Abstract
Bacterial populations that colonize a host can play important roles in host health, including serving as a reservoir that transmits to other hosts and from which invasive strains emerge, thus emphasizing the importance of understanding rates of acquisition and clearance of colonizing populations. Studies of colonization dynamics have been based on assessment of whether serial samples represent a single population or distinct colonization events. With the use of whole genome sequencing to determine genetic distance between isolates, a common solution to estimate acquisition and clearance rates has been to assume a fixed genetic distance threshold below which isolates are considered to represent the same strain. However, this approach is often inadequate to account for the diversity of the underlying within-host evolving population, the time intervals between consecutive measurements, and the uncertainty in the estimated acquisition and clearance rates. Here, we present a fully Bayesian model that provides probabilities of whether two strains should be considered the same, allowing us to determine bacterial clearance and acquisition from genomes sampled over time. Our method explicitly models the within-host variation using population genetic simulation, and the inference is done using a combination of Approximate Bayesian Computation (ABC) and Markov Chain Monte Carlo (MCMC). We validate the method with multiple carefully conducted simulations and demonstrate its use in practice by analyzing a collection of methicillin resistant Staphylococcus aureus (MRSA) isolates from a large recently completed longitudinal clinical study. An R-code implementation of the method is freely available at: https://github.com/mjarvenpaa/bacterial-colonization-model.
Highlights
This shows that the acceptance probability does not depend on realisation of b∗ and that the sampling procedure of used in the main text is equivalent to performing one blocked Metropolis-Hastings sampling with the proposal r in Eq 1
This ensures that the full algorithm is a valid Gibbs sampler
)−1, where wj is an unnormalised weight that is obtained from Eq 12 when c = 1
Summary
Because di is an integer, we use binomial formula and some algebra to obtain p(ηi | μ, zi, λ, D) = c(2ηi + μti)di ηik−1e−(2+λ/μ)ηi 1ηi≥0 di. Sampling from the conditional density of ηi can be done conveniently using the Algorithm 1, where wj are the unnormalised weights. This algorithm is fast (unless di is large) as it does not require numerical root finding, evaluating special mathematical functions or integration unlike standard methods such as e.g. inverse transform sampling which could be alternatively used. Di compute l = arg maxj=0,...,di {gj + log(wj )} return a sample from Gamma(l, 2 + λ/μ) end if
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