Survival time, time to first tumor, and total number of tumors in three groups
of animals in a photococarcinogenicity study.
Usage
photocar
Format
A data frame with 108 observations on 6 variables.
group
a factor with levels "A", "B", and "C".
ntumor
total number of tumors.
time
survival time.
event
status indicator for time: FALSE for censored observations
and TRUE otherwise.
dmin
time to first tumor.
tumor
status indicator for dmin: FALSE when no tumor was observed
and TRUE otherwise.
Details
The animals were exposed to different levels of ultraviolet radiation (UVR)
exposure (group A: topical vehicle and 600 Robertson–Berger units of UVR,
group B: no topical vehicle and 600 Robertson–Berger units of UVR and group
C: no topical vehicle and 1200 Robertson–Berger units of UVR). The data are
taken from Tables 1 to 3 in Molefe et al. (2005).
The main interest is testing the global null hypothesis of no treatment effect
with respect to survival time, time to first tumor and number of tumors.
(Molefe et al., 2005, also analysed the detection time of tumors, but
that data is not given here.) In case the global null hypothesis can be
rejected, the deviations from the partial null hypotheses are of special
interest.
Source
Molefe, D. F., Chen, J. J., Howard, P. C., Miller, B. J., Sambuco, C. P.,
Forbes, P. D. and Kodell, R. L. (2005). Tests for effects on tumor frequency
and latency in multiple dosing photococarcinogenicity experiments.
Journal of Statistical Planning and Inference129(1–2), 39–58.
References
Hothorn, T., Hornik, K., van de Wiel, M. A. and Zeileis, A. (2006). A Lego
system for conditional inference. The American Statistician60(3), 257–263.
Examples
## Plotting data
op <- par(no.readonly = TRUE) # save current settings
layout(matrix(1:3, ncol = 3))
with(photocar, {
plot(survfit(Surv(time, event) ~ group),
lty = 1:3, xmax = 50, main = "Survival Time")
legend("bottomleft", lty = 1:3, levels(group), bty = "n")
plot(survfit(Surv(dmin, tumor) ~ group),
lty = 1:3, xmax = 50, main = "Time to First Tumor")
legend("bottomleft", lty = 1:3, levels(group), bty = "n")
boxplot(ntumor ~ group, main = "Number of Tumors")
})
par(op) # reset
## Approximative multivariate (all three responses) test
it <- independence_test(Surv(time, event) + Surv(dmin, tumor) + ntumor ~ group,
data = photocar,
distribution = approximate(B = 10000))
## Global p-value
pvalue(it)
## Why was the global null hypothesis rejected?
statistic(it, type = "standardized")
pvalue(it, method = "single-step")