photocar | R Documentation |
Survival time, time to first tumor, and total number of tumors in three groups of animals in a photococarcinogenicity study.
photocar
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 right-censored
observations and TRUE
otherwise.
dmin
time to first tumor.
tumor
status indicator for dmin
: FALSE
when no tumor was observed
and TRUE
otherwise.
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 analyzed 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.
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 Inference 129(1–2), 39–58. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.jspi.2004.06.038")}
Hothorn, T., Hornik, K., van de Wiel, M. A. and Zeileis, A. (2006). A Lego system for conditional inference. The American Statistician 60(3), 257–263. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1198/000313006X118430")}
## 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(nresample = 10000))
## Global p-value
pvalue(it)
## Why was the global null hypothesis rejected?
statistic(it, type = "standardized")
pvalue(it, method = "single-step")
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