congruent_hbds_model {castor} | R Documentation |

Given a homogenous birth-death-sampling (HBDS) model (or abstract congruence class), obtain the congruent model (or member of the congruence class) with a specific speciation rate *λ*, or extinction rate *μ*, or sampling rate *ψ*, or effective reproduction ratio *R_e* or removal rate *μ+ψ* (aka. "become uninfectious"" rate). All input and output time-profiles are specified as piecewise polynomial curves (splines), defined on a discrete grid of ages. This function allows exploration of a model's congruence class, by obtaining various members of the congruence class depending on the specified *λ*, *μ*, *ψ*, *R_e* or removal rate. For more details on HBDS models and congruence classes see the documentation of `simulate_deterministic_hbds`

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congruent_hbds_model(age_grid, PSR, PDR, lambda_psi, lambda = NULL, mu = NULL, psi = NULL, Reff = NULL, removal_rate = NULL, lambda0 = NULL, CSA_ages = NULL, CSA_pulled_probs = NULL, CSA_PSRs = NULL, splines_degree = 1, ODE_relative_dt = 0.001, ODE_relative_dy = 1e-4)

`age_grid` |
Numeric vector, listing discrete ages (time before present) on which the various model variables (e.g., |

`PSR` |
Numeric vector, of the same size as |

`PDR` |
Numeric vector, of the same size as |

`lambda_psi` |
Numeric vector, of the same size as |

`lambda` |
Numeric vector, of the same size as |

`mu` |
Numeric vector, of the same size as |

`psi` |
Numeric vector, of the same size as |

`Reff` |
Numeric vector, of the same size as |

`removal_rate` |
Numeric vector, of the same size as |

`lambda0` |
Numeric, specifying the speciation rate at the present-day (i.e., at age 0). Must be provided if and only if one of |

`CSA_ages` |
Optional numeric vector, listing the ages of concentrated sampling attempts, in ascending order. Concentrated sampling is assumed to occur in addition to any continuous (Poissonian) sampling specified by |

`CSA_pulled_probs` |
Optional numeric vector of the same size as |

`CSA_PSRs` |
Optional numeric vector of the same size as |

`splines_degree` |
Integer, either 0,1,2 or 3, specifying the polynomial degree of the provided time-dependent variables between grid points in |

`ODE_relative_dt` |
Positive unitless number, specifying the default relative time step for internally used ordinary differential equation solvers. Typical values are 0.01-0.001. |

`ODE_relative_dy` |
Positive unitless number, specifying the relative difference between subsequent simulated and interpolated values, in internally used ODE solvers. Typical values are 1e-2 to 1e-5. A smaller |

The PDR, PSR and the product *λψ* are variables that are invariant across the entire congruence class of an HBDS model, i.e. any two congruent models have the same PSR, PDR and product *λψ*. Reciprocally, any HBDS congruence class is fully determined by its PDR, PSR and *λψ*. This function thus allows "collapsing" a congruence class down to a single member (a specific HBDS model) by specifying one or more additional variables over time (such as *λ*, or *ψ*, or *μ* and *λ_0*). Alternatively, this function may be used to obtain alternative models that are congruent to some reference model, for example to explore the robustness of specific epidemiological quantities of interest. The function returns a specific HBDS model in terms of the time profiles of various variables (such as *λ*, *μ* and *ψ*).

In the current implementation it is assumed that any sampled lineages are immediately removed from the pool, that is, this function cannot accommodate models with a non-zero retention probability upon sampling. This is a common assumption in molecular epidemiology. Note that in this function age always refers to time before present, i.e., present day age is 0, and age increases towards the root.

A named list with the following elements:

`success` |
Logical, indicating whether the calculation was successful. If |

`valid` |
Logical, indicating whether the returned model appears to be biologically valid (for example, does not have negative |

`ages` |
Numeric vector of size NG, specifying the discrete ages (time before present) on which all returned time-curves are specified. Will always be equal to |

`lambda` |
Numeric vector of size NG, listing the speciation rates |

`mu` |
Numeric vector of size NG, listing the extinction rates |

`psi` |
Numeric vector of size NG, listing the (Poissonian) sampling rates |

`lambda_psi` |
Numeric vector of size NG, listing the product |

`Reff` |
Numeric vector of size NG, listing the effective reproduction ratio |

`removal_rate` |
Numeric vector of size NG, listing the removal rate ( |

`Pmissing` |
Numeric vector of size NG, listing the probability that a past lineage extant during |

`CSA_probs` |
Numeric vector of the same size as |

`CSA_Pmissings` |
Numeric vector of the same size as |

Stilianos Louca

T. Stadler, D. Kuehnert, S. Bonhoeffer, A. J. Drummond (2013). Birth-death skyline plot reveals temporal changes of epidemic spread in HIV and hepatitis C virus (HCV). PNAS. 110:228-233.

A. MacPherson, S. Louca, A. McLaughlin, J. B. Joy, M. W. Pennell (in review as of 2020). A general birth-death-sampling model for epidemiology and macroevolution. DOI:10.1101/2020.10.10.334383

`generate_tree_hbds`

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`fit_hbds_model_parametric`

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`simulate_deterministic_hbds`

# define an HBDS model with exponentially decreasing speciation/extinction rates # and constant Poissonian sampling rate psi oldest_age= 10 age_grid = seq(from=0,to=oldest_age,by=0.1) # choose a sufficiently fine age grid lambda = 1*exp(0.01*age_grid) # define lambda on the age grid mu = 0.2*lambda # assume similarly shaped but smaller mu # simulate deterministic HBD model # scale LTT such that it is 100 at age 1 sim = simulate_deterministic_hbds(age_grid = age_grid, lambda = lambda, mu = mu, psi = 0.1, age0 = 1, LTT0 = 100) # calculate a congruent HBDS model with an alternative sampling rate # use the previously simulated variables to define the congruence class new_psi = 0.1*exp(-0.01*sim$ages) # consider a psi decreasing with age congruent = congruent_hbds_model(age_grid = sim$ages, PSR = sim$PSR, PDR = sim$PDR, lambda_psi = sim$lambda_psi, psi = new_psi) # compare the deterministic LTT of the two models # to confirm that the models are indeed congruent if(!congruent$valid){ cat("WARNING: Congruent model is not biologically valid\n") }else{ # simulate the congruent model to get the LTT csim = simulate_deterministic_hbds(age_grid = congruent$ages, lambda = congruent$lambda, mu = congruent$mu, psi = congruent$psi, age0 = 1, LTT0 = 100) # plot deterministic LTT of the original and congruent model plot( x = sim$ages, y = sim$LTT, type='l', main='dLTT', xlab='age', ylab='lineages', xlim=c(oldest_age,0), col='red') lines(x= csim$ages, y=csim$LTT, type='p', pch=21, col='blue') }

[Package *castor* version 1.7.0 Index]