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Seminar on Measurement of Risk and Modelling the Spread of AIDS

Copenhagen, Denmark, 2-4 June 1998
organized by the IUSSP Committee on AIDS


The Seminar on Measurement of Risk and Modelling the Spread of AIDS took place in Copenhagen, Denmark, on 2-4 June 1998. It was organised by the IUSSP Committee on AIDS in collaboration with the university of Copenhagen. In the opening ceremony, participants were welcomed by Professor Joan Conrad, Deputy Head of the university and Professor Tage Bild, Dean of the Faculty of Social Sciences. The meeting was hosted by the Economics Department, and the committee's thanks go to Professor Hans Oluf-Hansen, the local organiser, for the smooth running of the whole event.

The AIDS Committee had invited papers on the measurement of risk as considerable uncertainties remain as to the likely range of values of several important input variables in most models of the spread and impact of the AIDS epidemic. However, relatively few empirical papers were offered at this conference - only four of the seventeen presentations were concerned with presenting new data. It is a continuing dilemma faced by modellers, that empiricists feel they have little to contribute to their deliberations. Not only do modellers need empirical inputs, but also the insights of empiricists into the usefulness of model predictions, and their critiques of the questions addressed and the outputs produced would make for a lively and productive dialogue.

The presentations concerned with modelling covered a wide variety of applications. Two distinct types of modelling approaches were used - traditional demographic 'macro' models of population processes, and micro-simulation models in which aspects of individual life histories are generated, allowing for random branching patterns. Micro-simulation had much to offer as a method for representing the most complex processes, such as sexual network dynamics, which rapidly lead to intractable mathematical problems when approached with conventional demographic modelling techniques.

Measurement of risk

The empirical presentations included a paper by Arni Rao and Subhash Hira studying disease progression and AIDS related adult mortality in Mumbai, India. The progression of the disease was studied in a cohort of 520 HIV positive hospital patients between April 1994 and June 1997. The authors estimated annual incidence rates from asymptomatic HIV to ARC, from asymptomatic HIV or ARC to AIDS, and from asymptomatic HIV, ARC or AIDS to death. They found a median survival after attaining AIDS of just under a year (11.5 months). Extrapolating annual incidence rates to a hypothetical cohort of HIV asymptomatic individuals, they also estimated a median time from asymptomatic HIV to death of 7 years. The latter can only be interpreted as a minimum estimate of duration from infection to death as the initial cohort consists of HIV positive individuals at different durations since infection.

Another data-based paper by Kathleen Ford and Anne Noris presented new information on union formation among urban minority youth in the uS. The authors used partner histories drawn from a household probability sample of African American and Hispanic adolescents and young adults aged 15-24 from low-income areas of Detroit. The results were presented for three types of partnerships: married or cohabiting, partners knowing each other well, and casual partners. The data for each type of partnership included the frequency and duration of unions, the frequency of different types of intercourse, the age mixing patterns, the frequency of condom use and rate of concurrency. Such data are indeed essential to many models of the spread of the HIV epidemic and the differences found between the African American and Hispanic samples suggest wide variations across populations.

The paper by Babajide Olayinka studied the prevalence of high-risk sexual practices among men in Southwest Nigeria. The author interviewed 85 men in a high-density residential area of Ibadan on the frequency of condom use, number and type of sexual partners and history of past sexually transmitted diseases (STD's). This study found an appreciable and consistent rate of condom use: 78% reported ever having used this method, and 28% were consistent users - a much higher level than is usually recorded in studies in sub-Saharan Africa. A majority (57%) of respondents had more than one current sexual partner leading the author to infer that condoms were mostly used with non-regular sexual partners.

The final empirical paper was by John Potterat, Richard Rothenberg and Stephen Muth, who studied the dynamics of disease propagation within sexual networks and discussed how changes in risk-network structure affect STD and HIV transmission. Data from two uS cohort studies (injecting drug users in Colorado and adolescent heterosexuals in Georgia) were used to map the evolution of two different network structures, one in which network cohesion decreases over time and one in which it increases over time. Enhanced connectivity was associated with efficient syphilis transmission whereas segmentation impeded transmission. In either network, there were few personal risk behaviour changes over time. The results thus emphasise the need to re-evaluate purely individual behavioural explanations of STD or HIV transmission and consider the social network structure through which the epidemic must flow.

Partnership formation patterns

Two of the papers on modelling attempted to assess the effect which partnership formation patterns have on the spread of HIV. In the opening paper of the conference, Martina Morris and Mirjam Kretzschmar used a micro-simulation approach to study the effect of concurrent partnerships on the epidemic dynamic. The authors used data from the ugandan Sexual Network Study in the Rakai District of uganda where 2% of women and 12% of men reported ongoing concurrent partnerships. The simulations suggested that even such a modest rate of concurrent partnership increased the number of infections by 26% over a time span of 5 years. These results were obtained by comparing HIV prevalence in two populations: the first with the concurrency rates observed in Rakai, the second with no concurrency but the same overall number of partnerships. The authors emphasised the need for collecting data on concurrency and gave examples of questions geared to their ‘local network’ approach.

Marc Artzrouni approached the problem using a macro-modelling approach, presenting a two-sex model of population dynamics with HIV. The model was designed to study in depth the impact of the age-distribution of sexual partners, which was represented by a mixing matrix. using the framework of discrete-time multi-state population projections, the author assumed that both age-specific fertility rates and infection rates depend on the number of sexual partners, with the infection rates also depending on the age of the partner and the proportion infected in each age-group. He then studied the conditions of a long-term equilibrium comparing the intrinsic growth rates of the uninfected and infected growth rate. To maintain the epidemic, the average number of partners has to be large enough for both the infected and non-infected populations to reproduce fast enough not to become extinct. The uninfected population is shown to grow faster than the infected population when for a given sexual mixing matrix the number of partners is lower than a certain upper bound. Simulations showed that the value of this maximum number of partners increases with more age-homogeneous sexual preferences.

Commercial sex workers

The importance of contacts with commercial sex workers for the spread of HIV was the focus of several papers. Masayuki Kakehashi presented a model of pair formation where the population in reproductive ages consisted of four states: juveniles, single adults, adult pairs or couples and commercial sex workers. The author showed that the epidemic would only be sustained if a certain relationship existed between the minimum sexual transmission rate and the minimum contact rate of males with commercial sex workers. Below a certain set of minimum values for these parameters the epidemic would die out, but above this minimum the model suggested that the prevalence rate would increase for forty to fifty years before stabilising at an endemic level between 6% and 13%.

A paper by Bertran Auvert emphasised the impact of prostitution on the spread of HIV in sub-Saharan Africa. The author used a micro-simulation approach to study the relative importance of different sexual behaviours by varying their parameters within a range in broad agreement with currently available data from sub-Saharan Africa. The SimulAIDS model used for this exercise generates a population in which it is possible to define demographic features, sexual behaviour characteristics and the dynamics of HIV inter-action with other STD's. A sensitivity analysis showed that the most important factor in the long term was the proportion of males having contacts with sex workers.

Preventative strategies

The importance of focussing on high-risk groups in the design of preventative interventions was highlighted in a paper by Eline Korenromp, Carina van Vliet and Dik Habbema. The authors studied the potential impact on the spread of the epidemic of different prevention strategies for different population profiles of sexual behaviour. The profiles were defined by the extent of commercial sex, short-term relationships and concurrency. The authors describe how the pattern of HIV spread (initial pace and equilibrium level) depends on these different profiles. Focusing prevention strategies on increasing condom use among commercial sex workers and other high risk groups, depending on the population profile of sexual behaviour (e.g. males having multiple concurrent partners) is systematically the most effective strategy, as measured by the number of HIV cases prevented.

A paper by Travis Porco and Sally Blower modelled the effects of hypothetical vaccines. The authors compare two vaccines with different modes of action. The first was assumed to provide complete protection against a specific HIV subtype for a fraction of the vaccinated population and complete protection against another HIV subtype for a subgroup of this fraction. The second vaccine altered either the infectivity or the incubation period of the vaccinated individual but to a different degree for different HIV sub-types. Simulations showed that HIV eradication is possible in either case if vaccine coverage is complete enough, but the two modes of action have quite different implications when the coverage is too incomplete to eradicate the epidemic. If a vaccine fails to provide a protective response to a second subtype of HIV for a fraction of those protected against the first subtype, both subtypes may coexist. The second mode of action however does not allow this coexistence, so that only the subtype least affected by the vaccine persists.

HIV and fertility

Three papers were presented about the interaction between HIV infection and fertility. This theme has attracted much attention recently because differential fertility by HIV status may affect the measurement of current HIV prevalence, which is the most basic parameter in models of HIV spread. The problem arises because prevalence is often estimated from data on antenatal clinic patients. Also, the tendency of HIV to lower fertility would multiply the demographic impact of the epidemic by affecting not just the survival rates but also the reproductive rates in the infected population.

Eduard Bos examined whether HIV prevalence levels collected at antenatal clinic test sites can be used to represent HIV prevalence in the general population. He discussed two compensating biases. The first bias is a selection effect: HIV prevalence levels tend to be highest at the same ages at which fertility rates are highest as well, thus leading to an oversampling at antenatal clinics of age groups with the highest HIV prevalence. The similarity in the age pattern of fertility and the age pattern of HIV prevalence is so striking that, when plotted, the curves would in many cases be hard to distinguish. On the other hand, HIV has a depressing effect on fertility, so that women who are HIV positive are less likely to be pregnant and be included in antenatal clinic samples. With the exception of the under 20 age groups, community studies have shown that women who are HIV positive have lower fertility at every age, in comparison with women who are HIV negative. using a numerical example, Bos showed that the two biases are compensatory, so that the unweighted prevalence rate calculated from antenatal clinic test sites in many cases will be close to the rate in the adult female population.

In their paper, Geoff Garnett and Simon Gregson studied the dynamics of these biases in HIV prevalence estimates. They used a two-sex multi-state model of transmission dynamics with four sexual activity classes and five infection states within each (uninfected, three stages of asymptomatic HIV and AIDS) to replicate some of the factors known to influence prevalence among pregnant women. Three differential fertility effects were assumed: lower fertility in women with highest partner change rates because of their increased risk of other STD's, the lower overall fertility of HIV infected women due to foetal loss, and increasingly low fertility at longer durations of infection due to increased morbidity. Their model predicted complex changes over time, in which the relationship between seroprevalence in pregnant women and the general female population in the reproductive age range altered because of the changing age structures of infected and healthy women. The relationship would also vary between populations, depending on the level of co-infection with other STD's. They conclude that there is no consistent way to adjust antenatal clinic data. The authors found that in most cases, the prevalence of HIV infection among antenatal clinic patients was a reasonable representation of the prevalence among women in reproductive ages, with the underestimate ranging between 5% and 15% over the 30 year time span of their projections.

The other paper on this theme, by Susan Hunter and Basia Zaba presented a single-sex multi-state stable population model to study the determinants of the fertility differential between HIV positive and HIV negative women. Their model incorporates a proximate determinants approach to determine infection rates and fertility patterns for the HIV positive and HIV negative populations. Biological and behavioural parameters are allowed to differ by HIV status within ranges selected to represent East African conditions, with the default model calibrated to reproduce observed age specific fertility differentials, incorporating both the behavioural selection effects and the systematic fecundity reduction discussed in the other papers. A sensitivity analysis showed that among the biological determinants, menstrual disorders potentially have a large effect on differentials in total fertility, but that the contribution of behavioural factors, such as differences in stability of sexual unions and propensity to enter new unions could be even more important. The model predicted that extensive condom use would lower fertility differentials, because it would enhance the selection effect observed mainly in the youngest age groups in non-contracepting populations.

HIV and population mobility

Hans O. Hansen presented a stochastic one-parent model in continuous time that incorporates heterogeneity duration dependence in the hazards, the probabilities of transition being established by stochastic microsimulation with time and subsequent life state as the random elements. The model allows for transition between regions and three stages of infection (HIV negative, HIV positive and full-blown AIDS). The presentation includes the renewal theory required for obtaining consistent estimates of the stable growth rate and the age structure of multistate populations with AIDS. The basic simulation results in terms of a relational database (two tables) allow of consistent prediction of a wide range of complex demographic processes at the level of individuals and one-parent families. In an example based on recent population data from uganda, HIV positive women were assumed to have fertility rates 20% lower than HIV negative women, while women with AIDS had 60% lower fertility. Age-specific mortality rates were assumed to be the same for HIV negative and HIV positive persons until they develop AIDS. In three scenarios differentiated solely by the level of age-specific risk of infection, model-based predictions illustrated the dire demographic changes induced by the epidemic.

Reliability of data and analytical procedures

One important paper on measurement issues was concerned not so much with the presentation of new empirical results, as with a critique of the reliability of conventional data collection approaches. Benoit Ferry addressed himself to the problem of imbalance in levels of sexual activity reported by men and women. The frequency of changes of sexual partner appears to be one of the key factors in HIV transmission, but most studies of sexual behaviour have shown a glaring discrepancy between levels of partner change reported by men and women, and it is generally believed that women underreport their sexual activity and number of partners. The author singled out commercial sex workers' activity as one of the key factors, since CSWs attract a significant part of reported male sexual activity but typically are not interviewed in general population surveys. Additional factors such as non-response bias, sexual activity with partners outside the study area or outside the selected age range, definitions of sexual partners and recall errors can also add to the unbalance and complicate the reconciliation of sexual activity levels reported by males and females.

Two of the modelling papers were also concerned with aspects of data reliability and robustness of estimation procedures. Martina Morris and John O'Gorman studied the impact of response error on survey based estimates of the extent of concurrent partnerships. The authors discussed methods for collecting data on concurrency and the analytical problems encountered in estimating concurrency from reported starting and ending dates of past partnerships. Their paper studied the impact of inaccuracy in reported dates, focusing on unit heaping (i.e., reporting in a whole number of weeks, months or years) and random recall error for events occurring further back in the past. They assessed the impact of these errors by simulating histories of partnership formation and dissolution for 1,000 individuals and modelling the reporting errors affecting the dates defining each partnership. These simulations showed that if the median duration for periods separating two partnerships is much shorter than the median duration for periods of concurrency, random errors in date reporting create more false concurrent partnerships than false separated partnerships. In this case, survey estimates of concurrency based on partnership dates will be systematically biased upwards.

Not only are some crucial parameters of the spread of AIDS difficult to measure, but the HIV epidemic also complicates the routine measurement of demographic rates. Patrick Ward and Basia Zaba showed how the HIV epidemic may bias indirect estimates of child mortality made using the children surviving / children ever born technique. Three of the basic assumptions underlying the inference of child mortality rates from maternal reports of child survival no longer hold in an HIV-affected population: the correlation of mortality between mothers and their children is no longer sufficiently small to be ignored; children born to mothers of different ages experience different levels of mortality; and existing model lifetables are inadequate to describe the emerging relationships between infant and child mortality. The paper described the use of stable population modelling to simulate the application of the technique in populations with HIV and assessed the extent of the biases. To the usual stable population dynamics, the model adds constant age-specific HIV incidence rates and duration-independent excess mortality of HIV-positive women with a mean survival of 8 years for adults and 1.5 years for infants, with fertility assumed independent of infection status. The simulation exercises showed that significant errors could be introduced even with adult prevalence as low as 3 percent. The extent of the bias depends on seroprevalence levels, which suggests that the estimates can be corrected or at least improved by taking adult prevalence levels into account. The authors present regression based methods for making such corrections.

Patrick Heuveline