test {PK}

Function for hypothesis testing for objects of class PK

Description

Generic function for hypothesis testing based on an object of class PK.

Usage

test(obj, theta=0, method = c("t", "fieller", "z", "resample"), nsample = 1000) 

## S3 method for class 'PKtest'
print(x,hyp=FALSE,...)

## S3 method for class 'PKtest'
summary(object,...)

Arguments

obj

An output object of class PK.

x

An output object of class PKtest.

object

An output object of class PK test.

theta

The reference value to be tested against. If multiple parameters are to be tested a vector can be supplied.

method

A character string specifying the method for calculation of the test statistic. Possible values are t (the default) and fieller for a t-test based method, z for a z-test and resample for either a bootstrap or a permutation test.

nsample

Number of resamples for the permutation/bootstrap test (default=1000).

hyp

Logical variable indicating if hypothesis tests should be printed explicitly (default=FALSE).

...

Arguments to be passed to methods, such as graphical.

Details

Generic function to perform hypothesis test(s).

The reference value for the test is to be specified in theta. If multiple tests are performed theta can be a vector.

For method "resample" a permutation test is used for the difference of AUCs while a one-sample bootstrap test based on inverting a bootstrap-t statistic is implemented.

Value

An object of the class PKtest containing the following components:

stat

Test statistics.

p.value

p-values.

theta

Reference value(s) tested against.

conf.level

Confidence level.

alternative

Type of alternative used.

df

Degrees of freedom of method "t".

design

Sampling design used.

method

Type of test used.

Author(s)

Thomas Jaki

References

Efron B and Tibshirani R. J. (1993). An introduction to the bootstrap, Chapman and Hall, New York.

Holder D. J., Hsuan F., Dixit R. and Soper K. (1999). A method for estimating and testing area under the curve in serial sacrifice, batch, and complete data designs. Journal of Biopharmaceutical Statistics, 9(3):451-464.

Wolfsegger M. J. and Jaki T. (2009) Assessing systemic drug exposure in repeated dose toxicity studies in the case of complete and incomplete sampling. Biometrical Journal, 51(6):1017:1029.

See Also

auc, eqv and nca.

Examples

## example for a serial sampling data design from Wolfsegger and Jaki (2009)
conc <- c(0, 0, 0, 2.01, 2.85, 2.43, 0.85, 1.00, 0.91, 0.46, 0.35, 0.63, 0.39, 0.32, 
          0.45, 0.11, 0.18, 0.19, 0.08, 0.09, 0.06)
time <- c(rep(0,3), rep(5/60,3), rep(3,3), rep(6,3), rep(9,3), rep(16,3), rep(24,3))

obj <- nca(conc=conc, time=time, n.tail=4, dose=200, method="z", 
            conf.level=0.95, design="ssd")

## testing all parameters against different values using a z-test
res <- test(obj, theta=c(11, 12, 90, 7, 5, 16, 120), method="z")

print(res)

## a batch design example from Holder et al. (1999).
data(Rats)
data <- subset(Rats,Rats$dose==100)

obj <- auc(data=data,method=c('z','t'), design='batch')

## t-test
res <- test(obj, theta=100, method="t")

## making the hypothesis explicit
summary(res)

## bootstrap test for bioequivalence
# Note: This can take a few seconds
data(Glucose)
## one-sided permutation test
obj <- auc(conc=Glucose$conc, time=Glucose$time, group=Glucose$date, 
     method=c("t"), conf.level=0.90, alternative='less', 
     nsample=100, design="complete")

test(obj, theta=1, method="resample", nsample=100)