R0.Rd
The S3 generic function R0
defined in package surveillance is intended to
compute reproduction numbers from fitted epidemic models.
The package currently defines a method for the "twinstim"
class, which
computes expected numbers of infections caused by infected individuals depending on the event type
and marks attached to the individual, which contribute to the infection pressure
in the epidemic predictor of that class.
There is also a method for simulated "epidataCS"
(just a wrapper for the "twinstim"
-method).
R0(object, ...)
# S3 method for twinstim
R0(object, newevents, trimmed = TRUE, newcoef = NULL, ...)
# S3 method for simEpidataCS
R0(object, trimmed = TRUE, ...)
simpleR0(object, eta = coef(object)[["e.(Intercept)"]],
eps.s = NULL, eps.t = NULL, newcoef = NULL)
A fitted epidemic model object for which an R0
method exists.
an optional data.frame
of events for which the reproduction
numbers should be calculated. If omitted, it is calculated for the
original events from the fit. In this case, if
trimmed = TRUE
(the default), the result is just
object$R0
; however, if trimmed = FALSE
, the model
environment is required, i.e. object
must have been fitted
with model = TRUE
.
For the twinstim
method, newevents
must at least
contain the following columns:
the event time
(only for trimmed = TRUE
)
and type
(only for multi-type epidemics),
the maximum interaction ranges eps.t
and eps.s
,
as well as columns for the marks and stgrid
variables
used in the epidemic component of the fitted "twinstim"
object
as stored in formula(object)$epidemic
.
For trimmed
R0 values, newevents
must additionally
contain the components .influenceRegion
and, if using the
Fcircle
trick in the siaf
specification, also
.bdist
(cf. the hidden columns in the events
component of class "epidataCS"
).
logical indicating if the individual reproduction numbers should be
calculated by integrating the epidemic intensities over the
observation period and region only (trimmed = TRUE
) or over
the whole time-space domain R+ x R^2 (trimmed = FALSE
). By
default, if newevents
is missing, the trimmed R0
values stored in object
are returned. Trimming means that
events near the (spatial or temporal) edges of the observation
domain have lower reproduction numbers (ceteris paribus) because
events outside the observation domain are not observed.
the model parameters to use when calculating reproduction numbers.
The default (NULL
) is to use the MLE coef(object)
.
This argument mainly serves the construction of Monte Carlo
confidence intervals by evaluating R0
for parameter vectors
sampled from the asymptotic multivariate normal distribution of the MLE,
see Examples.
additional arguments passed to methods.
Currently unused for the twinstim
method.
a value for the epidemic linear predictor, see details.
the spatial/temporal radius of interaction.
If NULL
(the default), the original value from the data is
used if this is unique and an error is thrown otherwise.
For the "twinstim"
class, the individual-specific expected
number \(\mu_j\) of infections caused by individual (event) \(j\)
inside its theoretical (untrimmed) spatio-temporal range of interaction
given by its eps.t
(\(\epsilon\)) and eps.s
(\(\delta\)) values is defined as follows (cf. Meyer et al, 2012):
$$\mu_j = e^{\eta_j} \cdot
\int_{b(\bold{0},\delta)} f(\bold{s}) d\bold{s} \cdot
\int_0^\epsilon g(t) dt .$$
Here, \(b(\bold{0},\delta)\) denotes the disc centred at (0,0)' with
radius \(\delta\), \(\eta_j\) is the epidemic linear predictor,
\(g(t)\) is the temporal interaction function, and \(f(\bold{s})\)
is the spatial interaction function. For a type-specific
twinstim
, there is an additional factor for the number of event
types which can be infected by the type of event \(j\) and the
interaction functions may be type-specific as well.
Alternatively to the equation above,
the trimmed
(observed) reproduction numbers
are obtain by integrating over the observed infectious domains of the
individuals, i.e. integrate \(f\) over the intersection of the
influence region with the observation region W
(i.e. over \(\{ W \cap b(\bold{s}_j,\delta) \} - \bold{s}_j\))
and \(g\) over the intersection of the observed infectious period with
the observation period \((t_0;T]\) (i.e. over
\((0; \min(T-t_j,\epsilon)]\)).
The function simpleR0
computes
$$\exp(\eta) \cdot
\int_{b(\bold{0},\delta)} f(\bold{s}) d\bold{s} \cdot
\int_0^{\epsilon} g(t) dt ,$$
where \(\eta\) defaults to \(\gamma_0\) disregarding any epidemic
effects of types and marks. It is thus only
suitable for simple epidemic twinstim
models with
epidemic = ~1
, a diagonal (or secondary diagonal) qmatrix
,
and type-invariant interaction functions.
simpleR0
mainly exists for use by epitest
.
(Numerical) Integration is performed exactly as during the fitting of
object
, for instance object$control.siaf
is queried if
necessary.
For the R0
methods,
a numeric vector of estimated reproduction numbers from the fitted
model object
corresponding to the rows of newevents
(if
supplied) or the original fitted events including events of the prehistory.
For simpleR0
, a single number (see details).
Meyer, S., Elias, J. and Höhle, M. (2012): A space-time conditional intensity model for invasive meningococcal disease occurrence. Biometrics, 68, 607-616. doi: 10.1111/j.1541-0420.2011.01684.x
Sebastian Meyer
## load the 'imdepi' data and a model fit
data("imdepi", "imdepifit")
## calculate individual and type-specific reproduction numbers
R0s <- R0(imdepifit)
tapply(R0s, imdepi$events@data[names(R0s), "type"], summary)
## untrimmed R0 for specific event settings
refevent <- data.frame(agegrp = "[0,3)", type = "B", eps.s = Inf, eps.t = 30)
setting2 <- data.frame(agegrp = "[3,19)", type = "C", eps.s = Inf, eps.t = 14)
newevents <- rbind("ref" = refevent, "event2" = setting2)
(R0_examples <- R0(imdepifit, newevents = newevents, trimmed = FALSE))
stopifnot(all.equal(R0_examples[["ref"]],
simpleR0(imdepifit)))
### compute a Monte Carlo confidence interval
## use a simpler model with constant 'siaf' for speed
simplefit <- update(imdepifit, epidemic=~type, siaf=NULL, subset=NULL)
## we'd like to compute the mean R0's by event type
meanR0ByType <- function (newcoef) {
R0events <- R0(simplefit, newcoef=newcoef)
tapply(R0events, imdepi$events@data[names(R0events),"type"], mean)
}
(meansMLE <- meanR0ByType(newcoef=NULL))
## sample B times from asymptotic multivariate normal of the MLE
B <- 5 # CAVE: toy example! In practice this has to be much larger
set.seed(123)
parsamples <- MASS::mvrnorm(B, mu=coef(simplefit), Sigma=vcov(simplefit))
## for each sample compute the 'meanR0ByType'
meansMC <- apply(parsamples, 1, meanR0ByType)
## get the quantiles and print the result
cisMC <- apply(cbind(meansMLE, meansMC), 1, quantile, probs=c(0.025,0.975))
print(rbind(MLE=meansMLE, cisMC))
### R0 for a simple epidemic model
### without epidemic covariates, i.e., all individuals are equally infectious
mepi1 <- update(simplefit, epidemic = ~1, subset = type == "B",
model = TRUE, verbose = FALSE)
## using the default spatial and temporal ranges of interaction
(R0B <- simpleR0(mepi1)) # eps.s=200, eps.t=30
stopifnot(identical(R0B, R0(mepi1, trimmed = FALSE)[[1]]))
## assuming smaller interaction ranges (but same infection intensity)
simpleR0(mepi1, eps.s = 50, eps.t = 15)