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Cost-EflSectiveness Analysis of AIDS Prevention Programs: Concepts, Complications, and Illustrations Milton C. Weinstein, John D. Graham, - Joanna E. Siegel, and Harvey V. Fineberg The enormity of the AIDS problem ant! the limited resources avail- able to finance a potentially large number of intervention programs, each likely to have some degree of effectiveness in preventing future cases of AIDS, have led policymakers at national, state, and local levels to seek a rational basis for setting priorities for prevention. Cost-effectiveness analysis is a quantitative approach to resource al- Tocation under constrained resources (Weinstein and Stason, 1977; Warner and Luce, 1982; Drummond et al., 1987~. The premise of this paper is that cost-effectiveness analysis can be a useful too! in guiding resource allocation for AIDS prevention. Most AIDS prevention measures share the characteristic of pro- moting desirable behavioral changes that rerluce the risk of HIV transmission. Prevention measures may be applied in a variety of population groups, in a variety of ways. HIV antibody screening may be regarded as a preventive measure, to the degree that knowledge of one's HIV status results in desirable behavioral change. Screening of high-risk groups, such as homosexual men, intravenous (IV) drug users, and visitors to sexually transmitted disease clinics, as well as screening of more heterogeneous population segments at a time at which transmission would be especially likely for example, couples entering marriage and blood donors have all been advocated. Pro- The authors are from the Harvard School of Public Health. 471

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472 ~ BACKGROUND PAPERS motion of safer sex practices is exemplified by programs of condom distribution and safer sex education in schools, as well as community education through media such as television or the pamphlet recently mailed to all households by the U.S. Public Health Service. Programs to limit HIV spread among needIe-sharing drug users, such as bleach distribution by outreach workers or needle exchange, are also very much under consideration. Another type of prevention program is contact tracing, which has been used with some success in dealing with other sexually transmitted diseases. In this paper, the concepts, complications, and potential use of cost-effectiveness analysis in three of these areas are illustrated: premarital screening, conclorn promotion in secondary schools, and bleach distribution among {V drug users. Appendix A gives an illus- trative cost-effectiveness analysis for premarital screening, and Ap- penclix B illustrates an approach to modeling the benefits of condom promotion in schools. The authors' research on all three examples is used throughout the paper to illustrate key points. The paper is structured as follows: the first section is a brief exposition of the general mode] for cost-effectiveness, and the next section is a discussion of problems involved in assessing program effectiveness. One key issue in measuring effectiveness is the choice of outcome measure: What measures of final health outcome exist? Can intermediate outcome measures be used as proxies? Another set of issues in estimating effectiveness concerns modeling the spread of infection in populations: What data are needed? Are Tong-term effects different from short-term effects? Must secondary spread of infection be modeled? What types of heterogeneity in the target population influence program effectiveness? Still another set of issues in estimating effectiveness relates to the scientific uncertainty that surrounds the biological, epidemiological, and behavioral variables which determine the number of AIDS cases that will occur under different program scenarios: How can this uncertainty be reflected responsibly in cost-effectiveness analyses of prevention programs? Does this uncertainty vitiate the entire cost-effectiveness modeling approach? The third section introduces and illustrates the possibility of im- portant "collateral" program effects health or social consequences that relate to diseases or problems other than HTV (e.g., other sex- ually transmitted diseases or drug use) and that follow from in- terventions aimed at HIV. These collateral effects may significantly

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COST-EFFECTIVENESS ANALYSIS ~ 473 affect the relative desirability of a program option. In the fourth section, the emphasis changes from issues of program effects to issues of estimating program costs. Special problems of valuation, such as weighting effects on the quality of life, interpersonal comparisons across population groups inclu(ling some (e.g., IV drug users) that impose substantial externalities on the rest of society, and valuation of avoiding births of infected or uninfected infants, are described in the last section. A COST-EFFECTIVENESS MODEL FOR AIDS PREVENTION The purpose of applying cost-effectiveness analysis to AIDS preven- tion programs is to guide the setting of priorities for the use of finite resources, with the objective of achieving the maximum reduction in AIDS-related mortality and morbidity. The cost-effectiveness model user! herein assumes the societal perspective, according to which all program costs and consequences are recognized, irrespective of the beneficiary or payor. This is a broader perspective than that, for example, of a municipal health department (which does not realize all of the savings in AIDS treatment resources and which may not have to pay full program costs because of federal grants). However, the model is easily adapter! to other perspectives by excluding costs and consequences that are extraneous to a given decision maker and by including costs and savings realized by one decision-making entity at the expense of another. Cost-effectiveness analysis applies when four key ingredients are present: (1) an identifiable clecision-making entity; (2) a measure of program effectiveness, such as number of cases prevented, num- ber of years of life saved, or number of quality-adjusted years of life (QALYs) gained; (3) a constrained resource that limits the number of programs that can be implemented (e.g., cost); and (4) a set of independent programs from which to choose, each of which produces some degree of net expecter! effectiveness (e.g., lives saved or QALYs gained) and each of which consumes some of the constrained resource (e.g., dollars). When these conditions are met, the optimal alloca- tion rule (i.e., the allocation rule that achieves maximum effectiveness subject to the resource constraint) is to select programs in ascending order of their cost-effectiveness ratio (net program cost/net program

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474 ~ BACKGROUND PAPERS effectiveness) until the resource budget is exhausted. In other words, highest priority wouIc! go to the programs for which the net cost per unit of desired effect is lowest. When the societal perspective is adopted and QALYs are the measure of effect, the following formulation of a cost-effectiveness ratio for AIDS prevention may be used: /NetN {Programs' _ ~ Cases >` ~ Costs ~ (costJ _ ~ Cost J \~PreventedJ \`per CaseJ (~1) ~ Program `` ~ Cases `` ~ QALYs ~ ~ {Change in Quality`` kEffectiver~es~J VPreventedJ tper CaseJ \`of Life to OthereJ Each term in the ratio shouIcl be interpreted as a present value, at a suitable time discount rate, of a stream of future benefits or costs. This interpretation enables comparison of programs that may have different lags in the appearance of benefits and different patterns over time in the investments required to make them work. Issues that arise in estimating each term in this ratio, as well as refinements of the ratio to account for considerations such as population dynamics and collateral costs and consequences, are discussed in the following sections. ASSESSING PROGRAM EFFECTIVENESS Measures of Health Outcome Various measures of outcome can be used to assess the effectiveness of prevention programs directed at AIDS. These include both mea- sures of final outcome and intermediate outcome measures. Possible final outcome measures include number of lives saved, number and discounted number of life-years saved, and discounted QALYs saved. Intermediate outcome measures include reductions in risk-taking be- haviors and incidence of HIV infection. The virtues and limitations of these outcome measures, as they apply to AIDS prevention pro- grams, are discussed below. Final Outcome Measures The number of lives saved is a simple and intuitively appearing mea- sure because it corresponds with a basic and important purpose of public health intervention. Because lives are visibly lost as a result of AIDS, the number of lives saved offers a concrete representation of the success of a program. However, the number of lives saved has several drawbacks as an outcome measure. First, it does not

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COST-EFFECTIVENESS ANALYSIS ~ 475 reflect the timing of life saving. Cost-effectiveness analyses generally incorporate the assumption that it is preferable to use available resources to save a life now rather than in the future. This is both because improvements in technology will likely enable the savings of future lives at a Tower cost and because lives saved now can contribute to the pool of resources that will be available in the future. Authors such as Keeler and Cretin (1983) describe the logical impossibility of recognizing the greater present value of money, reflecting its potential for investment, without concurrently recognizing the greater value of saving present as opposed to future Ives. These authors recommend what has become a generally accepted practice, namely, (liscounting health effects to reflect the point at which they occur. As a measure of outcome, the number of lives saved also falls short in failing to reflect the proportion of a person's life that is saved or, more precisely, the amount of life expectancy saved. This quantity can be represented as the number of discounted life-years saved, rather than discounted lives saved. Using the number of life- years saved to evaluate program effectiveness is often controversial, because it seems to discriminate against groups with lower remaining life expectancy, notably the elderly. When comparing interventions against AIDS, this issue assumes secondary importance because a large proportion of AIDS cases fall within a narrow age range. The distinction becomes more important, however, when programs to pre- vent AIDS are compared with other programs such as those against heart disease or cancer. Using the number of discounted life-years saved is preferable to using the number of discounted lives saved because, in the opinion of the authors, the former more accurately reflects society's disproportionate concern about causes of untimely or premature death. One further complication of using discounted life-years saved as an outcome measure is that life expectancy may vary for groups of the same age, depending upon how groups are defined. This is an important concern in evaluating the effectiveness of AIDS prevention programs. For example, apart from any value judgments regarding the comparative worth of individuals to society, the life expectancy of a mate 35-year-ol(1 TV drug user is lower than that of a 35-year- old gay man. The difference is flue to the violence prevalent in the hazardous life-styTes associated with drug abuse. Use of this Tower life expectancy in calculating the effectiveness of AIDS programs, however, implies that preventing a case of AIDS among {V drug users is a less effective use of societal resources (i.e., results in fewer life- years saved) than preventing a case among the gay mate population.

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476 ~ BACKGROUND PAPERS Such an analysis might be perceived as biased against lifesaving programs targeted at drug users. Perhaps a greater dilemma arises when one considers the life expectancy of a drug user with AIDS, which is only about one-third that of a non-drug user with AIDS. To incorporate this differential into an analysis is to accept the current disadvantages faced-by drug users in recognizing AIDS and seeking care. The value judgments involved are discussed further in the section "Problems in Valuing Program Consequences." One additional characteristic that should arguably be includes! in an outcome measure is the quality of life-years saved. Using QALYs saved implies favoring preventive programs, which save healthy life- years, over treatment programs that allow increased survival with AIDS. Because both AIDS and AIDS-related complex (ARC) can be extremely debilitating, it would be clifficult to justify an equal prefer- ence for saving life-years with AIDS and saving the same number of life-years through prevention. Yet people with AIDS are identifiable individuals with visible neecis, and our society may find it difficult to assign a Tower priority to programs that benefit them. This dilemma can be mediated to some extent by adjusting the actual QALY value assigned to life with AIDS. A final use of QALYs that deserves mention is in assigning a societal valuation to life-years saved, apart from the relative valuation of life years with and without AIDS. The clearest example of this use is in evaluating programs for {V drug users. Some would argue that the value of a saver! life-year for a drug user is lower than that of a non-drug user because drug users impose substantial costs upon society (e.g., crime, fear). Alternatively, drug use can be seen as a disease that lowers the quality of life just as other illnesses do. One may, therefore, not believe it is appropriate to "penalize" drug users for suffering from a disease over which they may have limited control. Intermediate Outcome Measures Whereas final outcome measures reflect ultimate program goals, the effect of a given program on discounted life-years or QALYs saved is often difficult to assess. Programs are directed toward accomplishing intermediate objectives, which in turn are believed to achieve or contribute to the larger societal objectives. Intermediate outcome measures frequently have the advantage of being more immediate and potentially more measurable. Their disadvantage is that their relationship either to the larger goal or to the program itself is often indirect or elusive. This disadvantage will be described in greater

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COST-EFFECTIVENESS ANALYSIS ~ 477 detail as related to specific examples of two types of intermediate outcome, frequency of risk-taking behavior ant! incidence of HIV infection. Many programs designed to prevent AIDS are directed at elimi- nating or reducing the frequency of behaviors that place individuals at risk of exposure to HIV infection. To prevent infection by means of sexual transmission, for example, programs may promote condom use, encourage safer sex practices, or encourage having fewer part- ners. Intermediate outcome measures of the effectiveness of these programs may describe the frequency of condom use before and after an educational campaign or the numbers of partners before and after the circulation of a "safer sex" pamphlet. The importance of these and other behavioral changes, however, depends on how these results actually translate into prevention of AIDS cases. Although condom use is theoretically effective in preventing HIV infection, for exam- ple, effectiveness may actually depend on the number of partners, the stage of infection of an infected partner, and the number of ex- posures per partner. Measures of risk-taking behavior thus indicate the success of a program in achieving the intermediate objective, but do not necessarily predict the program's effectiveness in achiev- ing the larger societal goal. The value of this type of intermediate outcome measure for assessing program effectiveness depends on the relationship between the intermediate and the ultimate goals. The incidence of HIV infection is a type of intermediate out- come closely related to the incidence of AIDS. The problem with this measure is its distance from more immediate programmatic ob- jectives. There is no doubt that if a condom distribution program results in decreased incidence of HIV infection, it is a successful program. However, a causal link between such a program and HIV incidence is often difficult to establish. Many intervening factors may be involved, including other environmental influences (e.g., me- clia coverage, concurrent prevention activities), the timing of HIV testing and seroconversion, the prevalence of HIV positivity, and factors related to the sample selected. This type of measure thus provides information on the spread of the virus but is clifficult to relate to a particular program. Modeling Program Effects on HIV Transmission A major task in measuring the effectiveness of AIDS prevention is to estimate the number of incident cases of HIV infection expected to occur, over time, in both the presence and the absence of the

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478 ~ BACKGROUND PAPERS program being assessed. This task is complicated by gaps in our basic knowledge of the biology of HIV transmission, the epidemiology of the infection in populations, and especially, the determinants of high-risk behaviors and the use of protective measures. Data Requirements As illustrated in Appendix A, key variables for which estimates are required in order to calculate the number of cases prevented by a premarital screening program include the following: . current prevalence of HIV infection in theme and fe- maTe partner at the time of marriage (including possible transmission prior to marriage; . probability of HIV transmission during marriage, in the absence of preventive or protective action, from mate to female or from female to male; . probability of adopting preventive (e.g., abstention) or protective (e.g., condom use) action upon knowledge of a positive antibody test and appropriate counseling; . efficacy of protective action against sexual transmission . . Curing marriage; . sensitivity and specificity of HIV antibody test systems; and . probability of conception and ultimate infection of a child of the marriage. Some of these variables (e.g., test sensitivity and specificity, HIV prevalence) can be estimated from available data with reasonable precision and accuracy, although not entirely without uncertainty. (For example, HIV prevalence could vary considerably between pop- ulations of marriage candidates and populations of blood donors, al- though preliminary data from the premarital testing program in Illi- nois are consistent with prevalence estimates basest on blood donors.) Other variables (e.g., probability of transmission by sexual contact with and without protection) have been studied to a limited cle- gree, but wide variation in reported data exists. Still other variables (e.g., probability of adopting preventive or protective behavior) have hardly been studied at all. One value of performing cost-effectiveness analysis would be to identify those variables to which program cost- effectiveness is most sensitive, and thereby to identify areas in which field evaluations and further research would be most informative. Be- havioral response variables almost surely fall into the high-priority

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COST-EFFECTIVENESS ANALYSIS ~ 479 category for further research. Formal approaches to assessing cost- effectiveness in the face of uncertainty, and their implications for targeting areas of research, are described in the following subsection. Dynamic Modeling The cost-effectiveness formula (Equation 1) suggests a naive and potentially misreading approach to modeling benefits, namely, that the health benefit associated with the prevention of a case of HIV infection at any point in time is the difference between the number of (quaTity-adjustecI) years that wouic3 be liver! without infection and the number of (quaTity-adjusted) years that wouic! be lived with infection. The number of QALYs with infection can be estimated from models both of HIV latency prior to AIDS onset and of AIDS survival, but can the number of QALYs without infection be estimated from the usual method of life-table analysis in the general population? As a first-order approximation in Tow-risk populations (e.g., heterosexual partners of transfusion recipients), perhaps general life tables can be user! to estimate the number of life-years potentially saved by preventing an instance of HIV infection. However, in populations in which the risk of HIV infection is an ongoing process, preventing infection at time t does not guarantee a normal life expectancy if the risk at time t + 1 remains high. Dynamic, rather than static, models of the benefits of disease prevention are, therefore, needed. In general, more complex modeling techniques may be useful in generating the estimates of cost and effectiveness that enter the cost- effectiveness ratio. State-transition moclels (in which disease status is modeled probabilistically in a population), epidemic models based on differential equations, and other computer-based approaches are available to assist in the projection of cost and effectiveness through time. Assessment of the cost-effectiveness of prevention programs in {V drug user communities has revealed the importance of these con- siclerations. The aggregate gain in life expectancy attributable to preventing a case of HIV infection in a relatively Tow-prevaTence pop- ulation of drug users (as in Houston, where HIV prevalence among IV drug users is estimated at 3 percent) is greater than that attributable to preventing a case in New York City (where HIV prevalence among IV drug users exceeds 50 percent). The reason is that {V drug users in Houston have a higher probability of avoiding (or delaying) in- fection than their New York City counterparts and, therefore, have more years of life to gain if they are sparecl infection at a point in

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480 ~ BACKGROUND PAPERS time. Analogous considerations apply when comparing the life ex- pectancy gained per infection avoided among homosexuals in San Fiancisco versus that in communities with Tower HIV prevalence among homosexuals. An important insight from this reasoning is that the most cost- effective communities in which to implement AIDS prevention pro- grams may be those with intermediate levels of HIV prevalence. If prevalence is too Tow, resources are squandered in preventing very Tow probability events. However, if prevalence is too high, the gain (in terms of life expectancy) from preventing single-hit transmission today is attenuated by the high risk of eventual infection and pre- mature death. Even if programs continue at a high relative efficacy, residual infection rates with the program in place may be high enough to diminish consiclerably the benefit per infection prevented. Further modeling of this phenomenon will yield other specific guidelines for targeting prevention efforts according to preexisting spread in the community. Epidemic Control First-order estimates of program effectiveness may be based on the assumption that preventing the spread of infection to an individ- ual has the effect of averting the consequences of that single case of HIV infection. This assumption is correct only if that individual has a negligible probability of infecting others, either because anyone with whom the individual has intimate contact is already infected or because the individual engages in protective or preventive behavior immediately after becoming infected. In reality, the process of sec- ondary spread has the effect of producing a "multiplier effect"; that is, each primary case prevented would otherwise multiply into some larger number of cases over time. To estimate the effects of AIDS prevention accurately, models are required that can yield estimates of these multipliers under various assumptions about number of con- tacts, frequency of contact, and probability of transmission per con- tact. As long as these multipliers are approximately constant across AIDS prevention programs, however, their relative cost-effectiveness will not be distorted by omitting the multiplier from the calcula- tion. To the degree that multipliers do vary across programs, failure to consoler them will tend to result in underestimating the relative cost-effectiveness of programs with large multiplier effects.

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COST-EFFECTIVENESS ANALYSIS ~ 481 Heterogeneity The models the authors have used to estimate the effectiveness of protective measures such as condom use and needle sterilization are baser! on a number of parameters that govern the probability of HIV transmission in a population of interest. With regard to condom use (Appendix B), for example, such parameters include the probability of transmission during unprotected intercourse, the probability of condom use during a given sexual act, and the probability of preva- lent infection in a given sexual partner. The simplest model assumes that these parameters are constant across all members of a target population, such as a high school population. This homogeneity as- sumption, although simplifying the calculations and requiring only data on population means rather than frequency distributions, may distort the true effects of an intervention. It would be better to as- sume, for example, that the probability of transmission varies from inclividual to individual and that this probability is, in itself, dis- tributed in the population according to some frequency distribution. Although data do not permit estimation of these frequency dis- tributions, it is important to model the possibility of heterogeneity in order to obtain reasonable bounds on the likely effects of intervention. In general, heterogeneity in the probability of transmission tends to diminish the effectiveness of preventive interventions, if it is not pos- sible to identify the "superinfectors" and to target the interventions at them. Heterogeneity of compliance (e.g., condom use, needle ster- ilization) and heterogeneity of prevalence (e.g., nonrandom mixing within subpopulations with higher than average or lower than aver- age prevalence) cause smaller deviations from estimates of program effectiveness (Appendix B). Limited study populations make it extremely difficult to estimate underlying frequency distributions of such population characteristics as the infectivity rate. Therefore, in the absence of empirical data, modeling remains the only viable approach to exploring the implica- tions of heterogeneity. COLLATERAL PROGRAM EFFECTS An important issue in applying cost-effectiveness analysis to AIDS prevention programs is the appropriate treatment of collateral pro- gram effects. In particular, many programs designee! to prevent AIDS have other benefits or costs unrelated to AIDS itself. The behaviors that place individuals at risk for AIDS are frequently a source of risk for other illnesses and undesirable outcomes. To the extent that such

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COST-EFFECTIVENESS ANALYSIS ~ 489 condoms are not 100 percent effective in preventing preg- nancy, and misuse of the condom can result in a sub- stantial risk of pregnancy. Despite these drawbacks, it is well recognized that condoms have considerable virtues as a contraceptive method among teenagers. They are cheap, can be made readily available to adolescents, and can be used by teenagers without informing "establishment" figures such as physicians and parents. If used properly, condoms are quite effective at preventing both pregnancy and venereal (disease. Con- doms are perhaps the most effective contraceptive method during a couple's initial several encounters, before the girl elects a prescription metho(1 of contraception. In many adolescent relationships, women remain sexually active for more than a year before pursuing a pre- scription method. The emergence of the AIDS epidemic is causing a serious reap- praisal of the benefits and costs of increasing condom use among adolescents. Although the AIDS virus has so far penetrated only modestly beyond the traditional "high-risk" groups, there are reasons to target U.S. teenagers in the development of prevention activities. Adolescent life-styTe in the United States is characterized by sexual experimentation, multiple partners, frequent sexual intercourse, ex- posure to sexually transmitted diseases, and significant amounts of intravenous drug use. In light of all of the above, the potential role of condom use as an AIDS prevention strategy among teenagers needs to be analyzecI. A complete cost-benefit analysis of condom promotion anti dis- tribution programs is not attempted in this paper. Instead, some mathematical moclels are presented that are useful in simulating the potential HIV prevention benefits of increased condom use to the aclolescent. The purpose is not to produce precise estimates of an adolescent's absolute risk of HIV infection, but rather to determine how much conclom use might reduce an adolescent's risk of infec- tion. These analyses also highlight what the data requirements of a comprehensive benefit analysis of condom use might be. Because the economic facets of AIDS prevention have already been examined in the previous example (premarital screening), the focus here is on the interrelationships among patterns of sexual behavior, extent of condom use, and rates of HIV infection. Personal Risk of HIV Infection: A Simple Mode! of the Adolescent Let us take the perspective of an uninfected teenager at the start of ninth grade, for example, and simulate the cumulative probability

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490 ~ BACKGROUND PAPERS that he or she will become infected with the HIV virus prior to graduation (or four years later). In the equations that follow, let r be the risk of transmitting the virus (from an infected to an uninfected person) during a single act of vaginal intercourse, e the efficacy of condoms in preventing transmission of the virus, and f the fraction of sexual encounters protected (properly) by a condom. Given the above, the probability of becoming infected by an infected partner during a single act of intercourse is P = r(1fe). (1) If there are n exposures with the same infected partner, the risk of infection becomes P = 1[1r(1fe)]n. (2) If the uninfected teenager craws his or her partner randomly from the pool of U.S. adolescents and p is the prevalence of HIV infection among aclolescents, the cumulative risk of infection then becomes P = pl1[1r(1fe)InI. (3) Of course, many adolescents will have more than one partner. If the uninfected teenager has n exposures with each of m random partners, the cumulative risk of infection becomes P = 1{pL1r(1fell + (1p)) (4) Before computing some probabilities with Equation 4, the key simplifications made in this model will be summarized. They are . no intravenous drug use; . randomness in partner selection; no anal intercourse; . partners drawn only from the adolescent population; . a constant value of r, which applies to both males and females; and . a constant value of p during the period of sexual activity. To compute the cumulative probability of becoming infected during four years of adolescence, the following hypothetical values of the inputs are used:

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COST-EFFECTIVENESS ANALYSIS ~ 491 TABLE 1 Cumulative Probability of HIV Infection During Adolescence (Ages 15-18) as a Fraction of the Number of Sexual Partners, the Number of Sexual Exposures per Partner, and the Frequency of Condom Use Number of Frequency of Condom Usea Number of Exposures per Sexual Partners Partner - O 0.5 1.0 2 10 3.0 X 10-4 1.6 X 10-4 3.0 X 10-5 (-45%) ~-90%) 100 2.9 X 10-3 1.6 X 10-3 3.0 X 10-4 ~ - 44%) - ~ - 90~o) 750 1.6 X 10-2 1.0 X 10-2 2.2 X 10-3 ~ - 36%) ~ - 86%) 5 10 7.5 X 10-4 4.1 X 10-4 7.5 X 10-5 ~ - 45%) ~ - 90%) 100 7.1 X 10-3 4.0 X 10-3 7.5 X 10-4 (- 44%) ~ - 90%) 10 10 1.5 X 10-3 8.2 X 10-4 1.5 X 10-4 (-45%j (-90%) aValues in parentheses are percent reductions from the cumulative probability of HIV infec- tion under the baseline assumption of zero condom use. p = 0.015 (a constant rate) = 0.001 e = 0.90 f = to, 0.5, 1.04 n = [10,100, 750] m = t2, 5, 10] The corresponding hypothetical values of P are reporter! in Table 1. Note that hypothetical values have been used for the inputs because none of the true values for the U.S. teenage population is currently known with precision. The assumptions about teenage sexual behavior are roughly compatible with data reported in the 1987 National Academy of Sciences' report on adolescent sexuality and childbearing (Hayes, 1987; Hofferth and Hayes, 1987~. Given the hypothetical values for the inputs, condom use appears to be a highly effective AIDS prevention strategy. Among teenagers who are not very sexually active (e.g., m = 2, n = 10), half-time and full-time condom use cuts the cumulative risk of HIV infection by 45 and 90 percent, respectively. Among teenagers with a rela- tively large number of partners (e.g., m = 10, n = 10), half-time and

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492 ~ BACKGROUND PAPERS full-time condom use cuts the cumulative risk of infection by 45 and 90 percent, respectively. Among those with high frequency of inter- course (e.g., m = 2, n = 750), half-time and full-time condom use cuts the cumulative risk of infection by 36 and 86 percent, respectively. Whereas the absolute probabilities of HIV infection in Table 1 may be off the mark, there is nonetheless a strong suggestion that even halftime condom use produces significant reductions in the risk of HIV infection. In a recent analysis of 1,000 acts of anal intercourse with and without condoms, Fineberg (1988) showed that condom use is not always a highly effective prevention strategy. Where the prevalence of HIV infection is high among potential partners (e.g., 0.50), he found that half-time condom use produces virtually no benefit and full-time condom use cuts the cumulative risk of infection by 36 percent. He also found that the effectiveness of condoms against HIV infection diminishes rapidly among homosexuals who practice anal intercourse with large numbers of partners. It is reasonable to expect the relative effectiveness of condoms against HIV infection to be greater among heterosexual adolescents than among homosexuals. Heterosexual aclolescents draw partners from a population with relatively Tow rates of HIV prevalence com- pared to homosexuals. Moreover, homosexuals tend to practice sex more often and with more partners than heterosexual adolescents do. There is also reason to believe that anal intercourse is a more potent way to transmit the virus than vaginal intercourse. All of these factors help explain why the relative effectiveness of condom use (if not the absolute effectiveness) is larger among heterosexual adolescents than among homosexuals. Sensitivity Analysis of HIV Prevalence and Condom Efficacy To determine how confident one should be about condom effective- ness, sensitivity analysis was performed by increasing the value of p (HIV prevalence) from 0.015 to 0.2 and reducing the value of e (condom efficacy) from 0.9 to 0.5. The cumulative probabilities of HIV infection were then recalculated by using the same assumptions and Equation 4. Results of the sensitivity analysis are reported in Table 2. As expected, the absolute risk of infection is influenced significantly by the new values of p and e. However, the relative effectiveness of the

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COST-EFFECTIVENESS ANALYSIS ~ 493 TABLE 2 Sensitivity Analysis of P Under Alternative Assumptions About HIV Prevalence, Condom Efficacy, and Pattern of Sexual Activity Sexual Condom Activity Efficacy Frequency of Condom Usea f = O f = 0.5 f = 1.0 Assume HIV Prevalence = 0.015 m = 10, n = 10 m = 5, n = 100 m = 2,n = 750 m = 10, n = 10 m = 5, n = 100 m = 2, n = 750 0.9 0.5 0.9 0.5 0.9 0.5 0.9 0.5 0.9 0.5 0.9 0.5 1.5 X 10-3 1.5 X 10-3 7.1 X 10-3 7.1 X 10-3 1.6 X 10-2 1.6 X 10-2 Assume HIV Prevalence = 0.200 2.0 X 10-2 2.0 X 10-2 9.2 X 10-2 9.2 X 10-2 0.20 0.20 8.2 X 10-4 ( - 45%) 1.1 X 10-3 (-25%) 4.0 X 10-3 (- 44%) 5.4 X 10-3 (- 24%) 1.0 X 10-2 (-36%) 1.3 X 10-2 (- 18%) 1.1 x 10-2 ( - 45%) 1.5 X 10-2 ( - 25%) 5.2 X 10-2 ( - 43%) 7.0 X 10-2 (- 23%) 0.13 (-35%) 0.16 (- 18%) 1.5 X 10-4 ( - 90%) 7.5 X 10-4 ( - 50%) 7.5 X 10-4 ( - 90%) 3.7 X 10-3 (-49%) 2.2 X 10-3 (-86%) 9.4 X 10-3 ( -41%) 2.0 X 10-3 ( - 90%) 9.9 X 10-3 ( - 50%) 9.9 X 10-3 ( - 89%) 4.8 X 10-2 ( - 48%) 2.9 X 10-2 ( - 86%) 0.12 ( - 39%) NOTE: p = cumulative probability of HIV infection, m = number of partners, n = number of exposures. aValues in parentheses are percent reductions from the cumulative probability of HIV infec- tion under the baseline assumption of zero condom use.

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494 ~ BACKGROUND PAPERS condom remains quite significant. At p = 0.015 and e = 0.5, half- time and full-time condom use cut the cumulative risk of infection by 18-25 and 40-SO percent, respectively, (lepen(ling on the sexual activity assumptions. If e = 0.9 and p = 0.2, half-time and full-time condom use cut the risk by 40-50 and 86-90 percent, respectively, again depending upon the sexual activity assumptions. Because it is unlikely that any adolescent population is currently at p = 0.2 and it is likely that e > 0.5, condom use appears to be a promising strategy for reducing the risk of HIV infection among aclolescents. Accounting for Variations in Condom Use Among Adolescents Up to this point it has been assumed that condom use is uniform throughout the adolescent population (0, 50, or 100 percent). Sup- pose instead that condom use behavior in the population mirrors a probability distribution. To simplify, assume a discrete distribution, with three types of conclom users full-time users (fi), half time users (f2), and nonusers (fey. Each adolescent is assumer! to be in one of these three groups, Probi,F = fk3 = Xk. Given the constraint that ~3k=iXkfk = f, one must determine how different distributions of condom users influence the cumulative probability of HIV infection. Suppose, for example, that 50 percent of a(lolescent sexual expo- sures are protected by condoms (f = 0.5~. Although this coffin occur if all teens used condoms half the time, it could also result from half the teens using condoms all the time and the other half never using condoms. Under these circumstances, the probability of infection can be modeled in two ways: (1) the frequency of conclom use is linked to the person at risk of infection, or (2) the frequency of condom use is linked to the partners of those at risk. Both perspectives are modeled below. Taking the first perspective (the person at risk) and recalling Equation 4 lead to: P = 1{p[1r(1fee) + (1p j Am . (5) Here the value of f iS conditional on being in condom use group k; hence, the value of P is computed by assuming that the person at risk is in condom group k. If the person at risk exhibits all three types of condom use at different times, the cumulative risk of infection is

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COST-EFFECTIVENESS ANALYSIS ~ 495 obtained by: 3 P = 1~ Xk{p[1r(1fee)] + (1 p)} k=1 (6) This approach is somewhat awkward because it seems unnatural to assign the same person at risk to more than one condom-use group. The second approach defines condom-using groups in terms of the behavior of partners. The probability of no infection after n exposures with partners in group k is then: - p = pitr(1fEe)]n + (1p). If the partner is (lrawn randomly, the probability of infection is 3 P = p ~ Ok [1r(1fke)]n + (1p). k=1 Again, if m random partners are assumed 3 P = 1{P~Xk[lr(1fEe)]n + (1p)} k=1 . (7) (8) (9) The quantitative implications of this complication have been ex- plored for the case in which 50 percent of adolescent exposures are protected by condoms (f = 0.5~. It was assumed that either half of teens were full-time condom users and half nonusers or, alterna- tively, that all teens were half-time users. An attempt was made to determine which pattern of condom use would be most effective in preventing HIV infection. The hypothetical input values used to construct the probabilities in Table 1 were used again (p = 0.015, r = 0.001, e = 0.90), except that three groups of sexually active teens were examined (m = 10, n = 10; m = 5, n = 100; m = 2, n = 750~. The results, reported in Table 3, indicate that this refinement in the model does not make much difference. Given a particular value of f, it is only slightly better to see the average rate of condom use generate(1 by full-time condom users. Accounting for Heterogeneity of HIV Prevalence So far all members of the population at risk have been assumed to se- lect partners from the same HIV "prevalence pool." Suppose instead

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496 ~ BACKGROUND PAPERS TABLE 3 Cumulative Probability of HIV Infection Under Alternative Assumptions About the Fraction of Adolescents in Various Condom- Using Groups, Given That Half of Exposures Are Protected by Condoms Sexual Behavior Assumptions m = 10, m = 5, m = 2, Condom-Use Distribution - n - 10 n = 100 n = 750 1. (A =0,x2= 1.0,x3=0~: 2. (X} = 0.5, X2 = 0, x3 = 0.5) 8.2 X 10-4 8.2 X 10-4 4.0 X 10-3 3.9 X 10-3 1.0 X 10-2 9.0 X 10-3 NOTE: m = number of partners, n = number of exposures, xk = proportion of population in condom-use group k (1 = full-time user, 2 = half-time user, 3 = nonuser). aValues in parentheses are percent reductions from the cumulative probability of HIV infec- tion under the baseline assumption of zero condom use. that each member selects partners from one of several prevalence pools, in which the prevalence of HIV is pj. To simplify, let there be three pools with prevalence rates P~,P2, and pa. The probability that an at-risk adolescent draws from pool j is Vj. Let the constraint be that: 3 vjpj = p. j=1 (10) In previous calculations, it was assumed in effect that pi = P2 = pa = p = 0.015. Suppose instead that there is a small population of adolescents (v~ = 0.02) with high HIV prevalence Apt = 0.5), a large population (v2 = 0.48) with Tow prevalence (P2 = 0.01), and another large population (V3 = 0.50) with zero prevalence (p3 = 0~. The relative effectiveness of condom use uncler these circumstances must then be determinecl. To determine the cumulative probability of infection with three pools of HIV prevalence, 3 P = 1~vj{pj[1r(1fe)] + (1pi;)} j=1 (11) To estimate P. the hypothetical input values in Table 1 were used, and a sexually active group was the focus (m= 5, n = 100~. Condoms were still found to be quite effective. The figures in Table 4 for the m = 5, n = 100 group illustrate this point. If pi = 0.5, P2 = 0 01, pa = 0, and if vet = 0.02, v2 = 0.48, and V3 = 0.50,

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COST-EFFECTIVENESS ANALYSIS ~ 497 half-time and full-time condom use cut the risk of HIV infection by 42 and 89 percent, respectively. This rate of relative effectiveness is only slightly inferior to the relative effectiveness rates calculated in the case of a homogeneous HIV prevalence pool. Accounting for the Possibility of "Superinfectors" Suppose that all people infected with HIV are not equally infectious. In particular, assume that transmissibility (r) in the population of HIV positives exhibits a probability- distribution. To simplify, assume a discrete distribution with three levels of transmissibility fry. = highly infectious, r2 = somewhat infectious, r3 = not infectious) and ProbfR = ri) = wit Given that E3=~wiri = r, let us determine how the existence of "superinfectors" might influence the effectiveness of condoms against HIV. The probability of no infection given rz exposures with partner . in group ri IS P = p[1ri(1fe)]n + (1p)- If the partner is drawn randomly, 3 P = pit, witri(1fey)] + (1p). With m random partners, the probability of infection becomes (12) (13) TABLE 4 Cumulative Probability of HIV Infection if Three "Prevalence Pools" Are Assumed, Given Mean Prevalence of 0.015, Alternative Rates of Condom Use, and Specified Sexual Behavior Pattern (n = 100, m = 5) Frequency of One HIV Prevalence Three HIV Prevalence Condom Use Pool Pools 0 7.1 X 10-3 6.6 X 10-3 0.5 4.0 X 10-3 3.8 X 10-3 ~ - 44%) ~ - 42%) 1.0 7.5 X 10-4 7.3 X 10-4 ( - 89%~) ~ - 89%) NOTE: m = number of partners, n = number of exposures. aValues in parentheses are percent reductions from the cumulative probability of HIV infec- tion under the baseline assumption of zero condom use.

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498 ~ BACKGROUND PAPERS 3 P = 1 - {p~wi[1r:(1fe)] + (1P)} (14) i=1 The quantitative implications of this complication were explored for the case in which r = 0.001. In one scenario (Table 1), it was assumed that all HIV positives were infectious at the same rate, rat = r2 = r3 = r = 0.001. The alternative scenario presumes a small group Owl = 0.001) of "superinfectors" who are certain to infect their partners with a single unprotected sexual exposure Art = 1.0~. Everyone else who is infected is assumed not to be infectious (w2 = 0,W3 = 0.999,r3 = 01. Such an extreme case of heterogeneity in transmissibility substantially reduces the effectiveness of even full- time condom use, as Tong as n is fairly large (Table 5~. It is easy to visualize this phenomenon by considering the case in which the adolescent at risk has a "superinfectious" partner. Even if the person at risk is protected] by full-time condom use, the cu- mulative probability of infection increases rapidly as the number of exposures increases. Although the condom may be 90 percent effective per exposure, repeated exposures will ultimately infect the person at risk due to condom failure. The cumulative risk of infection is 0.65 from 10 "protected" exposures, 0.93 from 25 exposures, 0.995 from 50 exposures, and 0.99997 from 100 exposures. In a potential population of partners that is known to include such superinfectors, TABLE 5 Cumulative Probability of HIV Infection Under Alternative Assumptions About the Fraction of Partners in Various Transmissibility Groups ("superinfector" case) Sexual Behavior Assumptions Frequency of m = 10, m = 5, m = 2, Condom Use n = 10 n = 100 n = 750 0 1.5 X 10-4 7.5 X 10-5 3.0 X 10-5 0.5 1.5 X 10-4 7.5 X 10-5 3.0 X 10-5 (Togo) (~0%) (~0%) 1 9.8 X 10-5 7.5 X 10-5 3.0 X 10-5 (redo) (~0%) (~0%) NOTE: wl = 0.0G1, w2 = 0, W3 = 0.999 and r1 = 1, r2 = 0.5, r3 = 0, where Wok = propor- tion in population of transmissibility group k and rk = the risk of transmitting the virus. m = number of partners, n = number of exposures.

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