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.

Sequential Monte Carlo without likelihoods

“…Tanaka et al (7) previously implemented the ABC-MCMC algorithm with tolerance ⑀ ϭ 0.0025. Three Markov chains with an average acceptance rate of Ϸ0.3% were thinned and combined to form the final sample, utilizing Ͼ2.5 million data-generation steps.…”

“…Comparisons to the original ABC-MCMC analysis of Tanaka et al (7) can also be made in terms of the number of datageneration steps required to generate one uncorrelated particle. Here, the Markov nature of the sampler and the very low acceptance rates induce a strongly dependent sequence.…”

Increasing Viral Dose Causes a Reversal in CD8+ T Cell Immunodominance during Primary Influenza Infection due to Differences in Antigen Presentation, T Cell Avidity, and Precursor Numbers

“…Provided that the underlying model is close enough to the real system and the experimental observations are well captured by the summary statistics used to estimate the model parameters, this approach provides reliable and satisfying results. For example, previous applications of ABC showed that ABC estimates are accurate in scenarios in which likelihoodbased inference methods are also possible (38), and various groups have used ABC to estimate the evolutionary rates of human or bacterial populations (39,40), the transmission dynamics of Mycobacteria tuberculosis (41), and the fitness cost associated with bacterial drug resistance (36). In keeping with Bayesian statistics, ABC parameter estimates are represented as a posterior distribution that provides information on the likelihood that the unknown parameter falls within a certain range of values.…”

Inference in Epidemic Models without Likelihoods

“…These Approximate Bayesian Computation (ABC) techniques have already been employed with considerable success in various fields, for example: population genetics (Beaumont et al, 2002;Tallmon et al, 2004;Marjoram et al, 2003), systematics (Tavaré et al, 1997;Pritchard et al, 1999;Tavaré et al, 2002), molecular epidemiology (Tanaka et al, 2006;Sisson et al, 2007a) and stereology (Bortot et al, 2007).…”