Determining the contribution of recent transmission of Mycobacterium tuberculosis to the overall burden of tuberculosis (TB) cases is important both to understanding the impact of contemporary measures taken to control M. tuberculosis transmission and predicting the future course of the epidemic. Several studies conducted in various urban settings of the United States have estimated that the percentage of TB cases due to recent M. tuberculosis transmission is substantial; estimates range from 31% in San Francisco, to 37.5% in the Bronx, to 59% in Los Angeles. ^{1–3} These studies were based on the hypothesis that TB cases harboring M. tuberculosis strains with a common deoxyribonucleic acid (DNA) fingerprint (as determined by the number and pattern of copies of the insertion element IS6110, ^{4} supplemented by secondary typing methods in at least one study) ^{3} must be linked epidemiologically, that is, must be part of a recent chain of transmission. This hypothesis has received support from studies of outbreaks in institutions and within constrained social settings, which demonstrated that time- and space-linked TB cases do share a common DNA fingerprint. ^{5–9}

Whether cases with a common fingerprint necessarily represent a chain of recent transmission, however, remains uncertain. Investigators in San Francisco, finding no obvious association between TB cases sharing a common DNA fingerprint, inferred that in these cases, M. tuberculosis infection had been transmitted recently but through exposures that were neither prolonged nor intense. ^{2} Other investigators have concluded that the lack of an epidemiologic link between clustered TB strains may result from the difficulty in carrying out a retrospective epidemiologic study. ^{10} It is also possible, however, that multiple cases with similar fingerprints represent a high level of endemicity of the strain type in question. This uncertainty about interpretation underlies molecular studies aimed at understanding the dynamics of TB epidemics.

To evaluate the importance of recent M. tuberculosis transmission, we took an approach that is completely independent of DNA fingerprint results. Specifically, we constructed a mathematical model of the average number of secondary cases of active TB produced within 1 year of infection by a single active TB case. This quantity, which we call the short-term reproductive number of TB , is a modification of the reproductive number of TB, the average number of active TB cases ever produced by a single infectious TB case. ^{11} The short-term reproductive number generalizes the notion by Blower et al ^{11} of the reproductive number of “fast TB” in the absence of TB treatment to a context where a TB treatment program is operating. From our model, we calculated upper and lower bounds of the percentage of current TB cases estimated to be due to recent transmission in different neighborhoods of New York City for the years 1989–1993.

Subjects and Methods
The goal of our analysis was to estimate the percentage of current-year TB cases attributable to M. tuberculosis infections that were reported in the previous year, in a large geographic entity, New York City, of primary importance to recent TB trends in the United States. At its peak, in 1991, New York City accounted for 14.3% of all TB cases in the United States, with a rate of 52.0 cases per 100,000 person-years. ^{12}

We sought to accomplish this goal by estimating two quantities:n , the number of cases of infectious TB 1 year ago, and R _{s} , the short-term reproductive number. The short-term reproductive number can be thought of as the average number of active TB cases produced by a single infectious case within 1 year of contact. The product of n and R _{s} is the number of short-incubating current-year cases; dividing by the total TB case burden in the following year gives the percentage of new cases arising from infections acquired in the previous year.

Clearly, both the infectious-case burden and infectivity might vary with time and place. Temporal trends in these quantities might be ignored if TB occurrence is in a stable equilibrium in the population of interest, or smoothed if TB incidence is either rising or falling. Spatial variation is more problematic. Because we suspected that R _{s} might vary from one neighborhood to another in New York City, and we know that n (the case burden) varies appreciably with neighborhood, we set out to estimate these quantities in a way that would reflect the contribution of different parts of the city. And, because immune deficit from human immunodeficiency virus (HIV) infection can affect the transmission ^{13,14} and pathogeneticity ^{15} of M. tuberculosis , we carried out our estimation separately for HIV-infected and -uninfected cases and summed the results to arrive at a final estimate.

Data and Subjects
We studied all cases of infectious TB, that is, TB with pulmonary involvement, reported to the New York City Department of Health Bureau of Tuberculosis Control during the years 1988–1992. In these years, there were respectively 1,903, 2,131, 2,966, 3,117, and 3,261 infectious TB cases, representing respectively 83%, 84%, 85%, 85%, and 87% of all TB cases. The unit of analysis was the neighborhood. The United Health Fund defines 41 neighborhoods in New York City, which serve as a basis for reporting of health data. Here, we combined several neighborhoods with low TB incidence together, resulting in 33 units for analysis.

Mathematical Model 1: Prevalence of HIV Infection among TB Cases
Our first step was to estimate the prevalence of HIV infection among TB cases by neighborhood and by year. As data on HIV status of infectious TB cases by year and by neighborhood were not available for the years in question, we constructed a mathematical model of HIV seroprevalence among all TB cases, pulmonary and otherwise; first, we assumed that the distribution of HIV infection among cases with pulmonary involvement is similar to the distribution of HIV infection among all TB cases, even those with extrapulmonary TB only. Then we proceeded to model the spatial (that is, neighborhood-to-neighborhood) and temporal (that is, year-to-year) variation in HIV prevalence among TB cases. Thus, the model has two pieces.

Spatial Variation among Neighborhoods
We used data on cumulative HIV seroprevalence among TB patients who had been seen at New York City Department of Health TB clinics during the years 1988–1992. The Office of AIDS Research, New York City Department of Health, tested remnant blood samples from patients who had been seen at these clinics for the presence of antibodies to HIV. These results provided estimates of cumulative HIV seroprevalence for each neighborhood. We smoothed the set of estimates for the constituent neighborhoods using the method of median polish. ^{16} This procedure yielded 33 values of x _{i} , the neighborhood-specific smoothed HIV seroprevalence (i = 1–33).

We calculated weighted citywide mean JOURNAL/epide/04.03/00001648-200007000-00006/OV0335/v/2021-02-05T035758Z/r/image-png and weighted standard deviation s of HIV seropositivity from {x _{i} }, with weights given by the number of TB cases tested. We calculated a standard score for each neighborhood from its smoothed estimate x _{i} , the weighted mean JOURNAL/epide/04.03/00001648-200007000-00006/OV0335/v/2021-02-05T035758Z/r/image-png , and the weighted standard deviation s as z _{i} = (x _{i} – JOURNAL/epide/04.03/00001648-200007000-00006/OV0335/v/2021-02-05T035758Z/r/image-png)/s . We assumed spatial variation to be constant over time in the sense that the standard scores z _{i} are independent of calendar year.

Temporal Trends in New York Citywide HIV Seroprevalence among TB Cases
For each year (j ), we calculated an average (m _{j} ) from those studies having estimates of HIV seroprevalence among TB cases in New York City for year j . ^{17–20} (We excluded studies that investigated the seroprevalence of HIV in a limited geographic area of New York City, such as those that examined HIV seroprevalence of TB cases seen at a particular New York City hospital or Department of Health TB clinic.) From a collection of four studies, in any given year, there were a maximum of four and a minimum of two studies with estimates for that year.

Study-specific estimates of the citywide prevalence of HIV infection or AIDS among TB cases for the years 1988–1992 are presented in Figure 1 . Of the four studies cited, one conducted anonymous HIV-seroprevalence testing of cases seen at New York City Department of Health TB clinics, ^{19} one matched cases appearing on the New York City TB registry against cases appearing in the New York City AIDS registry, ^{18} and two examined International Classification of Diseases (9th revision) codes indicating an AIDS-defining illness among hospitalized TB patients in New York City. ^{17,20} In the study using matching as a surrogate for HIV infection among TB patients, the investigators noted that TB diagnoses tended to occur in close temporal proximity to AIDS diagnoses, ^{18} and thus HIV infection was likely to be already present at the time of TB diagnosis.

FIGURE 1: Percentage of TB cases with AIDS or HIV infection, New York City, 1988–1992: results of literature search. ♦, Arno et al ^{17} ; ○, Burwen et al ^{18} ; *, Greenberg et al ^{19} ; ▴, Kaufman et al . ^{20}

To construct the spatiotemporal model of the prevalence of HIV infection among TB cases, in addition to the standard score z _{i} and the annual citywide mean m _{j} we needed an annual estimate of the standard deviation of neighborhood-specific HIV prevalences, taken over all neighborhoods. We modeled temporal trends in the standard deviation s _{j} by assuming that the coefficient of variation c = s/ JOURNAL/epide/04.03/00001648-200007000-00006/OV0335/v/2021-02-05T035758Z/r/image-png was constant over time; thus, we calculated s _{j} as s _{j} = m _{j} × c . Then we calculated x _{ij} , the prevalence of HIV infection among TB cases in neighborhood i for year j , as x _{ij} = m _{j} + z _{i} × s _{j} . Finally, we calculated n _{ij} , the number of HIV-positive TB cases, as n _{ij} ^{+} = x _{ij} × N _{ij} , where N _{ij} is the number of TB cases in neighborhood i in year j . We calculated the number of HIV-negative TB cases by subtraction:n _{ij} ^{–} = N _{ij} – n _{ij} .

Mathematical Model 2: Short-Term Reproductive Number of TB
The next step was to calculate R _{s} , the short-term reproductive number of TB. R _{s} , the average number of active TB cases developing within 1 year of infection by a single TB index case, can be expressed as the product of three quantities: the average number of new infections caused by each case per year of infectiousness, the average duration of infectiousness, and the probability of progressing to active TB within 1 year after infection. Thus, R _{s} can be computed from the following formula : where I = the average number of infections caused by one TB case per year of infectiousness, t = the average duration of infectiousness, and P = the probability of progression to active TB within 1 year of infection.

As each of these quantities might be affected by the presence of HIV infection, we calculated R _{s} separately for HIV-positive and HIV-negative TB.

Blower et al ^{21} estimated the average duration of infectiousness of TB in the presence of treatment as MATH 2 where Φ = cumulative TB treatment rate, μ = death rate, and μ_{T} = rate of death due to untreated TB.

In other words, the average duration of infectiousness is given by the probability of not having been successfully treated times the average survival of people with untreated TB.

Estimation of R _{s}
We estimated I , P , Φ, μ, and μ_{T} separately for HIV-positive and HIV-negative persons and thereby calculated R _{s} and R _{s} ^{−} . Where possible, we derived parameter estimates from the existing literature or calculated from neighborhood-specific data. We estimated four of the five parameters, namely I , Φ, μ, and μ_{T} , according to the HIV status of the TB cases, whereas we estimated the remaining parameter P according to the HIV status of the those susceptible to TB. For estimates of the parameters I and I ^{−} , the average number of M. tuberculosis infections caused, respectively, by an HIV-positive or HIV-negative infectious TB case, we established highest and lowest reasonable values. We computed the highest (lowest) estimate of t in turn from the set of lowest (highest) estimates of Φ, μ, and μ_{T} . We calculated upper (lower) bounds on R _{s} by multiplying the estimate of P by the highest (lowest) estimates of I and t . Table 1 describes the parameters and gives sources of estimates.

Table 1: Parameter Values by HIV Status of TB Index Case/TB Susceptible

Estimates of the number of secondary infections caused by a single HIV-negative TB case, I ^{−} , are found in Styblo. ^{22} To estimate I , the average number of secondary infections caused by one infectious TB case with HIV infection over a year’s time, we calculated the ratio of prevalence of purified protein derivative (of tuberculin) positivity among contacts of HIV-positive index cases to the prevalence in contacts of HIV-negative index cases as described in Cauthen et al ^{13} and Elliot et al . ^{14} We multiplied estimates of the number of secondary infections caused by a single HIV-negative TB case by the resulting ratios to give a lower bound of 6 and an upper bound of 10 secondary infections per year.

We calculated neighborhood-specific death rates for non-AIDS/non-HIV causes of death for the years 1988–1992, as follows: the numerator is given by the annual number of non-AIDS, non-HIV deaths by neighborhood. The denominator is the annual neighborhood-specific population at risk of death from non-AIDS, non-HIV causes of death [= neighborhood population − (number of AIDS cases diagnosed in previous years still alive in the year of interest + number of AIDS cases diagnosed in the year of interest + number of persons likely to have advanced HIV disease in the year of interest, that is, the number of AIDS cases diagnosed in the following year)]. ^{23,24}

We estimated the annual death rate for persons at risk of death from HIV infection (that is, subsequent to a diagnosis of AIDS) from survival data presented in a study of New York City AIDS cases during the years 1980–1989. Two years after a diagnosis of AIDS, 31.9% of cases were still alive, and 22.5% were still alive after 3 years. ^{25} Assuming an exponential survival distribution, the upper bound for μ is 0.571, or 571 deaths per 1,000 AIDS cases per year [from the solution to the equation exp(–2μ) = 0.319]. From the equation exp(–3μ) = 0.225, the lower bound for μ is 0.497, or 497 deaths per 1,000 AIDS cases per year. Neighborhood-specific estimates of this death rate were not available.

We assumed a death rate of 50% within 5 years for untreated TB without HIV infection by relying on TB surveillance records assembled before the introduction of therapy. ^{26} Assuming an exponential survival model, as in Blower et al , ^{21} then exp(–5μ_{T} ) = 0.50, or μ_{T} = 0.139. For TB cases with HIV infection, we assumed that the rate of death due to untreated TB was the same as the rate of death due to untreated TB in persons without HIV infection, as the majority of deaths in patients with both TB and AIDS are due to non-TB causes. ^{27,28}

We assumed a cumulative TB treatment rate of 95% for TB cases without HIV infection and 80% for TB cases with HIV infection/AIDS. These rates are equivalent to those observed in an autopsy study that found that at most 5% of pulmonary TB vs 20% of extrapulmonary TB was diagnosed after death. ^{29} Pulmonary TB cases with AIDS are more likely than those without AIDS to have extrapulmonary involvement and anergy and less likely to have cavitary disease. ^{28,30,31} Thus, we assume that TB cases with AIDS are as unlikely to remain undiagnosed as TB cases with extrapulmonary involvement only.

The probability of progression from M. tuberculosis infection to active disease within 1 year of infection depends on the HIV status of those susceptible to TB. Thus, to quantify this probability, we need to make assumptions about the HIV status distribution among susceptible individuals coming into contact with HIV-negative and HIV-positive TB cases. For HIV-negative TB cases, we assumed that virtually all those susceptible to TB who came into contact with them were HIV negative. For HIV-positive TB cases, we assumed that 50% of susceptible individuals who came into contact with them were HIV negative and 50% were HIV positive. We based this last assumption on the results of studies showing that the HIV seroprevalence among intravenous drug users in New York City was approximately 50% during the years 1984–1992 ^{32} and that intravenous drug use is an important risk factor for HIV-associated TB in New York City. ^{19,20,30,31,33,34} Thus, for HIV-negative TB cases, the probability of progression in infected contacts is 0.05, whereas for TB cases with HIV infection, the average probability of progression in infected contacts is 0.05 × 0.50 + 0.10 × 0.50 = 0.075.

The Percentage of TB Cases Due to Infection Acquired 1 Year Ago
The annual number of cases of TB in a given year due to recent infection (that is, ≤1 year ago) is given by MATH 3 where n ^{–} (n ) is the number of cases of infectious TB in the previous year for TB cases without (with) HIV infection, and R _{s} ^{–} (R _{s} ^{+} ) is the short-term reproductive number for HIV-negative (HIV-positive) index cases.

We then obtained the percentage of TB cases due to recent infection by dividing the above expression by the total number of TB cases in a given year.

Results
Prevalence of HIV Infection among TB Cases
As estimated from remnant blood samples collected at Department of Health TB clinics, the mean cumulative prevalence of HIV infection for the years 1988–1992, JOURNAL/epide/04.03/00001648-200007000-00006/OV0335/v/2021-02-05T035758Z/r/image-png , was 44.4% (range = 6.7–68.4%), and the standard deviation, s , was 14.1%. The coefficient of variation, c , was thus 0.141/0.444 = 0.318. The annual citywide mean HIV seroprevalence among TB cases (as calculated from the five studies) was 27.4%, 36.1%, 32.9%, 34.3%, and 46.6%, respectively, for the years 1988–1992. Seroprevalence of HIV infection among TB cases by neighborhood (as predicted from our model) ranged from 3.9% to 42.3% in 1988, and 6.7% to 72.0% in 1992.

Percentage of TB Cases Due to Infection Acquired 1 Year Ago
Upper and lower bounds of the percentage of TB cases due to M. tuberculosis infection acquired 1 year ago by neighborhood of New York City for the years 1988–1992 are shown in Figure 2 . Using the lower bounds and averaging over time, neighborhood-specific percentages range from 10.1% to 15.5%, with an average over all neighborhoods and years of 13.2%. Using the upper bounds and averaging over time, neighborhood-specific percentages ranged from 17.5% to 23.3%, with an average over all neighborhoods and years of 20.4%.

FIGURE 2: Upper and lower bounds of the percentage of TB cases due to recent M. tuberculosis infection, by New York City neighborhoods, 1989–1993. a , Bronx neighborhoods;b , Brooklyn and Staten Island neighborhoods;c , Manhattan neighborhoods;d , Queens neighborhoods. Solid line, upper bounds; dashed line, lower bounds.

Discussion
Using a mathematical model that accounted for spatial variation, temporal trends, and the impact of the HIV epidemic on TB dynamics, we estimated that 13–20% of TB cases in New York City during a TB-epidemic period were attributable to TB infections acquired within the past year.

At least in some parts of New York City, the percentage of TB cases in 1989–1993 due to recent M. tuberculosis infection appeared to be lower than previously thought. For instance, one study based on molecular epidemiology estimated that 37.5% of TB cases diagnosed at a large hospital center in the Bronx were due to recent infection. ^{1} Even our upper-bound estimates for Bronx neighborhoods are substantially lower than this figure.

Such disparities might derive from several sources. First, investigators used DNA fingerprinting methods that rely solely on IS6110 to derive the above-cited estimates, and such methods may have been deficient. Burman et al ^{10} recently studied 86 TB patients in Colorado supplementing IS6110 with polymorphic GC-rich-sequence analysis. The use of two techniques reduced the frequency of strain clustering; that is, investigators showed that strains that seemed to be identical on IS6110 typing were actually distinct. It also increased the correlation with epidemiologically linked TB cases compared with the use of IS6110 alone. ^{10} It is possible that the use of an additional probe in the Bronx study would also have resulted in diminished estimates.

Second, the Bronx study’s use of data from TB cases diagnosed at a single center may have upwardly skewed the estimated proportion of TB due to recent infection. Referral biases that increase the representation of aggressive TB cases or cases diagnosed by a single hospital would inflate sample-based estimates of the importance of recently acquired tuberculous infection.

Third, there may have been deficiencies in our modeling or in our estimates of constants used in the model. A number of possible deficiencies can be cited, among which some of the more obvious are the following.

(a) Implicit to our modeling of the role of HIV was the assumption that the distribution of HIV infection among all TB cases was equal to that among pulmonary TB only. Studies of TB patients at two New York City hospitals showed that this distributional assumption was correct, at least for those patients who consented to an HIV test (Ref 31 and unpublished data at Bellevue Hospital Center); it seems reasonable to assume it was also true in the Bronx.

(b) Simplifying assumptions about mixing patterns between TB cases and those susceptible to TB in our model might have led us to underestimate the contribution of recently acquired M. tuberculosis infection. If a substantial proportion of HIV-negative pulmonary TB cases infect persons who already have HIV, then our modeling procedure would have underestimated the true value of R _{s} , as newly infected persons with HIV are presumed to develop active TB disease more rapidly. Although we allowed the HIV prevalence among TB cases to “wander” across the city’s neighborhoods, we assumed a single value for the HIV prevalence of case contacts, conditional only on the case’s HIV status. For certain neighborhoods of the Bronx, where some of New York City’s highest AIDS rates are extant, ^{35} this procedure might have been inadequate, and underestimates could have resulted.

Furthermore, the simplified mixing patterns used here reflected neither the host nor the susceptible population’s age structure. Thus, it was inappropriate to consider any age-dependent variation in infectivity or pathogenesis rates, as has been considered by Dye et al ^{36} and Vynnycky and Fine. ^{37}

(c) Other variables for which we assumed a single value include cumulative treatment rates and mortality due to TB, again conditional only on the HIV status of the case. No doubt there may have been some spatiotemporal variation in these variables as well. For example, Bureau of Tuberculosis Control data indicate that rates of directly observed therapy (DOT) varied from 13% to 40% by geographic region of New York City, and from 7% in 1991 to 47% in 1994. If rates of DOT in one time period can be regarded as a partial surrogate of treatment rates in another time period, then it is clear that there must have been some spatiotemporal variation in cumulative treatment rates in 1988–1992.

(d) Some further discrepancy might have arisen because we defined “recent” infection as that occurring within 1 year before case detection, whereas other investigators left the time frame open. In addition, the mathematical model of the basic reproductive rate of TB has been shown to be quite sensitive to one of the least certain of the input parameters, namely, I , the average number of infections caused by one TB case per year. ^{38} Sensitivity to I is also a problem for the short-term reproductive number. To tighten its estimation, we conclude, as did Sánchez and Blower, ^{38} that more work needs to be done to estimate and model the average number of infections caused by one infectious TB case per year. We have modeled this parameter by taking into account the influence of HIV on the infectiousness of pulmonary TB, but other biological parameters, such as age, the extent of cavitation, ^{39} sputum status, ^{40} and epidemiologic parameters governing contact rates, need to be incorporated as well. Future implementations of this model will also need to take into account the possibility of increasing post-AIDS survival time resulting from new retroviral treatments.

(e) We relied on reported TB cases. Estimates based on these data should be unbiased if there was no temporal trend in the fraction of cases reported each year and if parameter values for unreported cases are identical to parameter values for reported cases. These assumptions may not be valid.

It is important to resolve the issue of the contribution of recently acquired M. tuberculosis infection to the overall TB picture. Its disease-control significance is substantial; a heavy impact of rapidly progressing primary tuberculous infection implies that all possible measures must be taken to prevent pulmonary TB cases from infecting others. Some such interventions, for example, DOT and improved infection control in hospitals, jails, and other congregate settings, were greatly expanded in New York City during the epidemic years of the late 1980s and early 1990s. ^{41} A lesser contribution of recently acquired infection, however, would suggest that disease-control efforts should be shifted toward secondary prevention, for example, measures such as isoniazid chemoprophylaxis among groups likely to have latent tuberculous infection and a high likelihood of activation. In this context, the role of large, recent influxes of immigrants to New York City from regions of TB hyperendemicity cannot be overstated. ^{42}

Although model-based approaches carry substantial uncertainty, we suggest that they can be useful in both the elucidation and continuing monitoring of the impact of recent M. tuberculosis transmission on the TB-case picture. To reconcile model estimates with those obtained via DNA fingerprinting methods, the following steps need to be taken. First, more complete reporting of the HIV status of TB cases to TB registries is needed. Currently, HIV status is unknown for approximately 50% of reported TB cases in many important TB registries (for example, New York City, New Jersey, and San Francisco). More complete reporting will require greater coordination between TB and AIDS surveillance authorities as well as improved efforts by physicians to encourage all TB patients to undergo HIV testing.

Second, future model refinements need to take into account age-dependent variation in transmissibility and pathogenesis. In addition, a sensitivity analysis of mixing patterns that take age and HIV status into account should be conducted.

Third, model extensions that capture the possibility of active TB disease within, say, 2 or 3 years after infection, should be considered. Such models need to be developed in parallel with more intricate analyses of DNA fingerprint results that incorporate a time element, that is, analyses in which the heretofore loosely defined notion of “recent” transmission is quantified. Such analyses will in turn require insights into the molecular clock of M. tuberculosis as well as resourceful approaches to contact tracing.

Each of the currently available approaches to TB epidemiology—fingerprinting of cases or “molecular epidemiology,” surveillance, and modeling—has deficiencies. Models such as ours must sacrifice the ability to describe extraordinary or transitory situations for the sake of what they do best, that is, capturing a large picture with a few simple strokes. Case fingerprinting potentially provides very specific information, but, as practiced thus far, lacks a well-defined sampling frame and offers little basis for general inferences. Surveillance has the potential to provide a complete-catch population base, but it is not designed to be sensitive to nuances or abrupt changes in TB occurrence. A synthesis of these methods is needed—a methodological gap well illustrated by the lack of agreement on the question of the importance of recent TB transmission to recent urban TB outbreaks. Surveillance and modeling together have the potential both to provide the population reference that strain-typing studies lack and to allow group-level attributes to be considered in the light of the fingerprint data. Future work should be devoted to fusing these now-disparate approaches.

Acknowledgments
We thank Gordon Cook for preparing the figures; Peter Vavagiakis of the New York City Department of Health Office of AIDS Research for providing the data on remnant blood samples; and the New York City Department of Health’s Bureau of Tuberculosis Control, Office of AIDS Surveillance, and Office of Vital Statistics and Epidemiology for the provision of TB case records, AIDS case records and vital statistics, respectively.

References
1. Alland D, Kalkut GE, Moss AR, McAdam RA, Hahn JA, Bosworth W, Drucker E, Bloom BR. Transmission of tuberculosis in New York City: an analysis by DNA fingerprinting and conventional epidemiologic methods. N Engl J Med 1994; 330:1710–1716.

2. Small PM, Hopewell PC, Singh SP, Paz A, Parsonnet J, Ruston DC, Schecter GF, Daley CL, Schoolnik GK. The epidemiology of tuberculosis in San Francisco: a population-based study using conventional and molecular methods. N Engl J Med 1994; 330:1703–1709.

3. Barnes PF, Zhenhua Y, Preston-Martin S, Pogoda JM, Jones BE, Otaya M, Eisenach KD, Knowles L, Harvey S, Cave MD. Patterns of tuberculosis transmission in central Los Angeles. J Am Med Assoc 1997; 278:1159–1163.

4. Van Embden JDA, Cave MD, Crawford JT, Dale JW, Eisenach KD, Gicquel B, Hermans P, Martin C, McAdam R, Shinnick TM, Small PM. Strain identification of

Mycobacterium tuberculosis by DNA fingerprinting: recommendations for a standardized methodology. J Clin Microbiol 1993; 3:406–409.

5. Valway SE, Richards SB, Kovacovich J, Greifinger RB, Crawford JJ, Dooley SW. Outbreak of multi-drug−resistant tuberculosis in a New York State prison. Am J Epidemiol 1994; 140:113–122.

6. Coronado VG, Beck-Sague CM, Hutton MD, Davis BJ, Nicholas P, Villareal C, Woodley CL, Kilburn JO, Crawford JT, Frieden TR, Sinkowitz RL, Jarvis WR. Transmission of multidrug-resistant

Mycobacterium tuberculosis among persons with human immunodeficiency virus infection in an urban hospital: epidemiologic and restriction fragment length polymorphism analysis. J Infect Dis 1993; 168:1052–1055.

7. Frieden TR, Sherman LF, Maw KL, Fujiwara PI, Crawford JT, Nivin B, Sharp V, Hewlett D Jr, Brudney K, Alland D, Kreiswirth BN. A multi-institutional outbreak of highly drug-resistant tuberculosis: epidemiology and clinical outcomes. J Am Med Assoc 1996; 276:1229–1235.

8. Kline SE, Hedemark LL, Davies SF. Outbreak of tuberculosis among regular patrons of a neighborhood bar. N Engl J Med 1995; 333:222–227.

9. Daley CL, Small PM, Schecter GF, Schoolnik GK, McAdam RA, Jacobs WR Jr, Hopewell PC. An outbreak of tuberculosis with accelerated progression among persons infected with the human immunodeficiency virus: an analysis using restriction-fragment−length polymorphisms. N Engl J Med 1992; 326:231–235.

10. Burman WJ, Reves RR, Hawkes AP, Rietmeijer CA, Yang Z, El-Hajj H, Bates JH, Cave MD. DNA fingerprinting with two probes decreases clustering of

Mycobacterium tuberculosis . Am J Respir Crit Care Med 1997; 155:1140–1146.

11. Blower SM, McLean AR, Porco TC, Small PM, Hopewell PC, Sánchez MA, Moss AR. The intrinsic transmission dynamics of tuberculosis epidemics. Nat Med 1995; 1:815–821.

12. Bureau of Tuberculosis Control. Tuberculosis in New York City, 1995: Information Summary. New York: New York City Department of Health, 1996.

13. Cauthen GM, Dooley SW, Onorato IM, Ihle WW, Burr JM, Bigler WJ, Witte J, Castro KG. Transmission of

Mycobacterium tuberculosis from tuberculosis patients with HIV infection or AIDS. Am J Epidemiol 1996; 144:69–77.

14. Elliot AM, Hayes RJ, Halwiindi B, Luo N, Tembo G, Pobee JOM, Nunn PP, McAdam KPWJ. The impact of HIV on infectiousness of pulmonary tuberculosis: a community study in Zambia. AIDS 1993; 7:981–987.

15. Selwyn PA, Sckell BM, Alcabes P, Friedland GH, Klein RS, Schoenbaum EE. High risk of active tuberculosis in HIV-infected drug users with cutaneous anergy. JAMA 1992; 268:504–509.

16. Cressie NAC. Statistics for Spatial Data. New York: John Wiley, 1993.

17. Arno PS, Murray CJL, Bonuck KA, Alcabes P. The economic impact of tuberculosis in hospitals in New York City: a preliminary analysis. J Law Med Ethics 1993; 21:317–323.

18. Burwen DR, Bloch AB, Griffin LD, Ciesielski CA, Stern HA, Onorato IM. National trends in the concurrence of tuberculosis and acquired immunodeficiency syndrome. Arch Intern Med 1995; 155:1281–1286.

19. Greenberg BL, Weisfuse IB, Makki H, Adler J, El-Sadr W, Clarke L, Gainey S, Alford T, McFarlane K, Thomas PA. HIV-1 seroprevalence in chest clinic and hospital tuberculosis patients in New York City, 1989–1991. AIDS 1994; 8:957–962.

20. Kaufman G, Han Y, Agins BD. Hospitalization of patients infected with active TB in New York State, 1987–1992: the effect of the HIV epidemic. J Acquir Immune Defic Syndr 1996; 12:508–513.

21. Blower SM, Small PM, Hopewell PC. Control strategies for tuberculosis epidemics: new models for old problems. Science 1996; 273:497–500.

22. Styblo K. Recent advances in epidemiological research in tuberculosis. Adv Tuberc Res 1980; 29:1–63.

23. Office of Vital Statistics. Summary of Vital Statistics 1993. New York: New York City Department of Health, 1994.

24. Office of AIDS Surveillance. Data. New York: New York City Department of Health, New York. (Available on disk)

25. Blum S, Singh TP, Gibbons J, Fordyce EJ, Lessner L, Chiasson MA, Weisfuse IB, Thomas PA. Trends in survival among persons with acquired immunodeficiency syndrome in New York City: the experience of the first decade of the epidemic. Am J Epidemiol 1994; 139:351–361.

26. Reichman LB. HIV infection: the dominant new face of tuberculosis. Mt Sinai J Med 1992; 59:271–277.

27. Nunn P, Brindle R, Carpenter L, Odhiambo J, Wasunna K, Newnham R, Githui W, Gathua S, Omwega M, McAdam K. Cohort study of HIV infection in patients with tuberculosis in Nairobi, Kenya: analysis of early (6-month) mortality. Am Rev Respir Dis 1992; 146:849–854.

28. Chaisson RE, Schecter GF, Theuer CP, Rutherford GW, Echenberg DF, Hopewell PC. Tuberculosis in patients with the acquired immunodeficiency syndrome: clinical features, response to therapy, and survival. Am Rev Respir Dis 1987; 136:570–574.

29. Rieder HL, Kelly GD, Bloch AB, Cauthen GM, Snider DE Jr. Tuberculosis diagnosed at death in the United States. Chest 1991; 100:678–681.

30. Centers for Disease Control. Tuberculosis and acquired immunodeficiency syndrome: New York City. MMWR 1987; 36:785–790,795.

31. Shafer RW, Chirgwin KD, Glatt AE, Dahdouh MA, Landesman SH, Suster B. HIV prevalence, immunosuppression, and drug resistance in patients with tuberculosis in an area endemic for AIDS. AIDS 1991; 5:399–405.

32. Des Jarlais DC, Friedman SR, Sotheran JL, Wenston J, Marmor M, Yancovitz SR, Frank B, Beatrice S, Mildvan D. Continuity and change within an HIV epidemic: injecting drug users in New York City, 1984 through 1992. JAMA 1994; 271:121–127.

33. Friedman LN, Williams MT, Singh TP, Frieden TR. Tuberculosis, AIDS, and death among substance abusers on welfare in New York City. N Engl J Med 1996; 334:828–833.

34. Handwerger S, Mildvan D, Senie R, McKinley FW. Tuberculosis and the acquired immunodeficiency syndrome at a New York City hospital: 1978–1985. Chest 1987; 91:176–180.

35. Office of AIDS Surveillance. AIDS Surveillance Update: First Quarter 1997. New York: New York City Department of Health, 1997.

36. Dye C, Garnett GP, Sleeman K, Williams BG. Prospects for worldwide tuberculosis control under the WHO DOTS strategy. Lancet 1998; 352:1886–1891.

37. Vynnycky E, Fine PEM. The natural history of tuberculosis: the implications of age-dependent risks of disease and the role of reinfection. Epidemiol Infect 1997; 119:183–201.

38. Sánchez MA, Blower SM. Uncertainty and sensitivity analysis of the basic reproductive rate: tuberculosis as an example. Am J Epidemiol 1997; 145:1127–1138.

39. Kim TC, Blackman RS, Heatwole KM, Kim T, Rochester DF. Acid-fast bacilli in sputum smears of patients with pulmonary tuberculosis: prevalence and significance of negative smears pretreatment and positive smears post-treatment. Am Rev Respir Dis 1984; 129:264–268.

40. Shaw JB, Wynn-Williams N. Infectivity of pulmonary tuberculosis in relation to sputum status. Am Rev Tuberc 1954; 69:724–732.

41. Frieden TR, Fujiwara PI, Washko RM, Hamburg MA. Tuberculosis in New York City: turning the tide. N Engl J Med 1995; 333:229–233.

42. McKenna MT, McCray E, Onorato I. The epidemiology of tuberculosis among foreign-born persons in the United States, 1986 to 1993. N Engl J Med 1995; 332:1071–1076.