estimR {EpiLPS} | R Documentation |

This routine estimates the instantaneous reproduction number `R_t`

; the mean number
of secondary infections generated by an infected individual at time `t`

(White et
al. 2020); by using Bayesian P-splines and Laplace approximations (Gressani et al. 2022).
Estimation of `R_t`

is based on a time series of incidence counts and (a discretized) serial
interval distribution. The negative binomial distribution is used to model incidence
count data and P-splines (Eilers and Marx, 1996) are used to smooth the epidemic curve. The link
between the epidemic curve and the reproduction number is established via the renewal equation.

```
estimR(incidence, si, K = 30, dates = NULL, maxmethod = c("NelderMead","HillClimb"),
CoriR = FALSE, WTR = FALSE, optimstep = 0.3, priors = Rmodelpriors())
```

`incidence` |
A vector containing the incidence time series. If |

`si` |
The (discrete) serial interval distribution. |

`K` |
Number of B-splines in the basis. |

`dates` |
A vector of dates in format "YYYY-MM-DD" (optional). |

`maxmethod` |
The method to maximize the hyperparameter posterior distribution. |

`CoriR` |
Should the |

`WTR` |
Should the |

`optimstep` |
Learning rate for the "HillClimb" method to maximize the posterior distribution of the hyperparameters. |

`priors` |
A list containing the prior specification of the model hyperparameters as set in Rmodelpriors. See ?Rmodelpriors. |

The `estimR`

routine estimates the reproduction number in a
totally "sampling-free" fashion. The hyperparameter vector (containing the
penalty parameter of the P-spline model and the overdispersion parameter of
the negative binomial model for the incidence time series) is fixed at its
maximum a posteriori (MAP). By default, the algorithm for maximization is
the one of Nelder and Mead (1965). If `maxmethod`

is set to "HillClimb",
then a gradient ascent algorithm is used to maximize the hyperparameter posterior.

A list with the following components:

incidence: The incidence time series.

si: The serial interval distribution.

RLPS: A data frame containing estimates of the reproduction number obtained with the Laplacian-P-splines methodology.

thetahat: The estimated vector of B-spline coefficients.

Sighat: The estimated variance-covariance matrix of the Laplace approximation to the conditional posterior distribution of the B-spline coefficients.

RCori: A data frame containing the estimates of the reproduction obtained with the method of Cori (2013).

RWT: A data frame containing the estimates of the reproduction obtained with the method of Wallinga-Teunis (2004).

LPS_elapsed: The routine real elapsed time (in seconds) when estimation of the reproduction number is carried out with Laplacian-P-splines.

Cori_elapsed: The routine real elapsed time (in seconds) when estimation of the reproduction number is carried out with the method of Cori (2013).

penparam: The estimated penalty parameter related to the P-spline model.

K: The number of B-splines used in the basis.

NegBinoverdisp: The estimated overdispersion parameter of the negative binomial distribution for the incidence time series.

optimconverged: Indicates whether the algorithm to maximize the posterior distribution of the hyperparameters has converged.

method: The method to estimate the reproduction number with Laplacian-P-splines.

optim_method: The chosen method to to maximize the posterior distribution of the hyperparameters.

Oswaldo Gressani oswaldo_gressani@hotmail.fr

Gressani, O., Wallinga, J., Althaus, C. L., Hens, N. and Faes, C.
(2022). EpiLPS: A fast and flexible Bayesian tool for estimation of the
time-varying reproduction number. *Plos Computational Biology*,
**18**(10): e1010618.

Cori, A., Ferguson, N.M., Fraser, C., Cauchemez, S. (2013). A new
framework and software to estimate time-varying reproduction numbers during
epidemics. *American Journal of Epidemiology*, **178**(9):1505–1512.

Wallinga, J., & Teunis, P. (2004). Different epidemic curves for
severe acute respiratory syndrome reveal similar impacts of control measures.
*American Journal of Epidemiology*, **160**(6), 509-516.

White, L.F., Moser, C.B., Thompson, R.N., Pagano, M. (2021).
Statistical estimation of the reproductive number from case notification
data. *American Journal of Epidemiology*, **190**(4):611-620.

Eilers, P.H.C. and Marx, B.D. (1996). Flexible smoothing
with B-splines and penalties. *Statistical Science*,
**11**(2):89-121.

```
# Illustration on simulated data
si <- Idist(mean = 5, sd = 3)$pvec
datasim <- episim(si = si, endepi = 60, Rpattern = 5, dist="negbin", overdisp = 50)
epifit_sim <- estimR(incidence = datasim$y, si = si, CoriR = TRUE)
plot(epifit_sim, addfit = "Cori")
# Illustration on the 2003 SARS epidemic in Hong Kong.
data(sars2003)
epifit_sars <- estimR(incidence = sars2003$incidence, si = sars2003$si, K = 40)
tail(epifit_sars$RLPS)
summary(epifit_sars)
plot(epifit_sars)
```

[Package *EpiLPS* version 1.2.0 Index]