Projections of the course of the HIV/AIDS epidemic are needed to plan for health care needs and for developing and evaluating prevention strategies. Previous local and national projections have suggested that the annual incidence of AIDS would increase through the late 1980s and then plateau by the early- to mid-1990s(1-4). However, those studies did not account for the 1993 revision in the definition of AIDS(5), and also did not predict when the eventual peak and decline in the overall incidence of AIDS might occur.
In this report, we project the incidence of AIDS in San Francisco, California through 1998 using a model whereby the distribution of AIDS cases is calculated based on the HIV infection and incubation period distributions. Our model also takes into account the 1993 revision in the definition of AIDS. San Francisco is an important location to model the course of the HIV/AIDS epidemic, because good data are available on the incidence of HIV in the populations at highest risk of infection.
Overview of the Model
We projected AIDS incidence in San Francisco through 1998, based on assumed HIV infection and incubation period distributions as has been described previously(1,2,6).
We estimated annual HIV seroconversions for homosexual and bisexual men and for heterosexual injecting drug users by applying annual HIV seroincidence rates to estimates of population size for these groups. To project the number of persons diagnosed with AIDS under the 1987 or earlier case definitions through December 31, 1992, annual HIV seroconversion estimates were combined with a series of nonstationary incubation period distributions resulting from the gradual introduction of therapy into the population of HIV-infected persons. Models were developed only for homosexual and bisexual men and for heterosexual injecting drug users, because these two groups constitute the predominance of the epidemic in San Francisco and because much less information is available for other risk populations.
For persons with HIV who had not yet progressed to AIDS by December 31, 1992, we applied Markov model (stage-specific) estimates of progression to CD4+ cell count <200 cells/mm3 to project the theoretical number of persons who would be diagnosed under the 1993 AIDS case definition. This theoretical number was then modified, based on the assumption that only a portion of these persons would be receiving medical care and have CD4 counts available when they met the new case definition. The remaining persons would be diagnosed later under the 1987 definition. Markov model distributions of time from CD4+ cell count <200 cells/mm3 to 1987 definition AIDS were used to estimate this temporal lag in diagnosis.
Trends in previously reported AIDS cases in San Francisco were used to calculate ratios of homosexual and bisexual men and heterosexual injecting drug users to other risk groups. Based on these ratios, we estimated the number of AIDS cases among other risk groups. The numbers of persons projected by risk group were then summed to obtain projections of the total number of persons with AIDS. The projections assume no case-reporting delay.
Size of the At-Risk Populations
The size of the population of homosexual and bisexual men in San Francisco was determined using estimates from a random-digit telephone survey conducted in 1989, which estimated that there were 35,999 openly homosexual or bisexual men aged 18 years and older who resided in households with telephones(7). This estimate was increased to include the estimated number of sexually active homosexual and bisexual youth <18 years of age, persons living in residences without telephones, or men unwilling to disclose same gender sexual behavior during a telephone interview, resulting in a final estimate of 57,922 homosexual and bisexual men in San Francisco.
This total includes an estimated 3000 homosexual and bisexual men who injected drugs in the previous 3 years. We subdivided the number of homosexual and bisexual men into high- and low-risk groups, based on residence inside or outside of the 19 census tracts of San Francisco with the highest cumulative AIDS incidence through 1983 as defined by a previous multistage population-based survey(8).
Estimates of the number of injecting drug users were calculated by two methods. First, estimates of the percentage of current users (past year) were obtained from several population-based surveys of risk behaviors conducted in San Francisco between 1989 and 1991(9-14). These percentages were then applied to 1990 census data to generate an estimate of 13,472 current users residing in San Francisco. The second method was based on unduplicated counts of injecting drug users who resided in San Francisco and who entered drug treatment facilities in San Francisco in fiscal year 1990 to 1991 (current users) or in calendar years 1988 to 1990 (recent users). These counts were adjusted to account for the proportion of injecting drug users who were not in treatment. Adjustments were based on data from street-based surveys of injecting drug users(15) and from a multistage population-based household survey(16). Adjusted estimates ranged from 12,186 current users to 21,447 recent users. We averaged the three estimates generated through these two methods, yielding a midpoint estimate of ∼16,000 current or recent injecting drug users in San Francisco. This total includes an estimated 13,000 heterosexual and 3000 homosexual and bisexual male injecting drug users; the latter group is incorporated only in the homosexual and bisexual male models.
The size of the at-risk populations was assumed to be stable throughout the study period except for homosexual and bisexual men. For this group, the model allowed for immigration of 900 homosexual and bisexual men per year beginning in 1984.
HIV seroincidence rates were estimated separately for high- and low-risk homosexual and bisexual men, based on residence inside or outside of the 19 high-risk census tracts in San Francisco as defined previously(8). HIV seroconversion rates for high-risk homosexual and bisexual men were based primarily on data from the San Francisco Men's Health Study (SFMHS), a cohort of 1034 single men randomly sampled in 1984 from households in the 19 high-risk census tracts(8). Annual HIV seroconversion rates among homosexual and bisexual men in this cohort were estimated to have declined from 18.4% during 1982 to 1984, to 1.2% by 1987(17). Because the SFMHS was begun in 1984, the seroconversion rates for the years 1982 and 1983 were estimated by comparing HIV seroprevalence on entry into the study for those participants with and without recent histories of risk behaviors(18). The HIV seroconversion rates for 1978 to 1981 were estimated by extrapolating the known points for the SFMHS to simulate the shape of the HIV seroincidence curve observed for 320 homosexual and bisexual men in the San Francisco City Clinic Cohort Study(19). Although directly measured seroconversion rates were available from the City Clinic Cohort Study before 1984, we based our model on the population-based SFMHS, because its estimates of HIV seroincidence were more likely to be representative of men in the 19 high-risk census tracts.
HIV seroconversion rates were not available for homosexual and bisexual men residing outside the 19 high-risk census tracts. An estimated HIV seroincidence curve was developed, which retained the shape of the high-risk seroincidence curve but that was scaled to fit the HIV prevalence rates (32% to 39%) observed among homosexual and bisexual men in population-based household surveys conducted in San Francisco neighborhoods outside the 19 high-risk census tracts(16,20).
From 1988 through 1998, HIV seroincidence rates were estimated to remain constant at 2% per year for homosexual and bisexual men residing inside the 19 high-risk census tracts, and 1% per year for those residing outside. These estimates were based in part on evidence of continued seroconversions among some participants in the large cohorts of homosexual and bisexual men(17,19) and on evidence of recent infections among young homosexual and bisexual men(21,22).
Estimates of HIV seroincidence for heterosexual injecting drug users were based in part on observed trends from serial clinic- and street-based cross-sectional surveys conducted in San Francisco between 1983 and 1991. Clinic-based surveys of injecting drug users entering methadone maintenance and detoxification programs in San Francisco have shown that HIV seroprevalence rose from ∼4% in 1983 through 1984 to a high of 13.5% in 1986 and 1987, and then fell to 8.7% by 1990(23,24). Street-based surveys of injecting drug users have observed that HIV seroprevalence stabilized between 11% and 14% during 1988 to 1992(15). We used the observed rise in HIV seroprevalence to estimate an HIV seroincidence rate of ∼3% annually between 1983 to 1984 and 1986, with an estimated peak of 3.8% in 1985. Because no data were available before 1983, estimates for those years were extrapolated to fit the trend for injection drug users diagnosed with AIDS in San Francisco.
HIV seroincidence for calendar year 1985 and thereafter was also based in part on seroconversion rates observed among a subset of injecting drug users who were repeatedly tested in clinic- and street-based settings in San Francisco. HIV seroincidence in those studies was estimated to have declined from a high of 3.9% in 1985 to a rate of 1.9% by 1990(23). We assumed that the HIV seroconversion rate would remain at ∼2% annually between 1987 and 1998.
Estimates of HIV seroincidence were not available before 1988 for other populations in San Francisco, including infants and children, and heterosexuals who were not injecting drug users. To estimate the projected number of AIDS cases due to secondary transmission of HIV from bisexual men or injection drug users to their partners and/or children, we computed the ratios of the observed number of AIDS cases among women and children to the projected numbers of AIDS cases among bisexual men and heterosexual injection drug users by year. These ratios were based on AIDS cases previously reported in San Francisco through December 31, 1991.
Incubation Period Distributions
We estimated the incubation period distribution for persons not receiving therapy by fitting a log-logistic distribution (median, 9.0 years) to Kaplan-Meier product-limit(25) estimates of the time from seroconversion to AIDS for homosexual and bisexual men enrolled in the San Francisco City Clinic Cohort study(19) and followed through mid-1987. We adjusted this distribution to create a series of nonstationary incubation period distributions to account for the introduction and phasing in of the use of therapy beginning in 1987. Based on previous studies(26-29), we assumed that the efficacy of treatment was equal to a reduction of relative risk for progression to AIDS of 0.5, representing a halving of the rate of progression to AIDS. We also assumed that the treatment relative risk was maintained for a period of 4 years, followed by a gradual return to a treatment relative risk of 1.0. This is based on several studies showing that the treatment benefit is temporary and confers no long-term survival advantage(30,31). Based on a previous study of homosexual and bisexual men in the SFMHS(32), we assumed that therapy was gradually phased into the population beginning in 1987, such that individuals infected in later time periods would have a greater opportunity to receive effective therapy at an earlier stage in their incubation period. Therapy was estimated to have been received by 50% of those homosexual and bisexual men and 25% of those heterosexual injecting drug users who were infected in 1978. Persons seroconverting in subsequent years were estimated to have increasing access to therapy, reaching a high of 85% for homosexual and bisexual men and 65% for heterosexual injecting drug users who seroconverted in 1984 or later.
For persons with HIV who had not yet progressed to AIDS by December 31, 1992, we applied the Markov model(33) (incubation period partitioned into discrete stages) to estimate time to progression to CD4 count <200 (median, 9.1 years for those receiving therapy and 7.4 years for those not receiving therapy) (I. Longini Jr, personal communication, 1992) to project the theoretical number of patients who would be diagnosed under the 1993 AIDS case definition. This theoretical number was then modified, based on the assumption that only 42% of these patients would be receiving medical care and have CD4 counts available when they met the new case definition. The estimate of 42% was an average of the estimates from three surveys conducted in San Francisco between 1989 and 1993(7,21,34). The remaining 58% would be diagnosed later under the 1987 definition. Markov model(33) distributions of time from CD4 count <200 to 1987-definition AIDS(median, 2.2 years for those receiving therapy and 1.1 years for those who did not) were used to estimate this temporal lag in diagnosis (I. Longini Jr, personal communication, 1992).
Our model is based on estimates of several uncertain parameters, including the size of the at-risk populations, HIV seroincidence, incubation period distributions, and proportion of persons receiving treatment. Because the input parameters of the model are uncertain, the values we compute are uncertain as well. We represent the uncertainty in the parameters by sampling values of the parameters from a uniform probability distribution, the upper and lower bounds of which are represented in Table 1. The upper and lower bounds were chosen to reflect a plausible range of uncertainty for each parameter.
To compute the uncertainty in the model due to these uncertain inputs, we select a Latin Hypercube sample size of 1000 from the distribution of the input parameters(35-38). This process results in 1000 different choices of the parameters and thus 1000 different model inputs. The model is run for each of the 1000 input scenarios, and 1000 output values are calculated. The observed distribution of output values indicates the uncertainty in the model predictions that result from the uncertain inputs.
To select a Latin Hypercube sample size of 1000, the range of each input parameter is divided into 1000 intervals of equal probability. For each of these intervals, a value is drawn from the conditional distribution of the input parameter, given that the value is within the interval, yielding 1000 values for each parameter. The values for the different parameters are then grouped at random in such a way that if a value for a given parameter is chosen from the ith interval of its range, then no other parameter's value may be chosen from the ith interval of its range.
By stratifying the marginal distribution of each input parameter and sampling once from each stratum, Latin Hypercube sampling ensures that the full range of each input parameter is covered more thoroughly while otherwise selecting the input parameter combinations as randomly as possible(39).
Observed AIDS Cases
Observed AIDS cases represent San Francisco residents and non-residents diagnosed in San Francisco and reported to the San Francisco Department of Public Health through December 31, 1996. Nonresident cases are included because some San Francisco residents are diagnosed in other counties, and our projected model does not allow for outward migration. Cases are unadjusted for reporting delays. Most AIDS cases in San Francisco are reported through an active surveillance system that includes 8 of 11 San Francisco hospitals and two outpatient clinics. Laboratory record reviews at these hospitals include review for opportunistic infections as well as CD4 counts meeting the 1993 case definition. CD4 count data are also received from two additional hospitals and from one commercial laboratory. Prior(40) and more recent validation studies have indicated that >90% of diagnosed cases are reported(San Francisco Department of Public Health, January 1995).
Figure 1 shows the HIV seroincidence for gay and bisexual men and heterosexual injection drug users. For gay and bisexual men, incidence of HIV infection is estimated to have peaked at 7600 and reduced to ∼500 infections per year from 1987 onward. For heterosexual injection drug users, there has not been a sizable decrease in HIV incidence. Infections peaked at 490 infections in 1985 and have remained level at 260 infections per year since 1987.
Table 2 gives the projected annual incidence of AIDS by gender, race/ethnicity, and risk group for San Francisco through December 1998. All of the subgroups show similar trends, with a peak in 1992, followed by a sharp decline in 1993. A continued decline is predicted through 1998 for homosexual and bisexual men and for both whites and ethnic minorities. However, the incidence of AIDS is predicted to increase slightly between 1994 and 1998 among women, heterosexual injecting drug users, and persons in other risk groups.
Figure 2 compares the projected incidence of AIDS to the number of reported cases from 1980 to 1995. The error bars for the projected cases indicate the minimum and maximum results from the 1000 scenarios in the uncertainty analysis. The reported AIDS cases reflect those cases reported to the San Francisco Department of Public Health through December 31, 1996, and are otherwise unadjusted for reporting delay. In general, the observed and projected epidemic curves show similar trends, with a peak in 1992 followed by a decline in subsequent years. Compared with observed cases, our model overestimates the incidence of AIDS between 1987 and 1992 and underestimates it for 1993 and 1994. The observed number of cumulative AIDS cases by 1995(22,915) falls within the predicted minimum (22,559) and maximum (27,844) of the model.
Our data suggest that the incidence of AIDS peaked in San Francisco in 1992 and is projected to decline annually through 1998. These trends reflect the dramatic reductions in new HIV infections among homosexual and bisexual men that occurred a decade ago and that were achieved as a result of significant changes in high-risk behaviors(17,19,41-43). The number of new AIDS cases are only now reflecting this change, because of the median 10-year incubation period between infection with HIV and development of AIDS(1,2). The trends are also affected by the expansion of the definition of AIDS in 1993, which resulted in AIDS being defined earlier in the course of HIV infection for many people(5). The inclusion of persons with HIV infection and a CD4+ T-lymphocyte count <200 resulted, on average, in the diagnosis of AIDS ∼19 months earlier in the course of infection(33). This has caused the epidemic curve to shift, because many cases that would have been diagnosed during 1993 and thereafter were identified and retrospectively diagnosed during earlier years.
Despite the decline in the overall annual incidence of AIDS in San Francisco, the incidence of AIDS is predicted to increase slightly between 1993 and 1998 among women, heterosexual injecting drug users, and persons in other risk groups. In addition, high rates of new HIV infections among some populations, particularly among young homosexual and bisexual men and other high-risk youth, could cause a resurgence of the overall epidemic at some point in the future(21,22). These trends underscore the fact that the HIV/AIDS epidemic is comprised of several subepidemics among various populations at risk.
This study has several limitations. There is uncertainty in the estimates of the size of the populations at risk and the incidence of HIV infection. This is especially true with regard to HIV incidence among women and ethnic minorities, because the large studies of homosexual and bisexual men established in San Francisco in the early 1980s did not include women or persons with other risk factors and included few ethnic minorities(8,19,20). Because of this limitation, we were unable to create separate submodels for projecting the trends among women or persons with other HIV risk factors, but instead used extrapolations of trends in previously reported AIDS cases by gender, race, and ethnicity. However, recent studies have shown that incidence of HIV infection has remained relatively low among women since 1988(16,44). We also were not able to make projections for blood product recipients; however, given the universal screening of blood components for HIV beginning in 1985, we would expect there to be only a few AIDS cases due to this exposure route in future years. Even for heterosexual injecting drug users for whom estimates of population size and HIV seroincidence exist, these estimates are subject to greater variability than those for homosexual and bisexual men. However, the vast majority of cases in San Francisco are among homosexual and bisexual men, and thus trends in other populations would have a relatively small impact on the overall estimates.
The uncertainty analysis provides an indication of the impact of varying population size, HIV incidence, and proportion of persons on treatment. When these parameters are varied, the error bars are reasonably narrow, indicating that our model is robust to sizable changes in these parameters. However, there remains a significant lack of fit for the years 1987 to 1994 between the number of reported AIDS cases and the projected number of AIDS cases. The model overestimates observed cases between 1987 and 1992 and underestimates them for 1993 and 1994. There are several possible explanations for this discrepancy. The adoption of the 1993 AIDS case definition substantially complicates projections of the AIDS epidemic. Prior AIDS definitions considered only specific AIDS opportunistic infections and malignancies. The vast majority of such conditions require medical attention and thus result in a report of AIDS. In contrast, the 1993 definition includes CD4 lymphocyte count<200 cells/µl or percentage <14% as an AIDS diagnosis(5). Such cases can only be reported if the individual accesses CD4 testing. It is possible that we overestimated the proportion of persons who had CD4 counts performed at the time they met the case definition. If a smaller proportion of individuals had timely CD4 counts, the result would be that more cases would be reported in subsequent years when these counts were performed or when the individuals subsequently developed reportable opportunistic infections or malignancies.
Another possible reason for the discrepancy is that we underestimated the incubation period between seroconversion and AIDS, which would also result in cases being diagnosed later than our model predicts. This could occur if zidovudine monotherapy was more available or more effective than predicted in our model. Similarly, the availability of prophylaxis against Pneumocystis carinii pneumonia may have resulted in persons being diagnosed with AIDS significantly later than predicted in our model(45,46). Reporting delay in observed cases could be responsible for some of the discrepancy. However, we present our reported cases only through December 1995 with updates through December 1996, which would minimize missed cases as a result of reporting delay.
Given the lack of fit for the years 1987 to 1994, how accurate are our projections of what would have been expected (assuming availability of only zidovudine monotherapy) for the period 1996 to 1998 likely to be? In support of our projections, we note that the projected and reported cases show the same overall pattern of a peak in 1992 and subsequent fall in the number of cases. The number of reported AIDS cases for 1995 falls within the range of our estimated cases for 1995. Also, our reported cumulative number of AIDS cases by 1995 falls within the predicted ranges of our model. This is due to the equalizing effect of the overestimation between 1987 and 1992 and the underestimation in 1993 and 1994. Nonetheless, we believe our model illustrates the challenges of projecting AIDS cases in the context of the 1993 change in the AIDS definition and the availability of therapy, even in a city such as San Francisco with extensive data on HIV infection rates and highly complete AIDS reporting.
Both our projected model and our observed model indicate a peak and decline in AIDS incidence. Recent national reports have also demonstrated a decrease in AIDS incidence and mortality(47) among gay and bisexual men. Much of this decline is being attributed to the effect of therapy. Although combination antiretroviral therapy with protease inhibitors clearly improves survival(48), our analysis shows that San Francisco would have experienced a significant decline in AIDS cases, due to the decrease in HIV seroconversions, even if combination antiretroviral therapy had not been developed. In our model, we assumed that the benefit of treatment was sustained for a 4-year period, followed by a gradual return to no benefit of treatment. This is based on most studies of the effect of zidovudine monotherapy(30,31). Our projections do not include the efficacy of these new combination regimens, because too few patients without AIDS were treated with these medications until 1997. The value of our projections is that they serve as a bench-mark for how much decline in AIDS one would have expected in a city like San Francisco before the advent of protease inhibitors. Decreases beyond this level may well be due to the effect of these drugs.
One of the strengths of our model is that it illustrates how dependent AIDS incidence is on the rate of HIV seroincidence. We project that women and heterosexual injection drug users, in contrast to gay and bisexual men, will experience an increase in AIDS cases between 1993 and 1998. The reason is that HIV incidence did not decline precipitously in the early 1980s for this group. It is worth noting in this regard that the national decrease in AIDS cases and deaths has not occurred among women or injection drug users(47).
We are concerned that some policy makers may use our projections showing a decline in the numbers of AIDS cases in San Francisco as evidence that less funding is needed for AIDS treatment. It must be remembered that although the numbers of new cases is declining, the number of people living with AIDS is not declining because of the increases in survival(47). Moreover, the costs of caring for those living with AIDS is increasing(49). Factors contributing to the increased cost include longer hospitalizations, more expensive therapies, and the need to provide nonmedical services for an increasing proportion of AIDS patients who are living in poverty(50-52).
Acknowledgments: This study was funded by grant U62/CCU906255-03 from the Centers for Disease Control and Prevention. We thank Lowell Barnhart, David Makofsky, and Kurt Scheer for assistance with the analysis.
1. Bacchetti P, Moss AR. Incubation period
of AIDS in San Francisco.Nature
2. Lemp GF, Payne SF, Rutherford GW, et al. Projections of AIDS morbidity and mortality in San Francisco. JAMA
3. Brookmeyer R. Reconstruction and future trends of the AIDS epidemic in the United States. Science
4. Centers for Disease Control and Prevention. Projections of the number of persons diagnosed with AIDS and the number of immunosuppressed HIV
-infected persons, United States, 1992-1994.MMWR Morbid Mortal Wkly Rep
5. Centers for Disease Control and Prevention. 1993 Revised classification system for HIV
infection and expanded surveillance case definition for AIDS among adolescents and adults. MMWR Morbid Mortal Wkly Rep
6. Brookmeyer R, Gail MH. Minimum size of the acquired immunodeficiency syndrome (AIDS) epidemic in the United States. Lancet
7.HIV-related knowledge, attitudes, and behaviors among San Francisco gay and bisexual men: results from the fifth population-based survey
. San Francisco: Communication Technologies, 1990.
8. Winkelstein W Jr, Lyman DM, Padian N, et al. Sexual practices and risk of infection by the human immunodeficiency virus: the San Francisco Men's Health Study. JAMA
9.A report on the first tracking survey of AIDS knowledge, attitudes, and behaviors in San Francisco's Black communities: 1988-1989
. San Francisco: Polaris Research and Development, 1989.
10.Report on a tracking survey of AIDS knowledge, attitudes and behaviors in San Francisco's Latino Communities
. San Francisco: Fairbank, Bregman and Maullin, 1989.
11.AIDS knowledge, attitudes, beliefs and behaviors in Southeast Asian communities in San Francisco
. San Francisco: Center for Southeast Asian Refugee Resettlement, 1991.
12.AIDS knowledge, attitudes, beliefs and behaviors in a household survey of Filipinos in San Francisco
. San Francisco: The Asian American Health Forum and the Filipino Task Force on AIDS, 1990.
13.Report on a survey of AIDS knowledge, attitudes and behaviors in San Francisco's Japanese communities
. San Francisco: Asian American Recovery Services, 1990.
14.Report on a survey of AIDS knowledge, attitudes and behaviors in San Francisco's Chinese communities
. San Francisco: Asian American Recovery Services, 1990.
15. Watters JK. Trends in risk behavior and HIV
seroprevalence in heterosexual injection drug users in San Francisco, 1986-1992. J Acquir Immune Defic Syndr
16. Fullilove MT, Wiley J, Fullilove RE III, et al. Risk for AIDS in multiethnic neighborhoods in San Francisco, California: The population-based AMEN study. West J Med
17. Winkelstein W Jr, Wiley JA, Padian NS, et al. The San Francisco Men's Health Study: continued decline in HIV
seroconversion rates among homosexual/bisexual men. Am J Public Health
18. Winkelstein W Jr, Samuel M, Padian NS, et al. The San Francisco Men's Health Study: III. Reduction in human immunodeficiency virus transmission among homosexual/bisexual men, 1982-86. Am J Public Health
19. Hessol NA, Lifson AR, O'Malley PM, Doll LS, Jaffe HW, Rutherford GW. Prevalence, incidence, and progression of human immunodeficiency virus infection in homosexual and bisexual men in hepatitis B vaccine trials, 1978-1988. Am J Epidemiol
20. Moss AR, Bacchetti P, Osmond D, et al. Seropositivity for HIV
and the development of AIDS or AIDS related condition: three year follow up of the San Francisco General Hospital cohort. Br Med J
21. Lemp GF, Hirozawa AM, Givertz D, et al. Seroprevalence of HIV
and risk behaviors among young homosexual and bisexual men: The San Francisco/Berkeley Young Men's Survey. JAMA
22. Osmond DH, Page K, Wiley J, et al. HIV
infection in homosexual and bisexual men 18 to 29 years of age: The San Francisco Young Men's Health Study. Am J Public Health
23. Moss AR, Vranizan K, Gorter R, Bacchetti P, Watters J, Osmond D. HIV
seroconversion in intravenous drug users in San Francisco, 1985-1990. AIDS
24. Moss AR, Chaisson RE. AIDS and intravenous drug use in San Francisco. AIDS Public Policy
25. Benedetti J, Yuen K, Young L. Life tables and survival functions. In: Dixon WJ, ed. BMDP Statistical Software
. Berkeley, California: University of California Press, 1985:557-75.
26. Volberding PA, Lagakos SW, Koch MA, et al. Zidovudine in asymptomatic human immunodeficiency virus infection: a controlled trial in persons with fewer than 500 CD4-positive cells per cubic millimeter. N Engl J Med
27. Fischl MA, Richman DD, Hansen N, et al. The safety and efficacy of zidovudine (AZT) in the treatment of subjects with mildly symptomatic human immunodeficiency virus type 1 (HIV
) infection: a double-blind, placebo-controlled trial. Ann Intern Med
28. Golden JA, Chernoff D, Hollander H, Feigal D, Conte J. Prevention of Pneumocystis carinii pneumonia by inhaled pentamidine.Lancet
29. Graham NMH, Zeger SL, Park LP, et al. Effect of zidovudine and Pneumocystis carinii pneumonia prophylaxis on progression of HIV
-1 infection to AIDS. Lancet
30. Volberding PA, Lagakos SW, Grimes JM, et al. The duration of zidovudine benefit in persons with asymptomatic HIV
infection. Prolonged evaluation of Protocol 019 of the AIDS clinical trials group. JAMA
31. Concorde Coordinating Committee. Concorde: MRC/ANRS randomised double-blind controlled trial of immediate and deferred zidovudine in symptom-free HIV
32. Rosenberg PS, Gail MH, Schrager LK, et al. National AIDS incidence
trends and the extent of zidovudine therapy in selected demographic and transmission groups. J Acquir Immune Defic Syndr
33. Longini IM Jr, Clark WS, Gardner LI, Brundage JF. The dynamics of CD4+ T-lymphocyte decline in HIV
-infected individuals: a Markov modeling approach. J Acquir Immune Defic Syndr
34. A survey of AIDS knowledge, attitudes and behaviors in San Francisco's American Indian, Filipino and Latino gay and bisexual male communities. San Francisco: Fairbank, Bregman, and Maullin, 1991.
35. Blower SM, Bowlatabadi H. Sensitivity and uncertainty analysis of complex models of disease transmission. Int Stat Rev
36. Blower SM, McLean AR, Porco TC, et al. The intrinsic transmission dynamics of tuberculosis epidemics. Nature Med
37. Iman RL, Helton JC, Campbell JE. An approach to sensitivity analysis of computer models: Part I-introduction, input variable selection and preliminary variable assessment. J Qual Technol
38. Iman RL, Helton JC, Campbell JE. An approach to sensitivity analysis of computer models: Part II-ranking of input variables, response surface validation, distribution effect, and technique synopsis variable assessment. J Qual Technol
39. Stein M. Large sample properties of simulations using Latin Hypercube sampling. Technometrika
40. Lemp GF, Hirozawa AM, Cohen JB, Derish PA, McKinney KC, Hernandez SR. Survival for women and men with AIDS. J Infect Dis
41. McKusick L, Coates TJ, Morin SF, Pollack L, Hoff C. Longitudinal predictors of reductions in unprotected anal intercourse among gay men in San Francisco: The AIDS Behavioral Research Project. Am J Public Health
42. Katz MH. AIDS Epidemic in San Francisco among men who report sex with men: successes and challenges of HIV
43. Stryker J, Coates TJ, DeCarlo P, Haynes-Sanstad K, Shriver M, Makadon HJ. Prevention of HIV
infection: looking back, looking ahead. JAMA
44. San Francisco Department of Public Health AIDS Office. HIV Seroprevalence Report
45. Bozzette SA, Finkelstein DM, Spector SA, et al. A randomized trial of three antipneumocystis agents in patients with advanced human immunodeficiency virus infection. N Engl J Med
46. Clumeck N. Primary prophylaxis against opportunistic infections in patients with AIDS. N Engl J Med
47. Centers for Disease Control, and Prevention. Update: trends in AIDS incidence
, deaths, and prevalence-United States, 1996.MMWR
48. Deeks SG, Smith M, Holondiy M, Kahn JO. HIV
-1 protease inhibitors: A review for clinicians. JAMA
49. Hellinger FJ. Forecasts of the costs of medical care for persons with HIV
: 1992-1995. Inquiry
50. Smith NY, Rapkin BD. Unmet needs for help among persons with AIDS. AIDS Care
51. Piette JD, Fleishman JA, Stein MD, Mor V, Mayer K. Perceived needs and unmet needs for formal services among people with HIV
disease. J Community Health
52. Marx R, Katz MH, Park M-S, Gurley RJ. Meeting the service needs of HIV
-infected persons: is the Ryan White Care Act succeeding?JAIDS