The course of an HIV/AIDS epidemic in a given population is determined by a number of key parameters. Among these, the probability that the virus will be transmitted to an uninfected individual during the course of a single unprotected sexual contact with an HIV-infected individual remains one of the less well known. The continuing uncertainty concerning this important parameter derives from a number of reasons. Since infection can rarely be associated with a particular act of sexual intercourse, other than in cases involving single acts with an infected individual (1,2), direct estimation of the probability of transmission per contact is very difficult. In a few cases, individuals are known to have become infected during the course of a known number of contacts with one or more infected partners. However, this situation is very uncommon, as the exact date of infection of the partner is rarely known, while information concerning the number of sexual contacts in a given period may also be quite imprecise. A further source of uncertainty arises from the variability in the risk of transmission according to both intrinsic and time-varying characteristics of the couple.
Although somewhat counterintuitive, several studies have found no association between the number of contacts with a given partner and transmission of the virus (3-7). As a result, estimates of the probability of transmission per partnership, rather than per contact, have often been preferred in mathematical models of the epidemic (8,9). However, an analysis of data from the California Partners' Study (10) indicated the presence of an association, although not one consistent with a constant probability of transmission per contact. Similar data from a large European study (11,12) have been analyzed in an attempt to further elucidate the relationship between the number of unprotected sexual contacts and the probability of heterosexual transmission.
Between March 1987 and March 1991, a total of 563 heterosexual couples were enrolled in a European multi-center study involving 13 centers in nine different countries. Each couple consisted of an HIV-infected index case and a regular heterosexual partner, whose only known risk factor for HIV infection was sexual intercourse with the index case. Index cases were of either sex (72% men, 28% women) and of varying clinical status (24% with clinical symptoms or T4 count <200 × 106/L), and had been infected through various modes of transmission, a majority (65%) being past or present users of intravenous drugs. Serological testing and data collection through individual interviews were carried out at study entry and, for partners initially HIV seronegative, at 6-month follow-up intervals. Full details and principal results of the study have been published elsewhere (4,11,12).
Data collection included date of the start of the sexual relationship, date of termination of the relationship (where applicable), and date of any change in sexual behavior. Frequency of sexual contacts (no./week) and extent of condom use—never, sometimes (≈25% of the sexual contacts), about half of the time, most of the time (≈75% of contacts), or always—during these contacts were requested for the periods both before and after any reported change in behavior. Other information collected (when available) included date of infection (rarely known), date of latest HIV negative test, and date of first positive HIV test result.
Estimation of the Number of Unprotected Sexual Contacts
For each couple, the total number of unprotected sexual contacts that could involve transmission of the virus was estimated as Equation where f is the reported weekly frequency of sexual contacts, c is the reported proportion of these contacts for which a condom was used, and d is the length (in weeks) of the period of the relationship during which infective contacts could have occurred (i.e., when the index case was potentially infected). Any reported modification in the frequency of unprotected contacts was taken into account. Unless definite counter evidence was available, it was assumed that the index case was not infected earlier than January 1, 1982. Alternative estimates were obtained by varying this earliest possible infection date.
Nonparametric and parametric analyses were carried out to investigate male-to-female and female-to-male transmission. Data at study entry and follow-up data for initially discordant couples were analyzed separately.
Following an approach previously described by other authors (7,13), the dependence of the partner's HIV status upon the number of unprotected sexual contacts was investigated by isotonic regression using the pool adjacent violators algorithm. The couples were first ordered according to the number of unprotected contacts. The pool adjacent violators algorithm (14) was then used to group the couples in such a way that the proportion of partners infected in each group did not decrease as the mean number of contacts increased (isotonic regression). Nonparametric estimates were thus obtained of p(k), the proportion of partners infected after k contacts, subject to the constraint that p(k) is a nondecreasing function of k.
Parametric estimates were obtained by assuming a constant probability of transmission per contact, μ, both within and between couples. According to this (Bernoulli) model, the probability that a partner remains uninfected after N unprotected sexual contacts with an index case is given by (1 - μ)N and the probability that the partner is infected by 1 - (1 - μ)N. Estimates of μ were obtained by maximum likelihood estimation (LE) using the BMDP program LE (BMDP Statistical Software Inc., Los Angles, CA, U.S.A.), 1990 version. Confidence intervals were estimated (within the BMDP program) by means of the likelihood ratio statistic. Significance of difference between estimates of male-to-female and female-to-male transmission probabilities was assessed by the likelihood ratio test.
To investigate the possible effects of violation of the constant infectivity hypothesis, a simple alternative model, in which it was assumed that only a fraction q of the index cases were infectious, with infectivity μ, while the remainder were noninfectious, was also investigated. Under this model, the probability that a partner is infected after n contacts with the same partner is q[1 - (1 - μ)N].
Information was incomplete for 14 couples, and 24 couples reported only protected sexual contacts since January 1982 and were, therefore, excluded from the analysis. The remaining 525 couples comprised 377 with a male index case and 148 with a female index case. Overall, the estimated number of unprotected sexual contacts since January 1, 1982 ranged from 1 to 2,515 (mean 381) over periods of 1-101 months (mean: 38.0 months). At study entry, 17.1% (90/525) of the partners were HIV-positive. On average, female partners of male index cases had had more contacts (mean: 397 versus 342) over a longer period (mean: 41.2 versus 29.7 months) and were more often infected [19.6% (74/377) versus 10.8% (16/148)] than were male partners of female index cases. A more detailed breakdown of the data, grouped according to numbers of contacts, is presented in Table 1. Among the 435 initially discordant couples, 121, who did not systematically use condoms for each sexual contact, were followed for a mean of 23.7 months (range: 1-75 months). During the follow-up period, the estimated number of unprotected sexual contacts per couple ranged from three to 430 (mean: 84); 12 (9.9%) of the partners seroconverted: 8/73 (11.0%) female partners and 4/48 (8.3%) male partners.
Nonparametric (isotonic regression) analysis grouped the data at study entry into four exposure groups for both male-to-female and female-to-male transmission (Table 2). The percentage of female partners infected ranged from 10% among those with <10 unprotected contacts to 23% among those with ≈2,000 (1,447-2,515) unprotected contacts. The percentage of male partners infected ranged from 0% following <11 unprotected contacts to 36% after ≈1,500 (910-1,991) unprotected contacts. Female partners were more often infected than were male partners, except in the highest exposure group (which contained, however, very few couples). Analysis of follow-up data, generally involving smaller numbers of contacts, resulted in proportions of infected partners not very different from those obtained from the study entry data for similar number of contacts (Table 2). Results obtained by assuming the earliest date for potentially infective contacts to be the beginning of either 1981 or 1983 (instead of 1982) were very similar both in terms of the number and positioning of groups, and of the proportions of partners infected in each group.
Using the Bernoulli model, estimates of percontact transmission probabilities, based on data at study entry, were 0.0005 [95% confidence interval (CI): 0.0003-0.0007] for male-to-female transmission and 0.0003 (95% CI: 0.0002-0.0005) for female-to-male transmission. The difference was not significant at the 5% level (0.05 < p < 0.1; likelihood ratio test). Higher estimates were obtained when using follow-up data. While the probability of transmission was again estimated to be higher for male-to-female than for female-to-male transmission (0.0015 versus 0.0009), the difference remained nonsignificant (p > 0.3). Overall estimates, independent of the sex of the index case, were 0.0005 (0.0003-0.0006) from data at study entry and 0.0012 (0.0007-0.0021) from follow-up data. When the earliest possible infection date was taken to be January 1, 1983 rather than January 1, 1982, the estimate based upon data at study entry was also 0.0005.
The cumulative probability of infection corresponding to the constant per-contact transmission probability estimated using the Bernoulli model is plotted in Fig. 1 (data at study entry) and Fig. 2 (follow-up data), together with nonparametric estimates. Nonparametric and parametric estimates are strikingly different, particularly in the case of male-to-female transmission. In comparison with nonparametric estimates, the Bernoulli model appears to seriously underestimate the risk of transmission after very few contacts and to seriously overestimate the risk associated with a large number of contacts. This tendency was observed with both study entry and follow-up data.
Fitting the simple alternative model to the data at study entry (independently of the sex of the index case), it was estimated that only 17% of the index cases were infectious (q = 0.17), but that infectious individuals transmitted infection at the first contact with an uninfected partner (μ = 1.0). This alternative model fit the data significantly better than did the constant infectivity model [log(likelihood = -240.526 versus -300.046].
Our results appear to lend support to the conclusions of Padian et al. (10) that, while the number of unprotected sexual contacts with an HIV-infected person may indeed be associated with probability of infection, any such association is not well described by a model that assumes a constant per-contact infectivity. Indeed, the Bernoulli model shows a marked lack of fit to nonparametric estimates, even though the latter were deliberately obtained (by the algorithm used) in such a way that partners having had more contacts were more likely to be infected. Similar findings have been reported by other authors attempting to estimate the probability of transmission per contact, in relation to both male homosexual (7,15) and male-to-female heterosexual (7,13,16) transmission.
As has been pointed out elsewhere (3,17), interpretation of partner study data is hampered by a number of factors that could introduce bias into estimates of transmission probabilities. Of particular concern are the uncertainties concerning the dates of infection of the index cases and the problems associated with retrospective collection of sexual behavior data (frequency of contacts and condom use), all of which can lead to serious errors in the estimation of the number, N, of unprotected sexual contacts between the infected index case and his/her partner. In the present study, the lack of a known date of infection for a large majority of index cases means that exposure times (based upon the earliest possible time of infection) tended to be systematically overestimated. Measurement errors in the retrospectively reported number of sexual acts and extent of condom use are, on the other hand, more likely to be of a random nature. Jewell and Shiboski (13) have shown that systematic overestimation of n, while clearly leading to underestimation of infectivity, would not affect the fit of the model. Random measurement errors, however, would be expected to result in both overestimation of infectivity and a poorer fit of the model. While the latter effect would be qualitatively similar to that due to variability in infectivity (see below), Jewell and Shiboski concluded that measurement error was unlikely to account for more than a small part of the deviation obtained when fitting the data of the California Partners' Study (13). The European Study attempted to minimize measurement errors by obtaining data on sexual behavior separately from each of the two partners and excluding couples with discordant responses. Thus, although measurement error may be partly responsible, it seems highly unlikely that it would be sufficient to account for more than a small part of the lack of fit of the constant infectivity model in the present study.
Considerable variability in infectivity is believed to exist both between and within couples, over time. Apart from nonsystematic condom use, other well-identified risk factors for heterosexual transmission include anal sex (male-to-female transmission) and advanced disease stage of the infected partner, while sex during menses (female-to-male transmission), bleeding during sexual intercourse, age of the female partner (male-to-female transmission), and existence of genital infections in either partner have, in some studies (3-6,11,12,18-21), also been found to be independently associated with an increased risk of transmission. In a previous analysis of the European study data (11), the prevalence of HIV antibodies in partners ranged from 3% for female partners presenting none of the identified risk factors for HIV transmission to >50% for male and female partners presenting two or more risk factors. Variability of infectivity within a given couple over time is suggested both by epidemiological studies (increased risk when the partner has biological or clinical signs of advanced HIV infection) and virological studies, the latter of which have shown viremia levels to be much higher in the first few months of infection and later stages of HIV disease than in the intervening asymptomatic period (22-24). The present findings accord well with a variable infectivity hypothesis, in which the probability of being infected after relatively few contacts would be higher and the probability of being infected after many contacts lower, than that predicted by the constant infectivity model.
The fit of the Bernoulli model appears to be less unreasonable in the case of female-to-male than in the case of male-to-female transmission. However, the previously published multivariate analysis (11) of the data used here revealed a positive association between the number of unprotected contacts and disease stage in the index case for couples with a female index case. The presence of such an association, which was not found for couples in whom the index case was male, may well account for the present findings, particularly since the odds ratio for transmission from partners with late-stage disease compared with those who are asymptomatic was greater for female-to-male than for male-to-female transmission.
It has been pointed out elsewhere (25) that one of the consequences of interindividual variability in levels of infectivity is that results from studies based upon multiple sexual contacts with a given infected partner cannot easily be compared with those from studies involving contacts with many different partners. In the latter case, transmission can, indeed, be assumed to occur with a constant mean probability at each contact with a different partner of unknown infectivity. However, individual contacts with the same infected partner are not independent since, following initial contact with the selected partner, all subsequent contacts carry the probability of infection specific to that partner. Given the existence of interindividual variability, applying the Bernoulli model to data from regular partnerships could, therefore, be expected to underestimate the true mean probability of infection through a single unprotected sexual contact with a randomly selected HIV-infected person. The alternative model considered here, in which some individuals are totally noninfecting, is clearly highly oversimplified. For example, the follow-up study has shown that transmission can occur following many noninfecting contacts (12). Nevertheless, the fact that this model fit the data significantly better than did the constant infectivity model, suggests that it is probably much nearer the truth. On the basis of the estimates obtained, the probability of infection following a single unprotected contact with a randomly selected partner would be qμ = 0.17, >300 times greater than that estimated under the constant infectivity model.
Modeling the risk of transmission between female prostitutes and their clients, Mastro et al. (2), in Thailand, and Cameron et al. (1), in Kenya, estimated the per-contact probability of infection to be >0.01, an order of magnitude higher than obtained under the constant infectivity hypothesis both in the present analysis and in other analyses of European and North American partner study data (16,26). Probable reasons suggested by the authors for this large difference include a high prevalence of other sexually-transmitted diseases (1,2) and, among prostitutes in Thaïland (2), a history of recent infection with HIV, most infections being thought to have occurred within the previous 2 years. An alternative (and/or additional) explanation could be that, unless interindividual variability is adequately taken into account, estimates obtained from partner studies simply do not correspond to true estimates of the probability of infection in the course of a single unprotected contact with a randomly selected partner. Indeed, the evident lack of fit of the constant infectivity model and the potentially large effects of variable infectivity cast serious doubts on the validity of estimates obtained by fitting constant infectivity models to partner study data.
In conclusion, our findings suggest that estimates of average per-contact infection probabilities based on partner study data under the hypothesis of constant infectivity can be highly misleading at a public health level, particularly when extrapolated to multiple casual contacts. Only by taking into account, as fully as possible, the distribution of infectivity in given populations at given times can we hope to better elucidate the true risks associated with individual and multiple unprotected acts of heterosexual intercourse. More complex models are needed to fully investigate the extent of the variability due to specific characteristics of the couple and to the timing of the sexual contact in relation to the progression of disease in the infected partner.
Acknowledgment: The coordination of the study was supported by grants from the Commission of the European Communities, DG XII, and the participation of centers by national grants. The authors wish to thank Anne Johnson for helpful discussion and suggestions during the preparation of this article.
Members of the European Study Group on Heterosexual Transmission of HIV were Paolo Costigliola, Ennio Ricchi, and Francesco Chiodo, Istituto Malattie Infettive, Universita di Bologna, Italy; Anastasia Roumeliotou and George Papaevangelou, Athens School of Hygiene, Greece; Roel A. Coutinho and Harry J. A. van Haastrecht, Department of Public Health and Environment, Municipal Health Service, Amsterdam, Netherlands; Ray Brettle and Roy Robertson, Infectious Disease Unit, Drug Addiction Study and City Hospital, Edinburgh, United Kingdom; Michael Kraus and Wolfgang Heckmann, Socialpedagogishes Institut, Berlin, F.R. Germany; Alberto Saracco, Clinica delle Malattie Infettive, Ospedale L. Sacco, Milan, Italy; Anne M. Johnson, Academic Department of Genitourinary Medicine, University College London Medical School, London, United Kingdom; Marc Vandenbruaene and Johan Goeman, Institute of Tropical Medicine, Antwerp, Belgium; Jorge Cardoso, Service de Dermatologia, Hospital Curry Cabral, Lisbon, Portugal; Alain Sobel, Immunopathologie Clinique, Hopital H. Mondor, Creteil, France; Juan Gonzalez-Lahoz and Raphael Andres-Medina, Infectious Diseases Service CIC. Health Institut Carlos III, Madrid, Spain; Jordi Casabona and Jordi Tor, Programa del SIDA, Generalitat de Catalunya, Barcelona, Spain; and Isabelle De Vincenzi, Rosemary A. Ancelle-Park, and Jean-Baptiste Brunet, European Centre for the Epidemiological Monitoring of AIDS, Saint-Maurice, France (Coordinating center).
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Keywords:© Lippincott-Raven Publishers.
Heterosexual transmission; HIV; Infectivity