Epidemiologic Assumptions in the Model

The model’s structure, parameters, and assumptions have been published (6). Persons are assumed to be born uninfected. Infected persons are divided into those in whom primary disease has not yet developed (defined by convention as disease within 5 years of initial infection [7]), and those in the “latent” class, who are at risk for endogenous reactivation or for reinfection, which can be followed by exogenous disease. Exogenous disease is here defined as the first disease episode within 5 years of the most recent reinfection; endogenous disease includes disease occurring >5 years after the most recent (re)infection event, and second or subsequent disease episodes occurring <5 years after the most recent (re)infection event. (These definitions differ slightly from those of Sutherland et al. (8) to include the assumption that once persons have recovered from disease during the first 5 years after initial infection or reinfection, their risk of developing disease becomes the same as that of developing disease through reactivation, until they are newly reinfected.)

The infection and reinfection risks are assumed to be identical, but reinfection is less likely to lead to disease than is initial infection, due to some immunity induced by the prior infection (9). We explored the implications of four assumptions for the magnitude (and trend) in the annual risk for infection, namely, that the risk for infection 1) declined over time, as estimated for the Netherlands (from approximately 2% in 1940 to approximately 5/10,000 by 1979 [4,10]); 2) remained unchanged over time at a very low level (0.1%); 3) remained unchanged at 1%; or 4) remained unchanged at 3%. Infection risks of 1% have been found in several populations (e.g., Malawi [11]). Infection risks of 3% are uncommon today but have been reported in parts of South Africa (12). For simplicity, we assumed that persons cannot be reinfected during the period between initial infection (or reinfection) and onset of the first primary episode (or exogenous disease).

Figure 1

Figure 1. Summary of the main assumptions in the model relating to the risks of developing disease. 1) General relationship between the risk of developing the first primary episode (during the first year...

The risks of developing disease depend on age and sex (Figure 1A; [6]); they are based on previous analyses, in which we fitted predictions of disease incidence to observed notifications in the U.K (9). The risks of developing either a first primary episode or disease following exogenous reinfection also depend on the time since infection and reinfection, respectively (Figure 1B). The probability that a disease episode is infectious (sputum smear/culture-positive) is age dependent (Figure 1C) (9). The demography of the population described in the model is assumed to be that for the Netherlands. Analyses are restricted to respiratory (pulmonary) forms of tuberculosis, since these are far more likely than extrapulmonary forms to lead to transmission. Although additional factors such as immigration and HIV can influence the extent of clustering in complicated ways (14), these factors are not considered here, where the focus is upon the effect of the magnitude and trend in the annual risk for infection on clustering.

Derivation of Clustering Statistics

Recent studies suggest that the half-life of DNA fingerprint patterns based on IS6110 restriction fragment length polymorphism (RFLP, which has been used for the DNA fingerprinting conducted to date in most studies) is 2–5 years (5,15). If the molecular clock speed for IS6110 RFLP patterns of strains involved in latent infection (currently unknown) were to be similar, this relatively short half-life implies that most of the fingerprint patterns of the strains causing disease today differ from those that caused disease many years ago. Similarly, this short half-life implies that the M. tuberculosis fingerprint types and cluster distributions in tuberculosis cases today depend only loosely upon those that existed 50 years ago. Based on this assumption, to derive clustering estimates for a given population for recent years, we designed the model to simulate the introduction and subsequent transmission of strains with new DNA fingerprint patterns from a sufficiently distant time in the past (taken to be 1950), so that a) all cases with onset in recent years involved a strain whose DNA fingerprint pattern had first appeared since then and b) no assumptions would be required about the distributions of strains that existed before 1950. The general steps in the calculations are outlined briefly below.

The numbers of persons of each age in each of the epidemiologic categories for 1950 were calculated by using the model, based on described equations (9). From 1950, each of these age-sex classes was stratified to distinguish between those who had, versus those who had not, been (re)infected since 1950. Those who had been (re)infected since 1950 were subdivided further according to the time of infection or reinfection. The transmission dynamics were tracked simultaneously for all persons with the equations described in the Appendix and elsewhere (6), by using time steps of 6 months and 1 year for calendar year and age, respectively.

Figure 2

Figure 2. Summary of the assumptions defining contact between persons in the model. A, B, and C show the annual risk for infection, estimates of the average effective contact number in the model,...

In each interval, disease was assumed to develop in a proportion of infected persons, and a proportion of these disease episodes was attributed to a strain for which the DNA fingerprint pattern differed from that of the strain with which the persons were originally infected. This latter proportion depended on the time since infection (see below), and each of the new DNA fingerprint patterns was assigned a unique identity number. Each infectious patient with onset at a given time was assumed to contact a different number of persons (see Appendix and Figure 2). The frequency distributions of the number of persons contacted by each patient were used to derive the total number of persons who were newly (re)infected at this time. The corresponding equations were then applied to this number to determine the total number of persons in whom disease developed at a later time, T, among those who had been infected at time t. The DNA fingerprint patterns of the strains in these diseased persons were then determined by using the frequency distribution of the number of persons contacted by each case-patient at time t. These calculations are described further in the Appendix.

Estimating the Effect of the Annual Risk for Infection on Clustering as an Indicator of Recent Transmission

Our model was used to calculate the age-specific proportion of disease attributable to primary and exogenous disease from 1993 to 1997 for the Netherlands and for settings in which the annual risk for infection is assumed to have remained unchanged over time at 0.1%, 1%, and 3%. Primary and exogenous disease involve disease occurring during the first 5 years after the most recent (re)infection event, although the majority of persons in whom primary or exogenous (reinfection) disease develops acquire the disease within 2–3 years (Figure 1B). The clustering by sex and age for cases with onset in different periods between 1993 and 1997 for the Netherlands, and for settings in which the annual risk for infection is assumed to have remained unchanged over time at 0.1%, 1%, and 3%,was also calculated by using the age and sex distribution of the cases with onset in that period (see equations in [6]). For simplicity, we present age-specific levels of clustering for male patients only. Model predictions for male patients generally compared better against the observed data in the Netherlands than did those for female patients (6).

The predictive values of clustering for the identification of recent transmission were calculated as follows. The positive predictive value of clustering for identifying recent transmission in different age groups in different periods was calculated as the proportion of case-patients who were in a cluster in a given period who had been infected or reinfected <5 years before disease onset. The negative predictive value of clustering for identifying recent transmission in different age groups was calculated as the proportion of case-patients who were not in a cluster in a given period who had been infected or last reinfected >5 years before disease onset.

Model Predictions of the Extent of Clustering and Disease Attributable to Recent Transmission

Figure 3

Figure 3. Model predictions of the proportion of disease attributable to primary and exogenous disease during the period 1993–1997 in the Netherlands and settings in which the annual risk for infection has remained...

As shown in Figure 3, very different age patterns in the proportion of disease attributable to recent transmission were predicted for the Netherlands and for settings in which the annual risk for infection has remained unchanged over time. In the Netherlands, the proportion of disease attributed to recent infection decreased dramatically with age, e.g., from 100% in the young to approximately 50% and 10% for 45- to 54-year-old patients and persons >65 years of age, respectively. The proportion of disease attributed to recent reinfection was very low for all age groups (<3%). For constant infection risk settings, the predicted proportion of disease attributable to recent transmission (i.e., recent infection or reinfection) was very similar, falling from 100% in the young to 85%, 88%, and 90% in the oldest age groups for the 0.1%, 1%, and 3% infection risk scenarios, respectively. On the other hand, large differences between settings were predicted in the proportion of disease attributed to initial infection or to reinfection. In all instances, the proportion attributed to reinfection was zero in the youngest age groups, but this proportion increased with age to 3%, 35%, and 80% for the 0.1%, 1%, and 3% annual infection risk assumptions, respectively. The proportion attributed to recent initial infection in these settings decreased from 100% in the young to 80%, 50%, and 15%, respectively, in old patients.

Figure 4

Figure 4. Model predictions of A) the overall percentage of cases clustered during different time periods from 1993 to 1997 and B) the age-specific percentage of (male) cases clustered during the period 1993–1995...

As shown in Figure 4A, for each setting, the overall clustering (i.e., that seen among all age groups) was predicted to increase with study duration, e.g., from 15% for the Netherlands for a 1-year period to approximately 25% for a 5-year period. The clustering predicted for all the constant infection risk scenarios was similar in magnitude for each study period and increased from 60% to 70% for a 1-year period to 75% to 85% for a 5-year period. Since the overall clustering was not predicted to increase much for study periods of more than 3 years, clustering is defined using a 3-year period in the remainder of these analyses (represented by 1993–1995). As shown in Figure 4B, the clustering predicted for each age group was similar for each of the settings in which the annual risk for infection remained unchanged over time, and declined only slightly with age, e.g., from 83% for the youngest age group to approximately 75% for the oldest age category. In contrast, for the Netherlands, the clustering was predicted to decrease dramatically with age, from approximately 75% among young case-patients to approximately 15% in very old patients. This prediction is consistent with observed data (Figure 4B).

Reliability of Clustering as a Measure of the Extent of Recent Transmission

Figure 5

Figure 5. Comparison between model predictions of the clustering in different age groups and the proportion of disease attributable to recent infection or reinfection in the Netherlands and in settings in which the...

For settings in which the annual risk for infection remained unchanged over time at 0.1%, 1%, and 3%, the predicted clustering in each age group underestimated the proportion who had been recently infected or reinfected (Figure 5). In settings with an annual risk for infection of 0.1%, at least 90% of cases in each age group were predicted to have been recently (re)infected, whereas the proportion clustered decreased from about 85% in the youngest age group to approximately 70% for the oldest persons. For the Netherlands (described elsewhere [6]), clustering underestimated the proportion of disease attributable to recent transmission in the young (by up to 43%) and overestimated that for older patients (by up to 50%).

Figure 6

Figure 6. Summary of model predictions of the A) positive predictive values of clustering (proportion of cases who are in a cluster who have been infected or reinfected <5 years before onset) and...

The positive and negative predictive values of being in a cluster, as an indicator of recent transmission, depended both on age and the study setting (Figure 6). For settings with a high annual risk for infection that had remained unchanged over time, model predictions suggested that most patients clustered in each age group were likely to have been recently (re)infected, corresponding to a positive predictive value of clustering for recent transmission of almost 100% in each age group (Figure 6A). The positive predictive value was estimated to decrease with age in the Netherlands from 100% in the very young to about 20% for the oldest patients.

When unclustered cases were considered, the proportion of clinical case-patients who were estimated to have been infected >5 years previously was low (<5%) for young patients and increased with age for all settings, approaching 100% for patients ages >55 years in the Netherlands (Figure 6B). Almost all case-patients of ages >55 years who were not in a cluster in the Netherlands were therefore estimated to have been infected >5 years previously and thus owed their disease to reactivation of latent foci. Of the adult case-patients who were not in a cluster in the other settings, the proportion who had been infected >5 years previously was <45%, 35%, and 20% if the annual risk for infection was 0.1%, 1%, and 3%, respectively.