MCPAN (version 1.1-21)

poly3ci: Simultaneous confidence intervals for contrasts of poly-3-adjusted tumour rates

Description

Function to calculate simultaneous confidence intervals for several contrasts of poly-3-adjusted tumour rates in a oneway layout. Assuming a data situation as in Peddada(2005) or Bailer and Portier (1988). Simultaneous asymptotic CI for contrasts of tumour rates, assuming that standard normal approximation holds.

Usage

poly3ci(time, status, f, type = "Dunnett",
 cmat = NULL, method = "BP", alternative = "two.sided",
 conf.level = 0.95, dist="MVN", k=3, …)

Arguments

time

a numeric vector of times of death of the individuals

status

a logical (or numeric, consisting of 0,1 only) vector giving the tumour status at time of death of each individual, where TRUE (1) = tumour present, FALSE (0) = no tumour present

f

a factor, giving the classification variable

type

a character string, giving the name of a contrast method, as defined in contrMat(multcomp)

cmat

a optional contrast matrix

method

a single charcter string, specifying the method for adjustment, with options: "BP" (Bailer Portier: assuming poly-3-adjusted rates are binomial variables), "BW" (Bieler, Williams: delta method as in Bieler and Williams (1993)) "ADD1" (as Bailer Portier, including an add1-adjustment on the raw tumour rates) "ADD2" (as Bailer Portier, including an add2-adjustment on the raw tumour rates following Agresti and Caffo (2000) for binomials)

alternative

a single character string

conf.level

a single numeric value, simultaneous confidence level

dist

a character string, "MVN" invokes multiplicity adjustment via the multivariate normal distribution, "N" invokes use of quantiles of the univariate normal distribution

k

the exponent to calculate survival adjusted proportions, default is k=3

…

further arguments to be passed; currently only base, to be passed to contrMat to choose the control group with type="Dunnett"

Value

A object of class "poly3ci", a list containing:

conf.int

a matrix with 2 columns: lower and upper confidence bounds, and M rows

alternative

character string, as input

conf.level

single numeric value, as input

quantile

the quantile used to construct the CIs

estimate

a numeric vector with the point estimates of the contrasts

time

as input

status

as input

f

as input

method

as input

cmat

as input, with colnames= factor levels of f

sample.est

a list containing sample estimates

References

The implemented methodology is described in:

Schaarschmidt, F., Sill, M., and Hothorn, L.A. (2008): Approximate Simultaneous confidence intervals for multiple contrasts of binomial proportions. Biometrical Journal 50, 782-792.

Background references are:

Assumption for poly-3-adjustment: Bailer, J.A. and Portier, C.J. (1988): Effects of treatment-induced mortality and tumor-induced mortality on tests for carcinogenicity in small samples. Biometrics 44, 417-431.

Peddada, S.D., Dinse, G.E., and Haseman, J.K. (2005): A survival-adjusted quantal response test for comparing tumor incidence rates. Applied Statistics 54, 51-61.

Bieler, G.S. and Williams, R.L. (1993): Ratio estimates, the Delta Method, and quantal response tests for increased carcinogenicity. Biometrics 49, 793-801.

Statistical procedures and characterization of the coverage probabilities are described in: Sill, M. (2007): Approximate simultaneous confidence intervals for multiple comparisons of binomial proportions. Master thesis, Institute of Biostatistics, Leibniz University Hannover.

Examples

# NOT RUN {
#############################################################

### Methyleugenol example in Schaarschmidt et al. (2008) ####

#############################################################

# load the data:

data(methyl)

# The results in Table 5 (Schaarschmidt et al. 2008) can be
# reproduced by calling:


methylW<-poly3ci(time=methyl$death, status=methyl$tumour,
 f=methyl$group, type = "Williams", method = "ADD1", alternative="greater" )

methylW


methylWT<-poly3test(time=methyl$death, status=methyl$tumour,
 f=methyl$group, type = "Williams", method = "ADD1", alternative="greater" )

methylWT


plot(methylW, main="Simultaneous CI for \n Poly-3-adjusted tumour rates")

# The results in Table 6 can be reproduced by calling:

methylD<-poly3ci(time=methyl$death, status=methyl$tumour,
 f=methyl$group, type = "Dunnett", method = "ADD1", alternative="greater" )

methylD

methylDT<-poly3test(time=methyl$death, status=methyl$tumour,
 f=methyl$group, type = "Dunnett", method = "ADD1", alternative="greater" )

methylDT


plot(methylD, main="Simultaneous CI for Poly-3-adjusted tumour rates", cex.main=0.7)


############################################################


# unadjusted CI

methylD1<-poly3ci(time=methyl$death, status=methyl$tumour,
 f=methyl$group, type = "Dunnett", method = "ADD1", dist="N" )

methylD1

plot(methylD1, main="Local CI for Poly-3-adjusted tumour rates")

# }