Projecting the impact of variable MDR-TB transmission efficiency on long-term epidemic trends in South Africa and Vietnam

Whether multidrug-resistant tuberculosis (MDR-TB) is less transmissible than drug-susceptible (DS-)TB on a population level is uncertain. Even in the absence of a genetic fitness cost, the transmission potential of individuals with MDR-TB may vary by infectiousness, frequency of contact, or duration of disease. We used a compartmental model to project the progression of MDR-TB epidemics in South Africa and Vietnam under alternative assumptions about the relative transmission efficiency of MDR-TB. Specifically, we considered three scenarios: consistently lower transmission efficiency for MDR-TB than for DS-TB; equal transmission efficiency; and an initial deficit in the transmission efficiency of MDR-TB that closes over time. We calibrated these scenarios with data from drug resistance surveys and projected epidemic trends to 2040. The incidence of MDR-TB was projected to expand in most scenarios, but the degree of expansion depended greatly on the future transmission efficiency of MDR-TB. For example, by 2040, we projected absolute MDR-TB incidence to account for 5% (IQR: 4–9%) of incident TB in South Africa and 14% (IQR: 9–26%) in Vietnam assuming consistently lower MDR-TB transmission efficiency, versus 15% (IQR: 8–27%)and 41% (IQR: 23–62%), respectively, assuming shrinking transmission efficiency deficits. Given future uncertainty, specific responses to halt MDR-TB transmission should be prioritized.


LIST OF SUPPLEMENTARY FIGURES & TABLES
TB infection results from a density-dependent transmission process. Upon initial infection, populations may progress rapidly to incipient/preclinical/asymptomatic TB (hereafter referred to as early-active TB) or may develop latent infection; those latently infected may reactivate to early-active TB at a constant rate. Individuals in states of early-active TB, symptomatic active TB, ineffectively treated TB, or diagnosed-untreated TB contribute infectious person-time to transmission (with reduced infectiousness and mortality associated with early-active or ineffectively treated TB). Self-cure (with return to the susceptible state) may occur at a constant rate during early-active or active TB.
When TB patients develop fully symptomatic active TB, they may initiate first-line or (in cases of MDR-TB) second-line treatment. Upon initiating treatment, TB patients are separated into states of effective or ineffective treatment; those who complete effective treatment regimens experience culture conversion by the end of the treatment duration. (In the absence of DST, MDR-TB patients can only initiate ineffective first-line treatment). After effective treatment, TB patients may either achieve durable cure (becoming susceptible again) or may eventually relapse; after ineffective treatment, patients may either immediately re-initiate treatment or return to symptomatic active TB. During any TB treatment state, patients may be lost to follow-up; all S.4 those lost from ineffective treatment return to active TB, while those lost from effective treatment may return to active TB or (having received a sufficiently curative treatment before default) may achieve durable cure. HIV status also affects a variety of the dynamics of TB infection. HIV infected populations have higher rates of TB-independent mortality, and those with low CD4 status concurrent with active (untreated) TB experience an additional mortality associated with HIV/TB interactions. The probability of rapid TB progression upon initial infection is increased in HIV-infected populations, while the probability of TB self-cure is reduced. In populations latently infected with TB, HIV co-infection increases the rate of TB reactivation and reduces the S.5 degree of protection against a rapidly progressing superinfection. The infectiousness of each TB disease state is somewhat lower in populations with HIV co-infection than in their HIVuninfected counterparts. Finally, due to more rapid disease progression and more frequent encounters with the health system, active TB reaches diagnosis and treatment initiation more quickly for HIV-infected populations.

TB Transmission
TB transmission occurs as a function of time-varying transmission efficiency coefficients and the size of the infectious TB population. As previously described, we define the transmission efficiency of each strain (DS-TB vs. MDR-TB) as the number of new infections which would develop in a susceptible population from each infectious person-year contributed by prevalent infectious DS-TB or prevalent infectious MDR-TB, respectively. An initial coefficient β S 0 is used to define the equilibrium transmission efficiency of DS-TB cases. Due to secular trends in overall TB incidence in recent years, we allow for the overall transmission of DS-TB β S ( ) to decline at an annual geometric rate d S after the year t S . In Vietnam, we define t S as the first year with data used to calibrate our epidemics ( = 1996). In South Africa, due to the HIV/TB coepidemic over 1995-2010, we felt there was insufficient evidence for secular declines in DS-TB transmission in HIV-uninfected populations starting in the first year of survey data (2001).
Instead, we assumed any such declines would not occur until 2010 ( S = 2010). Therefore, we define the transmission efficiency of DS-TB as follows: In all MDR-TB scenarios we examined, the transmission efficiency of MDR-TB, β R ( ), is initialized at the start of the modern MDR-TB epidemic (in the year R 0 ) with an initial value determined by the initial transmission efficiency of DS-TB β S 0 and a relative efficiency term .
In the Shrinking Efficiency Deficit scenario, the transmission efficiency of MDR-TB is allowed to increase annually (through an annual percentage increase in the relative efficiency coefficient) beginning in the year . (The rate of increase term is set equal to zero in both the No Efficiency Deficit and Constant Efficiency Deficit scenarios, and the relative efficiency term is set equal to one in the No Efficiency Deficit scenario.) Therefore, the transmission efficiency of MDR-TB is defined as: In this way, any declines in DS-TB secular transmission efficiency (after time ) are not necessarily mirrored by MDR-TB, as trends in the transmission efficiency of DS-TB and MDR-TB are likely to occur through different processes (though β R ( ) is never permitted to exceed β S ( )). The general relationship between β S ( )and β R ( ) in each scenario is displayed diagrammatically in Fig. S1. S.7

Figure S1: Transmission Efficiency Scenarios
The assumed transmission efficiency (transmission events per 1,000 infectious person-years) of DS-TB over time is drawn in green; the downward slope recapitulates reductions in TB transmission efficiency due to secular trends unrelated to MDR-TB diagnosis and treatment (for example, reductions in crowding, improved socioeconomic conditions, etc.

Births and Deaths
We make a simplifying assumption of a steady-state population size. "Births" (entry of S.11 For reference, we use UNAIDS country-specific estimates of the prevalence of HIV among adults 15 years and older ̂( ) for the discrete time points ∈ {1990, 1991, … , 2016}. The expected HIV prevalence at time t2 is then calculated by linear interpolation between the two time points nearest in time to t2 (the maximum Y less than t2 and the minimum Y greater than t2): To reach the necessary ( 2 ) between [t1,t2), the number of new HIV infections in this interval ( 1 , 2 ) must therefore equal the expected prevalence minus the prevalence of surviving HIV infections multiplied by the population size: ( 1 , 2 ) = (̂( 2 ) − 0 ( 2 )) × initiation is derived such that the proportion of HIV-infected patients receiving ART are consistent with UNAIDS estimates (Fig. S3B below).
The rate of ART initiation is fitted to UNAIDS estimates in a similar manner used to fit HIV prevalence. We define the proportion of HIV-infected individuals receiving ART at any time A(t) as equal to the cumulative size of ART substates X A divided by the cumulative size of all HIV-infected substates V: After a time interval from [t1,t2), the number of survivors continuing to receive ART ,0 ( 2 ) would equal the number receiving ART at t1 minus the number of deaths (based on the state-specific cumulative mortality rates ) from all ART substates during the time interval: The total ART coverage (continued and newly initiated) expected at time t2 is again fitted to UNAIDS estimates. Based on the shape of UNAIDS estimates of this quantity (Fig. S3B), we used nonlinear (weighted) least squares regression to fit a sigmoid function (assuming ART coverage approaches a future asymptote A max at 60%) of the form: To reach this new level of ART coverage, the number of new ART initiations during the interval ( 1 , 2 ) can be calculated as the number of total individuals receiving ART at t2 minus the number continuing to receive ART: The time-varying rate of ART initiation After 2010, we allow for ART initiation to occur in both Low CD4 and High CD4 populations X H to reflect improved access to HIV care and changing national guidelines for ART provision.
However, ART initiation in High CD4 populations occurs at a lower rate than initiation in Low CD4 populations, according to an initiation coefficient kH (that is, for every one High CD4 patient, there are only kH High CD4 patients eligible for ART). Therefore, the time-varying rate of ART initiation is defined as follows: Finally, among HIV-infected patients receiving TB treatment, this rate of ART initiation is increased by a factor ktb to reflect increased HIV screening in patients diagnosed with TB. Therefore, the total rate of ART initiation in TB treatment states equals ktb ( 1 , 1 ). (Multiplicative factors with superscripts of U or N are set equal to one; thus ρ 0 ρ U = ρ 0 .)

Populations Susceptible to TB Infection
The total population is initiated at a size of 100,000 and forced to remain at steady-state.
The size of newly added populations is forced to equal the number of deaths in the population at any time, defined by the rates of background mortality (μ 0 ), HIV-associated mortality (μ ), and S.17 active-TB associated mortality (μ , reduced by factors associated with early/incompletely treated active TB): All newly added populations are divided between susceptible and latently infected states (described above). We define the forces of infection applied to individuals before entering the population at age 15 as using the approximate forces of infection distributed over the preceding 7.5 years: Transmission of TB Infection Transitions out of the new, latently infected state occur due to background mortality, reactivation to early-active TB (based on the constant rate of reactivation ( 0 )), or reinfection S.20 followed by rapid progression (despite the protection afforded by an existing latent infection As described above, all new 15-year olds are assumed to be initially uninfected. For V ∈ { , , }: Among previously-treated populations, latent infections LP result from new infections of previously-treated TB susceptible populations and superinfections of previously-treated, latently infected populations in the same manner as above. (Newly added 15-year olds are assumed to have negligible previous TB treatment history and are excluded from these populations upon initial entry.) Progression into early-active states E occur from a) a susceptible state S according to the force of infection and the proportion of infections which progress rapidly (ρ 0 ρ ); b) from a latent S.21 state L due to reactivation of endogenous infection according to the rate of reactivation ( 0 ); or c) from rapid progression of a recent, exogenous superinfection according to the proportion of infections which progress rapidly, reduced by the protection afforded by an existing latent infection ((1 − λ 0 λ )ρ 0 ρ ). Transitions from the early-active state occur due to death, spontaneous resolution, or progression to active TB.
Active TB Transitions into the symptomatic, active TB states A occur from the progression of earlyactive TB E according to the duration of early-active TB a. Transitions from the active disease state occur due to death, spontaneous resolution, or treatment initiation.
In those previously treated, active disease AP may additionally result from: a) relapse among those who will relapse W after the mean time to relapse (τ ω ); b) loss to follow-up (δ 1 ) during ineffective first-line treatment B1i ; c) loss to follow-up during effective treatment B1e provided that culture conversion has not yet occurred (δ 1 η 1 ); or d) failing ineffective first-line therapy provided that treatment has been completed without loss to follow-up (1 − δ 1 ) after treatment duration τ 1 = 6 months and that care is not immediately reinitiated (1 − γ). initiate successful treatment B2e1 but are subsequently lost to follow-up with probability δ 2 ; those who experience treatment failure B2i (due to ineffective second-line therapy after duration τ 21 = 6 months); or those complete treatment but subsequently relapse ZR (after a mean time to relapse τ ω ). Losses from F occur due to death.
Among those previously treated, effective first-line therapy B1eP may also be initiated following the failure of a previous first-line treatment regimen B1i. This only occurs provided the previous regimen was completed (after duration τ 1 = 6 months) without loss to follow-up (1 − δ 1 ), that retreatment is started immediately upon completion of the previous regiment (γ), and that MDR-TB was not acquired during the previous regimen (1 − α 0 α )). S.24 Among DS-TB patients, transitions into the state of ineffective first-line therapy B1iS occur from the same sources of effective first-line therapy above (according to the probability that treatment will not be successful 1 − σ 1 0 σ 1 ).
In those with MDR-TB, all first-line therapy is ineffective. Transitions into B1iR occur from treatment initiation or re-initiation based on the proportion of cases which do not receive subsequently acquired MDR-TB (with probability α 0 α ). In the case of failure, patients must have completed treatment (duration τ 1 = 6 months) without loss to follow-up followed by immediate retreatment(1 − 1 ) . Transitions from B2e1 occur due to death or finishing the initiation phase.
Transitions into ineffective second-line therapy for MDR-TB B2i occur from the same states as above.
Among those who complete effective second-line therapy B2e2 (culture negative at the end of treatment), a proportion ω 2 will eventually relapse to chronic (untreated) MDR-TB C.
Between the completion of second-line treatment and the time of relapse, these populations occupy an asymptomatic state Z for a mean duration of τ ω . This population differs from that of WR through a history of attempted second-line therapy; afterwards, those who relapse from Z will be ineligible for retreatment with second-line therapy. Losses from this state occur due to death or relapse.
HIV Infection In addition to the rates of change across states of TB infection (and births/deaths) HIV-infected populations are assumed to be unable to access ART before at least 2006.
After 2006, Low CD4 populations become eligible for ART at a time-varying rate ( ) S.28

Sampling & Calibration
To enrich our projections using simulated TB epidemics which were most consistent with empirical estimates of TB epidemics in South Africa and Vietnam, we implemented a two-stage semi-Bayesian Sampling/Importance-Resampling algorithm. 1 In the first stage of calibration, parameter sets were composed of a single value for each DS-TB or HIV parameter (drawn using Latin hypercube sampling 2 , Tables S1-S2 below) while values for MDR-TB parameters (Table   S3) (per 100,000) HIV-Infected Incident TB b,c (%)

MDR-TB d in New
Cases (%)

MDR-TB d in Previously-Treated Cases (%)
Year Year Mean (Range) South Africa (11.9-24.5) a Incidence estimates were taken from WHO country reports (as published with the 2016 Global TB Report) 3 . b These estimates were modeled as independent beta distributions with bounds defined by the estimated 95% confidence intervals. c HIV targets represent the proportion of HIV-infected populations among all incident TB cases. Estimates were taken from the 2012 TB drug resistance survey in South Africa 4 and the 2016 WHO estimate in Vietnam. d MDR-TB targets represent the proportion of MDR-TB cases among all recent TB diagnoses (defined as any population transitioning from a state of active, untreated TB to a state of TB diagnosis/treatment). Estimates were taken from national drug resistance surveys in South Africa 4,50 and Vietnam 51 . These estimates were modeled as independent normal distributions with two standard deviations set equal to half the widths of the estimated 95% confidence intervals

Bayesian Model Comparison
To compare the performance of our model scenarios, we calculated a Bayes Factor for each pair of scenarios in each country. A Bayes Factor is traditionally defined as the posterior odds to prior odds ratio 52 . For posterior distributions from any two models ( 1 | ) and ( 2 | ) and data y (our empirical calibration targets), a Bayes Factor can be defined as: S.34 (In this notation, ( 1 ) and ( 2 ) represent the prior distributions of each model.) As with common Monte Carlo approximations to Bayesian inference, if independent samples are drawn from ( 1 ) and ( 2 ), the BF may be consistently estimated by 52 : In our approach, the number of independent simulations run in each scenario's prior distribution was equal ( 1 = 2 ). Therefore, the BF is approximated by the ratio of the sums of likelihood values for the n prior simulations (before resampling) in each scenario (∑ =1 ( ; )). When presented in the text, the Constant Deficit scenario is used as the denominator model ( 2 | ) in calculating a BF unless noted otherwise.

Replication of Previous Findings
After review of our primary results, we noted important discrepancies in our projections of the MDR-TB epidemic in South Africa under the No Deficit scenario and those published in a similar study by Sharma and colleagues in which the transmission efficiency of DS-TB and MDR-TB were assumed to be identical 53 . Notably, their work projected the relative incidence of MDR-TB in South Africa to be 5.7% (95% UR: 3.0-7.6%) by 2040, significantly lower and with less variance than our estimates. In an attempt to reconcile these projections, we undertook to identify the source(s) of these discrepancies in our approach.

Sensitivity Analyses
We implemented two strategies in our sensitivity analyses. For each parameter in each scenario, we calculated the partial rank correlation coefficient (

Calibration
As described in the Methods, our scenarios were calibrated in a two-stage semi-Bayesian algorithm. The results of the first stage of calibrationusing estimates of absolute TB incidence and HIV among incident TB casesare presented in Fig. S4. The results of the second stage of calibrationusing empirical estimates of MDR-TB incidenceare presented in the Results ( Fig.   2 and Fig. 3). All Bayes Factors calculated between the three primary scenarios examined are presented in Table S5. S.38

B -Vietnam
Simulated epidemics are weighted according to how well each reproduced empirical calibration targets (historical estimates of absolute TB incidence and the proportion of incident TB cases infected with HIV). Red points represent median values and bounds for calibration targets drawn from WHO estimates and national survey data. IQR represents 25th to 75th percentiles and the 90% range represents the 5th to 95th percentiles of posterior simulations.

Model Projections
The primary outcomes of interest in our study were the projected changes in absolute and relative incidences of MDR-TB over time. Projections of the absolute MDR-TB incidence in the Constant Deficit and Shrinking Deficit scenarios are presented in the Results (Fig. 4). For these scenarios, we present projections of the relative incidence of MDR-TB (as a proportion of all TB) in Fig. S5. In the case of the No Deficit scenario, we present projections of the absolute and relative MDR-TB incidence in Fig. S6. Additionally, we investigated several secondary outcomes of interest in all scenarios. Projections of the absolute TB incidence (used to calculate the relative MDR-TB incidence presented in the Results and Fig. S5) are illustrated in Fig. S7.
The proportion of incident MDR acquired during recent first-line therapy is presented in Fig. S8. S.41

Replication of Previous Findings
In our attempt to replicate the findings of Sharma and colleagues 53 using our No Deficit scenario, we first altered prior distributions for two parametersthe probability of rapid progression upon initial TB infection and the rate of reactivation upon latent infectionsuch that simulated TB epidemics were driven less by rapidly progressing TB and driven more by the reactivation of latent TB, leading to a more slowly developing TB epidemic. A number of epidemiological studies have examined primary progressive TB and TB reactivation, with some variation in estimates between studies and between demographic groups within studies [7][8][9][10][11] .
These estimates may be parameterized in several ways, and the modified values that adopted for this Slower Epidemic scenario may be consistent with this body of literature.
The calibration results of this Slower Epidemic scenario are presented in Fig. S9   IQR represents 25th to 75th percentiles and the 90% range represents the 5th to 95th percentiles of posterior simulations.

S.48
These results were still meaningfully higher than the estimates published by Sharma and colleagues 53 . We therefore adjusted this scenario further by increasing the prior distribution of the duration of delay between the onset of TB and the initiation of care from a median of 12 months to a median of 10 years, comparable to the posterior probability of effective DS-TB treatment initiation published by Sharma and colleagues. In this Delayed Treatment scenario, few TB patients (DS-TB or MDR-TB) receive treatment of any kind, having died of TB or selfcured before treatment begins. As a result, MDR-TB exerts little competitive advantage over DS-TB (through lower probabilities of cure and longer durations of symptomatic, infectious disease).
With this additional adjustment, the Delayed Treatment scenario was better supported by empirical data than the Slower Epidemic scenario (BF>10 8 ) but still more poorly supported relative to our Constant Deficit scenario (BF=0.08) and our Shrinking Deficit scenario (BF=0.21) (for calibration results and projections of the Delayed Treatment scenario, see Results

Sensitivity Analyses
As described in the Supplementary Methods, we performed multivariate sensitivity analyses using PRCCs and univariate sensitivity analyses using parameter quintiles associated with two primary outcomes: the absolute incidence of MDR-TB in 2040 and the fold change in the relative incidence of MDR-TB between 2016 and 2040. Univariate analysis of the absolute incidence of MDR-TB in South Africa was presented in Fig. 6, and the univariate analysis of the relative incidence of MDR-TB in South Africa is presented in Fig. S11 below. Univariate analysis of the absolute incidence of MDR-TB in Vietnam is presented in Fig. S12. Multivariate analysis of the absolute incidence of MDR-TB in both countries is presented in Fig. S13 below.   Table S2.1 for full descriptions, sampling ranges, and references for each parameter and prior distribution. S.54