Using approximate Bayesian computation to estimate tuberculosis transmission parameters from genotype data

Abstract

Tuberculosis can be studied at the population level by genotyping strains of Mycobacterium tuberculosis isolated from patients. We use an approximate Bayesian computational method in combination with a stochastic model of tuberculosis transmission and mutation of a molecular marker to estimate the net transmission rate, the doubling time, and the reproductive value of the pathogen. This method is applied to a published data set from San Francisco of tuberculosis genotypes based on the marker IS6110. The mutation rate of this marker has previously been studied, and we use those estimates to form a prior distribution of mutation rates in the inference procedure. The posterior point estimates of the key parameters of interest for these data are as follows: net transmission rate, 0.69/year [95% credibility interval (C.I.) 0.38, 1.08]; doubling time, 1.08 years (95% C.I. 0.64, 1.82); and reproductive value 3.4 (95% C.I. 1.4, 79.7). These figures suggest a rapidly spreading epidemic, consistent with observations of the resurgence of tuberculosis in the United States in the 1980s and 1990s.

Figure 1.—

Marginal posterior densities of net transmission rate α − δ, doubling time log(2)/(α − δ), and reproductive value α/δ. The data used are from Small et al. (1994). The prior distribution of the mutation rate is p(θ) ∼ N(0.198, 0.06735²) and the tolerance level ɛ = 0.0025.

Figure 2.—

Joint posterior densities p(α, δ | D) (integrating over θ) and p(α − δ, θ | D).

Figure 3.—

Posterior densities of net transmission rate α − δ, doubling time log(2)/(α − δ), and reproductive value α/δ as prior mean of θ is varied. The prior means of θ are 0.15 (shaded dotted lines), 0.2 (shaded dashed lines), 0.25 (shaded solid lines), and 0.3 (dashed solid lines). The thick solid line corresponds to the analysis of Figure 1.

Figure 4.—

Posterior densities of net transmission rate α − δ, doubling time log(2)/(α − δ), and reproductive value α/δ as dependent on algorithm tolerance ɛ. The values of ɛ are 0.025 (shaded dashed lines), 0.015 (shaded solid lines), 0.005 (dashed solid lines), and 0.0025 (thick solid lines).