival, it was further discussed if and how this factor should be accounted for in the survival function that would be used in making estimates of HIV/AIDS and its impact. The factors, as well as the consensus view on their relationship to survival, are summarized in Table 1.

Table 1

In addition to the literature review, the findings of the three major incident cohort studies on adult survival in low and middle income countries were presented and discussed to identify explanations for differences in survival found in the three studies [^17-21]. Of particular interest were differences in age of infection and the level of health care services available to the members of the three cohorts.

Conclusions

In reviewing the non-treatment related factors that could affect survival from infection until death, the consensus view was that few factors had been conclusively shown to have a large impact on survival. The one exception was age at infection. The reference group judged that there was sufficient evidence that age of infection (for adults) had been shown to have a substantial impact on survival and that estimates of the scale of the HIV/AIDS pandemic and its impact could be improved by including the age of infection in the estimation process.

A major discussion focused on the possible effects of treatment and prophylaxis of opportunistic infections (OI) on survival. While it was noted that treatment and improved management of OI in the United States and other highly industrialized countries had increased survival, it was concluded that the level of case management available in most low and middle income countries would not be sufficient to appreciably affect survival. Also the main AIDS-defining condition and major cause of death was Pneumocystis carinii pneumonia (PCP), for which effective chemoprophylaxis was available. In low and middle income countries, PCP seems to be much rarer than in developed countries. This conclusion was supported by the findings on survival in the cohort studies, where case management and treatment were judged to be of a high quality compared to that available to most people living with HIV/AIDS in low and middle income countries.

Recommendations

It was recommended that for the purpose of the estimates of the scale of HIV/AIDS epidemics an overall median survival time of 9 years should be used, with a range of uncertainty of 8 to 11 years. The survival function should be Weibull distributed, based on findings from pre-HAART era cohort studies in industrialized countries. The resulting distribution is shown in Figure 3.

Figure 3

The reference group also recommended that age at acquiring HIV infection, which has a substantial impact on survival, be included in countries where there are sufficient data on age at infection. As a result, it was recommended that for countries in sub-Saharan Africa a different median survival function should be used for women and men. This is because in countries of this region, where the large majority of infections are spread heterosexually and the epidemics are more mature, there is a substantial difference in age of infection between women and men, with women becoming infected at an earlier age. Therefore it was recommended that for these countries a median survival time of 9.4 years for women and 8.6 years for men be used by UNAIDS/WHO in making estimates.

A further recommendation concerned the effects of provision of HAART on survival. As with overall management of opportunistic infections, the reference group concluded that quality of the health care system for management of treatment with antiretroviral therapy would have an effect on treatment success. At least in the early stages of provision of HAART therapy it was expected that treatment would not have as great of an impact on survival as it has in the highly industrialized countries. Therefore it was recommended that for the 2001 estimates it should be assumed that provision of HAART therapy would add roughly three years to median survival for those being treated. This would account both for treatment and adherence failures.

A final recommendation concerned how to treat background mortality when calculating AIDS-related mortality. The reference group recommended that the competing risk of mortality from other causes was accounted for in estimates of adult mortality directly attributable to AIDS by using the expected country-specific adult mortality rates for the 15-49 age group.

Survival distributions of children living with HIV-1 in low and middle income countries

Background

The methods previously used by UNAIDS for estimating the number of children living with HIV and dying of AIDS are described in detail elsewhere [¹]. To estimate the number of children infected with HIV, fertility rates were applied to the estimated number of HIV positive women, with the fraction of HIV infected infants determined by the probability of mother-to-child transmission. Three alternative survival curves were used to portray the mortality of HIV infected children, based on available studies. Under fast progression assumptions 84% developed AIDS within 5yrs of birth, 65% at medium progression rates and 46% at the slow rates. Accounting for country-specific background non-AIDS mortality, the number of child deaths attributable to AIDS was calculated.

The probability of mother-to-child HIV transmission has decreased in industrialized countries due to antiretroviral therapy (ART) and other preventive measures. In contrast, in low and middle income countries the probability of mother-to-child transmission remains high due to the absence of ART and almost universal breastfeeding. The high prevalence of HIV among pregnant women from many of these countries, together with high fertility rates, has led to continued escalation in the number of HIV infected children. As the number of perinatally infected children increases in countries with generalised heterosexual epidemics, it is essential to have accurate estimates of child mortality due to AIDS.

Process

A systematic literature review of studies published before June 2001 that included child survival and vertical transmission of HIV infection, was carried out by Brahmbhatt and colleagues at the Johns Hopkins School of Public Health, prior to the Reference Group meeting. Ambiguities in the diagnosis of HIV infection in infants, and insufficient follow-up time precluded the use of some of these studies. A total of 41 studies were identified that had collected information on mortality of infants born to HIV-positive mothers. The majority (25 studies) were from sub-Saharan Africa, five were from Europe, five from USA, three from Asia, two from the Caribbean and one study from Latin America. Most studies were conducted in urban areas, and were hospital based. Of these studies, six contained sufficient information on child HIV status and survival in the absence of ART to allow estimates of the impact of HIV on child survival (Table 2).

Table 2

At a meeting in July 2001, all studies were reviewed by members of the Reference Group and invited researchers (see Cited Here...), in order to assess study quality and determine a consensus on empirical estimates of child survival with HIV-1 in low and middle income countries. In addition, methods to derive the fraction of HIV positive child mortality directly attributable to HIV/AIDS were described, and the impact of a mother's HIV status on child mortality irrespective of child HIV status considered.

Recommendations

Children born to HIV positive mothers may die from causes unrelated to HIV or die from AIDS having been infected by vertical transmission of the virus. Because the former may be elevated by maternal death, a child with an HIV positive mother may have a higher risk of mortality irrespective of their own HIV status. To estimate the impact of HIV-1 on child mortality in different countries where background infant and child mortality may differ substantially, it is necessary to account for these competing risks of mortality. The Reference Group recommended that country-specific estimates of background mortality would be combined with a single best estimate of the impact of maternal HIV status and child HIV status on child survival, to provide an estimate of survival of HIV-positive children. To estimate the number of additional child deaths attributable to the HIV epidemic, the expected number of deaths ignoring the impact of HIV-related causes is subtracted from the expected number including HIV-related causes, in an analogous way to estimates of adult deaths attributable to AIDS.

After reviewing the outcomes of the selected studies, the group concluded that only one study, in Rakai, Uganda (Basia Zaba, unpublished work), provided concrete evidence about mortality differences between uninfected children of HIV positive and HIV negative mothers. This study suggests that mortality among uninfected children of HIV positive mothers is about 20% higher than that among children of uninfected mothers. Subsequent work suggests that the bulk of this extra mortality occurs if the mother dies from AIDS, in both the year of terminal illness preceding death and in the subsequent year [⁷]. Concerns about the generalisability of these results, and the small impact of changes in underlying non-AIDS mortality on numbers of deaths attributable to AIDS, led to the recommendation that for the end-2001 estimates the mortality rates of HIV negative children of HIV positive women in a given population could be represented by the mortality rates of children of uninfected women in that population.

Three studies from sub-Saharan Africa, indicated that approximately half of the HIV-infected children had died by about 24 months (Table 2). None of the studies provided enough detailed information about the timing of childhood infection (during pregnancy, delivery or breastfeeding), with a large enough sample size, to warrant the construction of separate survival schedules for children infected at different times. Another major limitation of many studies was a lack of long-term follow-up, with most studies ending their observations at around 24 to 36 months. Only one study following children up to 60 months, but with huge losses to follow-up [³]. In the absence of information on long term survival of children infected with HIV by vertical transmission, it is assumed that by age 15 all HIV-positive children will have died.

The group recommended that the shape of the survival curve for HIV infected children up to fifteen years old should be specified by a double Weibull distribution, subject to confirmation that predictions of mortality of children born to HIV positive mothers concur with any new cohort data generated as studies are extended to older ages. This formulation, described in the Cited Here..., allows for two periods of very high mortality: in infancy when HIV frequently overwhelms the immature immune system, and after age 9, when it is thought that the few remaining survivors will succumb to opportunistic infections and progress to AIDS in the same way as adults. This survival curve was fitted to the cohort data on HIV-positive child mortality from Table 2, where the competing risk of background mortality had been removed using data on survival of HIV negative children with HIV-positive mothers in these cohorts where available, or country-specific life tables if unavailable (Figure 4). This curve predicts ∼40% survival from HIV-related mortality at five years of age.

Figure 4

Methods to estimate numbers of AIDS orphans

Background

Estimates and projections of the numbers of children whose parents have died from AIDS or other causes are needed to inform policy-makers to take programmatic decisions. In the past, different organisations have produced differing estimates of AIDS orphans, for various countries or regions of the world [^1-3]. After accounting for differences in definitions (e.g. with respect to the orphans' ages, or whether the statistics are on the currently living or cumulative), and the geographical coverage of the statistics, the remaining discrepancies in these estimates are accounted for by differences in demographic and epidemiologic assumptions. For example, 56% of the difference between UN and US Census Bureau estimates of maternal orphans is due to different estimates of HIV prevalence, 14% due to different assumed survival times with AIDS, and 7% due to different assumptions about perinatal transmission probabilities [¹]. Differences also exist between projections of orphan numbers based on modelling the HIV epidemic, and the estimates from Demographic and Health Surveys (DHS; Macro International) and Multiple Indicator Cluster Surveys (MICS; UNICEF). These discrepancies are, in some cases, substantial. They probably result from inaccurate demographic and epidemiologic assumptions, but may also reflect problems with the survey data.

Most estimates of orphans have focused on 'maternal or dual (double) orphans' - those children whose mother has died irrespective of the survival status of the father. These estimates can be derived from information or assumptions about the mothers' mortality and fertility, child survival with and without HIV, and the probability of perinatal HIV transmission [⁴]. Estimating paternal orphans is made more difficult by a lack of data on male fertility, and the difficulty of allowing for differential child survival by the mother's HIV status (due to perinatal transmission of HIV), when it may differ from that of the father. Recognising that 'there is no generally accepted methodology for estimating paternal orphans…', Hunter and Williamson [¹] produced estimates of paternal orphans from all-causes for initially 23 countries and subsequently 34, by applying an empirically derived ratio for maternal+dual to paternal orphans of 40:60 in 1990 and 1995. This ratio was then assumed to shift by 5% every five years in favour of maternal and dual orphans (e.g. 45:55 in 2000), based on observed changes in this ratio for cohort studies in countries with severe HIV epidemics (Uganda and Tanzania). This assumption was favoured since it also gave a smooth change in the estimated number of orphans.

The ratio of maternal + dual to paternal orphan numbers changes during the course of an HIV epidemic and, as we show, depends on marriage patterns. Applying a single ratio for a given year to countries with different HIV epidemics at different stages leads to inaccuracies. In the worst cases it produces discrepancies between projections of men's mortality and paternal orphan estimates.

The discrepancy between demographic projections of orphan numbers and survey-based estimates, and the acknowledged short-comings of current methods prompted the UNAIDS reference group on estimates and projections to address these issues with the support and participation of interested agencies.

Process

Reference group members and invited researchers (see Cited Here...) met in July 2001 with the following aims: to ensure that the meaning of 'AIDS orphan' is clearly defined for all organisations [represented: UNAIDS, US Census Bureau, UNICEF], to reach consensus on methods to produce estimates of the numbers of AIDS orphans, to clarify the implications for estimates of all-cause orphans and to ensure information from model-based and analytical approaches is integrated with information from DHS and MICS. Following this meeting, work by Grassly and Timaeus [⁵], and a subsequent meeting in January 2002, led to a new approach to estimating maternal, paternal and dual AIDS and non-AIDS orphan numbers. This method was subsequently used by the US Census Bureau to produce orphan estimates for the countries of Africa, Latin America and Asia [⁶]. These estimates have been adopted by UNAIDS, UNICEF and USAID.

Recommendations

A consensus was reached on the definition of an AIDS orphan as 'a child who has at least one parent dead from AIDS', and a dual (or double) AIDS orphan as 'a child whose mother and father have both died, at least one due to AIDS.'

Maternal Orphans

A detailed paper on the recommended methods for estimating and projecting numbers of maternal, paternal and dual orphan numbers by cause has been submitted for publication [⁵]. Maternal orphans are estimated using a similar method to that previously described [⁴], by estimating the number of children born to women who have died over the preceding 14 years, and calculating the fraction of those children who are still alive and under 15 years old. When estimating maternal AIDS orphans from data on female AIDS mortality, this method needs to take account of the impact of HIV and AIDS on fertility, the probability of perinatal transmission of HIV and the impact of HIV on child survival (see preceding section). In countries with significant injecting drug use epidemics, it may also be important to account for the impact of injecting drug use on fertility, although little is known about this fertility impact. The expected time with HIV and AIDS before a woman's death, and hence the time during which fertility is reduced, is based on the adult progression rates described in this paper. The method also allows for the impact of the deaths of mothers on child survival, which has been found to have a detrimental effect in the year before as well as the year after the death, independent of the mother's HIV status [⁷]. Because the survival status of the father is unknown, this method estimates the number of children whose mother has died from AIDS, and whose father is either alive, dead from AIDS or dead from other causes.

The number of maternal orphans resulting from causes of death other than AIDS is estimated in a similar way. A complication arises in the presence of an HIV epidemic since the prevalence of HIV among women dying from causes other than AIDS is difficult to estimate. The prevalence of HIV among these women is important since it has an impact on their children's survival due to perinatal transmission. However, infection is likely to be less common than among pregnant women attending antenatal clinics (ANC) - the usual indicator of adult HIV prevalence. Older mothers who die from causes other than AIDS are unlikely to be infected with HIV since HIV prevalence falls rapidly with age. Because most non-AIDS deaths occur at older ages, we assume zero HIV prevalence among women who die from causes other than AIDS. The impact of this assumption is minimal, and at worse may overestimate maternal non-AIDS orphans by ∼5% [⁵].

Paternal Orphans

Numbers of paternal AIDS orphans can be estimated in a similar way to maternal AIDS orphans if we can specify the concordance of the HIV status of the mother and father, and have data on men's mortality and fertility. If an assumption is made about the age profile of male fertility, total births to men each year can be calculated from the population projection that underlies the estimates of maternal orphans (since every child must have a mother and a father). For countries with significant HIV epidemics among men who have sex with men, it is necessary to account for their lower fertility, currently assumed to be 10% of that of their heterosexual counterparts. Concordance of HIV status of parents must be derived from available empirical studies. Using estimates of HIV prevalence among the female partners of HIV positive men from 23 studies, Grassly and Timæus [⁵] derive the concordance of parents from a logistic regression on HIV prevalence in the adult population, as measured at ANC. Adult HIV prevalence determines the probability of pre-existing HIV in the partner of an HIV positive individual, but is also correlated with the probability of transmission of HIV between partners. This is because high HIV prevalence is correlated with risk factors for HIV transmission such as high STI prevalence or low condom use, and produces a non-linear relationship between adult HIV prevalence and concordance. Modelling the HIV status of the partners of men who die from AIDS in this way makes it possible to estimate the impact of HIV on men's fertility and on the mortality of their children through perinatal transmission.

Paternal non-AIDS orphans can be estimated in a similar way to maternal non-AIDS orphans. It is assumed that the prevalence of HIV among the partners of men dying from causes other than AIDS reflects that seen among pregnant women attending ANC. While men who die from causes other than AIDS may have a different prevalence of HIV from other men, the impact of this on estimates of non-AIDS orphans is likely to be trivial.

Dual Orphans

To estimate the number of dual AIDS orphans as defined above, we estimate the total number of children whose parents have both died and subtract those children where neither of these deaths were due to AIDS (Figure 5). If the probabilities of a mother's death and father's death were independent, then the number of dual orphans could simply be obtained as a product of the number of maternal and paternal orphans divided by the total number of children in the population of interest. In fact, these probabilities are not independent, as parents tend to be of a similar socio-economic status, exposed to the same environmental risks and may die together in an accident or violence. Disease transmission is also important, particularly the transmission of HIV. To estimate the excess risk of dual orphanhood over that expected if parental deaths were independent, a multi-level Poisson regression model was fitted to data on paternal, maternal and dual orphan numbers from 31 DHS surveys conducted in sub-Saharan Africa. Significant predictors of this excess risk are the children's age, HIV prevalence 5 years before the survey, and two indicators of the population's marriage patterns: the proportion of 15-19 year old women who are single and the proportion of married women in monogamous unions. This regression predicts dual orphan numbers to within 5% in the set of populations to which it is fitted.

Figure 5

Estimating dual orphan numbers using an elaboration of the model-based projections would require information about age differences in partnerships and how this affects HIV concordance. This is unavailable. Attempting to develop Hunter and Williamson's [¹] approach further by estimating paternal orphan numbers from maternal orphan numbers using a multi-level Poisson regression failed to predict paternal orphans to within ±20% more than a quarter of the time. The hybrid approach of using model-based projections of maternal and paternal orphans, and a regression model to predict dual orphans, is therefore appropriate.

Validation

Comparison of the total orphan numbers obtained using these methods with DHS data suggests that the new approach, together with the updated estimates presented in this paper of adult and child survival, gives estimates that are fairly consistent with empirical data (Figure 6). Projected maternal and dual orphan numbers, however, are consistently 40-110% higher than is found by the DHS. This may be because current projections overestimate women's mortality from AIDS and other causes. Equally, DHS surveys may under enumerate maternal orphans. Independent estimates for Zimbabwe and South Africa suggest that the female mortality data used in the projections are too high and rise too steeply. This would suggest that it is the existing projections that are too high. The latter explanation is also possible, particularly if it is maternal orphans who are most likely to become street children, enter child-headed households or institutions for orphans. In addition, the female caretakers of orphans may tend to be reported as their mothers in the DHS household survey, leading to under-reporting of maternal orphans. However, cross-checks with women's own reports in the birth history section of the individual survey reveal few discrepancies (Ann Blanc and Trevor Croft pers. comm.).

Figure 6

Inevitably the estimates of orphan numbers produced by the methods described here and in more detail elsewhere [⁵] are only as good as the demographic and epidemiologic data that they are based on. As these data improve, so too will the estimates of orphan numbers.

Overall conclusions

The recommendations that are contained in the four sections of this paper have all been implemented in the end of 2001 UNAIDS/WHO country-specific estimates of HIV/AIDS and its impact. New software (the Epidemic Projection Package, [EPP]) that was developed for epidemic modelling and short-term projections is currently available for download on various websites In addition, the demographic projection package Spectrum, has been updated to allow the conversion of EPP projections into age-structured projections that determine the demographic impact of HIV/AIDS. This package includes the recommended assumptions about survival time for adults and children (available at www.TFGI.com).

The Epidemiology Reference Group will continue to play a vital role in advising UNAIDS, WHO, and its partners on how to refine the assumptions and methodologies used to make estimates of HIV/AIDS and its impact. The improved methods for making estimates will strengthen the ability to track and predict the course of HIV/AIDS epidemic in countries and help monitor the impact of interventions.