PSI Tuberculosis Health Impact Estimation Model. Warren Stevens and David Jeffries Research & Metrics, Population Services International

Transcription

1 PSI Tuberculoss Health Impact Estmaton Model Warren Stevens and Davd Jeffres Research & Metrcs, Populaton Servces Internatonal June 2009

2 Ths document may be freely revewed, quoted, reproduced or translated, n part or n full, provded the source s acknowledged: Stevens W and Jeffres D (2009). PSI Tuberculoss Health Impact Estmaton Model. Washngton, DC: Populaton Servces Internatonal. Avalable at: PSI shares ts models wth all nterested ndvduals or organzatons. Please note that the models are updated perodcally based on the latest avalable epdemologcal, demographc, nterventon effectveness, and utlzaton data. As a result, numbers used n ths document should be consdered llustratve only. They show how the model works, but they are lkely to have changed snce the tme of wrtng. For more nformaton or the latest model updates, contact Amy Ratclffe at aratclffe@ps.org. Populaton Servces Internatonal, 2009 P S I 2

3 Contents Background... 4 Secton 1: Estmatng the Country Specfc Dsease Burden for Tuberculoss... 4 Secton 2: Estmatng the Impact of the PSI Tuberculoss Interventon... 6 Secton 3: Structure of Compartment Model... 7 Secton 4: Case Detecton Rates Secton 5: Runnng the Compartment Model Secton 6: Converson to Country Populaton Secton 7: Further Work References Appendces Appendx I Model Parameters for Calculaton of TB Burden Appendx II Model Parameters for Calculaton of Interventon Appendx III Compartment Model for Tuberculoss (TB) Appendx IV Startng Values for Compartment Model Appendx V Database Descrpton P S I 3

4 PSI Tuberculoss Health Impact Estmaton Model Background Populaton Servces Internatonal (PSI) s a socal marketng organzaton that promotes healthy behavors n low ncome and vulnerable populatons. PSI has programs n 65 countres ( and covers a wde range of health areas ncludng tuberculoss (TB) case detecton, referral, and treatment. PSI uses the dsablty adjusted lfe year (DALY) as the metrc for measurng the mpact of nterventons n health areas. A DALY model has been developed for each of PSI s product/servces and behavor change communcatons (BCC) nterventons. The DALY model presented here s the TB DALY model for early detecton, referral, and treatment. The TB DALY model uses country specfc data from publcly avalable data sources to calculate the burden of TB for HIVpostve and HIV negatve persons age 15 and over (15+), aggregated by 5 year age groups. Interventons are modelled usng a compartment model (Glazou, 2006) to compare predctons from standard and mproved TB treatment scenaros from the same baselne. Data nput tables and calculaton detals are produced by the model to facltate replcaton and comparson wth other predctve models. The model can be run ndvdually for specfc countres or n batch mode to calculate burdens and DALY coeffcents for multple PSI countres. Secton 1: Estmatng the Country-Specfc Dsease Burden for Tuberculoss The TB burden s calculated from the latest WHO data (WHO, 2008), 18 separate TB related parameters collected n The DALY model can be updated wth future datasets by replacng the relevant parameters descrbed n Appendx I. The WHO data ncludes TB ncdence, prevalence, and deaths for all populatons and for HIV postve populatons; the HIV negatve parameters are deduced from these data. The TB burden calculaton s then dvded nto HIV postve and HIV negatve subjects, and deaths and DALYs are estmated usng the followng approach: Death rate = deaths/(prevalence of TB cases + ncdence of TB cases), where death rate refers to the number of deaths per year. Duraton = prevalence of TB (all forms)/ncdence of TB (all forms) Calculaton of number of deaths from ncdence cases: Step 1: Deaths n frst year = Number of ncdence cases * death rate Step 2: Alve at end of year = Number of ncdence cases deaths n frst year Assume a Posson dstrbuton wth mean of estmated duraton (equals prevalence of TB/ncdence of TB), for the duraton of TB: Step 3: From Posson dstrbuton, calculate the probablty of those who survve the frst year havng TB for more than 1 year Step 4: Deaths n second year = Number alve at end of year * probablty of havng TB for more than 1 year * death rate Repeat Steps 3 and 4, cumulatng number of deaths untl convergence wthn 1*10 5 Note: Ths assumes that the death rate for TB remans constant throughout dsease duraton. EXAMPLE: Take the example of 1000 ncdent cases, a death rate of 0.13, for a perod of 18 months. P S I 4

5 Startng wth 1000 cases n the frst year, a death rate of 0.13 wll lead to the death of 130 subjects. Ths leaves 870 subjects n the cure set. Of these, 790 wll go on to second year (Posson dstrbuton). Startng the second year wth 790 subjects, of the 790 wll de (0.13*790) leavng 687 n the cure set. Of the 687 left n the cure set, 47 wll go on to thrd year (Posson dstrbuton). Startng the thrd year wth 47 subjects, 6.11 wll de, leavng 41 n the cure set. Of these, wll go through and after one addtonal loop the convergence condton wll be satsfed, gvng a total of deaths. Fgure 1 below llustrates how the number of cases contnung to the second year s estmated usng the Posson dstrbuton: Probablty of duraton >12 months = Therefore, for 870 subjects n a rsk set, the expected number of subjects wth TB duraton greater than 12 months s *870 = 790. Fgure 1: Posson dstrbuton showng probablty of case duraton greater than 12 months 0.1 posson dstrbuton wth mean = 18 months probablty month Deaths are calculated n the same way for both HIV postve and HIV negatve subjects. The populaton s dvded nto 5 year age groups, wth years of lfe lost (YLLs) calculated n the usual manner, usng 1) md pont age for each group, 2) lfe expectancy of 81.25, and 3) dscount rate of 3%. Note that for the 80+ age group, an age estmate of 81 was used. Years of lfe lved wth dsablty (YLDs) are calculated as ncdent cases * duraton for both HIV postve and HIV negatve groups The DALY s then calculated by combnng YLL and YLD, usng YLD weghtng of (Jamson et al., 2006). DALY = YLL *YLD P S I 5

6 Note that: São Tome s the only PSI country not avalable for analyss; ths s because of ncomplete data. Regonal estmates are not calculated because of the heterogenety of the datasets. They can of course be aggregated from relevant countres. Secton 2: Estmatng the Impact of the PSI Tuberculoss Interventon A compartment model (Glazou, 2006) s used to predct TB ncdence, prevalence, and deaths for a one year perod. The model s run for both exstng TB control parameters and an nterventon scenaro. The dfference n the total number of DALYs for each scenaro after one year s the estmated mpact of the nterventon. The PSI tuberculoss nterventon s assumed to do the followng: 1. Reduce treatment delay for TB cases; 2. Increase the case detecton rate (CDR); and 3. Improve the treatment success rate (TSR). Step 1: Estmatng reduced treatment delay. It s assumed that there wll be 9.5 nfectous contacts per person per year worldwde (Glazou, 2006). Assumng unformty, ths yelds an estmated 9.5/12 contacts per month. It s assumed that because of the PSI nterventon, TB cases are detected one month earler, reducng the number of nfectous contacts per person per year to 9.5*(1 1/12) = 8.71 contacts. Step 2: Estmatng ncreased case detecton. It s assumed that there s lnear mprovement n the case detecton rate (see Secton 5), wth an 18% mprovement for a case detecton rate (CDR) of 42%, and 0% mprovement for a casedetecton rate of 95%. The modellng s shown below n Fgure 2. Fgure 2 Relatonshp between case detecton rates (CDR) and PSI nterventons P S I 6

7 Although these mprovements are coded nto the model, a straghtforward modfcaton would allow them to be nput drectly. Alternatve relatonshps between percentage mprovement and actual CDR could also be mplemented. Note: The CDR for smear negatve TB was bounded at a maxmum of 85%. Stage 3: Estmatng mproved treatment success rate (TSR). The fnal assumpton s an ncrease n the treatment success rate (TSR) of 15%. Ths s assumed as unversal, but t can be altered n the edt parameters functon of the model. As wth all PSI Health Impact Estmaton Models, the nterventons delvered by PSI are assumed to be part of the wder health system structure. Each model s desgned to measure just the ncremental mpact of PSI s role n allevatng the epdemc. Real morbdty and mortalty data are used to ncorporate the lkelhood that other enttes wll treat dsease states outsde the scope of PSI n the health system. The assumpton s that wthout PSI s nterventon, cases would be detected at a rate equvalent to that of the Natonal TB Program (NTP) case detecton rate. In the TB DOTS nterventon model, t s assumed that the DALYs averted by PSI s nterventon are lmted to mprovements n the delvery of DOTS rather than the number of DALYs averted by each DOTS case. The mpact of the TB DOTS nterventon s measured as the sum of mprovements n 1) treatment delay, 2) case detecton rate (CDR), and 3) treatment success rate (TSR), NOT the resultng DALYs averted from DOTS as a whole. The latter s measured as the dfference between the outcomes from NTP only rates and PSI rates for delay, detecton, and treatment. Secton 3: Structure of Compartment Model Fgure 3 below shows the 10 compartments used to model the progresson of TB nfecton. There are separate models for HIV postve and HIV negatve populatons because of dfferences n the transmsson propertes of TB. Seroconverson wthn the past year s not modelled. The dfferental equatons descrbng ths model are presented n Appendx III. The flow of subjects through the 10 compartments depends on the followng parameters, whch are assumed to have the same values for all countres n the model. It s lkely that some of the parameters wll be country specfc and dffcult to obtan; however, they could easly be ncorporated nto the model. P S I 7

8 Table 3 Parameters for compartment models (fxed for all countres) Parameter Value Contact rate 9.5 Relatve contact rate for MDR 0.5 DST and DOTS plus coverage 0.5 Cure rate drug susceptble TB (DOTS) 0.87 Cure rate drug susceptble TB (non DOTS) 0.7 Cure rate of MDR wth DOTS frst lne regmen 0.25 Cure rate of MDR wth DOTS plus regmen 0.75 Death rate from causes other than TB per year Fracton of newly nfected persons who develop TB 0.14 Natural cure rate 0.08 Breakdown rate of MDR followng treatment falure 0.15 Relapse rate 0.02 Reactvaton rate Fracton of renfected persons who develop TB at reactvaton rate 0.35 Percentage of latent TB 0.17 Fracton of HIV+ pop wth nfectous TB 0.35 Fracton of HIV pop wth nfectous TB 0.45 Source: Glazou, 2006 The case detecton rates descrbed n the followng secton and the death rates are country specfc. P S I 8

9 Fgure 3 Compartment model for TB progresson (MDR = multple drug resstant) P S I 9

10 All nput parameters for the nterventon model, whether constants or calculated, can be dsplayed usng the dsplay nterventon button. The parameters extracted from the WHO dataset are lsted n Appendx II. P S I 10

11 Secton 4: Case-Detecton Rates The case detecton rate (CDR) s a key component of the TB model and country specfc rates from WHO 2006 data are avalable (WHO, 2008). The CDR s the number of TB cases notfed, dvded by the number of cases estmated for the year, expressed as a percentage. Estmates of ncdence rates are uncertan; therefore, CDR estmates can be naccurate. A partcular problem wth CDR estmates s that f TB programs are targetng prevalent cases, the CDR rate can exceed 100%. To allevate the problem, data from four consecutve years was averaged to obtan country specfc, casedetecton rates (rather than usng the WHO estmates from the 2006 survey). After averagng, four PSI countres stll had unrealstc CDRs for nfectous TB, as shown below n Table 4. Table 4 PSI countres wth unrealstc case detecton rate (CDR) for nfectous TB Country CDR for nfectous TB Costa Rca Mexco Belze Honduras Assumng that these four countres have 100% DOTS coverage, fttng a lnear regresson (sgnfcant at 5% level) on all PSI countres wth a CDR for nfectous TB under DOTS <94% gves: CDR for nfectous TB under DOTS = * CDR for all TB under DOTS Ths gves CDR estmates for nfectous TB of 72%, 72%, 58%, and 58%, respectvely, for Costa Rca, Mexco, Belze, and Honduras, replacng the Table 4 values n the model. Four case detecton rates are used n the model; they are the followng: CDR for DOTS nfectous TB CDR for DOTS non nfectous TB CDR for non DOTS nfectous TB CDR for non DOTS, non nfectous TB Note: The majorty of countres have 100% DOTS coverage. The followng example shows how each CDR s calculated for Angola. The black values are from the WHO data ncluded n the model; the orange values n talcs are derved. Part 1 Establsh the case detecton rates for DOTS and non DOTS Overall case detecton rate = 76% Case detecton rate for DOTS = 59% Case detecton rate for non DOTS = 76% 59% = 17% P S I 11

12 Part 2 Establsh the nfectous case detecton rates for both DOTS and non DOTS Case detecton rate for both DOTS and non DOTS nfectous = 90.59% Case detecton rate for DOTS nfectous = 88.93% Case detecton rate for non DOTS nfectous = 90.59% 88.93% = 1.66% Part 3 Establsh the non nfectous, case detecton rates for both DOTS and non DOTS Total number of ncdent nfectons = Number of ncdent smear postve nfectons = Number of ncdent smear negatve nfectons = = CDR rate for DOTS (or non DOTS) = [(CDR_smear_postve*smear postve_ncdence) +(X*smear negatve_ncdence)]/( smear postve_ncdence+ smearnegatve_ncdence), where X s the CDR for smear negatve subjects under DOTS or non DOTS. For DOTS: 0.59 = [0.8893* X* ]/ X = (0.59* * )/ = 35.06% Case detecton rate for DOTS non nfectous = 35.06% For non DOTS: 0.17 = [0.0166* X* ]/ X = (0.17* * )/ = 29.3% Case detecton rate for non DOTS, non nfectous = 29.3% As descrbed n Appendx III, the compartment model uses the patent dagnostc rate (PDR), whch has been proposed as an alternatve to the case detecton rate (Borgdorff, 2004). For the compartment model used n the model, the patent dagnostc rate and the case detecton rate are related through the followng defnton: PDR CDR = PDR + rate undagnosed patents For ths model, the rate of undagnosed patents s provded by the subjects who de from TB (whch s dependent on HIV status and type of TB) and those who self cure (whch s currently set as a global varable). CDR = PDR PDR + TB death rate per year + TB self cure rate per year P S I 12

13 Rearrangng the formula allows estmaton of the PDR from the CDR as follows: ( TB death rate per year + TB self cure rate per year) * CDR PDR = 1 CDR In contrast to the CDR, the patent dagnostc rate measures the number of newly reported cases dvded by the prevalence of new cases, as opposed to the ncdence of new cases, thus avodng havng to estmate ncdent rates. Prevalence s far easer to measure drectly than ncdence, whch s currently estmated. Clearly, from the defnton, the PDR s undefned as the CDR approaches 100% or s estmated at more than 100%, and cannot remedy napproprate case detecton rates. Usng the PDR smplfes the structure of the compartment model equaton, because subjects extng the compartments are calculated as products of the PDR and the prevalence. If the CDR s used, then those subjects extng the compartment are calculated by multplyng the CDR by the ncdence of subjects who enter a compartment (Laxmnarayan et al., 2007). Secton 5: Runnng the Compartment Model Intal startng values for compartments n the model are calculated from country specfc data usng the method descrbed n Appendx IV. Because the model s run from the same baselne for both current TB control and the nterventon, the DALYs averted are not senstve to small changes n the startng values. The nterventon effect s calculated by runnng the compartment model 1) from the baselne through one tme step, 2) wth and wthout an nterventon, 3) for a model populaton of 100,000 subjects, and 4) separately for HIV postve and HIV negatve populatons. The followng example shows how nterventon DALYs are calculated for Zamba. Note that all values are per 100,000 populaton and sales are 12,345 DOTS plus unts. Zamba baselne values for HIV negatve subjects: Prevalence: Incdence: Deaths: One tme step wth no nterventon: Prevalence: Incdence: Deaths: One tme step wth nterventon: Prevalence: P S I 13

14 Incdence: Deaths: These parameters are the same as those used to calculate the TB burden (descrbed n Secton 1 above) and the same method of calculaton can be used. Because the models are run from the same baselne, the numbers of deaths and DALYs averted are calculated by subtractng wth nterventon values from no nterventon values. In the Zamba example, calculatons are as follows: Total TB deaths (for year) = 4.85 ncdent deaths per 100,000 averted ( ) DALYs averted are calculated by estmatng the DALY TB burden (see calculaton of TB burden n Secton 1) and subtractng, to gve the followng: DALYs averted = per 100,000 ( ) Secton 6: Converson to Country Populaton The outcome from the compartment model s based on an dealzed populaton of 100,000 HIV negatve or HIV postve subjects, all of whom are exposed to the nterventon. Therefore, outcomes averted from the compartment model are based on: Populatons of 100, % HIV+ or HIV populatons 100% of TB subjects recevng the nterventon Step 1: The fgures above are converted to populaton values by nputtng current populaton estmates for specfc countres from the Unted Natons Populaton Dvson. Multply by (country populaton) / 100,000 Multply by estmated number [splt] HIV+ and HIV n the country populaton Multply by sales/total number of TB cases In the Zamba example, the number of DALYS averted per 100,000 populaton s: HIV+ populaton: = DALYs averted HIV populaton: = DALYs averted Step 2: From the data contaned n the table HIV_rate, 17% of the Zamban populaton s HIV postve. (Note that these data are dentcal to the HIV rates for regular partners n the HIV model calculatons.) Therefore, the populaton of Zamba s 11,696,160, gvng: DALYs averted n the HIV+ populaton = 0.17*(11,696,160/100,000)* DALYs averted n the HIV populaton = P S I 14

15 (1 0.17)*(11,696,160/100,000)* Step 3: All TB cases are assumed to have receved the nterventon. The absolute ncdence of TB n Zamba from the WHO data s and , gvng a total of 131,014.6 TB cases. Assumng that ths s the maxmum number of DOTS plus treatment courses that can be sold (wth10% wastage ncluded n the model), the values above must be multpled by sales (12,345 n ths example 10% = 11,110.5) over 131,014.6, gvng: DALYs averted n the HIV+ populaton = (11,110.5/131,014.6)* 0.17*(11,696,160/100,000)* DALYs averted n the HIV populaton = (11,110.5/131,014.6)* (1 0.17)*(11,696,160/100,000)* Total DALYs averted = ( ) The number of DALYs averted s confrmed to wthn roundng by model calculaton. Step 4: Ths stage of the model assumes equal nterventon effort n the HIV negatve and HIV postve populatons. A parameter n the model from WHO data (WHO, 2008) ndcates the number of TB cases that are HIV postve. For Zamba, 36.9 % of TB cases are HIV postve. For equal effort, the sales/total number of TB cases parameter has numerator and denomnator multpled by 36.9%; therefore, t remans as the orgnal rato. Suppose, however, that an nterventon s ntated amed at splttng the nterventon effort 2:1 n favor of the HIVpostve group. Then the ratos would be as follows: HIV+ group: (2/3)*patents recruted / (36.9% * total number of TB cases) HIV group: (1/3)*patents recruted / (63.1% * total number of TB cases) A DALY coeffcent could be based on ths scenaro, wth sales of 1, and 100% coverage n each group. The dsadvantage of ths approach s that the multpler for the coeffcents would not be sales, but would be the mnmum of (sales, TB cases n the relevant HIV group). P S I 15

16 Secton 7: Further Work The compartment models are not bounded so an unrealstc case detecton rate can remove all prevalent cases n one year. In realty, the resoluton of all prevalent cases n one year s unlkely and all hgh CDRs should be re evaluated before enterng them nto the model. When runnng the model for one year, any negatve prevalence estmates can smply be set to zero. If the model s run for more than one tme step, however, the model populaton wll no longer be stable and boundng wll be an ssue. Angola model Run the TB model for Angola (sellng 12,345 DOTS plus treatments) and open the compartment model detals to panel 34 for the nfectous drug susceptble compartment for the HIV postve group wth nterventon. P S I 16

17 The estmated prevalence after a one year tmestep s 4.18, whch s set to zero wthn n the code. The CDR rate for ths group s 89%, whch combned wth death rates gves a patent dagnostc rate (PDR) of 2.2 It s lkely that the effcency of the nterventon n Fgure 2 (see Secton 2) s nonlnear, and there may be heterogenety between the HIV negatve and HIV postve populatons. Small, negatve HIV postve compartment totals have been observed for Benn, Cameroon, and Vetnam, countres wth hgh nterventon CDRs and relatvely low baselne HIV+ populatons. Before confdence ntervals can be estmated, the followng areas need to be researched: Senstvty to parameters n Table 3 (see Secton 3) Dstrbutons for mportant parameters (Corbett et al., 2003) Senstvty to compartment startng values Confdence ntervals for WHO data the dstncton between surveyed and derved data s not clear It would be nterestng to compare the effects of recastng the nfectous and nonnfectous compartments n terms of the CDR actng on ncdence rather than the PDR actng on prevalence. Regardng DALY estmates, t s unlkely that recastng wll have much effect because the model s only run for one tme step. The key to accurate DALY estmates remans accurate assessment of the case detecton rate (CDR) or the patent dagnostc rate (PDR). P S I 17

18 References Borgdorff MW (2004). New measurable ndcator for tuberculoss case detecton. Emergng Infectous Dseases 10(9): Avalable at: htm Corbett EL, Watt CJ, Walker N, Maher D, Wllams BG, Ravglone MC, and Dye C (2003). The growng burden of tuberculoss: Global trends and nteractons wth the HIV Epdemc. Archves of Internal Medcne 163(9): Glazou P (2006). Mathematcal modellng of the TB epdemc n the Western Pacfc Regon. Manla: WHO/WPRO. ICF Macro (varous years). Demographc and Health Surveys (DHS) and Geographcal Health Informaton Surveys (GHIS). Calverton, Maryland: ICF Macro. Avalable at: Jamson DT, Breman JG, Measham AR, Alleyne G, Claeson M, Evans DB, Jha P, Mlls A, and Musgrov P, eds. (2006). Dsease control prortes n developng countres, 2 nd edton. Washngton, D.C.: World Bank. Avalable at: Laxmnarayan R, Klen E, Dye C, Floyd K, Darley S, and Adey O (2007). Economc beneft of tuberculoss control. Polcy Research Workng Paper Washngton, D.C.: The World Bank. World Health Organzaton (WHO) (2008). Global tuberculoss control 2008: Survellance, plannng and fnancng. Geneva, Swtzerland: WHO. Avalable at: P S I 18

19 Appendces Appendx I Model Parameters for Calculaton of TB Burden All stored n table TB_demography Parameter Descrpton Country Country lst, ncludes some non PSI countres for testng/possble expanson Regon SSA, FSS, LCA, South Asa, or East Asa breakdown_country Country used to provde age breakdown populaton nc_all Absolute TB ncdence n 2006 nc_hv Absolute TB ncdence n 2006 among HIV+ prev_all Absolute TB prevalence n 2006 prev_hv Absolute TB prevalence n 2006 among HIV+ Deaths_all Absolute number of deaths from TB n 2006 Deaths_hv Absolute number of deaths from TB n 2006 among HIV+ These data were obtaned from the WHO 2008 report, Global tuberculoss control 2008: Survellance, plannng and fnancng, va the fle annex3_global.xls. To facltate future updates the followng table gves the sheet and column d locatons. Parameter Locaton n WHO dataset populaton sheet A3.2 column B nc_all sheet A3.1 column 0 nc_hv sheet A3.1 column R prev_all sheet A3.1 column AA prev_hv sheet A3.1 column AD Deaths_all sheet A3.1 column AG Deaths_hv sheet A3.1 column AJ P S I 19

20 Appendx II Model Parameters for Calculaton of Interventon The parameter column gves the name of the varable n the TB demography set and the locaton s the locaton n the fle annex3_global.xls an annex to the WHO 2008 report. Parameter dots_coverage CDR_all CDR_dots CDR_nfect_all CDR_nfect_dots percent_tb_are_hiv_plus nfectous_rate_hv_plus nfectous_rate ncdent_rate prev_rate_all prev_rate_hv percent_of_ncdence_mdr percent_of_prevalance_mdr Locaton n WHO dataset sheet A3.3 column C sheet A3.2 column AD sheet A3.3 column AC sheet A3.2 column AE sheet A3.3 column AD sheet A3.1 column AL sheet A3.1 column X sheet A3.1 column U sheet A3.1 column O sheet A3.1 column AA sheet A3.1 column AC Source PSI Source PSI Note: The felds n table TB_demography other than those lsted n Appendx I and Appendx II are not currently used. P S I 20

21 Appendx III Compartment Model for Tuberculoss (TB) Ths model s taken from Glazou (2006), wth correctons to typographcal errors and converson to a dfference equaton. Unnfected: S( t) = S( t 1) ( ARI + ARI + μ 0 ) S( t 1) + μ0n + D( t 1) Where D s the total of TB deaths: Pr Ac D( t) = μ sp ( I p ( t) + I p ( t) + I p, ( t)) + μ sn ( I n ( t) + I n, ( )), t Latent nfectons: (Note that the Latent compartment s splt nto drug susceptble, L ds and multple drug resstant (MDR) compartments, L ) [(1 p) S( t 1) ] ( ARI p. x + v + ) L( t 1) L( t) = L( t 1) + ARI μ 0 for = 1,2 (drug susceptble, MDR) Infectous (drug susceptble): I p ( t) = I + p + ARI. p. f. S( t 1) + ( v. f + ARI. p. f. x) L PDRκ + μ0 + μ sp + (1 κ ) ρ. PDR ) I p ds + rl. f. C( t 1) ( ncr(1 PDR PDR n ) for = 1,2 (DOTS, non DOTS) Nonnfectous (drug susceptble): I n ( t) = I n + ARI. p.(1 ( ncr(1 PDR PDR f ). S( t 1) + ( v.(1 n ) + f ) + ARI. p.(1 PDRκ + μ0 + μ sn ) I n f ). x) L ds + rl.(1 f ). C( t 1) for = 1,2 (DOTS, non DOTS) Cured (drug susceptble): C( t) = C( t 1) + PDR. + (1.) κ ncr PDR I( t 1) j ( rl + μ0 ) C( t 1) j for = 1,2 (DOTS, non DOTS) and j = 1, 2 (nfectous and nonnfectous) P S I 21

22 Acqured MDR (nfectous): I Ac p, ( t) = I Ac p, + ( PDR( dst. κ Prmary MDR (nfectous): I Pr p, ( t) = I Pr p, ( ncr(1 Nonnfectous MDR: I n, ( t) = I Cured (MDR): C n, plus + ARI ( PDR( dst. κ + ARI PDR (1 κ ) ρ. I + (1 dst) κ PDR ) + PDR plus. κ p ) + PDR κ + rl. f. C n. p. f. S( t 1) + ( v + ARI n. p.(1 + (1 dst) κ + PDR( dst. κ + ncr(1. p. x). f. L plus f ). S( t 1) + ( v + ARI + PDR κ n + ncr(1 + (1 dst) κ PDR ) + μ + μ ) I. p. x).(1 0 sp + μ + μ ) I f ). L 0 sp PDR ) + μ + μ ) I 0 Ac p, Pr p, + rl.(1 sn n, k ( t) = C + PDR( dst. κ plus + (1 dst) κ ) + PDRnκ + ncr(1 PDR ) I j ( rl + μ ) C 0 k j, f ). C for = 1,2 (DOTS, non DOTS), j = 1, 2 (nfectous and nonnfectous), and k = 1, 2 (acqured, prmary) Annual rsk of nfecton (susceptble and MDR), where N s the model populaton: ARI c. I = N sp ARI c'. I p, = N The parameter defntons are gven below n Table A1; they are also shown n Table 3 (Secton 3 of the man text). Separate models are run for HIV postve and HIV negatve populatons; thus there are separate rates for the fractons of nfectous TB cases that are HIV postve and HIV negatve. P S I 22

23 Table A1: Defntons and values of parameters and varables used n the model Parameter Defnton Value c Per capta contact rate of nfectous, drug susceptble cases per year 9.5 c'/c Relatve contact rate of nfectous, MDR TB 0.5 x Fracton of renfected persons who develop TB at rate v 0.35 p Fracton of newly nfected persons who develop prmary progressve TB 0.14 f Fracton of TB cases that are nfectous: For HIV 0.45 Fracton of TB cases that are nfectous: For HIV ncr Per capta self cure rate 0.15 rl Relapse rate 0.02 v Reactvaton rate μ 0 Per capta death rate from causes other than TB per year μ sp Per capta death rate of nfectous TB 0.3 μ sn Per capta death rate of nonnfectous TB 0.1 ρ Breakdown rate of MDR TB followng treatment falure n nfectous TB 0.15 κ Cure rate of drug susceptble TB (DOTS) 0.85 κ n Cure rate of drug susceptble TB (non DOTS) 0.7 κ Cure rate of MDR wth DOTS frst lne regmen 0.25 κ plus Cure rate of MDR wth DOTS plus regmen 0.75 DST DST and DOTS plus coverage 0.5 Source: Glazou, 2006 P S I 23

24 Appendx IV Startng Values for Compartment Model The compartment model must have startng values for each of ts 10 compartments. These are calculated from the TB demographc data for each country to gve the correct overall nfecton, prevalence, and death rates for the countres. Zamba example: In the Zamba example below a smlar methodology s used for the HIV postve and HIV negatve populatons. Calculaton of TB (SS+) and TB (SS ) rates per 100,000 SS+ s nfectous TB SS s nonnfectous TB Black numbers are values from country specfc TB data Orange numbers are derved values Incdence rate of TB (SS+) = per 100,000 Incdence rate of TB (SS+) n HIV+ subjects = per 100,000 Therefore, the ncdence rate of TB (SS+) n HIV subjects = Percentage of TB subjects HIV+ = 36.9% Overall ncdence rate of TB = per 100,000 subjects Therefore, the ncdence rate of TB (SS ) n HIV subjects = ( )% * = The prevalent cases can be added n, assumng that the percentage of TB (SS ) and TB(SS+) subjects are the same as those n the ncdent cases. Percentage of TB (SS ) subjects = 191.9/( ) = 55% and TB (SS+) = 45% Prevalent rate of TB (SS+) = 45%*(TB prevalence rate TB prevalence rate for HIV) = 45%*( ) = Prevalent rate of TB (SS ) = 55%*(TB prevalence rate TB prevalence rate for HIV) = 55%*( ) = TB (SS+) rate per 100,000 = = TB (SS ) rate per 100,000 = = P S I 24

25 Calculaton of TB (SS+) and TB (SS ) rates per 100,000 for multdrug resstant tuberculoss (MDR TB) There are three compartments for multdrug resstant tuberculoss (MDR TB), acqured and prmary, whch are both nfectous and nonnfectous MDR. Zamba example for HIV negatve populaton: 1.8% of ncdent TB cases have MDR TB 2.3% of prevalent TB cases have MDR TB CDR for TB (SS+) = 53.9% (Note: CDR DOTS for both SS+ and SS = 71%) CDR for non DOTS TB (SS+) = 0% (Zamba s 100% DOTS) Cure rate for drug susceptble TB (DOTS) = 0.87 Cure rate for drug susceptble TB (non DOTS) = 0.7 Breakdown rate of MDR TB followng treatment = 0.15 Incdent rate of TB (SS ) subjects = Prevalent rate of TB (SS ) subjects = Fracton of TB cases that are nfectous = 0.45 Number of ncdent TB (SS+) cases = Number of prevalent TB (SS+) cases = Natural cure rate = 0.08 Death rate from TB (SS+) = 0.11 Death rate from TB (SS ) = Patent detecton rate (PDR) = (natural cure rate + death rate) *CDR/(1 CDR) MDR acqured (SS+) = PDR dots *(1 cure rate DOTS)*breakdown rate of MDR*Number of SS+ cases Incdent MDR acqured (SS+) = 0.23 * (1 0.87)*0.15*156.8 = 0.70 Prevalent MDR acqured (SS+) = 0.23 * (1 0.87)*0.15*209.5 = 0.94 Incdent MDR prmary (SS+) = % of ncdent case wth MDR TB*ncdent number of SS+ cases ncdent MDR acqured (SS+) = 0.018* = 2.12 Prevalent MDR prmary (SS+) = % of prevalent case wth MDR TB*prevalent number of SS+ cases prevalent MDR acqured (SS+) = 0.023* = 3.88 P S I 25

26 Incdent MDR prmary (SS ) = % of ncdent case wth MDR TB*ncdent number of SS cases = 0.018*191.9 = 3.45 Prevalent MDR prmary (SS ) = % of prevalent case wth MDR TB*prevalent number of SS cases = 0.023*256.0 = 5.89 Acqured nfectous MDR compartment = = 1.64 Prmary nfectous MDR compartment = = 6.00 Nonnfectous MDR compartment = = 9.34 Calculaton of nfectous and nonnfectous drug susceptble compartments Example for Zamba HIV negatve populaton: Infectous drug susceptble compartment = (ncdent + prevalent) (MDR acqured + MDR prmary) Infectous drug susceptble compartment = ( ) ( ) = Nonnfectous drug susceptble compartment = (ncdent + prevalent) nonnfectous MDR Nonnfectous drug susceptble compartment = ( ) 9.34 = Calculaton of cured compartments There are two cured compartments, one for drug susceptble TB and one for MDR TB. PDR = patent detecton rate Cured for drug susceptble = (PDR nfectous*cure rate)*number of nfectous TB cases + (PDR nonnfectous*cure rate)*number of nonnfectous TB cases Summed over DOTS and non DOTS for PDR and cure rate Cured for MDR = (PDR nfectous for DOTS*(1 DST coverage)*mdr cure rate + PDR nfectous for non DOTS*MDR cure rate)*(mdr acqured nfectons + MDR prmary nfectons) (PDR nonnfectous for DOTS*(1 DST coverage)*mdr cure rate + PDR nfectous for non DOTS*MDR cure rate)*mdr nonnfectous For Zamba HIV populaton, ths gves: Cured drug susceptble compartment = Cured MDR compartment = P S I 26

27 Calculaton of latent TB compartment In the latent TB model t s assumed that there are 100,000 subjects and 17% of the subjects have latent TB nfecton. Latent compartment = 0.17*(100,000 (sum of all subjects n drug susceptble, MDR, and cured compartments). Zamba example: 0.17*(100,000 ( ) = 16,909 (Note: Cured subjects are shown wth plus sgns because they can be renfected by latent TB nfecton). Assume that the splt of latent nto MDR TB s: (ncdent % of MDR*ncdent TB rate + prevalent % of MDR*prevalent rate of TB)/ (ncdent TB rate + prevalent TB rate) Ths gves 2.05% *16,909 = for the latent MDR compartment and 16,562.4 for the latent drug susceptble compartment. Calculaton of unnfected compartment Unnfected compartment = 100,000 (sum of all other compartments) = 81,998 P S I 27

28 Appendx V Database Descrpton The tables and ther purposes are shown to the rght. Yearly updates can be made by replacng the relevant data n the table TB_demography. The forms and ther descrptons are shown below: The calculator should be opened wth the form TB_calc. P S I 28

29 The code s contaned n the followng modules Note: Wthn the module TB_daly_burden, there s an excel worksheet functon that uses the exel lbrary. P S I 29

30 Publc Functon possy(lambda As Double, duraton As Double) As Double ' calcultes the prob that duraton dstrbuted as posson wth mean lambda months s greater than the nput valur duarton n months possy = 1 - WorksheetFuncton.Posson(duraton, lambda, True) End Functon Note: Ths model uses Mcrosoft Excel lbrary 10. If problems are encountered, the posson cdf functon can be hardcoded. P S I th Street, NW Sute 600 Washngton, DC ps.org blog: pshealthylves.com