Table 1. Summary of parameters and distributions.
| Definition | Mean and stratification | Distribution | Comments. References are listed as name of first author, year (Reference). |
|---|---|---|---|
| Population | |||
| Gender | 59.9% female | Represents trial population. Churchyard. 2015 [7] | |
| Age (IQR) | 37 (29–48) years | Fixed | Represents trial population. Churchyard. 2015 [7] |
| Initial population disease characteristics | HIVneg 0.314 (0.030); | Dirichlet | From trial population. Churchyard 2015 [7] Those with unknown self-reported HIV status are assumed to be HIV positive, not on ART. |
| HIVpos 0.531 (0.015); | |||
| ART 0.155 (0.005) | |||
| CD4 count in those with HIV (IQR) | 315 (192–480) cells/μL | Represents the microscopy arm of the trial population. Churchyard. 2015 [7] | |
| True TB prevalence (includes bacteriologically confirmed -, clinical—and undiagnosed TB) in the microscopy arm of the study. | 13.0% | Fixed | Estimated from XTEND trial and model calibration. Churchyard. 2015 [7] |
| Proportion of patients diagnosed with drug-resistant TB, any diagnosis | 4.0% (8/195) | Represents trial population. Churchyard. 2015 [7]. | |
| Proportion of patients starting MDR-TB treatment | 2.0% (3/195) | Represents what was observed in the XTEND trial. Churchyard. 2015 [7]. Time to starting MDR TB treatment was 11 and 33 days respectively. | |
| Diagnosis, transition probabilities | |||
| Probability of a positive Xpert test result if symptomatic and able to provide a sputum sample, mean (standard deviation) | HIVneg 0.077 (0.03); | Dirichlet | Estimated from XTEND trial. Churchyard. 2015 [7] |
| HIVpos 0.132 (0.05); | |||
| ART 0.135 (0.03) | |||
| Probability of TB if patient had a positive test result | HIVneg 0.877; | Fixed | Estimated based on GX sensitivity 0.86 in HIVneg; 0.79 in HIVpos, 0.94 for Rif resistance, and GX specificity of 0.99 in HIVneg, HIVpos, 0.98 for Rif resistance. Steingart 2014 [30], Steingart 2006 [31], and Boehme 2011 [32]. |
| HIVpos 0.936; | |||
| ART 0.938 | |||
| Probability of TB if patient had a negative test result | HIVneg 0.012; | Fixed | Unobserved parameter, estimated from model calibration. Based on GX sensitivity 0.86 in HIVneg; 0.79 in HIVpos, 0.94 for Rif resistance, and GX specificity of 0.99 in HIVneg, HIVpos, 0.98 for Rif resistance. Steingart 2014 [30], Steingart 2006 [31], and Boehme 2011 [32]. This includes a probability of a false negative test result; HIVneg 0.012; HIVpos pre-ART 0.038; HIVpos ART 0.039 as well as a probability of ‘undiagnosed TB’. Undiagnosed TB includes those who provide pauci-bacillary sputum or have extra-pulmonary TB. Probability of undiagnosed, “hard-to-diagnose” TB estimated to be 0.075 in those HIVpos pre-ART and 0.075 those HIVpos. |
| HIVpos 0.113; | |||
| ART 0.114 | |||
| Probability of starting treatment within 30 days of a positive test result, mean (standard deviation) | HIVneg 0.882 (0.325); | Dirichlet | Estimated from XTEND trial. Churchyard et al. 2015 [7] |
| HIVpos 0.802 (0.400); | |||
| ART 0.944 (0.236) | |||
| Probability of starting treatment within one month of a negative test result without further diagnostic tests | HIVneg_TB 0.535; HIVneg 0.002; HIVpos_TB 0.072; HIVpos 0.009; ART_TB 0.017; ART 0.003 | Fixed | Probability of starting treatment was estimated from XTEND trial, whether this clinical decision was correct (treatment started in those with TB vs those without) was estimated through model calibration. Churchyard et al. 2015 [7]. We therefore assume that clinicians are unlikely to start treatment empirically in those HIV negative. |
| Probability of receiving further investigations after a negative test result | HIVpos_TB 0.041; HIVpos 0.041; ART_TB 0.073; ART 0.073 | Fixed | Estimated from XTEND trial. Churchyard. 2015 [7]. McCarthy. 2016 [33]. |
| Probability of starting TB treatment after further diagnostic tests | HIVpos_TB 0.212; HIVpos 0.027; ART_TB 0.217; ART 0.037 | Fixed | Estimated from XTEND trial and the model calibration. Churchyard. 2015 [7]. McCarthy. 2016 [33]. |
| Probability of starting TB treatment from ‘out of care’, by month: from all who do not start TB treatment within one month of the diagnostic test | |||
| Month 2 | HIVneg_TB 0.928; HIVneg 0.005; HIVpos_TB 0.164; HIVpos 0.000; ART_TB 0.100; ART 0.000 | Fixed | Curve estimated from XTEND trial. Assume that the behaviour from out of care remains the same. Churchyard. 2015 [7]. |
| Month 3 | HIVneg_TB 0.756; HIVneg 0.000; HIVpos_TB 0.066; HIVpos 0.000; ART_TB 0.207; ART 0.000 | Fixed | Curve estimated from XTEND. Assume that the behaviour from out of care remains the same. Churchyard. 2015 [7]. |
| Month 4 | HIVneg_TB 0.000; HIVneg 0.005; HIVpos_TB 0.146; HIVpos 0.000; ART_TB 0.148; ART 0.000 | Fixed | Curve estimated from XTEND. Assume that the behaviour from out of care remains the same. Churchyard. 2015 [7]. |
| Month 5 | HIVneg_TB 0.000; HIVneg 0.015; HIVpos_TB 0.064; HIVpos 0.000; ART_TB 0.000; ART 0.000 | Fixed | Curve estimated from XTEND trial. Assume that the behaviour from out of care remains the same. Churchyard. 2015 [7]. |
| Month 6 | HIVneg_TB 0.000; HIVneg 0.010; HIVpos_TB 0.060; HIVpos 0.000; ART_TB 0.000; ART 0.000 | Fixed | Curve estimated from XTEND trial. Assume that the behaviour from out of care remains the same. Churchyard. 2015 [7]. |
| Probability of starting MDR-TB treatment if diagnosed with MDR-TB | HIVneg 0.025; HIVpos 0.019; ART 0.000 | Dirichlet | Estimated from XTEND trial. Churchyard. 2015 [7]. |
| Treatment, transition probabilities | |||
| Probability of drug sensitive TB regimen started if TB treatment started | HIVneg 0.952; HIVpos 0.969; ART_TB 0.834 | Dirichlet | Estimated from XTEND trial. Churchyard. 2015 [7]. |
| Probability of MDR-TB regimen started if TB treatment started, mean (standard deviation) | HIVneg 0.039 (0.208); HIVpos 0.023 (0.002); ART 0.000 (0.000); | Dirichlet | Estimated from XTEND trial. Churchyard. 2015 [7]. |
| Disease progression, transition probabilities | |||
| Average life expectancy at birth, South Africa | 63 years | Fixed | From the rapid mortality surveillance report 2014. Assumes that HIVpos patients who are on ART when they enter the model would have the same life expectancy as the general population (varied in the sensitivity analysis). HIV specific mortality considered in model through probabilities. Dorrington. 2015 [34]. Years of life remaining at death is estimated from the difference between current age in model (mean age of cohort + time in model) and the average life expectancy at birth. |
| All-cause mortality in those without TB, monthly, mean (standard deviation) | HIVneg 0.001 (0.0005); HIVpos 0.002 (0.000); ART 0.001 (0.001) | Dirichlet | From Statistics South Africa report (P0309.3), mortality and causes of death in South Africa: findings from death notification [35]. |
| Standardised mortality ratio for all-cause mortality in patients post-TB treatment | 3.76 | Fixed | Increased all-cause mortality in those with a previous episode of TB [36]. Estimated as part of a systematic review and meta-analysis. |
| Monthly mortality if living with TB, not currently receiving treatment, mean (standard deviation) | HIVneg 0.018 (0.020); HIVpos 0.132 (0.005); ART 0.039 (0.005) | Changes over time | Based on Tiemersma. 2011 [37]. Used half-cycle correction to adjust for earlier movement into treatment in month 1 of the model. |
| Monthly mortality on treatment for those with TB, mean (standard deviation) | HIVneg 0.002 (0.001); HIVpos 0.046 (0.002); ART 0.006 (0.003) | Changes over time | Andrews 2012 [38]. Mohr 2015 [39]. Monthly mortality reduction due to TB treatments added as distribution over time, where mortality reduces to 10% of the mortality of those with TB not on treatment at month 5 on treatment. Based on comparison with mortality on treatment observed in the XTEND trial. Churchyard 2015 [7]. |
| Disability weights, mean (standard deviation) | HIVneg_TB 0.331 (0.057); HIVpos_TB 0.399 (0.070); HIVpos 0.221 (0.041); ART 0.053 (0.011); ART_TB 0.331 (0.057) | Beta | Salomon. 2015 [40]. Kastien-Hilka. 2017 [41]. Assuming that disability weights are not cumulative, thus those on ART with TB have the same disability weight as someone with TB disease only. |
| The disability weight is a factor reflecting the severity of disease. | |||
| Cost and resource use | |||
| Microscopy, mean (standard deviation) | $6.30 ($1.34) | Gamma | Cunnama 2016 [42]. |
| Xpert, mean (standard deviation) | $16.90 ($6.10) | Gamma | Cunnama 2016 [42]. |
| Sputum liquid culture, mean (standard deviation) | $12.90 ($2.26) | Gamma | Cunnama 2016 [42]. |
| Digital radiograph, mean (standard deviation) | $15.17 ($7.74) | Gamma | Foster. Unpublished. |
| First-line drug sensitivity test, mean (standard deviation) | $20.30 ($7.28) | Gamma | Cunnama 2016 [42]. |
| Second-line drug sensitivity test, mean (standard deviation) | $25.10 ($20.22) | Gamma | Cunnama 2016 [42]. |
| Provider cost of clinic visit for initial diagnosis and monitoring | $8.63 | Fixed | Vassall 2017 [43]. |
| Provider cost of clinic visit for treatment | $3.89 | Fixed | Vassall 2017 [43]. |
| Patient cost of clinic visit | $2.90 | Fixed | Foster 2015 [44]. |
| Guardian cost per clinic visit | $10.04 | Fixed | Foster 2015 [44]. |
| Cost of caregiver per day | $0.69 | Fixed | Foster 2015 [44]. |
| Resource use along the diagnostic pathway | Detailed input available from S1 Text. | Gamma | Estimated by disease progression. Reported in Vassall 2017 [43]. Foster 2015 [44]. |
| Provider cost of drug sensitive TB treatment, episode | $192.99 | Fixed | Estimated based on patient movements through care observed in the trial. Reported in Vassall 2017 [43]. Foster 2015 [44]. |
| Provider cost of multi-drug resistant TB treatment, episode | $10 802.66 | Fixed | Estimated based on patient movements through care observed in the trial. Reported in Vassall 2017 [43]. Foster 2015 [44]. |
| Patient cost of drug sensitive TB treatment, episode | Cost of accessing care associated $459.16; | Time-dependent functions | Foster 2015 [44]. |
| Cost of illness $135.94 | |||
| Patient cost of multi-drug resistant TB treatment, episode | Cost of accessing care associated $3 592.27; | Time-dependent functions | Foster 2015 [44]. |
| Cost of illness $2 442.03 | |||
In the Table, a fixed distribution refers to a distribution one where no uncertainty interval is estimated in keeping with calibration practice in complex models. Furthermore, IQR = interquartile range; TB = tuberculosis; MDR-TB = multi-drug resistant tuberculosis; Xpert = Xpert MTB/RIF; HIVpos = individuals HIV positive not yet started on anti-retroviral therapy; HIVpos_TB = individuals HIV positive with tuberculosis; ART = individuals HIV positive started on anti-retroviral therapy; ART_TB = individuals HIV positive on anti-retroviral therapy with tuberculosis.