Introduction
Most HIV infections result from people engaging in high-risk sexual or drug use behaviors. Fortunately, behavioral science and health education research has shown that HIV-related risk behaviors can be averted or modified. Several scientifically sound intervention trials have demonstrated the effectiveness of rigorously developed and implemented behavioral modification programs. Successful behavioral interventions have been devised for women at high risk of HIV infection [1,2], at-risk youth [3,4], injecting drug users [5,6], and men who have sex with men [7-13].
These intervention studies demonstrate that HIV-risk behaviors are amenable to modification, and provide hope for future HIV-prevention programs. Demonstrations of behavioral change efficacy, however, are not enough to permit conclusions to be drawn about the relative merits of alternative intervention programs. Policy makers, program managers, community planning group members and other key decision makers need to balance the costs and effectiveness of various interventions when planning and evaluating HIV-prevention programs [14]. Resources to fund these programs are limited, and must be used judiciously in order to maximize the number of HIV infections averted [15-17]. Economic evaluation studies of HIV-prevention interventions can provide some of the information needed by key decision makers.
To date, very few cost-effectiveness studies of behavioral interventions to prevent the spread of HIV have been conducted [10,14]. With regard to sexual behavior modification, for example, Moses et al. [18] evaluated the cost-effectiveness of a sexually transmitted disease (STD) control and condom promotion campaign targeting core STD transmitters in Kenya. The authors estimated that it cost between $8 and $12 for each infection prevented by the intervention, in comparison with AIDS treatment costs of between $100 and $1600 per patient in east Africa [19]. More recently, Holtgrave and Kelly [20] retrospectively analysed a cognitive-behavioral skills intervention for at-risk urban women attending primary care clinics [1]. Although not cost-saving under base-case assumptions, the intervention was found to be cost-effective in comparison with other life-saving interventions. A second study by Holtgrave and Kelly [21] assessed the cost-effectiveness of a behavioral intervention for gay men in a mediumsized southern city [7]. The results of the analysis indicated that the program was cost-saving to society under base-case assumptions and most reasonable parameter variations.
The present report describes the results of an incremental, retrospective cost-utility analysis of a 1986-1987 intervention for men who have sex with men [9]. In the published study, 584 homosexual and bisexual men were recruited from the Pittsburgh area to participate in an AIDS prevention project and were then randomized into two intervention conditions. All participants attended a 60-90 minute lecture on safer sex and HIV transmission. In addition, some of the men (n = 319) participated in an 80-min skills-training session, during which they could discuss, rehearse, and role-play safer sex negotiation strategies. The safer sex lecture covered the following topics: HIV transmission and pathogenesis; clinical outcomes of HIV disease; relative risks of different sexual practices; the importance of practising safer sex; the proper way to use condoms; and interpretation of HIV antibody tests. The additional skills-training component employed role playing, psychodrama, and group process techniques to: promote the social legitimacy and acceptability of safer sex; teach men strategies to help them modify their high-risk sexual behaviors; and explore non-libidinous functions of gay sexuality. Sexual behavior data covering a 6-month recall period were collected at baseline, and at 6-month and 12-month follow-up. No differences in HIV/AIDS knowledge or behavior were noted at baseline. The main finding reported by the authors was a significant increase for the skills-training group, relative to the lecture-only condition, in the proportion of partners with whom condoms were used during anal intercourse.
The primary objectives of the incremental cost-utility analysis presented below are: (i) to determine the discounted medical costs averted by the skills-training component of the intervention, over and above the costs averted by the safer sex lecture component; and (ii) to assess the incremental cost per quality-adjusted life year (QALY) saved, and thereby to determine the incremental cost-effectiveness of the skills-training component. The main question addressed is, 'Do the additional benefits derived from including a skills-training component in the intervention outweigh the extra costs?'. This question is especially relevant to policy makers and program managers who must decide how to allocate resources among relatively brief and more intensive HIV-prevention interventions.
Methods
Standard methods of incremental cost-utility analysis (CUA) [22,23] employing a societal perspective were used to assess the economic consequences of adding skills training to a simpler educational intervention. Thus, the safer sex lecture acts as a comparison condition against which are compared the costs and benefits of the safer sex lecture plus skills-training intervention. The major analytic steps in the analysis are: retrospective estimation of the skills-training component's incremental cost; mathematical modeling to translate the observed behavioral effects into an estimate of the number of HIV infections averted by the intervention; estimation of the number of QALY saved and the cost per discounted QALY saved by the skills-training component; and multiple sensitivity analyses to explore the effects on results of deviations from base-case assumptions. Model parameters, base-case values, and data sources are listed in Table 1. The four steps outlined above are described individually in the following sections.
Retrospective cost estimation
Because the intervention, which was completed in 1987, did not collect cost data prospectively, these data were obtained by retrospective estimation (all costs are expressed here in 1992 dollars). Several cost categories contributed to the overall cost of the skills-training intervention, over and above costs associated with the safer sex lecture, including direct, indirect, transportation and opportunity costs, as indicated in Table 2. Because material costs were minimal (estimated at $1 per client), direct costs consisted mainly of the salaries and fringe benefits of senior project staff and facilitators who conducted the skills-training sessions.
Indirect (overhead) costs, such as utilities, rent, maintenance, and general administration, were obtained as a fixed percentage (25% in the base case) of the direct costs. Costs associated with the scientific objectives of the study (such as extensive survey work and study recruitment) were not included in these calculations; the unknown costs of recruitment to the intervention itself were assumed to be included in the indirect costs.
Possible opportunity costs for the clients participating in the intervention included 1.33 h (80 min) per client for the skills-training session, together with time spent in transit (see below). However, per standard practice in health services cost-effectiveness analyses, a $0 valuation was placed on client time spent in the intervention and en route to and from sessions [23]. This parameter was varied in the sensitivity analysis, where the client's time was valued at $17.27 per 1 h, in accordance with 1992 average hourly compensation in the US.
Direct transportation costs (e.g. bus fare, gas) and opportunity costs for time spent in transit were excluded from the base-case analysis. This is justified because skills-training clients were not required to travel to a new location to receive the additional intervention component, and therefore incurred no supplementary transit-associated costs. However, as a check on this assumption, transportation costs were included in the sensitivity analysis, both in their entirety and pro-rated to reflect the proportion of the clients' overall time spent in the skills-training component of the intervention (80 out of 140 total min - conservatively estimating the lecture at 60 min - or 57%).
Mathematical modeling
The principal benefit derived from the addition of the skills-training component to the intervention was a significant increase in the use of condoms during anal intercourse, relative to the control, lecture-only condition [9]. Condom use increased in the skills-training group to 62% at the 6-month follow-up, whereas men who received only the safer sex lecture increased condom use to 49% of all partners, as shown in Fig. 1. Although baseline condom use was less for the lecture-only group, this difference was not significant (unpublished analyses). Even more dramatic differences were observed at second (12-month) follow-up: men who received skills training used condoms with 84% of their partners, compared with 56% for men in the lecture-only condition. (It may seem curious that condom use continued to increase among the skills-training group long after the cessation of the intervention; however, this phenomenon is not unique to the present study [7,24]. Plausibly, the men's sexual negotiation and self-management skills continued to improve, with practice, over this period.) For the purposes of evaluating the incremental cost-effectiveness of the intervention, the 6-month and 12-month condom-use percentages were averaged to yield 52% and 73% for the lecture-only and skills-training conditions, respectively.
A Bernoulli-process model of the sexual transmission of HIV [25-28] can be used to translate the enhanced condom use observed in the skills-training group into an estimate of the number of potential HIV infections prevented by the skills-training component, in excess of the impact of the safer sex lecture [18,20,21]. Two classes of infections must be considered: 'primary infection' refers to transmission of HIV to a previously uninfected intervention client, whereas 'secondary infection' is transmission from an already-infected client to a partner. The total number of infections averted (A) is simply the sum of the primary and secondary infections prevented by the intervention (denoted Ap and As, respectively).
To apply the Bernoulli-process model requires estimates of the following parameters: first, the average number of sexual partners (m), acts of anal intercourse per partner (n), and frequency of condom use for members of the lecture-only and skills-training groups (f1 and f2, respectively); secondly, the per-contact probability of transmission from an infected man to his uninfected partner for unprotected anal intercourse (α); thirdly, the effectiveness of condoms in preventing the transmission of HIV (e); and fourthly, the prevalence of HIV in the intervention group (π) and among their sexual partners (π') (prevalence is used to estimate the probability that a randomly selected partner is infected). In the present application, the original condom-use measure, percentage of partners with whom condoms were used, is treated as an estimate of the per-contact frequency of use.
Once the requisite parameter values have been obtained, the probability of a particular client becoming infected can be calculated via the equation:
where x = (1 - e) is the condom failure rate, and f denotes the fraction of condom use (f = f1 in the lecture-only condition, and f = f2 for skills training). The difference, P(f1)-P(f2), measures the incremental risk reduction, or equivalently, the number of primary infections averted per client in the skills-training condition, relative to the lecture-only condition. The total number of primary infections incrementally averted by the skills training is then the product of the per-capita infections prevented and the number of susceptible (i.e. non-infected) clients:
where N is the number of clients. In this formulation, behavioral effects of the skills-training intervention are conservatively estimated to last only for the 12 months preceding second follow-up, and to return to comparison group (lecture-only) levels directly thereafter.
Similarly, for each already-infected man in the study, the expected number of secondary infections averted by skills training, relative to the lecture-only condition, is S(f1) - S(f2), where:
In this equation, {1 - π}m is the number of susceptible partners, and z is the 'partnership overlap factor', hence (1-z) is the fraction of partners that are unique to any one client. This factor is used to correct for possible overlap in the sexual partnership networks of the HIV-infected men in the study [20]. This correction is necessary because Equation 3 otherwise assumes that the susceptible partners of HIV-infected clients are unique. A base-case value of 0.25 has been assumed for this parameter; alternative values of z are explored in the sensitivity analyses. Multiplying the difference, S(f1)-S(f2), by the number of already-infected clients yields the total number of secondary infections incrementally averted by skills training:
Because condom use was the only behavioral variable found to differ significantly between intervention conditions [9], both the number of partners and the number of acts of sexual intercourse per partner are assumed equal in the two intervention conditions. The total number of acts of sexual intercourse (combining anal insertive and receptive) was not reported by Valdiserri et al. [9], hence it was necessary to estimate this parameter. Based on findings from several published studies [7,29,30], the annual number of acts of intercourse was estimated at 25.
Table 2 in the published report [9] indicates that the men had an average of about 2.3 (aggregate insertive and receptive) anal intercourse partners during the 6 months assessed at baseline, but reported a 6-month total of only 1.7 partners at 12-month follow-up. The average is thus about two partners per 6-month period. However, this average combines receptive and insertive anal intercourse partners, so some partners are probably counted twice. On the other hand, a total of two partners seems a reasonable, if not conservative, estimate for the 12-month period from baseline assessment to second follow-up.
Two variants of the basic Bernoulli model are also considered in order to reduce possible dependencies of the results on the particular model used to estimate the number of infections averted. The first variant compares increases in condom use from baseline to follow-up (rather than absolute levels of reported condom use at follow-up) to control for pre-intervention differences in condom-use frequency. The second alternative (a 'per-partner' rather than 'per-act' model) is used in the sensitivity analyses presented below to provide a check on the feasibility of results suggested by the peract model. The equations associated with these variants are presented in the Appendix.
Estimation of QALY saved
The expected number of HIV infections averted by the skills-training component of the intervention can be converted into an estimate of the number of QALY saved by dividing the life course of an HIV-infected person into several phases (e.g. unaware of infection; aware with CD4 count ≥ 200 × 106/l; CD4 < 200 × 106/l; clinically-defined AIDS), and associating each with a reduction in quality of life as reported in the literature [31]. Using this method, Holtgrave and Qualls [31] obtained an estimate of 9.26 QALY saved for each infection prevented, after discounting at a 5% yearly rate. Adjusting for differences in mean age between the hypothetical cohort in their study and the skills-training group considered here (26 versus 33, respectively), yields a revised estimate of 6.97 discounted QALY saved per infection averted. In these calculations, perfect health was assigned a quality valuation of 0.9 rather than the maximum 1.0 because empirical evidence indicates that this value better approximates the average health of an arbitrarily drawn sample at any given time (i.e. perfect health is not necessarily the norm) [32].
The following formula was used to calculate the costutility ratio (R):
where C is the total incremental societal cost of the skills-training intervention component, A is the total expected number of infections averted, Q is the discounted number of QALY saved per prevented infection, and T is the lifetime medical care cost of treating a case of HIV disease and AIDS in the US. (see also Tables 1 and 2). Guinan and colleagues [33] estimated the present value of T at $56 000 in 1992 dollars, discounted at a 5% rate. ('Present value' refers to the discounting of future monetary outlays to reflect that resources are more highly valued in the present than in the future, independent of inflation [22,34].) Notice that although the time horizon of the cost component of the analysis is only 12 months, the intervention itself yields downstream benefits over 10 or more years for each HIV infection averted.
Because the cost-utility ratio provides an index of the cost per discounted QALY saved that is not specific to HIV prevention, it facilitates comparison of HIV-prevention interventions with other health service programs. The US Public Health Service's Panel on Cost-Effectiveness in Health and Medicine recommends utilizing QALY in the reference case of all costeffectiveness analyses to increase between-study comparability, and because QALY explicitly incorporate intervention effects on morbidity and impaired physical, mental, and emotional functioning [35].
Although there is no universally accepted cost-utility ratio threshold below which a program is judged costeffective, there is general agreement regarding the labeling of cost-utility ratios of certain magnitudes [36-39]. Ratios less than zero indicate that the program is cost-saving, and by convention, are simply labeled as such [36]. Health service programs with cost-utility ratios that exceed zero but are less than approximately $30 000 are usually considered cost-effective [37-39], but programs with ratios over $140 000 are difficult to justify as cost-effective.
Sensitivity analyses
Although a diligent effort was made to procure the most accurate estimates available, there nevertheless remains some residual uncertainty in the values of several of the parameters utilized in the base-case analysis. Multiple sensitivity analyses were therefore undertaken to explore how variations in base-case assumptions impact the result obtained. Simple one-way analyses, in which a single parameter is varied while the remaining parameters remain fixed, were undertaken first to determine the direction and magnitude of the associated effect. These unitary analyses were supplemented with multi-way analyses in which the effects of different value combinations of particular groups of variables were examined. Threshold and worst-case analyses provided further checks on the reasonableness of the base-case results.
Results
Under the base-case assumptions summarized in Table 1, the incremental societal cost of the skills-training component was $12 657, or just under $40 per client. The number of (primary and secondary) infections averted was 3.05 (57% of which were primary), at an incremental cost of approximately $4150 per averted infection. The intervention saved a total of 21.29 discounted QALY, and over $170 000 in direct medical care costs. The incremental cost per discounted QALY saved was negative, which suggests that the skills-training component was a cost-savings addition to the overall intervention program.
As indicated in Equation 5, the cost-utility ratio (R) is a function of four primary components: the total incremental cost of the intervention (C), the total number of infections averted (A), the medical treatment cost (T), and the number of QALY saved per averted infection (Q). The last two (T and Q) are molar parameters of the model in that they cannot be reduced to other parameters, as can C and A. Both C and A are determined by the interactions of numerous other parameters, as illustrated in Tables 3 and 4, which summarize the sensitivity of C and A to several essential constituent parameters. As shown in Table 3, the intervention remains cost-saving under all conditions considered, including the extreme case when: facilitator fringe benefits equal half the salary; indirect costs equal direct costs; and clients are paid for 100% of the time spent in the intervention (including the safer sex lecture component) and in transit, as well as being reimbursed for transportation costs. Even in this worst-case scenario, total incremental intervention costs are less than $40 000, well below the cost-saving threshold of $171 048 (under base-case assumptions for the remaining parameters).
Similarly, the intervention remains incrementally costsaving within the range of values of the sexual behavior and epidemiological parameters shown in Table 4. (It should be noted that the base-case per-contact probability of HIV transmission, α= 0.009, is assumed in this Table. As discussed further below, the results are sensitive to variation in this parameter.) As indicated in Table 4, the intervention is cost-saving provided that at least 0.23 infections are averted. A similar, though somewhat larger, number of infections (0.31) are prevented under worst-case assumptions, which include: (i) a 20 to 25% reduction in the actual number of partners and sex acts per partner (to account for possible under-reporting by clients); (ii) an increment in reported condom use among men in the lecture-only condition and a decrement for men in the skills-training group; (iii) an HIV prevalence among both sexual partners and clients of 0.075, one-half the base-case value; (iv) condom effectiveness of 0.9 rather than 0.95; and (v) substantial overlap (z = 0.5) among clients' sex partners.
Table 5 shows the result of combining the base-case value of one parameter (C, A, T, or Q) with worst-case values for the remaining three parameters. As indicated, the intervention is cost-saving when the base-case value of C is combined with worst-case values for A, T, and Q, and likewise when A is combined with C, T, and Q. However, the cost-utility ratio is greater than zero when worst-case values are assumed for either C, A, and Q (with the base-case value for T), or for C, A, and T (with the base-case-value for Q). When all four parameters are set to worst-case values, the cost-utility ratio is about $16 000, which suggests cost-effectiveness, but not cost-savings.
Although the intervention remains cost-saving if the base-case number of infections averted (A) is combined with the worst-case values of C, T, and Q, the model is, in fact, relatively sensitive to this measure of pro-grammatic effectiveness. Figure 2 illustrates the effect that varying A has on the base-case and worst-case values of the cost-utility ratio. For relatively large values of A (e.g., A>1), the effect is minimal and the skills-training intervention is incrementally cost-saving. The cost-utility ratio is very sensitive, however, to small changes in this parameter for A less than about 0.2 in the base case and 0.5 in the worst case.
As indicated in Table 4, A is relatively insensitive to changes in most sexual behavior and epidemiological parameters; A is about 2.0 or more in all the one-way sensitivity analyses, and drops below 0.5 only when nearly all of the parameters are assigned their worst-case values. In fact, the sensitivity of the cost-utility ratio to the number of infections averted is almost entirely due to its dependence on the per-contact probability of transmission (α). However, even when worst-case values are assumed for C, T, and Q, skills training is incrementally cost-effective for α > 0.0006, and is cost-saving for α > 0.0027, and thus for the base-case assumption of α= 0.009. By way of comparison, in Brookmeyer and Gail's review [40] of reported estimates of the per-contact transmission probability for anal intercourse, α ranges from 0.008 to 0.32 [40,41]. In summary, although the model is sensitive to the per-contact probability of transmission, the base-case value would need to err by at least an order of magnitude, and there would have to be substantial errors in the remaining parameters (all biased against the intervention), to reverse the indicated conclusion of cost-effectiveness.
Furthermore, the base-case number of infections averted is much greater for the alternative 'delta-delta' model defined in the Appendix than for the basic model (5.32 versus 3.05, respectively). Thus, controlling for baseline differences in condom use only strengthens the finding of cost-effectiveness. (This result is not surprising in lieu of the condom-use patterns illustrated in Fig. 1.)
Although the estimated number of infections averted is slightly smaller for the per-partner model (see the Appendix) than for the per-act model (2.83 versus 3.05, respectively), the cost-effectiveness ratio is still considerably less than zero for the skills-training per-partner probability of transmission, β= 0.1 [40,42]. Moreover, the skills-training intervention remains incrementally cost-saving for β>0.033, and cost-effective for β>0.007, assuming worst-case values of C, T and Q. Thus, consideration of this alternative form of the Bernoulli-process model does not substantially alter the findings.
Discussion
The above analyses indicate that the skills-training component is incrementally cost-saving in the base case and under most reasonable variations in parameter values. The results, however, are somewhat sensitive to the number of infections averted, which is largely determined by the single-contact probability of HIV transmission (α). Nevertheless, the intervention remains cost-saving or at least cost-effective for a wide range of epidemiologically feasible values of α.
Limitations of the study include the retrospective (rather than prospective) collection of cost data, the need to estimate key epidemiological parameters, and reliance on self-reported sexual behavior data. However, these concerns are substantially mitigated by the sensitivity analyses, which show that the results are generally robust to changes in the relevant parameters over a range of reasonable values (and in some cases values that were unreasonably biased against the intervention). Thus, even uncertainty in the cost and epidemiological estimates, and possible bias in the self-reporting of sexual behavior data, does not alter the basic finding that the skills-training component was a cost-saving addition to the intervention. Of course, by their very nature, cost-utility analyses do not incorporate in a satisfactory way the important issues of equity, access, and community support [43].
Another possible limitation of the study is the use of a cumulative probability model to estimate the number of HIV infections averted (A). Unfortunately, the relevant clinical outcome data (i.e., seroconversion rates) are seldom available for this type of study, and therefore the number of infections prevented must be modeled. Two different forms of the Bernoulli-process model were used to estimate A, one in which the individual sexual act is taken as the basic probabilistic unit, and another based on partners rather than acts. It is reassuring to note that the obtained results were consistent across models. Neither of these simple models, however, adequately captures temporal features of the epidemic (for example, the prevalence of infection is assumed static throughout the 12-month follow-up period). Although more complex, dynamic models of the epidemic could have been utilized [44,45], the present method yields a conservative estimate of the number of infections averted because it ignores partnership chains beyond the first link (i.e. only primary and secondary infections are included in A, not higher-order infections), as well as infections arising outside the 12-month assessment period (intervention effects are assumed to vanish completely at the completion of follow-up). Another limitation of the particular models used here is that the extreme heterogeneity usually observed in sexual behavior data has been averaged out, in essence combining high-risk with low-risk individuals to obtain 'average-risk' individuals. The impact of this simplification on the estimated number of infections averted is not known.
Finally, the cost-utility analysis presented above focused on the incremental costs incurred in adding a skills-training component to an existing intervention, in the context of a larger epidemiological study of the natural history of HIV infection, and therefore does not incorporate start-up costs that a community-based organization or other service provider would incur before being able to deliver such a program. The substantial difference, however, between incremental cost (about $38 000 in the worst case) and the cost-saving threshold (over $170 000), suggests a large tolerance for additional costs.
Care should also be exercised in generalizing the results of this study to other behaviorally-based HIV-prevention interventions for men who have sex with men, or to other populations. The effectiveness, hence cost-effectiveness, of an intervention is inexorably linked with the risk level of the target population, as jointly determined by behavioral practices and the prevalence of HIV in the community. In the analysis above, 3.05 infections were averted under the base-case assumption of 15% HIV prevalence. If this same intervention were implemented in a community with a much lower HIV prevalence, say 1%, then the expected number of infections averted would decrease to 0.24 and the intervention would barely be cost-saving (at a prevalence of about 0.1% the cost-utility ratio climbs to nearly $68 000, indicating questionable cost-effectiveness). Thus, this (and other) HIV interventions are most cost-effective when applied to high-risk communities. Similar comments apply to individual risk. For example, the intervention analysed here was undertaken in 1986-1987, when information on safer sex and HIV transmission was less widely disseminated among gay and bisexual men than it is now. If the intervention were replicated today among men whose sexual practices place them at lower risk than the men in this study, fewer infections would be averted. Unfortunately, however, not all men who have sex with men consistently practice safer sex, especially younger gay men, gay men of colour, and men who do not self-identify as gay [46-49]. Careful matching of interventions with target population risk levels is therefore needed to ensure maximal effectiveness.
These limitations also suggest several areas of additional research. First, the cost-effectiveness analysis reported here was retrospective; future HIV-prevention interventions should include a prospective economic evaluation component to permit the collection of accurate cost data. Second, additional epidemiological research is required to provide more accurate characterizations of the per-act (or per-partnership) probability of HIV transmission during anal or vaginal intercourse. Third, detailed analyses of the sensitivity of probabilistic models, such as the Bernoulli-process model, to parameter variations are also needed, as are comparisons with more complex models of HIV transmission.
As the behavior-change effectiveness of additional HIV-risk reduction interventions is established, it will become increasingly important to establish their economic efficiency as well. Cost-effectiveness analyses should be conducted for a range of HIV intervention types (e.g., informational, cognitive-behavioral), modes of delivery (community-level versus individual or small group), and target populations. Once a foundation has been laid of solid economic evaluation studies involving different intervention types and populations, public health decision makers will be better able to determine the kinds of HIV prevention approaches that produce the greatest benefits given resource constraints.
The foregoing analysis strongly suggests that the extra cost of adding a skills-training component to an otherwise lecture-only HIV-prevention intervention is well worth the investment of fiscal resources. Decision makers responsible for resource allocation should give strong consideration to this type of intervention. Sometimes making an intervention more expensive is well worth the additional cost.
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Appendix
Two variants of the basic Bernoulli model (Equations 1-4) are introduced below. The first variant controls for pre-intervention disparities in condom-use frequency by considering differences rather than absolute levels of condom use. In this alternative model, Equations 2 and 4 are modified to read:
Equation (Uncited)Image Tools
where f and g are the frequencies of condom use at follow-up and baseline, respectively, and the subscript indicates the intervention condition, as above. For the lecture-only condition, f1 = 0.52 and g1 = 0.47, whereas for skills training, f2 = 0.73 and g2 = 0.31 (using the average values calculated above for follow-up, and baseline values from Table 2 in the published report [9]). This variant is referred to in the main text as the 'delta-delta' model.
The basic model is considered a 'per-act' model [28] because each act of intercourse is treated as a potentially risky, independent trial. Other Bernoulli-process models focus instead on the overall probability of transmission per partnership [45,50,51]. The per-partnership equations corresponding to Equations 1 and 3 are:
Equation (Uncited)Image Tools
where β is the probability of HIV transmission from an infected person to his partner at any time during the duration of the partnership, and f the proportion of partners with whom condoms are used.
Keywords: Cost analysis; cost-effectiveness; HIV; prevention; risk behaviors; homosexuality
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