PointEstimator-class {adestr} | R Documentation |
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.
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)
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 first-stage 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 about the point estimators can be found in (our upcoming paper).
SampleMean()
)The sample mean is the maximum likelihood estimator for the mean and probably the 'most straightforward' of the implemented estimators.
WeightedSampleMean()
)The first- and second-stage (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).
AdaptivelyWeightedSampleMean()
)The first- and second-stage (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).
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.
RaoBlackwell
and PseudoRaoBlackwell
)The conditional expectation of the first-stage sample mean given the overall sample mean and the second-stage sample size. See (Emerson and Kittelson 1997).
BiasReduced()
)This estimator is calculated by subtracting an estimate of the bias from the MLE. See (Whitehead 1986).
The implemented median-unbiased 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).
an object of class PointEstimator
. This class signals that an
object can be supplied to the evaluate_estimator
and the
analyze
functions.
Brannath W, König F, Bauer P (2006).
“Estimation in flexible two stage designs.”
Statistics in Medicine, 25(19), 3366-3381.
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:10.1007/978-3-319-32562-0.
Whitehead J (1986).
“On the bias of maximum likelihood estimation following a sequential test.”
Biometrika, 73(3), 573–581.
doi:10.2307/2336521.
PointEstimator(g1 = \(smean1, ...) smean1,g2 = \(smean2, ...) smean2, label="My custom estimator")