. 2015 Mar 19;181(8):619–632. doi: 10.1093/aje/kwu320

Table 1.

Summary of the Parameter Values Used in the Base-Case and the Ranges Explored in Sampling Parameter Combinations When Modeling a Cluster Randomized Trial of Mass Tuberculosis Screening Known as “Thibela TB,” 2006–2011

Definition	Symbol^a	Base-Case Value^b	Range^b,c	Comment^b
Transmission
Effective contact rate (average number of individuals effectively contacted by each person per unit of time)	c_e	Adjusted to give an annual risk of infection averaged across clusters of 20%/year before the start of the intervention	5–25/year	No available data
Force of infection that is attributable to contact with the outside community	λ_o	0.29%/year	Fixed	Based on report by Wood et al. (31)^d
Infectiousness of sm− TB cases compared with that of sm+ cases	f	22%	Fixed	Based on report by Behr et al. (32)
Disease Onset
Rate of onset of reactivation disease for HIV− miners without radiologically confirmed silicosis	d_n_,z−,a,h−	Estimated	0.0001–0.014/year	Based on reports by Vynnycky and Fine (7), Sutherland et al. (33), Clark and Vynnycky (34), and Vynnycky et al. (35). The upper limit was set to ensure biological plausibility with the rate of disease following reinfection.
Rate of onset of (exogenous) disease in the first year after reinfection	d_x_,z−,a,h− (0)	Estimated	0.01–0.11/year	Based on reports by Vynnycky and Fine (7), Sutherland et al. (33), Clark and Vynnycky (34), and Vynnycky et al. (35).
Proportion of miners of age a that have radiologically confirmed silicosis	p_si_,a	Varies by age and between clusters: ≤1% (<40 years of age); 2%–10% (≥40 years of age)	Fixed	Based on baseline prevalence survey^d,e
Relative risk of developing TB among miners with radiologically confirmed silicosis, compared with that among miners without radiologically confirmed silicosis	ρ_si_,h	HIV−: 2.6	1–6.5	Based on report by Corbett et al. (36). For biological plausibility, the selected value for the relative risk for HIV+ was higher than that for HIV−.
	ρ_si_,h	HIV+: 4.1	2.4–7.1
Rate at which sm− cases become sm+	o_s₊_,h	HIV−: 0.6%/week	0.3%–0.9%/week	Based on data from the report by Corbett et al. (37)^d,f
Rate at which sm− cases become sm+	o_s₊_,h	HIV+: 1.78%/week	0.89%–2.7%/week	Based on data from the report by Corbett et al. (37)^d,f
HIV and ART
HIV prevalence in the workforce	h₊	0.3	0.2–0.45	Based on the report by Lewis et al. (38)
ART coverage among miners with a CD4 count of <200 cells/mL at time t	g_ART,<200(t)	Varies between clusters. Increases from 0 in 2003 to 50%–100% by 2008	Fixed	Calculated from observed data. Refer to Figure 3A^d,g
Protection provided by ART against TB disease among those not on IPT	TT_z₋_,ART+	65%	48%–83%	Based on the report by Suthar et al. (39)^d,h
Factor by which the rate of disease onset among those with a CD4+ cell count in the range c_i − c_i₊₁ cells/µL differs from that among HIV− individuals	$ρ_{h, c_{i} - c_{i + 1}}$	CD4 <200: 17	8.5–25.5	Consistent with estimates in the report by Williams et al. (40). The value for those with a CD4 count of <200 cells/mL was constrained to be at least as high as that for miners with a CD4 count of ≥200 cells/mL
	$ρ_{h, c_{i} - c_{i + 1}}$	CD4 ≥200: 6	2.9–8.8
Proportion of HIV+ miners who have a CD4+ count in the range c_i − c_i₊₁	$p_{h, c_{i} - c_{i + 1}}$	CD4 <200: 0.25	Fixed	Consistent with data in reports by Wlliams et al. (40, 41)^d
	$p_{h, c_{i} - c_{i + 1}}$	CD4 ≥200: 0.75	Fixed
Case Detection
Proportion of new employees with TB disease joining the workforce that are detected (“found”)	p_in_,f,s	sm−: company A, 14%; companies B/C: 1.4%	sm−: 0.7%–20%	Calculated by using the sensitivity of radiographs, proportion of miners followed up, and the sensitivity of the method for subsequent follow-up (culture for company A; smear for company B/C)^b,i
	p_in_,f,s	sm+ (both companies): 25%	sm+: 12.5%–37.5%
Rate at which cases with smear-status s are detected (found) through the routine medical examination	r_f_,s,h,y	Company A: sm−, 0.22%/week; sm+, 0.42%/week. Company B/C: sm−, 0.02%/week; sm+, 0.42%/week	Company A: sm−, 0.1%–0.3%/week; sm+, 0.2%–0.42%/week. Company B: sm−, 0.01%–0.3%/week; sm+, 0.2%–0.42%/week	Calculated by using the sensitivity of radiographs, proportion of miners followed up, and the sensitivity of the method for subsequent follow-up (culture for company A; smear for company B/C)^b,i
Rate at which sm+ cases are detected (found) through passive presentation to the health services	r_f_,s+,h,p	HIV+: 13%/week	6%–19%/week	Calculated by using data from the report by Corbett et al. (37)^b,i
	r_f_,s+,h,p	HIV−: 1.6%/week	0.7%–2.3%/week
Rate at which sm− cases are detected (found) through passive presentation to the health services	r_f_,s−,h,p	Company A: HIV−, 0.4%/week; HIV+, 1.2%/week. Company B/C: HIV−, 0.6%/week; HIV+, 1.4%/week	All companies: HIV−, 0.2%–0.9%/week; HIV+, 0.6%–2.2%/week	Calculated by using data from the report by Corbett et al. (37)^b,i
Treatment
Rate at which TB cases with smear status s who have been detected (found) for duration s_f start TB treatment	T_s(s_f)	Refer to Figure 3B	Fixed	Based on observed data; depends on mining company^d,j
Duration of TB (disease) treatment	$T_{τ_{max}}$	6 months	Fixed	Based on observed data. Note that in reality, cases who have previously experienced TB and cases with multiple drug resistance are treated for 8 months and 2 years, respectively. However, such cases make up a small proportion of all TB cases (10% and 2%–2.5%, respectively, based on observed data in the report by van Halsema et al. (2))
Intervention
Rate at which individuals of age a start IPT	i_z_+,a(t)	Varies between clusters, with the peak proportion on IPT reaching between 10% and 70%^k	Fixed	Based on observed data. Differs between clusters and changes over time^d,k,l
Rate at which individuals of age a stop taking IPT	i_z_−,a(t)	Varies between clusters with the peak proportion on IPT reaching between 10% and 70%^k	Fixed	Based on observed data. Differs between clusters and changes over time^d,k,l
Rate at which cases are detected through the screening carried out on recruitment into Thibela TB	q(t)	Varies between clusters	Fixed	Based on observed data. Differs between clusters and changes over time^d
Protection against disease provided by IPT for those not on ART	TT_d_,z+,ART−	63%	25%–81%	Based on the analyses of individual-level data in Thibela TB in the report by Churchyard et al. (5)
Protection against disease provided by IPT for those on ART	TT_d_,z+,ART+	82.5%	41%–83%	Calculated by assuming that IPT provides an additional 50% protection to that provided by ART. Consistent with reports by Samandan et al. (13), Rangaka et al. (42), and Golub et al. (43, 44)
Proportion of infections that are cured (i.e., so that reactivation cannot occur) as a result of 6 months of IPT	$p_{z_{c}, h}$	100% for IPT assumption 1	0%–100%	For biological plausibility, the values for HIV− were constrained to be at least as high as those for HIV+.
	$p_{z_{c}, h}$	Estimated (IPT assumptions 2 and 3)	0%–100%
Protection provided against reinfection for individuals while they are on IPT	z_r_,h	100% for IPT assumptions 1 and 2	0%–100%	No available data
	z_r_,h	Estimated (IPT assumption 3)	0%–100%	No available data
Minimum duration of IPT required in order to cure infection	$T_{z_{\min}}$	6 months	Fixed	Consistent with the report by Comstock (14)
Maximum duration of IPT	$T_{z_{\max}}$	9 months	Fixed	Determined by Thibela TB
Mortality and Migration
Average mortality rate among TB cases before they start TB treatment	μ_s_,h,tr−	HIV−: sm−, 0.2%/month; sm+, 1%/month. HIV+ (both sm+ and sm−): 5%/month	HIV–: sm−, 0.1%–0.3%/month; sm+: 0.5%–1.5%/month. HIV+ (both sm+ and sm−): 2.5%–7.5%/month	Consistent with the report by Tiemersma et al. (45)^d
Average mortality rate among TB cases while they are on TB treatment	μ_h_,tr+	HIV−: 0.13%/month; HIV+: 1.3%/month	HIV−: 0.06%–0.19%/month; HIV+: 0.6%–1.9%/month	Consistent with the report by Churchyard et al. (46)
Average rate at which miners who are not on TB treatment leave the workforce because of out-migration or non-TB-related death	m_tr_−,a	Varies by age between clusters: 2%–4%/month (<30 years); 1%–2%/month (≥30 years)	Fixed	Based on human resources data^d,m
Average rate at which miners who are on TB treatment leave the workforce because of out-migration or non-TB-related death	m_tr₊	Varies between clusters in the range of 2%–7%/month	Fixed	Based on human resources data^d,m
Factor by which the prevalence of TB among new mining employees differs from that in the final prevalence survey (after adjustment for the observed impact)	p_in	1.0	0.3–1.5	No data available

Abbreviations: ART, antiretroviral therapy; HIV− and HIV+, human immunodeficiency virus-negative and -positive, respectively; IPT, isoniazid preventive therapy; sm− and sm+, smear-negative and smear-positive, respectively; TB, tuberculosis.

^a Several of the symbols have subscripts h, z−, z+, or a. h refers to HIV status (which can be positive or negative); z− and z+ refer to those not on IPT and on IPT, respectively; a refers to the age group.

^b The 3 mining companies are denoted by “A,” “B,” and “C.”

^c The parameters were sampled from the uniform distribution. Unless otherwise stated, the base-case values and ranges are identical for each cluster. The upper and lower limits of the ranges were taken to be 50% and −50% of the base-case value, unless confidence limits were available or the values were constrained for consistency with other parameter values.

^d Web Appendix 2.

^e Web Figure 2.

^f Web Figure 3.

^g Web Figure 4.

^h Web Table 2.

ⁱ Web Table 3.

^j Web Tables 4 and 5.

^k Web Figure 1.

^l Web Figures 5 and 6.

^m Web Figure 7.