The relative fitness of drug-resistant Mycobacterium tuberculosis: a modelling study of household transmission in Peru

The relative fitness of drug-resistant versus susceptible bacteria in an environment dictates resistance prevalence. Estimates for the relative fitness of resistant Mycobacterium tuberculosis (Mtb) strains are highly heterogeneous and mostly derived from in vitro experiments. Measuring fitness in the field allows us to determine how the environment influences the spread of resistance. We designed a household structured, stochastic mathematical model to estimate the fitness costs associated with multidrug resistance (MDR) carriage in Mtb in Lima, Peru during 2010–2013. By fitting the model to data from a large prospective cohort study of TB disease in household contacts, we estimated the fitness, relative to susceptible strains with a fitness of 1, of MDR-Mtb to be 0.32 (95% credible interval: 0.15–0.62) or 0.38 (0.24–0.61), if only transmission or progression to disease, respectively, was affected. The relative fitness of MDR-Mtb increased to 0.56 (0.42–0.72) when the fitness cost influenced both transmission and progression to disease equally. We found the average relative fitness of MDR-Mtb circulating within households in Lima, Peru during 2010–2013 to be significantly lower than concurrent susceptible Mtb. If these fitness levels do not change, then existing TB control programmes are likely to keep MDR-TB prevalence at current levels in Lima, Peru.


Time of follow-up in study
Households were followed-up for variable lengths of time in the original household study (Supplementary Figure 1). The raw data is included in the Electronic Supplementary Material.

Detailed overview of simulation
A detailed overview of all the stages used in the simulation are provided in Figure 2.    The model initially sampled 700 household sizes from the distribution of household sizes in the trial. 1 213 of these had an initial MDR-TB case, 487 an initial DS-TB case. Tuberculin skin test (TST) prevalence surveys across Lima have found 52% (95% CI: 48-57%) to be infected with Mtb. 2 Hence, the number of cases initially latently infected was sampled from a normal distribution with mean 0.5 and standard deviation of 0.1. Informed by the TB prevalence in Lima, it was assumed that initially, 98% of these latent infections were with DS-TB strains, 2% with MDR-TB strains in all households. 2 This proportion was varied in scenario analysis. Random sampling from a binomial distribution, with this 98% DS-TB, determined the distribution of latent DS-TB and MDR-TB cases across the 700 households. The proportion of latent cases that were "latently fast" cases ( Figure 1) was taken to be 3% to reflect that although the proportion of new infections that are fast latent is 15%, over time these will change state more rapidly than latent slow.

Models 2 & 3: Fit to data
Model 1-3 structures could all replicate the data from the household study as shown in Figure

Probability of remaining free from tuberculosis
We compared the probability of remaining free from TB in our model to that presented in the original study ( Figure 2 in the original paper by Grandjean et al. 1 ). We had highly similar dynamics to those in the main study ( Figure 5).
The total follow-up time of MDRTB contacts was 1,425 person-years (mean follow-up time per MDRTB contact 494 d, standard deviation 199 d), during which 35 second cases arose, equating to an incidence of 2,456 per 100,000 contact follow-up person-years. The total followup time of drug-susceptible tuberculosis contacts was 2,620 person-years (mean follow-up time per drug-susceptible tuberculosis contact 406 d, standard deviation 189 d), during which 114 second cases arose, equating to an incidence of 4,351 per 100,000 contact follow-up person-years (multivariate analysis, HR 0.56, 95% CI 0.34-0.90, p = 0.017; Fig 2).

Trace and density plots for each unknown parameter for main models
The trace and density for each unknown parameter, from the three models are shown in Supplementary Scenario analysis used the structure from Model 1 with altered parameters. All four could replicate the data from the household study as shown in Supplementary Figures 9 -11.

Trace and density plots for each unknown parameter for scenario analysis
The trace and density for each unknown parameter, from the three models are shown in Supplementary Figures 14-18.

Scenario analysis results
The parameters estimates for the five scenarios are given in Table 1 and Figure 19. Our first scenario analysis explored increasing the initial proportion of households that were initially infected with latent MDR-Mtb from 2% to 10% (in the pre-study). Fitting the four unknown parameters revealed that this increased MDR-Mtb latency proportion had very little impact on the estimates.
Our correlation analysis revealed four parameters (other than the four unknown parameters) to be correlated with TB incidence: the proportion of (re)infected individuals which progress to "latent fast" (p), the protection from developing active TB upon re-infection (χ), the proportion of new active cases which directly become infectious (d) and the progression rate of latent fast individuals to active disease (pf). The second scenario set these four parameters to be (p, χ, d, pf) = (0.25, 0.25, 0.75, 0.9) (high TB incidence) and the third (low TB incidence) to be (0.08,0.45,0.25,0.1). These second and third scenarios affected the estimates for the external force of infection and per capita transmission rate as would be expected due to the nature of the change in the natural history parameters. However, the estimates for the relative fitness (f) remain relatively consistent with our initial parameter set in Model 1 at approximately 0.30. Scenario 3 has a lower mean fitness at 0.22.
The fourth scenario, extended the initial run-in period from 10 to 30 years. All parameter estimates are similar to those of Model 1, including the relative fitness.
The fifth scenario removed the saturating household effect. The parameter estimates from this were also highly similar to the main analysis, except for the per capita transmission parameter, which was lower, reflecting the change to the model structure (no longer divided by household size).

Effective Reproduction Number estimates
The effective reproduction number (R) can be defined as the average number of secondary infections produced by an infected individual during the entire period of infectiousness. For our model, this can be approximated by taking the product of the transmission rate and the duration of infectiousness. This gives an approximate number of secondary cases generated by a single case of DS-or MDR-TB. The ratio of these two numbers (R r for MDR-TB : R s for DS-TB) provides another estimate of the impact of the resistance on MDR-TB transmission. In the pre-study period of our simulation, the ratio for Model i is: For our three models, inputting the estimates for f i , gives ratios of approximately 0.49, 0.59 or 0.86. This suggests that MDR-TB has a substantially lower effective reproduction number than DS-TB in this setting, matching the results of the reduction in per capita transmission rate.
This calculation is only an approximation as it does not take into account the complexity of the latent states nor disease progression variation. We chose to use values from the pre-study period, as the case detection rate increased during the study.