a simple procedure to compute the sample size needed to compare two independent groups when the population variances are unequal the usual methods of sample size determination which assume the homogeneity of within group variances are not sufficiently robust against the violation of this assumption a method using satterthwaite s correction for unequal variances is given it is shown that in the case of unequal variances the minimum total sample size is attained when the allocation ratio is equal to the proportion of the standard deviations

coding for additive white noise channels with feedback corrupted by quantization or bounded noise we present coding strategies which are variants of the schalkwijk kailath scheme for communicating reliably over additive white noise channels in the presence of corrupted feedback our framework comprises an additive white forward channel and a feedback link we consider two types of corruption mechanisms in the feedback link the first is quantization noise i e the encoder receives the quantized values of the past outputs of the forward channel the quantization is uniform memoryless and time invariant the second corruption mechanism is an arbitrarily distributed additive bounded noise here we allow symbol by symbol encoding at the input to the feedback link we propose explicit schemes featuring positive information rate and positive error exponent if the forward channel is additive white gaussian awgn then as the amplitude of the noise at the feedback link decreases to zero the rate of our schemes converges to the capacity of the channel moreover the probability of error is shown to converge to zero at a doubly exponential rate if the forward channel is awgn and the feedback link consists of an additive bounded noise channel with signal to noise ratio snr constrained symbol by symbol encoding then our schemes achieve rates arbitrarily close to capacity in the limit of high snr at the feedback link

brief paper estimation of the disturbance structure from data using semidefinite programming and optimal weighting designing a state estimator for a linear state space model requires knowledge of the characteristics of the disturbances entering the states and the measurements in odelson b j rajamani m r rawlings j b 2006 a new autocovariance least squares method for estimating noise covariances automatica 42 2 303 308 the correlations between the innovations data were used to form a least squares problem to determine the covariances for the disturbances in this paper we present new and simpler necessary and sufficient conditions for the uniqueness of the covariance estimates we also formulate the optimal weighting to be used in the least squares objective in the covariance estimation problem to ensure minimum variance in the estimates a modification to the above technique is then presented to estimate the number of independent stochastic disturbances affecting the states this minimum number of disturbances is usually unknown and must be determined from data a semidefinite optimization problem is solved to estimate the number of independent disturbances entering the system and their covariances

optimal allocation for the comparison of proportions optimal allocation strategies for the comparison of proportions p1 and p2 in two groups are discussed allocations which i maximize the precision in the estimation of the difference p1 p2 ii maximize the precision in the estimation of the ratio p1 p2 iii maximize the power to detect a group difference and iv minimize the total cost of a study are compared the recommended allocation varies markedly with the desired objective furthermore there is a wide range of allocation schemes which are effectively optimal with regard to each criterion considered a study of congenital malformations occurring in pregnancies of diabetic women is used to illustrate how these considerations apply to the planning of a study

secrecy capacity of colored gaussian noise channels with feedback in this paper the finite order autoregressive moving average arma gaussian wiretap channel with noiseless causal feedback is considered in which an eavesdropper receives noisy observations of signals in both forward and feedback channels it is shown that the generalized schalkwijk kailath scheme a capacity achieving coding scheme for the gaussian feedback channel achieves the same maximum rate for the same channel even with the presence of an eavesdropper therefore the secrecy capacity is equal to the feedback capacity without the presence of an eavesdropper for the gaussian feedback channel furthermore the results are extended to the additive white gaussian noise awgn channel with quantized feedback it is shown that the proposed coding scheme achieves a positive secrecy rate our result implies that as the amplitude of the quantization noise decreases to zero the secrecy rate converges to the capacity of the awgn channel

a studentized permutation test for three arm trials in the gold standard design the gold standard design for three arm trials refers to trials with an active control and a placebo control in addition to the experimental treatment group this trial design is recommended when being ethically justifiable and it allows the simultaneous comparison of experimental treatment active control and placebo parametric testing methods have been studied plentifully over the past years however these methods often tend to be liberal or conservative when distributional assumptions are not met particularly with small sample sizes in this article we introduce a studentized permutation test for testing non inferiority and superiority of the experimental treatment compared with the active control in three arm trials in the gold standard design the performance of the studentized permutation test for finite sample sizes is assessed in a monte carlo simulation study under various parameter constellations emphasis is put on whether the studentized permutation test meets the target significance level for comparison purposes commonly used wald type tests which do not make any distributional assumptions are included in the simulation study the simulation study shows that the presented studentized permutation test for assessing non inferiority in three arm trials in the gold standard design outperforms its competitors for instance the test based on a quasi poisson model for count data the methods discussed in this paper are implemented in the r package threearmedtrials which is available on the comprehensive r archive network cran copyright 2016 john wiley sons ltd

a general approach for sample size calculation for the three arm gold standard non inferiority design in the three arm gold standard non inferiority design an experimental treatment an active reference and a placebo are compared this design is becoming increasingly popular and it is whenever feasible recommended for use by regulatory guidelines we provide a general method to calculate the required sample size for clinical trials performed in this design as special cases the situations of continuous binary and poisson distributed outcomes are explored taking into account the correlation structure of the involved test statistics the proposed approach leads to considerable savings in sample size as compared with application of ad hoc methods for all three scale levels furthermore optimal sample size allocation ratios are determined that result in markedly smaller total sample sizes as compared with equal assignment as optimal allocation makes the active treatment groups larger than the placebo group implementation of the proposed approach is also desirable from an ethical viewpoint

conditional rank tests for the two sample problem under random censorship for the two sample problem with randomly censored data there exists a general asymptotic theory of rank statistics which are functionals of stochastic integrals with respect to certain empirical martingales in the present paper a conditional counterpart of this theory is developed the conditional martingales are versions of the original ones reduced to the unit interval having their jumps at fixed lattice points the resulting conditional tests are strictly distribution free under the null hypothesis of randomness if the censoring distributions in both samples are equal and are asymptotically equivalent to their unconditional counterparts even if the censoring distributions are different simulations for linear rank statistics and kolmogorov smirnov type statistics show superiority of the conditional versions over their unconditional counterparts with respect to size and robustness under unequal censoring in both samples at the same time the power of the conditional and unconditional tests is very similar in most cases

a two stage sample size recalculation procedure for placebo and active controlled non inferiority trials many non inferiority trials of a test treatment versus an active control may also if ethical incorporate a placebo arm inclusion of a placebo arm enables a direct assessment of assay sensitivity it also allows construction of a non inferiority test that avoids the problematic specification of an absolute non inferiority margin and instead evaluates whether the test treatment preserves a pre specified proportion of the effect of the active control over placebo we describe a two stage procedure for sample size recalculation in such a setting that maintains the desired power more closely than a fixed sample approach when the magnitude of the effect of the active control differs from that anticipated we derive an allocation rule for randomization under which the procedure preserves the type i error rate and show that this coincides with that previously presented for optimal allocation of the sample size among the three treatment arms

asymptotic permutation tests in general factorial designs summary in general factorial designs where no homoscedasticity or a particular error distribution is assumed the well known wald type statistic is a simple asymptotically valid procedure however it is well known that it suffers from a poor finite sample approximation since the convergence to its 2 limit distribution is quite slow this becomes even worse with an increasing number of factor levels the aim of the paper is to improve the small sample behaviour of the wald type statistic maintaining its applicability to general settings as crossed or hierarchically nested designs by applying a modified permutation approach in particular it is shown that this approach approximates the null distribution of the wald type statistic not only under the null hypothesis but also under the alternative yielding an asymptotically valid permutation test which is even finitely exact under exchangeability finally its small sample behaviour is compared with competing procedures in an extensive simulation study

bootstrapping frequency domain tests in multivariate time series with an application to comparing spectral densities summary we propose a general bootstrap procedure to approximate the null distribution of non parametric frequency domain tests about the spectral density matrix of a muitivariate time series under a set of easy to verify conditions we establish asymptotic validity of the bootstrap procedure proposed we apply a version of this procedure together with a new statistic to test the hypothesis that the spectral densities of not necessarily independent time series are equal the test statistic proposed is based on an 2 distance between the non parametrically estimated individual spectral densities and an overall pooled spectral density the latter being obtained by using the whole set of m time series considered the effects of the dependence between the time series on the power behaviour of the test are investigated some simulations are presented and a real life data example is discussed

quantifying nanoparticle mixing state to account for both location and size effects abstractripley s k function is commonly used to characterize the homogeneity of spatial point distribution not surprisingly it becomes a favored tool in quantifying the nanoparticles mixing state in composite materials a parameter that material scientists believe is of close relevance to certain properties of the nanoparticle embedding material ripley s k function assumes that the spatial points are dimensionless in reality the nanoparticles once mixed in a host material form clusters or agglomerates of various sizes and shapes our analysis shows that using the original k function falls short of ranking or distinguishing the homogeneity of nanoparticle mixing we therefore propose to revise the k function to account for both particle location and size effects we apply the revised function to electron microscopy images of material samples and conduct analysis and comparison of nanoparticle mixing the analysis shows that the revised function is a better index to quantify the mixing states

simultaneous confidence intervals for ratios with application to the gold standard design with more than one experimental treatment considering a study design with two experimental treatments a reference treatment and a placebo we extend a previous approach considering the ratios of effects to a procedure for analyzing multiple ratios the technical framework for constructing tests and compatible simultaneous confidence intervals is set in a general manner besides a single step procedure and its extension to a stepdown procedure also an informative stepwise procedure in the spirit of our previous work is developed the latter is especially interesting because noninferiority studies require informative confidence intervals to infer more information than just noninferiority at the prespecified margin results from a simulation study for the three methods are shown we also argue that an extension to more than two experimental treatments is straightforward

a kpss test for stationarity for spatial point processes we propose a formal method to test stationarity for spatial point processes the proposed test statistic is based on the integrated squared deviations of observed counts of events from their means estimated under stationarity we show that the resulting test statistic converges in distribution to a functional of a two dimensional brownian motion to conduct the test we compare the calculated statistic with the upper tail critical values of this functional our method requires only a weak dependence condition on the process but does not assume any parametric model for it as a result it can be applied to a wide class of spatial point process models we study the efficacy of the test through both simulations and applications to two real data examples that were previously suspected to be nonstationary based on graphical evidence our test formally confirmed the suspected nonstationarity for both data

new tests for equality of several covariance functions for functional data in this article we propose two new tests for the equality of the covariance functions of several functional populations namely a quasi gpf test and a quasi fmax test whose test statistics are o

inference in vars with conditional heteroskedasticity of unknown form we derive a framework for asymptotically valid inference in stable vector autoregressive var models with conditional heteroskedasticity of unknown form we prove a joint central limit theorem for the var slope parameter and innovation covariance parameter estimators and address bootstrap inference as well our results are important for correct inference on var statistics that depend both on the var slope and the variance parameters as e g in structural impulse response functions irfs we also show that wild and pairwise bootstrap schemes fail in the presence of conditional heteroskedasticity if inference on functions of the unconditional variance parameters is of interest because they do not correctly replicate the relevant fourth moments structure of the error terms in contrast the residual based moving block bootstrap results in asymptotically valid inference we illustrate the practical implications of our theoretical results by providing simulation evidence on the finite sample properties of different inference methods for irfs our results point out that estimation uncertainty may increase dramatically in the presence of conditional heteroskedasticity moreover most inference methods are likely to understate the true estimation uncertainty substantially in finite samples

nonparametric non inferiority analyses in the three arm design with active control and placebo the three arm design with test treatment reference treatment and placebo offers internal assay sensitivity for a proof of non inferiority in this design the relative effects known from nonparametric theory are robust tools allowing the assessment of non inferiority in a range of situations an asymptotic nonparametric theory is established in the three arm design based on the asymptotic distribution of rank means under alternative a rank test for non inferiority is derived fieller s formula is used to calculate a respective confidence interval the approach is expanded to multicentre studies the simulation studies are conducted demonstrating the accuracy of the methods and an example is discussed

blinded sample size re estimation in three arm trials with gold standard design in this article we study blinded sample size re estimation in the gold standard design with internal pilot study for normally distributed outcomes the gold standard design is a three arm clinical trial design that includes an active and a placebo control in addition to an experimental treatment we focus on the absolute margin approach to hypothesis testing in three arm trials at which the non inferiority of the experimental treatment and the assay sensitivity are assessed by pairwise comparisons we compare several blinded sample size re estimation procedures in a simulation study assessing operating characteristics including power and type i error we find that sample size re estimation based on the popular one sample variance estimator results in overpowered trials moreover sample size re estimation based on unbiased variance estimators such as the xing ganju variance estimator results in underpowered trials as it is expected because an overestimation of the variance and thus the sample size is in general required for the re estimation procedure to eventually meet the target power to overcome this problem we propose an inflation factor for the sample size re estimation with the xing ganju variance estimator and show that this approach results in adequately powered trials because of favorable features of the xing ganju variance estimator such as unbiasedness and a distribution independent of the group means the inflation factor does not depend on the nuisance parameter and therefore can be calculated prior to a trial moreover we prove that the sample size re estimation based on the xing ganju variance estimator does not bias the effect estimate copyright 2017 john wiley sons ltd

point estimation for multi spectral distributed random matrices abstract in this communication we consider a p n random matrix x x 1 x 2 x n which is normally distributed with mean matrix m and covariance matrix where the multivariate observation x i y i i with p dimensions on an object consists of two components the signal y i with mean vector and covariance matrix s and noise i i 1 2 n with mean vector zero and covariance matrix then the covariance matrix of x i and x j is given by cov x i x j b i j s c i j where is a correlation matrix b i j and c i j are diagonal constant matrices the statistical objective is to consider the maximum likelihood estimate of the mean matrix m and various components of the covariance matrix as well as their statistical properties that is the point estimates of s and more importantly some properties of these estimators are investigated in slightly more general models

the covariance matrix of a general symmetric second degree matrix polynomial under normality assumptions abstract a matrix expression for the covariance matrix of a general second degree matrix polynomial under normality assumptions is derived by applying methods of matrix differentiation to the cumulant generating function

estimation of parameters for normally distributed random matrices abstract consider the p n random matrix x which is normally distributed with mean m and let the covariance matrix between any two columns of x say x i and x j be ij expectations and convariances of the maximum likelihood estimators of m and are given for the situation when ij and are known

sample size determination for proving equivalence based on the ratio of two means for normally distributed data equivalence trials aim to demonstrate that two treatments do not differ by more than a prespecified clinically irrelevant amount we consider the problem when equivalence is defined in terms of the ratio of population means and the original untransformed data are normally distributed application of the intersection union principle to the test proposed by sasabuchi results in a two one sided tests procedure of size we give the associated 100 1 2 per cent confidence interval and derive the exact methods for calculation of power and sample sizes for the parallel group design and the two period cross over we present tables and figures of required sample sizes and achieved power copyright 1999 john wiley sons ltd

exact and asymptotically robust permutation tests given independent samples from p and q two sample permutation tests allow one to construct exact level tests when the null hypothesis is p q on the other hand when comparing or testing particular parameters of p and q such as their means or medians permutation tests need not be level or even approximately level in large samples under very weak assumptions for comparing estimators we provide a general test procedure whereby the asymptotic validity of the permutation test holds while retaining the exact rejection probability in finite samples when the underlying distributions are identical a quite general theory is possible based on a coupling construction as well as a key contiguity argument for the binomial and hypergeometric distributions the ideas are broadly applicable and special attention is given to a nonparametric k sample behrens fisher problem whereby a permutation test is constructed which is exact level under the hypothesis of identical distributions but has asymptotic rejection probability under the more general null hypothesis of equality of means a monte carlo simulation study is performed 2010 msc subject classifications primary 62e20 secondary 62g10

formulae and tables for the determination of sample sizes and power in clinical trials for testing differences in proportions for the two sample design a review this paper is a compendium of exact and asymptotic formulae and tables for estimating the sample size in a clinical trial with two treatment groups and a dichotomous outcome the paper provides separate formulae for equal and unequal treatment group sizes formulae for the calculation of power given the sample size and complete references for all formulae and tables cited

achievable error exponents in the gaussian channel with rate limited feedback we investigate the achievable error probability in communication over an awgn discrete time memoryless channel with noiseless delayless rate limited feedback for the case where the feedback rate rfb is lower than the data rate r transmitted over the forward channel we show that the decay of the probability of error is at most exponential in blocklength and obtain an upper bound for increase in the error exponent due to feedback furthermore we show that the use of feedback in this case results in an error exponent that is at least rfb higher than the error exponent in the absence of feedback for the case where the feedback rate exceeds the forward rate rfb r we propose a simple iterative scheme that achieves a probability of error that decays doubly exponentially with the codeword blocklength n more generally for some positive integer l we show that a l th order exponential error decay is achievable if rfb l 1 r while the above results are proved under an average feedback rate constraint we show that all the achievability results for rfb r hold in a more restrictive case where the feedback constraint is expressed in terms of the per channel use feedback rate our results show that the error exponent as a function of rfb has a strong discontinuity at r where it jumps from a finite value to infinity

multivariate and multiple permutation tests abstract in this article we consider the use of permutation tests for comparing multivariate parameters from two populations first the underlying properties of permutation tests when comparing parameter vectors from two distributions p and q are developed although an exact level test can be constructed by a permutation test when the fundamental assumption of identical underlying distributions holds permutation tests have often been misused indeed permutation tests have frequently been applied in cases where the underlying distributions need not be identical under the null hypothesis in such cases permutation tests fail to control the type 1 error even asymptotically however we provide valid procedures in the sense that even when the assumption of identical distributions fails one can establish the asymptotic validity of permutation tests in general while retaining the exactness property when all the observations are i i d in the multivariate testing problem for testing the global null hypothesis of equality of parameter vectors a modified hotelling s t 2 statistic as well as tests based on the maximum of studentized absolute differences are considered in the latter case a bootstrap prepivoting test statistic is constructed which leads to a bootstrapping after permuting algorithm then these tests are applied as a basis for testing multiple hypotheses simultaneously by invoking the closure method to control the familywise error rate lastly monte carlo simulation studies and an empirical example are presented

power and sample size computations in simultaneous tests for non inferiority based on relative margins in this paper we address the problem of calculating power and sample sizes associated with simultaneous tests for non inferiority we consider the case of comparing several experimental treatments with an active control the approach is based on the ratio view where the common non inferiority margin is chosen to be some percentage of the mean of the control treatment two power definitions in multiple hypothesis testing namely complete power and minimal power are used in the computations the sample sizes associated with the ratio based inference are also compared with that of a comparable inference based on the difference of means for various scenarios it is found that the sample size required for ratio based inferences is smaller than that of difference based inferences when the relative non inferiority margin is less than one and when large response values indicate better treatment effects the results are illustrated with examples

fourth order properties of normally distributed random matrices abstract three results are given involving a normally distributed matrix x namely 1 the expectation of x axcx bx 2 the covariance of vec x ax and vec x bx and 3 the expectation of x x x x

how do bootstrap and permutation tests work resampling methods are frequently used in practice to adjust critical values of nonparametric tests in the present paper a comprehensive and unified approach for the conditional and unconditional analysis of linear resampling statistics is presented under fairly mild assumptions we prove tightness and an asymptotic series representation for their weak accumulation points from this series it becomes clear which part of the resampling statistic is responsible for asymptotic normality the results leads to a discussion of the asymptotic correctness of resampling methods as well as their applications in testing hypotheses they are conditionally correct iff a central limit theorem holds for the original test statistic we prove unconditional correctness iff the central limit theorem holds or when symmetric random variables are resampled by a scheme of asymptotically random signs special cases are the m n out of k n bootstrap the weighted bootstrap the wild bootstrap and all kinds of permutation statistics the program is carried out for convergent partial sums of rowwise independent infinitesimal triangular arrays in detail these results are used to compare power functions of conditional resampling tests and their unconditional counterparts the proof uses the method of random scores for permutation type statistics

robust permutation tests for correlation and regression coefficients abstractgiven a sample from a bivariate distribution consider the problem of testing independence a permutation test based on the sample correlation is known to be an exact level test however when used to test the null hypothesis that the samples are uncorrelated the permutation test can have rejection probability that is far from the nominal level further the permutation test can have a large type 3 directional error rate whereby there can be a large probability that the permutation test rejects because the sample correlation is a large positive value when in fact the true correlation is negative it will be shown that studentizing the sample correlation leads to a permutation test which is exact under independence and asymptotically controls the probability of type 1 or type 3 errors these conclusions are based on our results describing the almost sure limiting behavior of the randomization distribution we will also present asymptotically robust randomization tests for regression coeffi

resampling based inference methods for comparing two coefficients alpha the two sample problem for cronbach s coefficient formula see text as an estimate of test or composite score reliability has attracted little attention compared to the extensive treatment of the one sample case it is necessary to compare the reliability of a test for different subgroups for different tests or the short and long forms of a test in this paper we study statistical procedures of comparing two coefficients formula see text and formula see text the null hypothesis of interest is formula see text which we test against one or two sided alternatives for this purpose resampling based permutation and bootstrap tests are proposed for two group multivariate non normal models under the general asymptotically distribution free adf setting these statistical tests ensure a better control of the type i error in finite or very small sample sizes when the state of affairs adf large sample test may fail to properly attain the nominal significance level by proper choice of a studentized test statistic the resampling tests are modified in order to be valid asymptotically even in non exchangeable data frameworks moreover extensions of this approach to other designs and reliability measures are discussed as well finally the usefulness of the proposed resampling based testing strategies is demonstrated in an extensive simulation study and illustrated by real data applications

on the dispersion matrix of a matrix quadratic form connected with the noncentral wishart distribution recently magnus and neudecker 3 derived the dispersion matrix of vec x x when x is a p n random matrix n p and vec x has the distribution nnp vec m in v this note is concerned with the matrix quadratic form x ax where x is a defined above and a is a nonrandom not necessarily symmetric matrix the dispersion matrix of vec x ax is then derived by applying results of magnus and neudecker 3 and neudecker and wansbeek 4 this generalizes an earlier result of giguere and styan 2 which assumes a symmetric a

a studentized permutation test for the comparison of spatial point patterns in this study a new test is proposed for the hypothesis that two or more observed point patterns are realizations of the same spatial point process model to this end the point patterns are divided into disjoint quadrats on each of which an estimate of ripley s k function is calculated the two groups of empirical k functions are compared by a permutation test using a studentized test statistic the proposed test performs convincingly in terms of empirical level and power in a simulation study even for point patterns where the k function estimates on neighboring subsamples are not strictly exchangeable it also shows improved behavior compared with a test suggested by diggle et al for the comparison of groups of independently replicated point patterns in an application to two point patterns from pathology that represent capillary positions in sections of healthy and cancerous tissue our studentized permutation test indicates statistical significance although the patterns cannot be clearly distin

the assessment of non inferiority in a gold standard design with censored exponentially distributed endpoints the objective of this paper is to develop statistical methodology for non inferiority hypotheses to censored exponentially distributed time to event endpoints motivated by a recent clinical trial in depression we consider a gold standard design where a test group is compared to an active reference and to a placebo group the test problem is formulated in terms of a retention of effect hypothesis thus the proposed wald type test procedure assures that the effect of the test group is better than a pre specified proportionof the treatment effect of the reference group compared to the placebo group a sample size allocation rule to achieve optimal power is presented which only depends on the pre specifiedand the probabilities for the occurrence of censoring in addition a pretest is presented for either the reference or the test group to ensure assay sensitivity in the complete test procedure the actual type i error and the sample size formula of the proposed tests is explored asymptotically and by means of a simulation study showing good small sample characteristics to illustrate the procedure a randomized double blind clinical trial in depression is evaluated an r package for implementation of the proposed tests and for sample size determination accompanies this paper on the author s web page

feedback capacity of finite state machine channels we consider a finite state machine channel with a finite memory length e g finite length intersymbol interference channels with finite input alphabets also known as partial response channels for such a finite state machine channel we show that feedback dependent markov sources achieve the feedback capacity and that the required memory length of the markov process matches the memory length of the channel further we show that the whole history of feedback is summarized by the causal posterior channel state distribution which is computed by the sum product forward recursion of the bahl cocke jelinek raviv bcjr baum welch discrete time wonham filtering algorithm these results drastically reduce the space over which the optimal feedback dependent source distribution needs to be sought further the feedback capacity computation may then be formulated as an average reward per stage stochastic control problem which is solved by dynamic programming with the knowledge of the capacity achieving source distribution the value of the capacity is easily estimated using markov chain monte carlo methods when the feedback is delayed we show that the feedback capacity can be computed by similar procedures we also show that the delayed feedback capacity is a tight upper bound on the feedforward capacity by comparing it to tight existing lower bounds we demonstrate the applicability of the method by computing the feedback capacity of partial response channels and the feedback capacity of run length limited rll sequences over binary symmetric channels bscs

some fundamental issues with non inferiority testing in active controlled trials in an active controlled non inferiority trial without a placebo arm it is often not entirely clear what the primary objective is in many cases the considered goal is to demonstrate that the experimental treatment preserves at least some fraction of the effect of the active control the active control effect is a parameter the value of which is unknown to test the hypothesis of effect preservation the classical confidence interval approach requires specification of a non inferiority margin which is a function of the unknown active control effect when the margin is estimated it is also not clear what is the relevant type i error of making a false assertion about preservation of the active control effect the statistical uncertainty of the estimated margin arguably needs to be incorporated in evaluation of the type i error in this paper we discuss these fundamental issues we show that the classical confidence interval approach cannot attain the target type i error exactly since this error varies as the sample size or as the values of the nuisance parameters in the active controlled trial change in contrast the preservation tests as proposed in literature can attain the target type i error rate exactly regardless of the sample size and the values of the nuisance parameters but can do so only at the price of several strong assumptions holding that may not be directly verifiable one assumption is the constancy condition holding whereby the effect of the active control in the historical trial populations is assumed to carry to the population of the active control trial when this condition is violated both the confidence interval approach and the preservation test method may be problematic

a bootstrap semiparametric homogeneity test for the distributions of multigroup proportional data with applications to analysis of quality of life outcomes in clinical trials this article is concerned about the test for the difference in the distributions of multigroup proportional data which is motivated by the problem of comparing the distributions of quality of life qol outcomes among different treatment groups in clinical trials the proportional data such as qol outcomes assessed by answers to questions on a questionnaire are bounded in a closed interval such as 0 1 with continuous observations in 0 1 and in addition excess observations taking the boundary values 0 and or 1 common statistical procedures used in practice such as t and rank based tests may not be very powerful since they ignore the specific feature of the proportional data in this article we propose a three component mixture model for the proportional data and a density ratio model for the distributions of continuous observations in 0 1 a semiparametric test statistic for the homogeneity of distributions of multigroup proportional data is derived based on the empirical likelihood ratio principle and shown to be asymptotically distributed as a chi squared random variable under null hypothesis a nonparametric bootstrap procedure is proposed to further improve the performance of the semiparametric test simulation studies are performed to evaluate the empirical type i error and power of the proposed test procedure and compare it with likelihood ratio tests lrts under parametric distribution assumptions rank based kruskal wallis test and wald type test the proposed test procedure is also applied to the analysis of qol outcomes from a clinical trial on colorectal cancer that motivated our study

nonparametric testing for multiple survival functions with non inferiority margins new nonparametric tests for the ordering of multiple survival functions are developed with the possibility of right censorship taken into account the motivation comes from non inferiority trials with multiple treatments the proposed tests are based on nonparametric likelihood ratio statistics which are known to provide more powerful tests than wald type procedures but in this setting have only been studied for pairs of survival functions or in the absence of censoring we introduce a novel type of pool adjacent violator algorithm that leads to a complete solution of the problem the limit distributions can be expressed as weighted sums of squares involving projections of certain gaussian processes onto the given ordered alternative a simulation study shows that the new procedures have superior power to a competing combined pairwise cox model approach we illustrate the proposed methods using data from a three arm non inferiority trial

comparing the performances of diggle s tests of spatial randomness for small samples with and without edge effect correction application to ecological data summary diggle s tests of spatial randomness based on empirical distributions of interpoint distances can be performed with and without edge effect correction we present here numerical results illustrating that tests without the edge effect correction proposed by diggle 1979 biometrics35 87 101 have a higher power for small sample sizes than those with correction ignoring the correction enables detection of departure from spatial randomness with smaller samples down to 10 points vs 30 points for the tests with correction these results are confirmed by an example with ecological data consisting of maps of two species of trees in a west african savanna tree numbers per species per map were often less than 20 for one of the species for which maps strongly suggest an aggregated pattern tests without edge effect correction enabled rejection of the null hypothesis on three plots out of five vs on only one for the tests with correction

comparative analysis of two rates in this paper we examine comparative analysis of rates with a view to each of the usual comparative parameters rate difference rd rate ratio rr and odds ratio or and with particular reference to first principles for rd and rr we show the prevailing statistical practices to be rather poor we stress the need for restricted estimation of variance in the chi square function underlying interval estimation and also point estimation and hypothesis testing for rr analysis we propose a chi square formulation analogous to that for rd and thus one which obviates the present practice of log transformation and its associated use of taylor series approximation of the variance as for or analysis we emphasize that the chi square function introduced by cornfield for unstratified data and extended by gart to the case of stratified analysis is based on the efficient score and thus embodies its optimality properties we provide simulation results to evince the better performance of the proposed parameter constrained procedures over the traditional ones

assessing non inferiority of a new treatment in a three arm clinical trial including a placebo in non inferiority trials where non inferiority of a new experimental drug compared to an active control has to be shown it may be advisable to use an additional placebo group for internal validation if ethically justifiable the focus of this paper is on such designs assuming normality and homogeneity of variances we will derive a statistical test procedure which turns out to be equivalent to the assessment based on fieller s confidence interval based on the power function of this test sample size calculations are carried out to achieve a given power additionally the optimal allocation of the total sample size is derived as an alternative to this parametric procedure the bootstrap percentile interval is discussed and finally compared with fieller s confidence interval in a study on mildly asthmatic patients

capacity region of the finite state multiple access channel with and without feedback the capacity region of the finite state multiple access channel fs mac with feedback that may be an arbitrary time invariant function of the channel output samples is considered we characterize both an inner and an outer bound for this region using massey s directed information these bounds are shown to coincide and hence yield the capacity region of indecomposable fs macs without feedback and of stationary and indecomposable fs macs with feedback where the state process is not affected by the inputs though multiletter in general our results yield explicit conclusions when applied to specific scenarios of interest for example our results allow us to do the following 1 identify a large class of fs macs that includes the additive mod2 noise mac where the noise may have memory for which feedback does not enlarge the capacity region 2 deduce that for a general fs mac with states that are not affected by the input if the capacity region without feedback is zero then so is the capacity region with feedback 3 deduce that the capacity region of a mac that can be decomposed into a multiplexer concatenated by a point to point channel with without or with partial feedback the capacity region is given by sigmam rm les c where c is the capacity of the point to point channel and m indexes the encoders moreover we show that for this family of channels source channel coding separation holds

finite state channels with time invariant deterministic feedback we consider capacity of discrete time channels with feedback for the general case where the feedback is a time invariant deterministic function of the output samples under the assumption that the channel states take values in a finite alphabet we find a sequence of achievable rates and a sequence of upper bounds on the capacity the achievable rates and the upper bounds are computable for any n and the limits of the sequences exist we show that when the probability of the initial state is positive for all the channel states then the capacity is the limit of the achievable rate sequence we further show that when the channel is stationary indecomposable and has no intersymbol interference isi its capacity is given by the limit of the maximum of the normalized directed information between the input xn and the output yn i e c limnrarrinfin 1 n max i xnrarryn where the maximization is taken over the causal conditioning probability q xnparzn 1 defined in this paper the main idea for obtaining the results is to add causality into gallager s results on finite state channels the capacity results are used to show that the source channel separation theorem holds for time invariant determinist feedback and if the state of the channel is known both at the encoder and the decoder then feedback does not increase capacity

box type approximations in nonparametric factorial designs abstract linear rank statistics in nonparametric factorial designs are asymptotically normal and in general heteroscedastic in a comprehensive simulation study the asymptotic chi squared law of the corresponding quadratic forms is shown to be a rather poor approximation of the finite sample distribution motivated by this problem we propose simple finite sample size approximations for the distribution of quadratic forms in factorial designs under a normal heteroscedastic error structure these approximations are based on an f distribution with estimated degrees of freedom that generalizes ideas of patnaik and box simulation studies show that the nominal level is maintained with high accuracy and in most cases the power is comparable to the asymptotic maximin wald test data driven guidelines are given to select the most appropriate test procedure these ideas are finally transferred to nonparametric factorial designs where the same quadratic forms as in the parametric case are applied to the vector

planning and analysis of three arm non inferiority trials with binary endpoints three arm trials including an experimental treatment an active control and a placebo group are frequently preferred for the assessment of non inferiority in contrast to two arm non inferiority studies these designs allow a direct proof of efficacy of a new treatment by comparison with placebo as a further advantage the test problem for establishing non inferiority can be formulated in such a way that rejection of the null hypothesis assures that a pre defined portion of the unknown effect the reference shows versus placebo is preserved by the treatment under investigation we present statistical methods for this study design and the situation of a binary outcome variable asymptotic test procedures are given and their actual type i error rates are calculated approximate sample size formulae are derived and their accuracy is discussed furthermore the question of optimal allocation of the total sample size is considered power properties of the testing strategy including a pre test for assay sensitivity are presented the derived methods are illustrated by application to a clinical trial in depression

comparison of tests and sample size formulae for proving therapeutic equivalence based on the difference of binomial probabilities to prove the hypothesis that a new treatment is as effective as a standard one a possibility is to test the one sided null hypothesis of a clear inferiority of the new treatment against the alternative hypothesis that if at all it is only negligibly inferior such a problem is of clinical relevance if for instance a new treatment with an effectiveness which is comparable to that of the standard one would be preferred if it is less toxic if the difference between the two treatments is measured by the difference of failure rates approximate statistical tests and sample size formulae have to be used this paper reports the results of an extensive empirical investigation comparing the well known calculations proposed by blackwelder rodary comnougue and tournade which propose a sample size formula for the test of dunnett and gent and farrington and manning the investigation was conducted in order to allow more comprehensive conclusions than those which may be drawn from the limited examples given by the last authors for the usual settings in clinical trials the formulae of farrington and manning are recommended however there are combinations of statistical parameters for which they are not preferred

test statistics and sample size formulae for comparative binomial trials with null hypothesis of non zero risk difference or non unity relative risk when it is required to establish a materially significant difference between two treatments or alternatively to show that two treatments are equivalent standard test statistics and sample size formulae based on a null hypothesis of no difference no longer apply this paper reviews some of the test statistics and sample size formulae proposed for comparative binomial trials when the null hypothesis is of a specified non zero difference or non unity relative risk methods based on restricted maximum likelihood estimation are recommended and applied to studies of pertussis vaccine

analysis of small sample size studies using nonparametric bootstrap test with pooled resampling method experimental studies in biomedical research frequently pose analytical problems related to small sample size in such studies there are conflicting findings regarding the choice of parametric and nonparametric analysis especially with non normal data in such instances some methodologists questioned the validity of parametric tests and suggested nonparametric tests in contrast other methodologists found nonparametric tests to be too conservative and less powerful and thus preferred using parametric tests some researchers have recommended using a bootstrap test however this method also has small sample size limitation we used a pooled method in nonparametric bootstrap test that may overcome the problem related with small samples in hypothesis testing the present study compared nonparametric bootstrap test with pooled resampling method corresponding to parametric nonparametric and permutation tests through extensive simulations under various conditions and using real data examples the nonparametric pooled bootstrap t test provided equal or greater power for comparing two means as compared with unpaired t test welch t test wilcoxon rank sum test and permutation test while maintaining type i error probability for any conditions except for cauchy and extreme variable lognormal distributions in such cases we suggest using an exact wilcoxon rank sum test nonparametric bootstrap paired t test also provided better performance than other alternatives nonparametric bootstrap test provided benefit over exact kruskal wallis test we suggest using nonparametric bootstrap test with pooled resampling method for comparing paired or unpaired means and for validating the one way analysis of variance test results for non normal data in small sample size studies copyright 2017 john wiley sons ltd

a randomization based perspective on analysis of variance a test statistic robust to treatment effect heterogeneity summary fisher randomization tests for neyman s null hypothesis of no average treatment effect are considered in a finite population setting associated with completely randomized experiments involving more than two treatments the consequences of using the f statistic to conduct such a test are examined and we argue that under treatment effect heterogeneity use of the f statistic in the fisher randomization test can severely inflate the type i error under neyman s null hypothesis we propose to use an alternative test statistic derive its asymptotic distributions under fisher s and neyman s null hypotheses and demonstrate its advantages through simulations

on second order and fourth order moments of jointly distributed random matrices a survey abstract the study is concerned with second order and fourth order moments of jointly distributed random matrices when distributional properties are required normality is adopted some of the results can also be applied to elliptical or wishart distributions the developments are entirely algebraic full use is made of the kronecker product repeated vectorization commutation matrices and related items there are a few references in the main text but many additional references to other work in which the same or kindred results obtained by other methods procedures or concepts can be found have been included in the references

randomization tests for weak null hypotheses in randomized experiments the fisher randomization test frt is appropriate for any test statistic under a sharp null hypothesis that can recover all missing potential outcomes however it is often sought after to test a

qualms about bootstrap confidence intervals abstract the percentile method and bias corrected percentile method of efron 1981 1982 are discussed when these methods are used to construct nonparametric confidence intervals for the variance of a normal distribution the coverage probabilities are substantially below the nominal level for small to moderate samples this is due to the inapplicability of assumptions underlying the methods these assumptions are difficult or impossible to check in the complicated situations for which the bootstrap is intended therefore bootstrap confidence intervals should be used with caution in complex problems

linear hypothesis testing with functional data in real data analysis it is often interesting to consider a general linear hypothesis testing glht problem for functional data which includes the one way anova post hoc or contrast analysis a

minimization of sample size when comparing two small probabilities in a non inferiority safety trial in clinical trials success rates of two treatments to be compared often range from 10 to 90 per cent when the comparison probabilities are much smaller than 10 per cent standard methods for sample size and power calculations may provide invalid results this situation may occur when there is interest in safety rather than in efficacy in such trials no more patients should be included than strictly necessary we compared the results of maximum likelihood methods for the computation of sample sizes in a non inferiority trial including exact procedures and considered unequal sample sizes for experimental and reference treatment an exact unequal sample size maximum likelihood procedure is advocated when the specified non zero risk difference under the null hypothesis is not too large such a procedure is also indicated when the parameter of interest is the relative risk rather than the risk difference

penalized fieller s confidence interval for the ratio of bivariate normal means constructing a confidence interval for the ratio of bivariate normal means is a classical problem in statistics several methods have been proposed in the literature the fieller method is known as an exact method but can produce an unbounded confidence interval if the denominator of the ratio is not significantly deviated from 0 while the delta and some numeric methods are all bounded they are only first order correct motivated by a real world problem we propose the penalized fieller method which employs the same principle as the fieller method but adopts a penalized likelihood approach to estimate the denominator the proposed method has a simple closed form and can always produce a bounded confidence interval by selecting a suitable penalty parameter moreover the new method is shown to be second order correct under the bivariate normality assumption that is its coverage probability will converge to the nominal level faster than other bounded methods simulation results show that our proposed method generally outperforms the existing methods in terms of controlling the coverage probability and the confidence width and is particularly useful when the denominator does not have adequate power to reject being 0 finally we apply the proposed approach to the interval estimation of the median response dose in pharmacology studies to show its practical usefulness

two guidelines for bootstrap hypothesis testing two guidelines for nonparametric bootstrap hypothesis testing are highlighted the first recommends that resampling be done in a way that reflects the null hypothesis even when the true hypothesis is distant from the null the second guideline argues that bootstrap hypothesis tests should employ methods that are already recognized as having good features in the closely related problem of confidence interval construction violation of the first guideline can seriously reduce the power of a test sometimes this reduction is spectacular since it is most serious when the null hypothesis is grossly in error the second guideline is of some importance when the conclusion of a test is equivocal it has no direct bearing on power but improves the level accuracy of a test