Data on the 188 cases in the measles outbreak among children in the German city of Hagelloch (near Tübingen) 1861. The data were originally collected by Dr. Albert Pfeilsticker (1863) and augmented and re-analysed by Dr. Heike Oesterle (1992). This dataset is used to illustrate the twinSIR model class in vignette("twinSIR").

data("hagelloch")

## Format

Loading data("hagelloch") gives two objects: hagelloch and hagelloch.df. The latter is the original data.frame of 188 rows with individual information for each infected child. hagelloch has been generated from hagelloch.df via as.epidata (see the Examples below) to obtain an "epidata" object for use with twinSIR. It contains the entire SIR event history of the outbreak (but not all of the covariates).

The covariate information in hagelloch.df is as follows:

PN:

patient number

NAME:

patient name (as a factor)

FN:

family index

HN:

house number

AGE:

age in years

SEX:

gender of the individual (factor: male, female)

PRO:

Date of prodromes

ERU:

Date of rash

CL:

class (factor: preschool, 1st class, 2nd class)

Date of death (with missings)

IFTO:

number of patient who is the putative source of infection (0 = unknown)

SI:

serial interval = number of days between dates of prodromes of infection source and infected person

C:

complications (factor: no complications, bronchopneumonia, severe bronchitis, lobar pneumonia, pseudocroup, cerebral edema)

PR:

duration of prodromes in days

CA:

number of cases in family

NI:

number of initial cases

GE:

generation number of the case

TD:

day of max. fever (days after rush)

TM:

max. fever (degree Celsius)

x.loc:

x coordinate of house (in meters). Scaling in metres is obtained by multiplying the original coordinates by 2.5 (see details in Neal and Roberts (2004))

y.loc:

y coordinate of house (in meters). See also the above description of x.loc.

tPRO:

Time of prodromes (first symptoms) in days after the start of the epidemic (30 Oct 1861).

tERU:

Time upon which the rash first appears.

Time of death, if available.

tR:

Time at which the infectious period of the individual is assumed to end. This unknown time is calculated as $$tR_i = \min{tDEAD_i,tERU_i+d_0},$$ where -- as in Section 3.1 of Neal and Roberts (2004) -- we use $$d_0=3$$.

tI:

Time at which the individual is assumed to become infectious. Actually this time is unknown, but we use $$tI_i = tPRO_i - d_1,$$ where $$d_1=1$$ as in Neal and Roberts (2004).

The time variables describe the transitions of the individual in an Susceptible-Infectious-Recovered (SIR) model. Note that in order to avoid ties in the event times resulting from daily interval censoring, the times have been jittered uniformly within the respective day. The time point 0.5 would correspond to noon of 30 Oct 1861.

The hagelloch "epidata" object only retains some of the above covariates to save space. Apart from the usual "epidata" event columns, hagelloch contains a number of extra variables representing distance- and covariate-based weights for the force of infection:

household:

the number of currently infectious children in the same household (including the child itself if it is currently infectious).

nothousehold:

the number of currently infectious children outside the household.

c1, c2:

the number of children infectious during the respective time block and being members of class 1 and 2, respectively; but the value is 0 if the individual of the row is not herself a member of the respective class.

Such epidemic covariates can been computed by specifying suitable f and w arguments in as.epidata at conversion (see the code below), or at a later step via the update-method for "epidata".

## Source

Thanks to Peter J. Neal, University of Manchester, for providing us with these data, which he again became from Niels Becker, Australian National University. To cite the data, the main references are Pfeilsticker (1863) and Oesterle (1992).

## References

Pfeilsticker, A. (1863). Beiträge zur Pathologie der Masern mit besonderer Berücksichtigung der statistischen Verhältnisse, M.D. Thesis, Eberhard-Karls-Universität Tübingen. Available as https://archive.org/details/beitrgezurpatho00pfeigoog.

Oesterle, H. (1992). Statistische Reanalyse einer Masernepidemie 1861 in Hagelloch, M.D. Thesis, Eberhard-Karls-Universitäat Tübingen.

Neal, P. J. and Roberts, G. O (2004). Statistical inference and model selection for the 1861 Hagelloch measles epidemic, Biostatistics 5(2):249-261

data class: epidata

point process model: twinSIR

illustration with hagelloch: vignette("twinSIR")

## Examples

data("hagelloch")
head(hagelloch.df)   # original data documented in Oesterle (1992)
head(as.data.frame(hagelloch))   # "epidata" event history format

## How the "epidata" 'hagelloch' was created from 'hagelloch.df'
stopifnot(all.equal(hagelloch,
as.epidata(
hagelloch.df, t0 = 0, tI.col = "tI", tR.col = "tR",
id.col = "PN", coords.cols = c("x.loc", "y.loc"),
f = list(
household    = function(u) u == 0,
nothousehold = function(u) u > 0
),
w = list(
c1 = function (CL.i, CL.j) CL.i == "1st class" & CL.j == CL.i,
c2 = function (CL.i, CL.j) CL.i == "2nd class" & CL.j == CL.i
),
keep.cols = c("SEX", "AGE", "CL"))
))

### Basic plots produced from hagelloch.df

# Show case locations as in Neal & Roberts (different scaling) using
# the data.frame (promoted to a SpatialPointsDataFrame)
coordinates(hagelloch.df) <- c("x.loc","y.loc")
plot(hagelloch.df, xlab="x [m]", ylab="x [m]", pch=15, axes=TRUE,
cex=sqrt(multiplicity(hagelloch.df)))

# Epicurve
hist(as.numeric(hagelloch.df$tI), xlab="Time (days)", ylab="Cases", main="") ### "epidata" summary and plot methods (s <- summary(hagelloch)) head(s$byID)
plot(s)

if (FALSE) {
# Show a dynamic illustration of the spread of the infection
animate(hagelloch, time.spacing=0.1, sleep=1/100,
legend.opts=list(x="topleft"))
}