testing hypotheses in order in certain circumstances one wishes to test one hypothesis only if certain other hypotheses have been rejected this ordering of hypotheses simplifies the task of controlling the probability of rejecting any true hypothesis in an example from an observational study a treated group is shown to be further from both of two control groups than the two control groups are from each other

two stage tests for studying monotherapy and combination therapy in two by two factorial trials two stage testing involves a preliminary test of a nuisance parameter prior to testing main hypothesis in a two by two factorial trial the treatment interaction is the nuisance to the inference about the efficacy of one of the treatments given alone in comparing a combination therapy to both of its component therapies the nuisance parameter is the difference in the component effects when the preliminary test is an integral part of inference about the main parameter the actual level of significance for the two stage test procedure can be much higher than the desired nominal level if one places no restriction on the value of the nuisance parameter then any two stage test with its significance level properly controlled has undesirable properties this applies to comparative studies of combination agents relative to the component agents when the interaction with an ineffective treatment is null two stage testing may have some power advantage for assessing monotherapy efficacy

a sharper bonferroni procedure for multiple tests of significance summary a simple procedure for multiple tests of significance based on individual p values is derived this simple procedure is sharper than holm s 1979 sequentially rejective procedure both procedures contrast the ordered p values with the same set of critical values holm s procedure rejects an hypothesis only if its p value and each of the smaller p values are less than their corresponding critical values the new procedure rejects all hypotheses with smaller or equal p values to that of any one found less than its critical value

large sample tests for binary outcomes in fixed dose combination drug studies several test statistics are developed for testing the hypothesis that the combination of two drugs at a fixed dose regimen is more effective than both of the single drugs used alone with respect to a dichotomous response variable the response probability logit and arcsine root scales are considered the power function and the significance level are derived for large samples for the sample size per group of 20 or greater the power and type i error rate can be accurately calculated using the large sample power function when the response probability ranges from 0 2 to 0 8 these tests have similar power behaviors in small samples the large sample power functions of two of the tests can severely underestimate the type i error rate while overestimation can occur with one other test the utilities of these tests are extended to unbalanced sample size cases generally speaking there is a loss of power with unequal sample size allocation but the loss is not severe

on the discriminant of a hyperelliptic curve the minimal discriminant of a hyperelliptic curve is defined and used to generalize much of the arithmetic theory of elliptic curves over number fields this leads to a higher genus version of szpiro s conjecture analytically the discriminant is shown to be related to siegel modular forms of higher degree

evaluation of a combination drug with multiple doses in unbalanced factorial design clinical trials flexibilities for sample size allocation are often demanded for achieving multiple study objectives in combination drug trials the global tests of hung chi and lipicky are extended for analysis of unbalanced factorial design trials to test the hypothesis that at least one of the non zero dose combinations of two drugs is more effective than the respective component doses when the dose combinations have heterogeneous effect sizes an unbalanced design may induce greater power than the balanced design an adjusted p value approach is proposed for testing the individual dose combinations under the condition that the maximum type i error probability is protected

second variation of zhang s λ invariant on the moduli space of curves we compute the second variation of the invariant recently introduced by s zhang on the complex moduli space mg of curves of genus g 2 using work of n kawazumi as a result we prove that 8g 4 is equal up to a constant to the invariant introduced some time ago by r hain and d reed we deduce some consequences for example we calculate the invariant for each hyperelliptic curve expressing it in terms of the petersson norm of the discriminant modular form 1 introduction recently independently s zhang 27 and n kawazumi 16 introduced a new interesting real valued function on the moduli space mg of complex curves of genus g 2 its value at a curve x m g is given as follows let h 0 x x be the space of holomorphic differentials on x equipped with the

testing for the existence of a desirable dose combination we consider the problem of studying several dose combinations of two drugs for a therapeutic endpoint in a multilevel factorial clinical trial two test statistics are constructed to test whether there exists at least one dose combination that is more effective than its component doses their distributions involve nuisance parameters quantifying the mean differences among the doses of the two component drugs it is shown that their power functions achieve maxima as all the nuisance parameters approach infinity in absolute value the significance levels of the two tests are derived and two alpha level tests are proposed tables are given to provide the alpha level critical values for these tests and to gain insights into their power performances

jacobian nullwerte and algebraic equations abstract we present two applications of jacobian nullwerte both related with the resolution of algebraic equations of any degree we give a very simple expression of the roots of a polynomial of arbitrary degree in terms of derivatives of hyperelliptic theta functions this expression can be understood as an explicit proof of torelli s theorem in the hyperelliptic case we also give geometrical expressions of the discriminant of a polynomial both applications are based on a jacobian version of thomae s formula

closure procedures for monotone bi factorial dose response designs les essais en doses multiples ont deux buts i demontrer une amelioration de l efficacite pour une combinaison donnee de chacun des composants ii identifier un intervalle de doses efficaces et sures les auteurs s interessent aux deux aspects quoique avec un interet plus marque pour le second avec une procedure de cloture qui garantit un controle fort du risque global d erreur on etudie deux familles differentes d hypotheses nulles pour des dispositifs bi factoriels monotones par rapport a un ordre partiel l une est adaptee a la recherche d une ou plusieurs doses efficaces minimums l autre est suffisamment large pour permettre d identifier les doses efficaces les plus elevees on applique des tests du rapport de vraisemblance et des contrastes multiples appropries a un exemple d essai clinique tire de hung 2000 statistics in medicine 19 2079 2087 le code ecrit en langage r est disponible dans sa totalite sur internet

challenge of multiple co primary endpoints a new approach there are many disorders where regulatory agencies have required a new treatment to demonstrate efficacy on multiple co primary endpoints all significant at the one sided 2 5 per cent level before accepting the treatment s effect for the disorder this requirement rooted in the intersection union iu test has led many researchers to increase the study sample size to make up for the reduction in the statistical power at the study level unfortunately the increase in sample size could be substantial when the endpoints are minimally correlated and the treatment effects on the multiple endpoints are comparable in this paper we demonstrate that the frequentist concept of controlling the maximum false positive rate even when applied to a restricted null space has only limited success in keeping the sample size increase at a reasonable level we therefore propose an approach that is based on the notion of controlling an average type i error rate by employing an upper bound for the average type i error rate the new approach provides an adjustment to the significance level that depends only on the correlation among the endpoints for the most common case of two or three co primary endpoints the adjusted significance level is at most 5 per cent one sided when the endpoints are moderately correlated we show how sample size could be calculated under the proposed approach and contrast the needed sample size with that required under the iu test we provide additional comments and discuss why the new approach is consistent with the principle requiring evidence of significance in the drug development and approval process

simultaneous confidence intervals on multivariate non inferiority we discuss the analysis of non inferiority trials based on a multi armed design with multiple correlated endpoints we consider five different scenarios 1 global non inferiority 2 non inferiority for subsets of comparisons 3 global non inferiority for a treatment group 4 global non inferiority for an endpoint and 5 local non inferiority we describe and compare related approaches which are based on the union intersection and intersection union test principles alone and in combination because non inferiority thresholds for many differently scaled endpoints are rarely available in practice the approaches described focus on the estimation of simultaneous confidence limits and their post hoc interpretation on non inferiority we discuss and demonstrate pros and cons by means of a real data example

comparison of several testing strategies for combination drug efficacy trials based on the closure principle the author discusses three multiple testing procedures for identifying the minimum efficacious doses in a balanced factorial combination drug trial all of these procedures utilize the closed testing principle and hence strongly control the overall error rate and satisfy the coherence property that is if a hypothesis is retained then any hypothesis implied by it is also retained while coherence is an essential requirement for any multiple testing procedure consonance is a highly desirable characteristic in the considered settings if a testing procedure is consonant then it always provides a set of all minimum efficacious combinations as a result otherwise it may lead to ambiguity although the coherence property is satisfied for any closed testing procedure and thus does not depend on the test used for an individual hypothesis whether the considered procedures satisfy the consonance property depends entirely on the nature of the test statistic the author identifies the consonant and non consonant procedures among the presented procedures and discusses possible drawbacks of non consonant procedures with respect to combination drug efficacy trials additional properties of these procedures are assessed by simulations

the asymptotics of the arakelov geen s function and faltings delta invariant we study the behavior of the arakelov green s function and faltings delta invariant on degenerating riemann surfaces

sample size determination for testing whether an identified treatment is best laska and meisner 1989 biometrics 45 1139 1151 dealt with the problem of testing whether an identified treatment belonging to a set of k 1 treatments is better than each of the other k treatments they calculated sample size tables for k 2 when using multiple t tests or wilcoxon mann whitney tests both under normality assumptions in this paper we provide sample size formulas as well as tables for sample size determination for k or 2 when t tests under normality or wilcoxon mann whitney tests under general distribution assumptions are used

new explicit formulas for faltings delta invariant in this paper we give new explicit formulas for faltings delta invariant in terms of integrals of theta functions and we deduce an explicit lower bound for delta only in terms of the genus and an explicit upper bound for the arakelov green function in terms of delta furthermore we give a canonical extension of delta and the zhang kawazumi invariant varphi to the moduli space of indecomposable principally polarised complex abelian varieties

calculus on arithmetic surfaces in a2 and a3 arakelov introduces an intersection calculus for arithmetic surfaces that is for stable models of curves over a number field in this paper we intend to show that his intersection product has a lot of useful properties more precisely we show that the following properties from the theory of algebraic surfaces have an analogue in our situation

multiple testing for a combination drug with two study endpoints a combination drug product with two or more active compounds may be superior to each of its components with higher dose levels and therefore is preferred in terms of efficacy cost and safety to study a combination drug researchers often conduct trials by using a factorial design with combinations of dose levels of each drug component by applying some bootstrap methods we construct multiple testing procedures to simultaneously identify combinations superior to each drug component with any dose level these multiple testing procedures are more powerful than holm s step down procedure that is known to be very conservative when there is only one study endpoint applying the bootstrap is straightforward in many studies however there are two or more study endpoints and it is not simple to apply the bootstrap we apply one version of the bootstrap and then use an upper bound to control the familywise error defined as the probability of rejecting at least one true null hypothesis properties of the bootstrap multiple testing procedures are discussed and examined in some simulation studies

optimal designs for dose response models with restricted design spaces in dose response studies the dose range is often restricted due to concerns over drug toxicity and or efficacy we present restricted and unrestricted interval locally optimal designs with respect to a very general class of optimality criteria for estimating the underlying dose response curve the underlying curve belongs to a diversified set of link functions suitable for the dose response studies and having a common canonical form these include the fundamental binary response models the logit and the probit as well as the skewed versions of these models the results are illustrated through the re design of a dose ranging trial conducted at the merck research laboratories zeng and zhu 1997 this work is a generalization of the results of dai and zhu 2002 in terms of the design interval the underlying dose response curve and the optimality criterion

traditional multiplicity adjustment methods in clinical trials this tutorial discusses important statistical problems arising in clinical trials with multiple clinical objectives based on different clinical variables evaluation of several doses or regiments of a new treatment analysis of multiple patient subgroups etc simultaneous assessment of several objectives in a single trial gives rise to multiplicity if unaddressed problems of multiplicity can undermine integrity of statistical inferences the tutorial reviews key concepts in multiple hypothesis testing and introduces main classes of methods for addressing multiplicity in a clinical trial setting general guidelines for the development of relevant and efficient multiple testing procedures are presented on the basis of application specific clinical and statistical information case studies with common multiplicity problems are used to motivate and illustrate the statistical methods presented in the tutorial and software implementation of the multiplicity adjustment methods is discussed copyright 2013 john wiley sons ltd

measuring uncertainty under prior information there are various situations where prior information is available on parameters in the form of order relations one needs to take into account this information to obtain superior estimators shannon modeled uncertainty mathematically and called it entropy in this paper we study the problem of estimating entropy of two exponential populations associated with a common scale parameter and unknown but ordered location parameters in particular the unrestricted best affine equivariant estimator is shown to be inadmissible under order restricted location parameters with respect to a class of location invariant loss functions under some specific location invariant loss functions various improved estimators are obtained applications of this problem are developed for various sampling schemes i i i d sampling ii record values iii type ii censoring and iv progressive type ii censoring numerically we have compared the risk performance of the proposed estimators for the squared error and linex loss functions

on estimating the scale parameter of the selected gamma population under the scale invariant squared error loss function let x1 and x2 be two independent random variables representing the populations 1 and 2 respectively and suppose that the random variable xi has a gamma distribution with shape parameter p same for both the populations and unknown scale parameter i i 1 2 define m 1 if x1 x2 m 2 if x2 x1 and j 3 m we consider the component wise estimation of random parameters m and j under the scale invariant squared error loss functions l1 1 1 m 1 2 and l2 2 2 j 1 2 respectively sufficient conditions for the inadmissibility of equivariant estimators of m and j are derived as a consequence various natural estimators are shown to be inadmissible and better estimators are obtained

step up multiple testing of parameters with unequally correlated estimates we consider the problem of simultaneously testing k or to 2 hypotheses on parameters theta 1 theta k using test statistics t 1 t k such that a specified familywise error rate alpha is achieved dunnett and tamhane 1992a proposed a step up multiple test procedure in which testing starts with the hypothesis corresponding to the least significant test statistic and proceeds towards the most significant stopping the first time a significant test result is obtained and rejecting the hypotheses corresponding to that and any remaining test statistics the parameter estimates used in the t statistics were assumed to be normally distributed with a common variance which was a known multiple of an unknown sigma 2 and known correlations which were equal in the present article we show how the procedure can be extended to include unequally correlated parameter estimates unequal correlations occur for example in experiments involving comparisons among treatment groups with unequal sample sizes we also compare the step up and step down multiple testing approaches and discuss applications to some biopharmaceutical testing problems

bounds on faltings s delta function through covers let x be a compact riemann surface of genus gx 1 in 1984 g faltings introduced a new invariant fal x associated to x in this paper we give explicit bounds for fal x in terms of fundamental dierential geometric invariants arising from x when gx 1 as an application we are able to give bounds for faltings s delta function for the family of modular curves x0 n in terms of the genus only in combination with work of a abbes p michel and e ullmo this leads to an asymptotic formula for the faltings height of the jacobian j0 n associated to x0 n

improved time censored reliability test plans for k out of n gamma systems abstract relevant prior knowledge supported by historical data and expert judgments is common in many manufacturing processes the classical viewpoint to the determination of acceptance sampling plans for k out of n gamma systems is generalized to those situations in which the available previous information is appreciable a beta distribution with a reduced parameter space is adopted to describe the stochastic behavior of the fraction of defective systems an integer nonlinear programming problem is stated to find the inspection scheme that minimizes the required number of components to test and keeps the average producer and consumer risks below specified thresholds first lower and upper bounds as well as an approximate solution are derived then an efficient step by step procedure which finds the best acceptance sampling plan in a finite number of iterations is provided the inclusion of prior information into the decision process provides substantial savings in the sample size required for demonstrating system reliability and also more accurate assessments of the actual producer and consumer risks a system of five water pumps for cooling a reactor is analyzed for illustrative and comparative purposes

a superiority equivalence approach to one sided tests on multiple endpoints in clinical trials this paper considers the problem of comparing a new treatment with a control based on multiple endpoints the hypotheses are formulated with the goal of showing that the treatment is equivalent i e not inferior on all endpoints and superior on at least one endpoint compared to the control where thresholds for equivalence and superiority are specified for each endpoint roy s 1953 union intersection and berger s 1982 intersection union principles are employed to derive the basic test it is shown that the critical constants required for the union intersection test of superiority can be sharpened by a careful analysis of its type i error rate the composite test is illustrated by an example and compared in a simulation study to alternative tests proposed by bloch et al 2001 and perlman wu 2004 the bloch et al test does not control the type i error rate because of its nonmonotone nature and is hence not recommended the and the perlman wu tests both control the type i error rate but the latter test generally has a slightly higher power

testing whether an identified treatment is best summary we consider the problem of testing whether an identified treatment is better than each of k treatments suppose there are univariate test statistics si that contrast the identified treatment with treatment i for i 1 2 k the min test is defined to be the a level procedure that rejects the null hypothesis that the identified treatment is not best when for all i si rejects the one sided hypothesis at the a level that the identified treatment is not better than the ith treatment in the normal case where si are t statistics the min test is the likelihood ratio test for distributions satisfying mild regularity conditions if attention is restricted to test statistics that are monotone nondecreasing functions of si then regardless of their covariance structure the min test is an optimal a level test tables of the sample size needed to achieve power 5 8 90 and 95 are given for the min test when the si are student s t and wilcoxon

inadmissibility results for the selected scale parameters let x 1 x 2 ldots x k be k independent gamma random variables with different scale parameters but with a common known shape parameter suppose the population corresponding to the largest x 1 or the smallest x k observation is selected the problem of estimating the scale parameter theta 1 or theta k of the selected population is considered we derive using the method of differential inequalities explicit estimators that dominate the natural or the existing estimators the improved estimators of theta 1 are similar to that of dasgupta estimators for the usual simultaneous estimation problem an implication of this result for the simultaneous estimation of the selected subset is also considered