D
Description and Mathematical Statement of the HIV Prevention Resource Allocation Model

This appendix presents a brief description and mathematical statement of the model the Committee used to produce the examples discussed in Chapter 3. The Committee structured our analysis around four steps, which are briefly described below: estimating aggregate HIV incidence, estimating the efficacy and reach of HIV prevention programs, estimating the costs of HIV prevention, and allocating the HIV prevention budget to prevent as many new infections as possible.

ESTIMATING AGGREGATE HIV INCIDENCE

HIV incidence data broken down by location and HIV risk group are sorely lacking. The only description the Committee found of a systematic attempt to provide such estimates was a paper in the American Journal of Public Health (Holmberg, 1996). Our analysis uses estimates of HIV incidence broken down by injection drug users, men who have sex with men, and high-risk heterosexuals for 96 Standard Metropolitan Statistical Areas in the United States, aggregated to the state level. As discussed in Chapter 2 in this report, however, the systematic estimation of HIV incidence remains a crucial data need to effectively plan and evaluate HIV prevention programs.



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No Time to Lose: Getting More from HIV Prevention D Description and Mathematical Statement of the HIV Prevention Resource Allocation Model This appendix presents a brief description and mathematical statement of the model the Committee used to produce the examples discussed in Chapter 3. The Committee structured our analysis around four steps, which are briefly described below: estimating aggregate HIV incidence, estimating the efficacy and reach of HIV prevention programs, estimating the costs of HIV prevention, and allocating the HIV prevention budget to prevent as many new infections as possible. ESTIMATING AGGREGATE HIV INCIDENCE HIV incidence data broken down by location and HIV risk group are sorely lacking. The only description the Committee found of a systematic attempt to provide such estimates was a paper in the American Journal of Public Health (Holmberg, 1996). Our analysis uses estimates of HIV incidence broken down by injection drug users, men who have sex with men, and high-risk heterosexuals for 96 Standard Metropolitan Statistical Areas in the United States, aggregated to the state level. As discussed in Chapter 2 in this report, however, the systematic estimation of HIV incidence remains a crucial data need to effectively plan and evaluate HIV prevention programs.

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No Time to Lose: Getting More from HIV Prevention ESTIMATING THE EFFICACY AND REACH OF HIV PREVENTION PROGRAMS The Committee reviewed peer-reviewed publications reporting evaluations of HIV prevention programs. It has proven challenging to interpret such studies in terms of the relative reduction in the rate of new HIV infections implied by the programs examined. Yet, it is precisely this information about new infections that is required to sensibly consider the overall impact of alternative plans for distributing HIV prevention dollars. To develop data for this analysis, we reviewed in detail a subset of HIV prevention studies with an eye toward estimating the relative reduction in exposure to HIV risk as a result of prevention interventions aimed at men who have sex with men, injection drug users, and women at high risk for heterosexual transmission (see references at the end of this appendix for a listing of the studies reviewed). These three risk groups were selected to coincide with the risk group classification employed by Holmberg in estimating HIV incidence (Holmberg, 1996). Prevention efficacy, defined as the percentage reduction in new HIV infections, was estimated under the assumption that HIV incidence is proportional to the product of HIV prevalence and risky exposure rates (or “contact rates,” as defined in the mathematical epidemiology literature; see Anderson and May, 1991, and Kahn, 1996, for an example). There is little question that more work along these lines is needed in order to better understand the value of HIV prevention interventions. The Committee’s review of these studies also revealed that there were the high rates of subject attrition from the interventions evaluated. This observation led us to question the ability of many prevention programs to effectively reach and retain program participants over time. An intervention might be effective for program participants, but unable to reach more than, say, 10 percent of the total population. While many discussions of HIV prevention assume, in fact, that all persons at risk can be contacted, the Committee felt it was important to build into the analysis the recognition that not all of those at risk can be reached by interventions. Because no data exist on program reach, the Committee made some assumptions in the analysis to account for this fact. We assumed: 50 percent in the base case; 75 percent in the optimistic case; and 25 percent in the pessimistic case. THE COSTS OF HIV PREVENTION PROGRAMS The Committee notes that very few evaluations of HIV prevention programs report the costs of providing such services, though there are

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No Time to Lose: Getting More from HIV Prevention some exceptions (see Holtgrave, 1998). For each of the HIV prevention studies reviewed, a research assistant working with the Committee produced an estimate of the average cost per client enrolled, using resource-based costing (see Gorsky, 1996, for a description of the approach). Typical resources included the labor costs for program staff, materials, and administrative overhead. Low, medium, and high cost estimates for programs providing services to each of the three risk groups were developed. To complete Table 3.1, the low cost estimates were assigned to the optimistic scenario, high cost estimates to the pessimistic scenario, and medium cost estimates to the base case scenario. Note that we are not claiming that inexpensive programs are actually more effective than expensive programs. Rather, we have developed a range of scenarios reflecting optimistic, base, and pessimistic assumptions regarding HIV prevention. The optimistic scenario has high-end effectiveness estimates combined with low costs, while the pessimistic scenario has low-end effectiveness estimates combined with high costs. Nor are we claiming that the most expensive programs are least effective, or that the most effective programs are least expensive. Rather, the idea was to cover a wide range of possibilities with a very small number of scenarios. Some of the types of interventions used to construct the scenarios for the analysis include: individual risk reduction education, group counseling and skills training, community-level interventions in housing projects, identification and training of peer leaders to endorse and recommend safer-sex practices, counseling and HIV testing, partner notification, drug treatment, the provision of bleach for needle cleaning, needle exchange, and syringe access (e.g., via pharmacies).1 ALLOCATING RESOURCES FOR HIV PREVENTION Following the development of these data, the Committee employed a standard model to allocate resources in order to maximize the number of infections averted. The input quantities rij and nij were obtained from Holmberg’s 1996 study (see above). The input quantities cj, fj, and ej are all summarized in Table 3.1. The input parameter B, the budget, is varied in the analysis from $0 to $1 billion. The decision variables xij were optimally determined via the linear program. Once determined, the number of infections averted follows. The mathematical statement of this model is presented below: 1   For a complete list of interventions used in the analysis, see references at the end of this appendix.

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No Time to Lose: Getting More from HIV Prevention Let: xij = $ allocated for programs targeting risk group j in state i cj = cost per program participant in programs for risk group j ej = % reduction in the rate of new HIV infections for those in programs for risk group j fj = maximum % of population reachable in risk group j rij = annual number of new HIV infections in risk group j, state i nij = number of person in risk group j, state i B = HIV prevention budget Any proposed allocation of funds corresponds to specifying numerical values for the variables xij defined above. Estimating the number of infections averted that corresponds to a proposed funding allocation to programs for risk group j in state i requires four computational steps: (i) First, divide allocated amounts by per capita program costs to obtain the number of persons that could be reached: The number of persons reached with programs in j, state (ii) Second, compare the result of (i) to the maximum number of persons who can be reached to determine the actual number reached: The actual number of persons reached equals the minimum of and nij fj. (iii) Third, apply the percentage reductions in the rate of new infections to the appropriate HIV incidence base rate to obtain the annual number of new HIV infections averted per program participant: The number of HIV infections averted per program participant equals (iv) Fourth, multiply the number of program participants [from (ii)] by the number of HIV infections averted per program participant [from (iii)] to obtain the total number of infections averted. The number of infections prevented with programs in group j, state i = the number reached × rate of new infections × % reduction

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No Time to Lose: Getting More from HIV Prevention Cumulating over all locations and risk groups leads to an estimate of the total number of infections prevented under any given funding allocation. We have used the four-step procedure above to estimate the effectiveness of proportional allocation schemes in the examples discussed in Chapter 3 by choosing the funding amounts xij to be proportional to the rates of new infection rij in the Holmberg (1996) data set. To determine the allocation scheme that prevents as many infections as possible subject to a budget constraint requires selecting the funding amounts xij that solve the following linear program: In words, this formula says that funds should be allocated to programs for different risk groups in different states so as to maximize the number of HIV infections prevented. The constraints state: that the number of persons reached in any risk group and in any state cannot exceed the maximum number that can be reached; that the entire amount of money allocated cannot exceed the total HIV prevention budget; and that the amounts allocated toward any risk group in any state are nonnegative. For related technical literature describing the application of such models to HIV prevention, see Kahn (1996), Kaplan (1998), Kaplan and Pollack (1998), Paltiel and Stinnett (1998), and Richter, Brandeau and Owens (1999). For a didactic discussion of economic evaluation as it applies to HIV prevention, see Kaplan (1998). SPECIFIC REFERENCES USED IN DEVELOPING MODEL SCENARIOS FOR HIV PREVENTION Belcher L, Kalichman S, Topping M, Smith S, Emshoff J, Norris F, Nurss J. 1998. A randomized trial of a brief HIV risk reduction counseling intervention for women. Journal of Consulting and Clinical Psychology 66(5):856-861. Carey MP, Maisto SA, Kalichman SC, Forsyth AD, Wright EM, Johnson BT. 1997. Enhancing motivation to reduce the risk of HIV infection for economically disadvantaged urban women. Journal of Consulting and Clinical Psychology 65(4):531-541.

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No Time to Lose: Getting More from HIV Prevention Carey MP, Maisto SA, Kalichman SC, Forsyth AD, Wright EM, Johnson BT. 1997. Enhancing motivation to reduce the risk of HIV infection for economically disadvantaged urban women. Journal of Consulting and Clinical Psychology 65(4):531–541. Choi KH, Lew S, Vittinghoff E, Catania JA, Barrett DC, Coates TJ. 1996. The efficacy of brief group counseling in HIV risk reduction among homosexual Asian and Pacific Islander men. AIDS 10(1):81–87. DiClemente RJ and Wingood GM. 1995. A randomized controlled trial of an HIV sexual risk-reduction intervention for young African-American women. Journal of the American Medical Association 274(16):1271–1276. Hobfoll SE, Jackson AP, Lavin J, Britton PJ, Shepherd JB. 1994. Reducing inner-city women’s AIDS risk activities: a study of single, pregnant women. Health Psychology 13(5):397–403. Holtgrave DR (Ed.). 1998. Handbook of Economic Evaluation of HIV Prevention Programs. New York: Plenum Press. Holtgrave DR and Kelly JA. 1996. Preventing HIV/AIDS among high-risk urban women: The cost-effectiveness of a behavioral group intervention. American Journal of Public Health 86(10):1442–1445. Ickovics JR, Morrill AC, Beren SE, Walsh U, Rodin J. 1994. Limited effects of HIV counseling and testing for women. A prospective study of behavioral and psychological consequences. Journal of the American Medical Association 272(6):443–448. Kahn JG. 1998. Economic Evaluation of Primary HIV Prevention in Injection Drug Users. In Holtgrave DR, (Ed.), Handbook of Economic Evaluation of HIV Prevention Programs. New York: Plenum Press. Pp. 45–62. Kegeles SM, Hays RB, Coates TJ. 1996. The Mpowerment Project: A community-level HIV prevention intervention for young gay men. American Journal of Public Health 86(8 Pt 1):1129–1136. Kegeles SM, Hays RB, Pollack LM, Coates TJ. 1999. Mobilizing young gay and bisexual men for HIV prevention: A two-community study. AIDS 13(13):1753–1762. Kelly JA, Murphy DA, Sikkema KJ, McAuliffe TL, Roffman RA, Solomon LJ, Winett RA, Kalichman SC. 1997. Randomised, controlled, community-level HIV-prevention intervention for sexual-risk behaviour among homosexual men in U.S. cities. Community HIV Prevention Research Collaborative. Lancet 350(9090):1500–1505. Kelly JA, Murphy DA, Washington CD, Wilson TS, Koob JJ, Davis DR, Ledezma G, Davantes B. 1994. The effects of HIV/AIDS intervention groups for high-risk women in urban clinics. American Journal of Public Health 84(12):1918–1922. Kelly JA, St. Lawrence JS, Betts R, Brasfield TL, Hood HV. 1990. A skills-training group intervention model to assist persons in reducing risk behaviors for HIV infection. AIDS Education and Prevention 2(1):24–35. Kelly JA, St. Lawrence JS, Diaz YE, Stevenson LY, Hauth AC, Brasfield TL, Kalichman SC, Smith JE, Andrew ME. 1991. HIV risk behavior reduction following intervention with key opinion leaders of population: An experimental analysis. American Journal of Public Health 81(2):168–171. Kelly JA, St. Lawrence JS, Hood HV, Brasfield TL. 1989. Behavioral intervention to reduce AIDS risk activities. Journal of Consulting and Clinical Psychology 57(1):60–67. Kelly JA, St. Lawrence JS, Stevenson LY, Hauth AC, Kalichman SC, Diaz YE, Brasfield TL, Koob JJ, Morgan MG. 1992. Community AIDS/HIV risk reduction: the effects of endorsements by popular people in three cities. American Journal of Public Health 82(11):1483–1489.

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No Time to Lose: Getting More from HIV Prevention Peterson JL, Coates TJ, Catania J, Hauck WW, Acree M, Daigle D, Hillard B, Middleton L, Hearst N. 1996. Evaluation of an HIV risk reduction intervention among African-American homosexual and bisexual men. AIDS 10(3):319–325. Pinkerton SD, Holtgrave DR, DiFranceisco WJ, Stevenson LY, Kelly JA. 1998. Cost-effectiveness of a community-level HIV risk reduction intervention. American Journal of Public Health 88(8):1239–1242. Pinkerton SD, Holtgrave DR, Valdiserri RO. 1997. Cost-effectiveness of HIV-prevention skills training for men who have sex with men. AIDS 11(3):347–357. Richter A, Brandeau ML, Owens DK. 1999. An analysis of optimal resource allocation for prevention of infection with human immunodeficiency virus (HIV) in injection drug users and non-users. Medical Decision Making 19(2):167–179. Shain R, Piper J, Newton E, Perdue S, Ramos R, Champion J, Guerra F. 1999. A randomized controlled trail of a behavioral intervention to prevent sexually transmitted disease among minority women. New England Journal of Medicine 340(2):93–100. Sikkema KJ, Kelly JA, Winett RA, Solomon LJ, Cargill VA, Roffman RA, McAuliffe TL, Heckman TG, Anderson EA, Wagstaff DA, Norman AD, Perry MJ, Crumble DA, Mercer MB. 2000. Outcomes of a randomized community-level HIV prevention intervention for women living in 18 low-income housing developments. American Journal of Public Health 90(1):57–63. Stein JA, Nyamathi A, Kingston R. 1997. Change in AIDS risk behaviors among impoverished minority women after a community-based cognitive behavioral outreach program. Journal of Community Psychology 25:519–533. Valdiserri RO, Lyter DW, Leviton LC, Callahan CM, Kingsley LA, Rinaldo CR. 1989. AIDS prevention in homosexual and bisexual men: Results of a randomized trial evaluating two risk reduction interventions. AIDS 3(1):21–26. REFERENCES Anderson RM and May RM. 1991. Infectious Diseases of Humans: Dynamics and Control. Oxford University Press: Oxford, England. Gorsky RD. 1996. A method to measure the costs of counseling for HIV prevention. Public Health Reports 111(Suppl 1):115–122. Holmberg SD. 1996. The estimated prevalence and incidence of HIV in 96 large U.S. metropolitan areas. American Journal of Public Health 86:642–654. Holtgrave DR (Ed.). 1998. Handbook of Economic Evaluation of HIV Prevention Programs. New York: Plenum Press. Kahn JG. 1996. The cost-effectiveness of HIV prevention targeting: How much more bang for the buck? American Journal of Public Health. 86:1709–1712. Kaplan EH. 1998. Economic Evaluation and HIV Prevention Community Planning—A Policy Analyst’s Perspective. In Holtgrave DR (Ed.), Handbook of Economic Evaluation of HIV Prevention Programs. New York: Plenum Press. Pp. 177–193. Kaplan EH and Pollack H. 1998. Allocating HIV prevention resources. Socio-Economic Planning Sciences 32:257–263. Paltiel AD and Stinnett AA. 1998. Resource allocation and the funding of HIV prevention. In Holtgrave DR (Ed.), Handbook of Economic Evaluation of HIV Prevention Programs. New York: Plenum Press. Richter A, Brandeau ML, Owens DL. 1999. An analysis of optimal resource allocation for prevention of infection with human immunodeficiency virus (HIV) infection in drug users. Medical Decision Making 19(2):167–179.