Technical Appendix (as supplied by author):
Modelling Costs and Effects of TB Control
Introduction
This technical appendix explains the estimation of costs and health effects of TB control strategies in 14 epidemiological sub-regions. It starts with a detailed description of the model, and then discusses the calibration of the model, the projections, and the estimation of costs and health effects at the population level.
Model
The study employs the simplified TB-HIV model as developed by John Stover of Futures Group International (Stover et al. 1998), and as applied by Dye et al. (1998). The model structure is a state-transfer compartmental model, includes age-structures and allows for exogenous reinfection (Fig. 1). The present analysis differs from previous applications in two respects. First, its focus is on the evaluation of both costs and effects of interventions, whereas previous applications assessed the impact of interventions in effects only. Second, it employs different epidemiological sub-regions (i.e. 14 epidemiological regions of the world, developed for the assessment of a wide range of health interventions by the WHO-CHOICE project) and a different, more recent, base-year (year 2000). Definitions of variables and transition parameters are in Table 1.
Figure 1. Flow diagram of the age-structured compartmental
model for tuberculosis
 |
The flow chart in Fig. 1 represents the following set of difference equations. Variables and parameters are defined in Table 1. For brevity, we write S(t,a) as S, and S(t+1, a+1) – S(t,a) as S¢ , with similar mappings leading to L and L’, Ti and Ti,’, and so forth:
(1)
(2)
(3)
(4)
i (5)
(6)
(7)
(8)
(9)
Equation (9) represents immunity in the simplest way. The justification is that we are not primarily concerned with the effect of acquired immunity on TB incidence, but rather with the way in which immunity might influence the impact of DOTS.
The birth of susceptibles requires a boundary condition, S(t,0) = 1, and the maximum lifespan is taken to be 80 years, after which everyone dies. Equations (1)-(9) exclude deaths from causes other than TB because these have no influence on incidence and prevalence rates by age. However, population age structure is an important determinant of transmission, and is therefore included in the force of infection:
(10)
where 
.
The case detection ‘rate’ (d) is the ratio of the treated cases/yr to incident cases/yr. From equations (1)-(9), for example, the incidence rate of infectious cases at age a is:
(11)
Table 1. Definitions of variables and parameters in the age-structured TB model.
|
Symbol |
Interpretation |
|
S(t,a) |
Never before infected, susceptible to infection |
|
L(t,a) |
Latently infected, or cured of TB under good chemotherapy |
|
Ti(t,a) |
Infectious (smear positive) TB; primary, endogenous, exogenous or relapse |
|
Tn(t,a) |
Non-infectious (smear negative) pulmonary and extra-pulmonary TB |
|
Ni(t,a) |
Self-cured, from infectious TB; non-infectious |
|
Nn(t,a) |
Self-cured, from non-infectious TB; non-infectious |
|
Fi(t,a) |
Proportion of Ti whichis not cured under treatment (classed as having ‘failed’, ‘defaulted’ or ‘transferred out’ in cohort analysis) |
|
Fn(t,a) |
As Fi, but from Tn |
|
M(t,a) |
Immune to infection, naturally (MOTT) or following vaccination |
|
I(t,a) |
Incidence rate of infectious (sub I) or non-infectious (sub n) TB |
|
λ (t) |
Incidence rate (all rates per capita) or force of infection, or annual risk of infection (ARI) |
|
β (t) |
Per capita contact rate between Tiand other individuals |
|
θ |
Exponential rate of decline in β , reflecting ‘socio-economic improvement’ |
|
π (t,a) |
Proportion of population in age class a at time t |
|
m+(a) |
Rate at which immunity is acquired by S as a result of non-specific natural infection (age-independent) or vaccination (age-independent, or children < 1 yr) |
|
m- |
Rate at which protective immunity is lost |
|
μ |
Death rates; subscripts i, n, HIV and TB/HIV refer to different rates for Ti , Tn, THIV and TTB/HIV |
|
f(a) |
Proportion of progressive primary cases which becomes infectious |
|
φ |
Proportion of Fiwhich is infectious |
|
n(a) |
Rate of natural cure for Ti and Tn |
|
p(a) |
Proportion of infected S which develop progressive primary TB (within 1 yr), infectious or non-infectious |
|
r |
Rate of relapse from F to T |
|
rn |
Rate of relapse after self-cure, from N to T |
|
v(a) |
Rate at which L progress to TB by endogenous reactivation |
|
w |
Rate of smear conversion, from non-infectious to (Tn ) to infectious TB (Ti) |
|
x(a) |
Proportion of (exogenously) re-infected L which is susceptible to developing TB within 1yr |
|
d |
Rate at which TB cases are found and treated |
|
k |
Proportion of treated cases given curative chemotherapy |
|
ε |
Relative case detection rate of non-infectious cases |
|
δ |
Proportion of failed treatment cases that are multi-drug resistant |
|
l |
Rate of cure for multi-drug resistant cases |
|
y |
Rate at which multi-drug resistant cases are found and treated |
Table 2. Estimates for transition parameters in Table 1.
|
Parameters |
Value (range) |
Sources |
|
μI |
0.3 (0.2-0.4) |
Rutledge & Crouch 1919, Berg 1939, Drolet 1938, Thompson 1943, Tatersall 1947, Lowe 1954, Springett 1971, NTI 1974, Grzybowski & Enarson 1978 |
|
μn |
0.21 (0.18-0.25) |
Lindhart 1939, Murray et al 1993 |
|
μHIV |
0.25 (0.1-0.33) |
Nunn et al 1992, Nunn & Felten 1994, Edlin et al 1992, Allen et al 1992, Mulder et al 1994, Perriens et al 1995, Whalen et al 1995 |
|
μTB/HIV |
1.0 (0.75-1.0) | |
|
f(£ 15) |
0.08 (0.012-0.1) |
Styblo 1977, Murray et al 1993, Barnett & Styblo 1991 |
|
f(>15) |
0.65 (0.5-0.65) | |
|
f(HIV) |
0.3 (0.19-0.4) |
Colebunders et al 1989, Meeran 1989, DeCock et al 1991, Githui et al 1992, Elliot et al 1993, Sassan Morokro et al 1994, Nunn et al 1994, Cauthen et al 1996, Espinal et al 1996 |
|
n |
0.2 (0.15-0.25) |
Springett 1971, Olakowski 1973, NTI 1974, Enarson & Rouillon 1994, Grzybowski & Enarson 1978 |
|
p(£ 15) |
0.04 (0.015-0.14) |
Sutherland 1968, 1976 Ferebee 1970, Comstock 1982, Sutherland et al 1982, Styblo 1986, Krishnamurthy et al 1976, Krishnamurthy & Chaudhuri 1990, Vynnycky 1996, Vynnycky & Fine 1997, Dye et al 1998 |
|
p(>15) |
0.14 (0.08-0.25) | |
|
p(HIV) |
0.67 (0.36-0.8) |
DiPerri et al 1989, Daley et al 1992, Edlin et al 1992, Coronado et al 1993 |
|
r |
0.3 (0-0.5) |
Grzybowski et al 1965, Horwitz 1969, Ferebee 1970, Chan-Yeung et al 1971 |
|
rn |
0.03 (0.02-0.04) |
Springett 1961, Grzybowski et al 1965, Ferebee 1970, Chan-Yeung et al 1971, Campbell 1974, Nakielna et al 1975, Styblo 1986 |
|
v(£ 15) |
5’ 10-5 (0-10-4) |
Horwitz et al 1969, Barnett et al 1971, Sutherland et al 1982, Styblo 1991, Vynnycky 1996, Vynnycky & Fine 1997, Dye et al. 1998 |
|
v(>15) |
1.13’ 10-4 (10-4-3’ 10-4) | |
|
v(HIV) |
0.17 (0.04-0.2) |
Schulzer et al 1992 |
|
x(£ 15) |
1.0 (0.5-1.0) |
Sutherland 1968, Sutherland et al 1982, Vynnycky 1996, Vynnycky & Fine 1997, Dye et al 1998 |
|
x(>15) |
0.35 (0.1–0.6) | |
|
x(HIV) |
0.75 (0.5-1.0) |
Assumed (no data) |
|
w |
0.015 (0.007-0.02) |
Ferebee 1970, HKCS 1974 |
|
m+(a) |
0.2 (0-0.5) for infant vaccination; natural immunity excluded from calculations in this paper |
Colditz et al 1994, Fine 1994, 1995 |
|
m- |
0.15 (0.06-0.2) |
MRC 1972, Hart & Sutherland 1977, BTTA 1975 |
|
δ |
0.58 (0..29-0.8) |
Suarez et al 2002 |
|
l |
0.48 (0.3-0.7) |
Suarez et al 2002, Leimane et al. 2005 |
|
y |
1 |
Assumed (no data) |
Note: All rates are per capita per year; ranges have been subjected to (one way) sensitivity analysis (see Main text)
Calibration
We calibrated the model to produce TB incidence, prevalence and mortality rates for each region for the period 1950-2000 that matched those actually observed in the same period, based on the best and most recent available evidence (WHO 2004). This was done by establishing equilibrium rates by age (0-80 years) in the starting year of analysis by dropping the time dependence in equations (1)-(9), and then solving numerically. The equilibrium value of β was calculated from the relation between force of infection and the prevalence of smear positives (equation 10). We chose 1950 of starting year of analysis for all regions (approximately when drugs became widely available). We applied similar transition parameters and regional case detection and cure rates for the period 1950-2000 to those specified in Dye et al. (1998), with 1995 values to be similar to year 2000 values. Regional population estimates, including background mortality rates, were based on WHO estimates (WHO 2000). Regional HIV/AIDS estimates of incidence, prevalence and case-fatality for the period were based on UNAIDS internal projections, and were applied to each of the 9 classes of individuals in Figure 1. We then have a parallel 9-class TB/HIV model, with the different transfer rates indicated in Table 2. A number of indicators can be used to describe the model, and are presented in Table 3.
Table 3. Model indicators, year 2000.
|
Epidemiological sub-regions | |||
|
|
AFRO E |
SEARO D | |
|
Indicators | |||
|
Annual risk of infection (ARI %) |
2,5 |
2,6 | |
|
Incidence rates (new cases per 105 per year) | |||
|
All forms |
369 |
155 | |
|
Infectious cases |
180 |
107 | |
|
Ratio incidence rate infectious cases/ARI |
73 |
42 | |
|
Prevalence rate (infectious cases per 105 per year) |
236 |
161 | |
|
Death rate (all forms per 105 per year) |
361 |
96 | |
|
Change in annual risk of infection (% per year) |
7,5 |
-1,7 | |
|
Change in incidence rate (% per year) |
8,5 |
-1,1 | |
|
Change in contact rate (% per year) |
-0,3 |
|
-0,6 |
Projection
We used the calibrated model to make a number of projections. To allow the effectiveness of current practices to be evaluated, we first estimated what would happen to transmission, morbidity and deaths if all current interventions ceased. By then introducing all possible interventions against this background of no interventions being implemented, we estimated the population health effects (and costs) of those interventions.
Each projection simulated the change from equilibrium (steady state with respect to time), accounting for (a) the initial incidence rate in each country, (b) the duration and background rate of decline in TB (based on ARI data and modelled by reducing β ) (Cauthen et al 1988, Murray et al 1993), (c) the recent history of, and prospects for improving, case finding and cure rates, (d) demography. We assume that DOTS programmes for treatment of smear-postive and smear-negative cases provides cure rates of 85% for everyone treated (the same for HIV-positive and negative; Grosset 1992, Harries 1997), and that case detection increases from year 2000 levels to 70% (except for Western European regions that have higher rates) over a period of ten years (Evans et al. 2005). We assumed that 100% of treatment failures with MDR are identified and that the cure rate is 48% over the period (Suarez et al. 2002).
Numerical simulations of equations (1)-(9) were carried out for a population of constant, arbitrary size, in each of the 14 epidemiological sub-regions. Population age-structures for the 14 epidemiological sub-regions were then used to convert rates (incidence, prevalence etc) to numbers; these different age-structures reflect births and deaths (all causes, including TB).
Estimating population health and costs
On the basis of the projected incidence, prevalence and mortality data, we estimated the population impact of the different scenarios in terms of healthy years lived (HYL). To do so, we used a population model PopMod (Lauer et al. 2003). Health state valuations were taken from the Burden of Disease study (Murray et al. 1996). The model was run for 100 years, i.e. the length of time necessary for all people affected by the interventions over the ten years of the analysis to have died. The difference between the HYL in each intervention scenario and the no-intervention scenario is the health gain of the intervention. This can also be interpreted as the number of disability adjusted life-years (DALYs) averted.
To estimate total patient costs, the project numbers of patients for each intervention were multiplied by the cost per patient. Details on the calculations of patient costs are provided in Tables 4 and 5. Programme costs were estimated independent of the model, and its details are reported elsewhere (WHO-CHOICE website).
Table 6 shows the results for patient and programme costs.
Table 4. Resource use patterns for treatment of smear-positive, smear-negative, and MDR cases
|
Intervention component |
Resource use |
Volume/costs* |
|
DIAGNOSTICS † ‡ |
|
|
|
Treatment of smear-positive cases |
# smears to detect one smear+ |
30 |
|
# X-rays per smear+ to detect 1 smear- |
9 | |
|
DRUGS§ |
|
|
|
Treatment of smear-positive cases |
Intensive phase | |
|
regimen |
2/HRZE(3) | |
|
# weeks |
8 | |
|
# days per week |
3 | |
|
cost per regimen |
$4.39 | |
|
Continuation phase | ||
|
regimen |
4/HR(3) | |
|
# weeks |
16 | |
|
# days per week |
3 | |
|
cost per regimen |
$3.45 | |
|
total doses |
72 | |
|
Treatment of smear-negative cases |
Intensive phase | |
|
regimen |
2/HRZ(3) | |
|
# weeks |
8 | |
|
# days per week |
3 | |
|
cost per regimen |
$2.33 | |
|
Continuation phase | ||
|
regimen |
4/HR(3) | |
|
# weeks |
16 | |
|
# days per week |
3 | |
|
cost per regimen |
$3.45 | |
|
Treatment of MDR cases |
regimen | |
|
# weeks |
78 | |
|
# days per week |
7 | |
|
cost per regimen |
$264.49 | |
|
HEALTH CENTRE VISITS |
|
|
|
Treatment of smear-positive cases |
Intensive phase | |
|
# weeks |
8 | |
|
days per week |
3 | |
|
# visits |
24 | |
|
Continuation phase | ||
|
# weeks |
16 | |
|
days per week |
1 | |
|
# vists |
16 | |
|
Intensive + Continuation phase |
40 | |
|
Monitoring visits |
# visits |
3 |
|
Total (supervision + monitoring) |
|
43 |
|
monitoring diagnostics |
smears |
6 |
|
Treatment of smear-negative cases |
Intensive phase | |
|
# weeks |
8 | |
|
days per week |
3 | |
|
# visits |
24 | |
|
Continuation phase | ||
|
# weeks |
16 | |
|
days per week |
0.25 | |
|
# visits |
4 | |
|
Intensive + Continuation phase |
28 | |
|
Treatment of MDR cases |
Intensive phase | |
|
# weeks (3 months) |
12.5 | |
|
# days per week |
6 | |
|
# visits |
75 | |
|
Continuation phase | ||
|
# weeks (15 months) |
62 | |
|
# days per week |
6 | |
|
# visits |
375 | |
|
intensive + Continuation phase |
450 | |
|
Monitoring visits |
# visits |
18 |
|
Total (supervision + monitoring) |
|
468 |
|
monitoring diagnostics |
# smears |
18 |
|
# culture |
9 | |
|
# X-ray |
3 |
* Costs are presented in I$. Because drugs are traded goods, these costs are equivalent to US$. Details of this approach are reported elsewhere.12
† Based on the assumption that one per 10 TB suspects presenting to health centres is tested smear-positive. Since each suspect is tested with three smear tests, this means that 30 smears are used to detect one smear-positive case. The remaining nine suspects remain suspect cases and are tested with an X-ray. This means that for every case that is tested smear-positive, 9 X-rays are performed which will detect x number of smear-negative cases. The number of X-rays used for case-detection of x smear-negative cases is then equal to 9*smear-positive cases detected (and is then independent of x).
‡ #=number
§ H=Isoniazid R= Rifampicin Z=Pyrazinamide E=Ethambutol K=Kanamycin Cx=Ciprofloxacin Et=Ethionamide
Table 5. Unit costs (I$)*
|
Region |
Coverage |
Health facility† |
Laboratory tests | ||||||
|
Outpatient visit |
Inpatient day |
Smear test |
X-ray |
Culture test | |||||
|
Afr-E ‡ |
50% |
$3.98 |
$15.94 |
$1.99 |
$34.55 |
$24.68 | |||
|
80% |
$5.84 |
$15.94 |
$2.00 |
$34.67 |
$24.77 | ||||
|
95% |
$7.18 |
$15.94 |
$2.01 |
$34.80 |
$24.86 | ||||
|
Sear-D § |
50% |
$3.85 |
$14.95 |
$1.14 |
$23.91 |
$17.08 | |||
|
80% |
$3.85 |
$14.95 |
$1.14 |
$23.91 |
$17.08 | ||||
|
95% |
$3.85 |
$14.95 |
$1.14 |
$23.91 |
$17.08 | ||||
|
* Costs are expressed in I$ and can be converted in US$ for a reference country in a region. For example, cost estimates in Afr-E in I$ should be divided by a factor 4.5 to obtain US$ cost estimates for Kenya. In Sear-D, this factor is 5.2 to obtain US$ cost estimates for India. Details of this approach are discussed elsewhere .12 | |||||||||
|
†Estimates may seem low because of the assumption of technical efficiency.26 | |||||||||
|
‡ Costs of smear tests and X-rays based on 1998 Malawi data (converted to year 2000 prices using GDP deflators), costs of culture test based on 2000 Peru data. All cost estimates are converted to country-specific estimates using purchasing power parity exchange rates. Differences in costs vary by coverage level because of local distribution costs. | |||||||||
|
§ Costs of smear tests based on 2000 China data, costs of X-rays based on 1998 Malawi data (converted to year 2000 prices using GDP deflators), costs of culture test based on 2000 Peru data. All cost estimates are converted to country-specific estimates using purchasing power parity exchange rates. | |||||||||
Table 6 Cost (in international dollars ($Int)) and DALYs averted per patient for different strategies for tuberculosis control in the two regions Afr-E and Sear-D
|
Region and coverage level |
Patient costs for treatment ($Int)* |
Programme costs for treatment ($Int)† |
DALYs averted by intervention strategy‡ | |||||||||
|
Smear-positive cases |
Smear-negative and extra-pulmonary cases |
After treatment failure |
Smear-positive cases |
Smear-negative and extra-pulmonary cases |
After treatment failure |
Minimal DOTS |
Full DOTS |
Minimal DOTS plus resistant cases |
Full combination | |||
|
Afr-E: | ||||||||||||
|
50% |
209 |
327 |
2284 |
266 |
32 |
711 |
72 |
42 |
72 |
42 | ||
|
80% |
280 |
374 |
3068 |
257 |
45 |
934 |
72 |
42 |
72 |
42 | ||
|
95% |
332 |
408 |
3633 |
300 |
86 |
1703 |
72 |
42 |
72 |
42 | ||
|
Sear-D: | ||||||||||||
|
50% |
186 |
321 |
2170 |
236 |
75 |
214 |
55 |
45 |
51 |
43 | ||
|
80% |
186 |
321 |
2171 |
476 |
70 |
1427 |
55 |
45 |
51 |
43 | ||
|
95% |
186 |
321 |
2171 |
493 |
77 |
1551 |
55 |
45 |
51 |
43 | ||
Costs are given in international dollars (a hypothetical unit of currency that has the same purchasing power that the US$ has in the United States at a given point in time). Details of this approach are discussed elsewhere.18
*Patient cost may differ by coverage level because of differences in costs of outpatient visits and local distribution costs of goods.
†Programme costs may differ by coverage level because of differences in cost functions and number of patients treated.
‡See methods section for details of interventions.
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