PointEstimatorclass {adestr}  R Documentation 
Point estimators
Description
This is the parent class for all point estimators implemented in this package.
Currently, only estimators for the parameter \mu
of a normal distribution
are implemented.
Usage
PointEstimator(g1, g2, label)
SampleMean()
FirstStageSampleMean()
WeightedSampleMean(w1 = 0.5)
AdaptivelyWeightedSampleMean(w1 = 1/sqrt(2))
MinimizePeakVariance()
BiasReduced(iterations = 1L)
RaoBlackwell()
PseudoRaoBlackwell()
MidpointStagewiseCombinationFunctionOrderingCI()
MidpointMLEOrderingCI()
MidpointLikelihoodRatioOrderingCI()
MidpointScoreTestOrderingCI()
MidpointNeymanPearsonOrderingCI()
MedianUnbiasedStagewiseCombinationFunctionOrdering()
MedianUnbiasedMLEOrdering()
MedianUnbiasedLikelihoodRatioOrdering()
MedianUnbiasedScoreTestOrdering()
MedianUnbiasedNeymanPearsonOrdering(mu0 = 0, mu1 = 0.4)
Arguments
g1 
functional representation of the estimator in the early futility and efficacy regions. 
g2 
functional representation of the estimator in the continuation region. 
label 
name of the estimator. Used in printing methods. 
w1 
weight of the firststage data. 
iterations 
number of bias reduction iterations. Defaults to 1. 
mu0 
expected value of the normal distribution under the null hypothesis. 
mu1 
expected value of the normal distribution under the null hypothesis. 
Details
Details about the point estimators can be found in (our upcoming paper).
Sample Mean (SampleMean()
)
The sample mean is the maximum likelihood estimator for the mean and probably the 'most straightforward' of the implemented estimators.
Fixed weighted sample means (WeightedSampleMean()
)
The first and secondstage (if available) sample means are combined via fixed, predefined weights. See (Brannath et al. 2006) and (Section 8.3.2 in Wassmer and Brannath 2016).
Adaptively weighted sample means (AdaptivelyWeightedSampleMean()
)
The first and secondstage (if available) sample means are combined via a combination of fixed and adaptively modified weights that depend on the standard error. See (Section 8.3.4 in Wassmer and Brannath 2016).
Minimizing peak variance in adaptively weighted sample means (MinimizePeakVariance()
)
For this estimator, the weights of the adaptively weighted sample mean are chosen to
minimize the variance of the estimator for the value of \mu
which maximizes
the expected sample size.
(Pseudo) RaoBlackwell estimators (RaoBlackwell
and PseudoRaoBlackwell
)
The conditional expectation of the firststage sample mean given the overall sample mean and the secondstage sample size. See (Emerson and Kittelson 1997).
A biasreduced estimator (BiasReduced()
)
This estimator is calculated by subtracting an estimate of the bias from the MLE. See (Whitehead 1986).
Medianunbiased estimators
The implemented medianunbiased estimators are:

MedianUnbiasedMLEOrdering()

MedianUnbiasedLikelihoodRatioOrdering()

MedianUnbiasedScoreTestOrdering()

MedianUnbiasedStagewiseCombinationFunctionOrdering()
These estimators are constructed by specifying an ordering of the sample space
and finding the value of \mu
, such that the observed sample is the
median 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).
Value
an object of class PointEstimator
. This class signals that an
object can be supplied to the evaluate_estimator
and the
analyze
functions.
References
Brannath W, König F, Bauer P (2006).
“Estimation in flexible two stage designs.”
Statistics in Medicine, 25(19), 33663381.
doi:10.1002/sim.2258.
Emerson SS, Fleming TR (1990).
“Parameter estimation following group sequential hypothesis testing.”
Biometrika, 77(4), 875–892.
doi:10.2307/2337110.
Emerson SS, Kittelson JM (1997).
“A computationally simpler algorithm for the UMVUE of a normal mean following a group sequential trial.”
Biometrics, 53(1), 365–369.
doi:10.2307/2533122.
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:10.1007/9783319325620.
Whitehead J (1986).
“On the bias of maximum likelihood estimation following a sequential test.”
Biometrika, 73(3), 573–581.
doi:10.2307/2336521.
See Also
Examples
PointEstimator(g1 = \(smean1, ...) smean1,g2 = \(smean2, ...) smean2, label="My custom estimator")