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Inference of epidemiological dynamics based on simulated phylogenies using birth-death and coalescent models.

Boskova V, Bonhoeffer S, Stadler T - PLoS Comput. Biol. (2014)

Bottom Line: The coverage of the coalescent decreases with decreasing basic reproductive ratio and increasing sampling probability of infecteds.Both methods performed reasonably well when analyzing trees simulated under the coalescent.The methods can also identify other key epidemiological parameters as long as one of the parameters is fixed to its true value.

View Article: PubMed Central - PubMed

Affiliation: Department of Biosystems Science & Engineering (D-BSSE), Eidgenössische Technische Hochschule (ETH) Zürich, Basel, Switzerland.

ABSTRACT
Quantifying epidemiological dynamics is crucial for understanding and forecasting the spread of an epidemic. The coalescent and the birth-death model are used interchangeably to infer epidemiological parameters from the genealogical relationships of the pathogen population under study, which in turn are inferred from the pathogen genetic sequencing data. To compare the performance of these widely applied models, we performed a simulation study. We simulated phylogenetic trees under the constant rate birth-death model and the coalescent model with a deterministic exponentially growing infected population. For each tree, we re-estimated the epidemiological parameters using both a birth-death and a coalescent based method, implemented as an MCMC procedure in BEAST v2.0. In our analyses that estimate the growth rate of an epidemic based on simulated birth-death trees, the point estimates such as the maximum a posteriori/maximum likelihood estimates are not very different. However, the estimates of uncertainty are very different. The birth-death model had a higher coverage than the coalescent model, i.e. contained the true value in the highest posterior density (HPD) interval more often (2-13% vs. 31-75% error). The coverage of the coalescent decreases with decreasing basic reproductive ratio and increasing sampling probability of infecteds. We hypothesize that the biases in the coalescent are due to the assumption of deterministic rather than stochastic population size changes. Both methods performed reasonably well when analyzing trees simulated under the coalescent. The methods can also identify other key epidemiological parameters as long as one of the parameters is fixed to its true value. In summary, when using genetic data to estimate epidemic dynamics, our results suggest that the birth-death method will be less sensitive to population fluctuations of early outbreaks than the coalescent method that assumes a deterministic exponentially growing infected population.

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Influence of branch length extension in various parts of the tree on the growth rate parameter estimation.For setting  and  (), we modified all 100 birth-death trees (A) and all 100 coalescent trees (B) by branch extension. The unchanged tree is denoted as “orig” on x-axis. We added 48 units of time, roughly corresponding to the full length of the longest trees, to the branches. We extended the branches that were present in the tree at 10% of the tree (going from the root), at 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90% (see x-axis from left to right). We then re-estimated the growth rate parameter for each such tree. Unlike in previous plot, here we display a summary in form of the median values of the start and the end of the 95% HPD intervals, and the median of the medians of the posterior estimates for all 100 trees per setting.
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pcbi-1003913-g002: Influence of branch length extension in various parts of the tree on the growth rate parameter estimation.For setting and (), we modified all 100 birth-death trees (A) and all 100 coalescent trees (B) by branch extension. The unchanged tree is denoted as “orig” on x-axis. We added 48 units of time, roughly corresponding to the full length of the longest trees, to the branches. We extended the branches that were present in the tree at 10% of the tree (going from the root), at 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90% (see x-axis from left to right). We then re-estimated the growth rate parameter for each such tree. Unlike in previous plot, here we display a summary in form of the median values of the start and the end of the 95% HPD intervals, and the median of the medians of the posterior estimates for all 100 trees per setting.

Mentions: To investigate the impact of long early branches on parameter estimation under each model further, we changed the simulated trees systematically. We looked at trees simulated under and . In these trees, we extended each branch existing after 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90% of the time between the root an the present. We extended branches in all these cases by 48 for and by 0.18 for , which was approximately the full length of the birth-death tree (Figure 2 and Figure S5).


Inference of epidemiological dynamics based on simulated phylogenies using birth-death and coalescent models.

Boskova V, Bonhoeffer S, Stadler T - PLoS Comput. Biol. (2014)

Influence of branch length extension in various parts of the tree on the growth rate parameter estimation.For setting  and  (), we modified all 100 birth-death trees (A) and all 100 coalescent trees (B) by branch extension. The unchanged tree is denoted as “orig” on x-axis. We added 48 units of time, roughly corresponding to the full length of the longest trees, to the branches. We extended the branches that were present in the tree at 10% of the tree (going from the root), at 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90% (see x-axis from left to right). We then re-estimated the growth rate parameter for each such tree. Unlike in previous plot, here we display a summary in form of the median values of the start and the end of the 95% HPD intervals, and the median of the medians of the posterior estimates for all 100 trees per setting.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4222655&req=5

pcbi-1003913-g002: Influence of branch length extension in various parts of the tree on the growth rate parameter estimation.For setting and (), we modified all 100 birth-death trees (A) and all 100 coalescent trees (B) by branch extension. The unchanged tree is denoted as “orig” on x-axis. We added 48 units of time, roughly corresponding to the full length of the longest trees, to the branches. We extended the branches that were present in the tree at 10% of the tree (going from the root), at 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90% (see x-axis from left to right). We then re-estimated the growth rate parameter for each such tree. Unlike in previous plot, here we display a summary in form of the median values of the start and the end of the 95% HPD intervals, and the median of the medians of the posterior estimates for all 100 trees per setting.
Mentions: To investigate the impact of long early branches on parameter estimation under each model further, we changed the simulated trees systematically. We looked at trees simulated under and . In these trees, we extended each branch existing after 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90% of the time between the root an the present. We extended branches in all these cases by 48 for and by 0.18 for , which was approximately the full length of the birth-death tree (Figure 2 and Figure S5).

Bottom Line: The coverage of the coalescent decreases with decreasing basic reproductive ratio and increasing sampling probability of infecteds.Both methods performed reasonably well when analyzing trees simulated under the coalescent.The methods can also identify other key epidemiological parameters as long as one of the parameters is fixed to its true value.

View Article: PubMed Central - PubMed

Affiliation: Department of Biosystems Science & Engineering (D-BSSE), Eidgenössische Technische Hochschule (ETH) Zürich, Basel, Switzerland.

ABSTRACT
Quantifying epidemiological dynamics is crucial for understanding and forecasting the spread of an epidemic. The coalescent and the birth-death model are used interchangeably to infer epidemiological parameters from the genealogical relationships of the pathogen population under study, which in turn are inferred from the pathogen genetic sequencing data. To compare the performance of these widely applied models, we performed a simulation study. We simulated phylogenetic trees under the constant rate birth-death model and the coalescent model with a deterministic exponentially growing infected population. For each tree, we re-estimated the epidemiological parameters using both a birth-death and a coalescent based method, implemented as an MCMC procedure in BEAST v2.0. In our analyses that estimate the growth rate of an epidemic based on simulated birth-death trees, the point estimates such as the maximum a posteriori/maximum likelihood estimates are not very different. However, the estimates of uncertainty are very different. The birth-death model had a higher coverage than the coalescent model, i.e. contained the true value in the highest posterior density (HPD) interval more often (2-13% vs. 31-75% error). The coverage of the coalescent decreases with decreasing basic reproductive ratio and increasing sampling probability of infecteds. We hypothesize that the biases in the coalescent are due to the assumption of deterministic rather than stochastic population size changes. Both methods performed reasonably well when analyzing trees simulated under the coalescent. The methods can also identify other key epidemiological parameters as long as one of the parameters is fixed to its true value. In summary, when using genetic data to estimate epidemic dynamics, our results suggest that the birth-death method will be less sensitive to population fluctuations of early outbreaks than the coalescent method that assumes a deterministic exponentially growing infected population.

Show MeSH
Related in: MedlinePlus