Interval estimators

This is the parent class for all confidence intervals implemented in this package. Currently, only confidence intervals for the parameter \(\mu\) of a normal distribution are implemented. Details about the methods for calculating confidence intervals can be found in (our upcoming paper).

Usage

IntervalEstimator(two_sided, l1, u1, l2, u2, label)

RepeatedCI(two_sided = TRUE)

StagewiseCombinationFunctionOrderingCI(two_sided = TRUE)

MLEOrderingCI(two_sided = TRUE)

LikelihoodRatioOrderingCI(two_sided = TRUE)

ScoreTestOrderingCI(two_sided = TRUE)

NeymanPearsonOrderingCI(two_sided = TRUE, mu0 = 0, mu1 = 0.4)

NaiveCI(two_sided = TRUE)

Arguments

two_sided: logical indicating whether the confidence interval is two-sided.
l1: functional representation of the lower boundary of the interval in the early futility and efficacy regions.
u1: functional representation of the upper boundary of the interval in the early futility and efficacy regions.
l2: functional representation of the lower boundary of the interval in the continuation region.
u2: functional representation of the upper boundary of the interval in the continuation region.
label: name of the estimator. Used in printing methods.
mu0: expected value of the normal distribution under the null hypothesis.
mu1: expected value of the normal distribution under the null hypothesis.

Value

an object of class IntervalEstimator. This class signals that an object can be supplied to the evaluate_estimator and the analyze functions.

Details

The implemented confidence intervals are:

MLEOrderingCI()
LikelihoodRatioOrderingCI()
ScoreTestOrderingCI()
StagewiseCombinationFunctionOrderingCI()

These confidence intervals are constructed by specifying an ordering of the sample space and finding the value of \(\mu\), such that the observed sample is the \(\alpha/2\) (or (\(1-\alpha/2\))) quantile of the sample space according to the chosen ordering. Some of the implemented orderings are based on the work presented in (Emerson and Fleming 1990) , (Sections 8.4 in Jennison and Turnbull 1999) , and (Sections 4.1.1 and 8.2.1 in Wassmer and Brannath 2016) .

References

Emerson SS, Fleming TR (1990). “Parameter estimation following group sequential hypothesis testing.” Biometrika, 77(4), 875–892. doi:10.2307/2337110 .

Jennison C, Turnbull BW (1999). Group Sequential Methods with Applications to Clinical Trials, 1 edition. Chapman and Hall/CRC., New York. doi:10.1201/9780367805326 .

Wassmer G, Brannath W (2016). Group Sequential and Confirmatory Adaptive Designs in Clinical Trials, 1 edition. Springer, Cham, Switzerland. doi:10.1007/978-3-319-32562-0 .

Examples