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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(1—fe).
(1)
If there are n exposures with the same infected partner, the risk of
infection becomes
P = 1—[1—r(1—fe)]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—[1—r(1—fe)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—{pL1—r(1—fell + (1—p))
(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[1—r(1—fee) + (1—p 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[1—r(1—fee)] + (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 = pit—r(1—fEe)]n + (1—p).
If the partner is (lrawn randomly, the probability of infection is
3
P = p ~ Ok [1—r(1—fke)]n + (1—p).
k=1
Again, if m random partners are assumed
3
P = 1—{P~Xk[l—r(1—fEe)]n + (1—p)}
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[1—r(1—fe)] + (1—pi;)}
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[1—ri(1—fe)]n + (1—p)-
If the partner is drawn randomly,
3
P = pit, wit—ri(1—fey)] + (1—p).
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[1—r:(1—fe)] + (1—P)} (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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