parfm (version 2.7.7)

ecf: East Coast Fever transmission dynamics

Description

Theileriosis or East Coast Fever (ECF) is a major cattle disease in East and Southern Africa. The disease is caused by Theileria parva which is transmitted by the ticks Rhipicephalus appendiculatus and the closely related Rhipicephalus zambeziensis.

In order to study the transmission of the disease, cows were followed up from birth until time of first ECF contact in Nteme, a region in Southern Zambia. On weekly basis, blood is collected and tested for the presence of antibodies to Theileria parva using the Indirect Fluorescent Antibody test. After three consecutive positive IFA test results an animal is considered seroconverted. The time to first ECF contact is defined as the timespan from birth to one month before the first of the three consecutive positive test results (i.e., we set the date of contact with Theileria parva one month before the time of the first positive test result). Animals are followed up until one year after birth; if they do not seroconvert by that time, their time of seroconversion is right-censored. We also consider the binary covariate breed.

Usage

data(ecf)

Format

A dataframe containing 212 observations.

Cowid:

Cow's identifyier.

Time:

Time to ECF contact (in days).

Status:

Censored (0) or observed (1) event time.

Breed:

The cow's breed.

References

Duchateau L, Janssen P (2008). The frailty model. Springer. New York: Springer--Verlag.

Examples

# \donttest{
data(ecf)
head(ecf)

################################################################################
#Example 3.8: Population and conditional hazard for time to ECF contact        #
#Duchateau and Janssen (2008, page 113)                                        #
################################################################################
pfm1 <- parfm(Surv(Time, Status) ~ 1, cluster = "Cowid", data = ecf,
              dist = "weibull", frailty = "gamma")
pfm2 <- parfm(Surv(Time, Status) ~ Breed, cluster = "Cowid", data = ecf,
              dist = "weibull", frailty = "gamma")
curve(pfm1["lambda", 1] * pfm1["rho", 1] * x ^ (pfm1["rho", 1] - 1),
      from = 0, to = 400, ylim = c(0, .15), 
      ylab = "Hazard function", xlab = "Time (days)")
curve(qgamma(.75, shape = 1 / pfm1["theta", 1],
             scale = pfm1["theta", 1]) * pfm1["lambda", 1] * pfm1["rho", 1] *
                x ^ (pfm1["rho", 1] - 1),
      add = TRUE, lty = 2)
curve(qgamma(.25, shape=1 / pfm1["theta", 1],
             scale = pfm1["theta", 1]) * pfm1["lambda", 1] * pfm1["rho", 1] *
               x ^ (pfm1["rho", 1] - 1),
      add = TRUE, lty = 3)
curve(pfm1["lambda", 1] * pfm1["rho", 1] *
        x ^ (pfm1["rho", 1] - 1) / (
            1 + pfm1["theta", 1] * pfm1["lambda", 1] * x ^ (pfm1["rho", 1])
      ),
      add = TRUE, lwd = 2)
legend("top", lwd = c(1, 1, 1, 2), lty = c(1, 2, 3, 1), ncol = 2,
       legend = c("Mean frailty", "Q75 frailty", "Q25 frailty", "Population"))
# }