# Continuous Space-Time Marked Point Patterns with Grid-Based Covariates

`epidataCS.Rd`

Data structure for **c**ontinuous **s**patio-temporal event
data, e.g. individual case reports of an infectious disease.
Apart from the actual `events`

, the class simultaneously
holds a spatio-temporal grid of endemic covariates (similar to
disease mapping) and a representation of the observation region.

The `"epidataCS"`

class is the basis for fitting
spatio-temporal endemic-epidemic intensity models with the function
`twinstim`

(Meyer et al., 2012).
The implementation is described in Meyer et al. (2017, Section 3),
see `vignette("twinstim")`

.

## Usage

```
as.epidataCS(events, stgrid, W, qmatrix = diag(nTypes),
nCircle2Poly = 32L, T = NULL,
clipper = c("polyclip", "rgeos"), verbose = interactive())
# S3 method for epidataCS
print(x, n = 6L, digits = getOption("digits"), ...)
# S3 method for epidataCS
nobs(object, ...)
# S3 method for epidataCS
head(x, n = 6L, ...)
# S3 method for epidataCS
tail(x, n = 6L, ...)
# S3 method for epidataCS
[(x, i, j, ..., drop = TRUE)
# S3 method for epidataCS
subset(x, subset, select, drop = TRUE, ...)
# S3 method for epidataCS
marks(x, coords = TRUE, ...)
# S3 method for epidataCS
summary(object, ...)
# S3 method for summary.epidataCS
print(x, ...)
# S3 method for epidataCS
as.stepfun(x, ...)
getSourceDists(object, dimension = c("space", "time"))
```

## Arguments

- events
a

`"SpatialPointsDataFrame"`

of cases with the following obligatory columns (in the`events@data`

`data.frame`

):- time
time point of event. Will be converted to a numeric variable by

`as.numeric`

. There should be no concurrent events (but see`untie`

for an ex post adjustment) and there cannot be events beyond`stgrid`

(i.e.,`time<=T`

is required). Events at or before time \(t_0\) =`min(stgrid$start)`

are allowed and form the prehistory of the process.- tile
the spatial region (tile) where the event is located. This links to the tiles of

`stgrid`

.- type
optional type of event in a marked

`twinstim`

model. Will be converted to a factor variable dropping unused levels. If missing, all events will be attribute the single type`"1"`

.- eps.t
maximum

*temporal*influence radius (e.g. length of infectious period, time to culling, etc.); must be positive and may be`Inf`

.- eps.s
maximum

*spatial*influence radius (e.g. 100 [km]); must be positive and may be`Inf`

. A compact influence region mainly has computational advantages, but might also be plausible for specific applications.

The

`data.frame`

may contain columns with further marks of the events, e.g. sex, age of infected individuals, which may be used as epidemic covariates influencing infectiousness. Note that some auxiliary columns will be added at conversion whose names are reserved:`".obsInfLength"`

,`".bdist"`

,`".influenceRegion"`

, and`".sources"`

, as well as`"start"`

,`"BLOCK"`

, and all endemic covariates' names from`stgrid`

.- stgrid
a

`data.frame`

describing endemic covariates on a full spatio-temporal region x interval grid (e.g., district x week), which is a decomposition of the observation region`W`

and period \(t_0,T\). This means that for every combination of spatial region and time interval there must be exactly one row in this`data.frame`

, that the union of the spatial tiles equals`W`

, the union of the time intervals equals \(t_0,T\), and that regions (and intervals) are non-overlapping. There are the following obligatory columns:- tile
ID of the spatial region (e.g., district ID). It will be converted to a factor variable (dropping unused levels if it already was one).

- start, stop
columns describing the consecutive temporal intervals (converted to numeric variables by

`as.numeric`

). The`start`

time of an interval must be equal to the`stop`

time of the previous interval. The`stop`

column may be missing, in which case it will be auto-generated from the set of`start`

values and`T`

.- area
area of the spatial region (

`tile`

). Be aware that the unit of this area (e.g., square km) must be consistent with the units of`W`

and`events`

(as specified in their`proj4string`

s).

The remaining columns are endemic covariates. Note that the column name

`"BLOCK"`

is reserved (a column which will be added automatically for indexing the time intervals of`stgrid`

).- W
an object of class

`"SpatialPolygons"`

representing the observation region. It must have the same`proj4string`

as`events`

and all events must be within`W`

. Prior simplification of`W`

may considerably reduce the computational burden of likelihood evaluations in`twinstim`

models with non-trivial spatial interaction functions (see the “Note” section below).- qmatrix
a square indicator matrix (0/1 or

`FALSE`

/`TRUE`

) for possible transmission between the event types. The matrix will be internally converted to`logical`

. Defaults to an independent spread of the event types, i.e. the identity matrix.- nCircle2Poly
accuracy (number of edges) of the polygonal approximation of a circle, see

`discpoly`

.- T
end of observation period (i.e. last

`stop`

time of`stgrid`

). Must be specified if the start but not the stop times are supplied in`stgrid`

(=> auto-generation of`stop`

times).- clipper
polygon clipping engine to use for calculating the

`.influenceRegion`

s of events (see the Value section below). Default is the polyclip package (called via`intersect.owin`

from package spatstat.geom). In surveillance <= 1.6-0, package gpclib was used, which has a restrictive license. This is no longer supported.- verbose
logical indicating if status messages should be printed during input checking and

`"epidataCS"`

generation. The default is to do so in interactive R sessions.- x
an object of class

`"epidataCS"`

or`"summary.epidataCS"`

, respectively.- n
a single integer. If positive, the first (

`head`

,`print`

) / last (`tail`

)`n`

events are extracted. If negative, all but the`n`

first/last events are extracted.- digits
minimum number of significant digits to be printed in values.

- i,j,drop
arguments passed to the

`[-method`

for`SpatialPointDataFrame`

s for subsetting the`events`

while retaining`stgrid`

and`W`

.

If`drop=TRUE`

(the default), event types that completely disappear due to`i`

-subsetting will be dropped, which reduces`qmatrix`

and the factor levels of the`type`

column.

By the`j`

index, epidemic covariates can be removed from`events`

.- ...
unused (arguments of the generics) with a few exceptions: The

`print`

method for`"epidataCS"`

passes`...`

to the`print.data.frame`

method, and the`print`

method for`"summary.epidataCS"`

passes additional arguments to`print.table`

.- subset, select
arguments used to subset the

`events`

from an`"epidataCS"`

object like in`subset.data.frame`

.- coords
logical indicating if the data frame of event marks returned by

`marks(x)`

should have the event coordinates appended as last columns. This defaults to`TRUE`

.- object
an object of class

`"epidataCS"`

.- dimension
the distances of all events to their potential source events can be computed in either the

`"space"`

or`"time"`

dimension.

## Details

The function `as.epidataCS`

is used to generate objects of class
`"epidataCS"`

, which is the data structure required for
`twinstim`

models.

The `[`

-method for class `"epidataCS"`

ensures that the subsetted object will be valid, for instance, it
updates the auxiliary list of potential transmission paths stored
in the object. The `[`

-method is used in
`subset.epidataCS`

, which is implemented similar to
`subset.data.frame`

.

The `print`

method for `"epidataCS"`

prints some metadata
of the epidemic, e.g., the observation period, the dimensions of the
spatio-temporal grid, the types of events, and the total number of
events. By default, it also prints the first `n = 6`

rows of the
`events`

.

## Value

An object of class `"epidataCS"`

is a list containing the
following components:

- events
a

`"SpatialPointsDataFrame"`

(see the description of the argument). The input`events`

are checked for requirements and sorted chronologically. The columns are in the following order: obligatory event columns, event marks, the columns`BLOCK`

,`start`

and endemic covariates copied from`stgrid`

, and finally, hidden auxiliary columns. The added auxiliary columns are:`.obsInfLength`

observed length of the infectious period (possibly truncated at

`T`

), i.e.,`pmin(T-time, eps.t)`

.`.sources`

a list of numeric vectors of potential sources of infection (wrt the interaction ranges eps.s and eps.t) for each event. Row numbers are used as index.

`.bdist`

minimal distance of the event locations to the polygonal boundary

`W`

.`.influenceRegion`

a list of influence regions represented by objects of the spatstat.geom class

`"owin"`

. For each event, this is the intersection of`W`

with a (polygonal) circle of radius`eps.s`

centered at the event's location, shifted such that the event location becomes the origin. The list has`nCircle2Poly`

set as an attribute.

- stgrid
a

`data.frame`

(see description of the argument). The spatio-temporal grid of endemic covariates is sorted by time interval (indexed by the added variable`BLOCK`

) and region (`tile`

). It is a full`BLOCK`

x`tile`

grid.- W
a

`"SpatialPolygons"`

object representing the observation region.- qmatrix
see the above description of the argument. The

`storage.mode`

of the indicator matrix is set to logical and the`dimnames`

are set to the levels of the event types.

The `nobs`

-method returns the number of events.

The `head`

and `tail`

methods subset the epidemic data using
the extraction method (`[`

), i.e. they return an object of class

`"epidataCS"`

, which only contains (all but) the first/last

`n`

events.

For the `"epidataCS"`

class, the method of the generic function

`marks`

defined by the spatstat.geom package
returns a `data.frame`

of the event marks (actually also
including time and location of the events), disregarding endemic
covariates and the auxiliary columns from the `events`

component
of the `"epidataCS"`

object.

The `summary`

method (which has again a `print`

method)
returns a list of metadata, event data, the tables of tiles and types,
a step function of the number of infectious individuals over time
(`$counter`

), i.e., the result of the

`as.stepfun`

-method for `"epidataCS"`

, and the number
of potential sources of transmission for each event (`$nSources`

)
which is based on the given maximum interaction ranges `eps.t`

and `eps.s`

.

## Note

Since the observation region `W`

defines the integration domain
in the point process likelihood,
the more detailed the polygons of `W`

are the longer it will
take to fit a `twinstim`

. You are advised to
sacrifice some shape details for speed by reducing the polygon
complexity, for example via the `mapshaper`

JavaScript library
wrapped by the R package rmapshaper, or via
`simplify.owin`

.

## References

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

Meyer, S., Held, L. and Höhle, M. (2017):
Spatio-temporal analysis of epidemic phenomena using the R package
surveillance.
*Journal of Statistical Software*, **77** (11), 1-55.
doi:10.18637/jss.v077.i11

## See also

`vignette("twinstim")`

.

`plot.epidataCS`

for plotting, and
`animate.epidataCS`

for the animation of such an epidemic.
There is also an `update`

method for the
`"epidataCS"`

class.

To re-extract the `events`

point pattern from `"epidataCS"`

,
use `as(object, "SpatialPointsDataFrame")`

.

It is possible to convert an `"epidataCS"`

point pattern to
an `"epidata"`

object (`as.epidata.epidataCS`

),
or to aggregate the events into an `"sts"`

object
(`epidataCS2sts`

).

## Examples

```
## load "imdepi" example data (which is an object of class "epidataCS")
data("imdepi")
## print and summary
print(imdepi, n=5, digits=2)
print(s <- summary(imdepi))
plot(s$counter, # same as 'as.stepfun(imdepi)'
xlab = "Time [days]", ylab="Number of infectious individuals",
main=paste("Time course of the number of infectious individuals",
"assuming an infectious period of 30 days", sep="\n"))
plot(table(s$nSources), xlab="Number of \"close\" infective individuals",
ylab="Number of events",
main=paste("Distribution of the number of potential sources",
"assuming an interaction range of 200 km and 30 days",
sep="\n"))
## the summary object contains further information
str(s)
## a histogram of the spatial distances to potential source events
## (i.e., to events of the previous eps.t=30 days within eps.s=200 km)
sourceDists_space <- getSourceDists(imdepi, "space")
hist(sourceDists_space); rug(sourceDists_space)
## internal structure of an "epidataCS"-object
str(imdepi, max.level=4)
## see help("imdepi") for more info on the data set
## extraction methods subset the 'events' component
## (thereby taking care of the validity of the epidataCS object,
## for instance the hidden auxiliary column .sources)
imdepi[101:200,]
tail(imdepi, n=4) # reduce the epidemic to the last 4 events
subset(imdepi, type=="B") # only consider event type B
## see help("plot.epidataCS") for convenient plot-methods for "epidataCS"
###
### reconstruct the "imdepi" object
###
## observation region
load(system.file("shapes", "districtsD.RData", package="surveillance"),
verbose = TRUE)
## extract point pattern of events from the "imdepi" data
## a) as a data frame with coordinate columns via marks()
eventsData <- marks(imdepi)
## b) as a Spatial object via the coerce-method
events <- as(imdepi, "SpatialPointsDataFrame")
## plot observation region with events (may require package 'sf')
if (requireNamespace("sf")) {
plot(stateD, axes=TRUE); title(xlab="x [km]", ylab="y [km]")
points(events, pch=unclass(events$type), cex=0.5, col=unclass(events$type))
legend("topright", legend=levels(events$type), title="Type", pch=1:2, col=1:2)
summary(events)
}
## space-time grid with endemic covariates
head(stgrid <- imdepi$stgrid[,-1])
## reconstruct the "imdepi" object from its components
myimdepi <- as.epidataCS(events = events, stgrid = stgrid,
W = stateD, qmatrix = diag(2), nCircle2Poly = 16)
if (FALSE) {
## This reconstructed object is equal to 'imdepi' as long as the internal
## structures of the embedded classes ("owin", "SpatialPolygons", ...), and
## the calculation of the influence regions by "polyclip" have not changed:
stopifnot(all.equal(imdepi, myimdepi))
}
```