on the sample size for studies based upon mcnemar s test when computing the sample size for studies using mcnemar s test one needs to know the probability of discordance and the odds ratio to be detected in many studies the investigator is unable to specify the probability of discordance but can state at least approximately the marginal probabilities of each variable this information leads to restrictions on the possible values of the cell probabilities and provides a range of admissible values for the off diagonal cells we compute the sample size needed in these circumstances and compare them to the results cited by schlesselman and connett et al these sample sizes for the method are quite close to those found in the monte carlo study of connett et al

testing non inferiority and equivalence between two diagnostic procedures in paired sample ordinal data before adopting a new diagnostic procedure which is more convenient and less expensive than the standard existing procedure it is essentially important to assess whether the diagnostic accuracy of the new procedure is non inferior or equivalent to that of the standard procedure in this paper we consider the situation where test responses are on an ordinal scale with more than two categories we give two definitions of non inferiority one in terms of the probability of correctly identifying the case for a randomly selected pair of a case and a non case over all possible cut off points and the other in terms of both the sensitivity and specificity directly on the basis of large sample theory we develop two simple test procedures for detecting non inferiority we further conduct monte carlo simulation to evaluate the finite sample performance of these test procedures we note that the two asymptotic test procedures proposed here can actually perform reasonably well in a variety of situations even when the numbers of studied subjects from the diseased and non diseased populations are not large to illustrate the use of the proposed test procedures we include an example of determining whether the diagnostic accuracy of using a digitized film is non inferior to that of using a plain film for screening breast cancer finally we note that the extension of these results to accommodate the case of detecting two sided equivalence is simply straightforward

equivalence test and confidence interval for the difference in proportions for the paired sample design summary this paper considers a model for the di erence of two proportions in a paired or matched design of clinical trials case control studies and also sensitivity comparison studies of two laboratory tests this model includes a parameter indicating both interpatient variability of response probabilities and their correlation under the proposed model we derive a one sided test for equivalence based upon the e cient score equivalence is defined here as not more than 100 per cent inferior mcnemar s test for significance is shown to be a special case of the proposed test further a score based confidence interval for the di erence of two proportions is derived one of the features of these methods is applicability to the 2 2 table with o diagonal zero cells all the mcnemar type tests and confidence intervals published so far cannot apply to such data a monte carlo simulation study shows that the proposed test has empirical significance levels closer to the nominal a level than the other tests recently proposed and further that the proposed confidence interval has better empirical coverage probability than those of the four published methods 1998 john wiley sons ltd

sample size and power for pair matched case control studies a new sample size formula is derived herein for matched pair case control studies this result is based on an unconditional approach to the use of mcnemar s statistic we contrast this method for determining sample size and power with schlesselman s conditional approach and compare the results numerically in a monte carlo study

reduced fusion systems over 2 groups of small order we prove when s is a 2 group of order at most 29 that each reduced fusion system over s is the fusion system of a finite simple group and is tame it then follows that each saturated fusion system over a 2 group of order at most 29 is realizable what is most interesting about this result is the method of proof we show that among 2 groups with order in this range the ones which can be sylow 2 subgroups of finite simple groups are almost completely determined by criteria based on bender s classification of groups with strongly 2 embedded subgroups

reduced fusion systems over p groups with abelian subgroup of index p ii abstract for an odd prime p we look at simple fusion systems over a finite nonabelian p group s which has an abelian subgroup a of index p when s has more than one such subgroup we reduce this to a case already studied by ruiz and viruel when a is the unique abelian subgroup of index p in s and is not essential equivalently is not radical in the fusion system we give a complete list of all possibilities which can occur this includes several families of exotic fusion systems including some which have proper strongly closed subgroups

equivalences between fusion systems of finite groups of lie type when g is a finite group and p is a prime the fusion system fp g is the category whose objects are the p subgroups of g and whose morphisms are the homomorphisms between subgroups induced by conjugation in g if g is another finite group then fp g and fp g are isotypically equivalent if there is an equivalence of categories between them which commutes up to natural isomorphism of functors with the forgetful functors from fp to the category of groups alternatively fp g and fp g are isotypically equivalent if there is an isomorphism between sylow p subgroups of g and of g which is fusion preserving in the sense of definition 1 2 below the goal of this paper is to use methods from homotopy theory to prove that certain pairs of fusion systems of finite groups of lie type are isotypically equivalent our main result is the following theorem

coordination complexity of parallel price directive decomposition the general block angular convex resource sharing problem in k blocks and m nonnegative block separable coupling constraints is considered applications of this model are in combinatorial optimization network flows scheduling communication networks engineering design and finance this paper studies the coordination complexity of approximate price directive decomposition pdd for this problem i e the number of iterations required to solve the problem to a fixed relative accuracy as a function of k and m first a simple pdd method based on the classical logarithmic potential is shown to be optimal up to a logarithmic factor in m in the class of all pdd methods that work with the original unrestricted blocks it is then shown that logarithmic and exponential potentials generate a polylogarithmically optimal algorithm for a wider class of pdd methods which can restrict the blocks by the coupling constraints as an application the fastest currently known deterministic approximation algorithm for minimum cost multicommodity flows is obtained

non inferiority tests for clustered matched pair data non inferiority tests for matched pair data where pairs are mutually independent may not be appropriate when pairs are clustered the tests may require an adjustment to account for the correlation within a cluster we consider the adjusted score and wald type tests and a modification of obuchowski s method for non inferiority and compare them with the non inferiority test based on a method of moments estimate in terms of type 1 error rate and power by simulations for a small cluster size under various correlation structures in general the score test adjusted by an inflation factor and the modified obuchowski s method perform as good as the test based on moments estimate in the accuracy of type 1 error rates the latter does not provide reasonably close type 1 error rates to the nominal level when the number of clusters is 25 or smaller and a positive response rate for the standard procedure is 20 per cent or lower the adjusted score test the method based on moments estimate and the modified test are comparable in power the adjusted wald type test is too anti conservative and we should caution use of the test since number of clusters is strongly related to the accuracy of empirical type 1 error rate and power it is very important to have a sufficiently large number of clusters in designing a clustered matched pair study for non inferiority

the classification of p compact groups for p odd a p compact group as defined by dwyer and wilkerson is a purely homotopically defined p local analog of a compact lie group it has long been the hope and later the conjecture that these objects should have a classification similar to the classification of compact lie groups in this paper we finish the proof of this conjecture for p an odd prime proving that there is a one to one correspondence between connected p compact groups and finite reflection groups over the p adic integers we do this by providing the last and rather intricate piece namely that the exceptional compact lie groups are uniquely determined as p compact groups by their weyl groups seen as finite reflection groups over the p adic integers our approach in fact gives a largely self contained proof of the entire classification theorem for p odd

a more powerful exact test of noninferiority from binary matched pairs data assessing the therapeutic noninferiority of one medical treatment compared with another is often based on the difference in response rates from a matched binary pairs design this paper develops a new exact unconditional test for noninferiority that is more powerful than available alternatives there are two new elements presented in this paper first we introduce the likelihood ratio statistic as an alternative to the previously proposed score statistic of nam biometrics 1997 53 1422 1430 second we eliminate the nuisance parameter by estimation followed by maximization as an alternative to the partial maximization of berger and boos am stat assoc 1994 89 1012 1016 or traditional full maximization based on an extensive numerical study we recommend tests based on the score statistic the nuisance parameter being controlled by estimation followed by maximization

on tests of equivalence via non unity relative risk for matched pair design matched pair design is often used in clinical trials to increase the efficiency of treatment comparison we consider the problem of equivalence test with a relative risk endpoint in matched pair studies with binary outcomes and develop several score and wald type statistics for testing a hypothesis of non unity relative risk examples from an assessment of hiv screening test and a cross over clinical trial of soft contact lenses are used to illustrate the proposed methods through simulations we compare the empirical performance of these tests with the test proposed by lachenbruch and lynch we show that a score test based on a reparameterized multinomial model by tango performs best in the sense that the test satisfactorily controls the type i error rate and its empirical type i error rates are generally much closer to the prespecified nominal significance level than those of the other tests

improved confidence intervals for the difference between binomial proportions based on paired data existing methods for setting confidence intervals for the difference theta between binomial proportions based on paired data perform inadequately the asymptotic method can produce limits outside the range of validity the exact conditional method can yield an interval which is effectively only one sided both these methods also have poor coverage properties better methods are described based on the profile likelihood obtained by conditionally maximizing the proportion of discordant pairs a refinement methods 5 and 6 which aligns 1 alpha with an aggregate of tail areas produces appropriate coverage properties a computationally simpler method based on the score interval for the single proportion also performs well method 10

sample size for testing differences in proportions for the paired sample design miettinen 1968 biometrics 24 339 352 presented an approximation for power and sample size for testing the differences between proportions in the matched pair case duffy 1984 biometrics 40 1005 1015 gave the exact power for this case and showed that miettinen s approximation tends to slightly overestimate the power or underestimate the sample size necessary for the design power a simple alternative approximation that is more conservative is presented here in many cases the sample size for the independent sample case provides a conservative approximation for the matched pair design

power and sample size evaluation for the mcnemar test with application to matched case control studies various expressions have appeared for sample size calculation based on the power function of mcnemar s test for paired or matched proportions especially with reference to a matched case control study these differ principally with respect to the expression for the variance of the statistic under the alternative hypothesis in addition to the conditional power function i identify and compare four distinct unconditional expressions i show that the unconditional calculation of schlesselman for the matched case control study can be expressed as a first order unconditional calculation as described by miettinen corrections to schlesselman s unconditional expression presented by fleiss and levin and by dupont which use different models to describe exposure association among matched cases and controls are also equivalent to a first order unconditional calculation i present a simplification of these corrections that directly provides the underlying table of cell probabilities from which one can perform any of the alternative sample size calculations also i compare the four unconditional sample size expressions relative to the exact power function the conclusion is that miettinen s first order expression tends to underestimate sample size while his second order expression is usually fairly accurate though possibly slightly anti conservative a multinomial based expression presented by connor among others is also fairly accurate and is usually slightly conservative finally a local unconditional expression of mitra among others tends to be excessively conservative

faster approximation algorithms for the unit capacity concurrent flow problem with applications to routing and finding sparse cuts this paper describes new algorithms for approximately solving the concurrent multicommodity flow problem with uniform capacities these algorithms are much faster than algorithms discovered previously besides being an important problem in its own right the uniform capacity concurrent flow problem has many interesting applications leighton and rao used uniform capacity concurrent flow to find an approximately sparsest cut in a graph and thereby approximately solve a wide variety of graph problems including minimum feedback arc set minimum cut linear arrangement and minimum area layout however their method appeared to be impractical as it required solving a large linear program this paper shows that their method might be practical by giving an o m 2 log m expected time randomized algorithm for their concurrent flow problem on an m edge graph raghavan and thompson used uniform capacity concurrent flow to solve approximately a channel width minimization problem in very large scale integration an o k 3 2 m n log n expected time randomized algorithm and an o k min n k m n log n log k deterministic algorithm is given for this problem when the channel width is omega log n where k denotes the number of wires to be routed in an n node m edge network

fast approximation schemes for convex programs with many blocks and coupling constraints this paper presents block coordinate descent algorithms for the approximate solution of large structured convex programming problems the constraints of such problems consist of k disjoint convex compact sets b k called blocks and m nonnegative valued convex block separable inequalities called coupling or resource constraints the algorithms are based on an exponential potential function reduction technique it is shown that feasibility as well as min mix resource sharing problems for such constraints can be solved to a relative accuracy varepsilon in o k ln m varepsilon 2 ln k iterations each of which solves k block problems to a comparable accuracy either sequentially or in parallel the same bound holds for the expected number of iterations of a randomized variant of the algorithm which uniformly selects a random block to process at each iteration an extension to objective and constraint functions of arbitrary sign is also presented the above results yield fast approximatio

analysis of clustered matched pair data for a non inferiority study design hypothesis testing of matched pair data has been adapted for equivalence one and two sided study designs however a statistical problem arises when more than one measurement is recorded for each study subject ignoring the correlation between the repeated measurements per subject may underestimate the standard error of the parameter estimate a method of testing for non inferiority or equivalence of clustered matched pair data is not yet available this paper proposes a wald type test statistic for a non inferiority hypothesis and applies it to the comparison of two diagnostic procedures

the maximum concurrent flow problem the maximum concurrent flow problem mcfp is a multicommodity flow problem in which every pair of entities can send and receive flow concurrently the ratio of the flow supplied between a pair of entities to the predefined demand for that pair is called throughput and must be the same for all pairs of entities for a concurrent flow the mcfp objective is to maximize the throughput subject to the capacity constraints we develop a fully polynomial time approximation scheme for the mcfp for the case of arbitrary demands and uniform capacity computational results are presented it is shown that the problem of associating costs distances to the edges so as to maximize the minimum cost of routing the concurrent flow is the dual of the mcfp a path cut type duality theorem to expose the combinatorial structure of the mcfp is also derived our duality theorems are proved constructively for arbitrary demands and uniform capacity using the algorithm applications include packet switched networks 1 4 8 and cluster analysis 16

fast approximation algorithms for fractional packing and covering problems this paper presents fast algorithms that find approximate solutions for a general class of problems which we call fractional packing and covering problems the only previously known algorithms for solving these problems are based on general linear programming techniques the techniques developed in this paper greatly outperform the general methods in many applications and are extensions of a method previously applied to find approximate solutions to multicommodity flow problems our algorithm is a lagrangian relaxation technique an important aspect of our results is that we obtain a theoretical analysis of the running time of a lagrangian relaxation based algorithm we give several applications of our algorithms the new approach yields several orders of magnitude of improvement over the best previously known running times for algorithms for the scheduling of unrelated parallel machines in both the preemptive and the nonpreemptive models for the job shop problem for the held and karp bound for the tr

sample size for individually matched case control studies the standard formulas used to calculate sample size for an individually matched case control study assume a constant probability of exposure throughout the pool of possible controls we propose new formulas that allow for heterogeneity in the probability of exposure among controls in different matched sets since matching factors are suspected of being confounders they are expected to divide the total population into subgroups with different proportions exposed thus the assumption of homogeneity of exposure among controls made by the currently used formulas is inconsistent with the assumptions used to design a matched study the proposed formulas avoid this inconsistency we present an example to illustrate how heterogeneity can affect the required sample size

unconditional exact tests for equivalence or noninferiority for paired binary endpoints problems of establishing equivalence or noninferiority between two medical diagnostic procedures involve comparisons of the response rates between correlated proportions when the sample size is small the asymptotic tests may not be reliable this article proposes an unconditional exact test procedure to assess equivalence or noninferiority two statistics a sample based test statistic and a restricted maximum likelihood estimation rmle based test statistic to define the rejection region of the exact test are considered we show the p value of the proposed unconditional exact tests can be attained at the boundary point of the null hypothesis assessment of equivalence is often based on a comparison of the confidence limits with the equivalence limits we also derive the unconditional exact confidence intervals on the difference of the two proportion means for the two test statistics a typical data set of comparing two diagnostic procedures is analyzed using the proposed unconditional exact and asymptotic methods the p value from the unconditional exact tests is generally larger than the p value from the asymptotic tests in other words an exact confidence interval is generally wider than the confidence interval obtained from an asymptotic test

establishing equivalence of two treatments and sample size requirements in matched pairs design statistical methods for testing the null hypothesis of a nonzero difference between two treatments and the sample size determination for matched pairs studies are investigated a wald type test proposed by lu and bean 1995 statistics in medicine 14 1831 1839 is anticonservative i e its false positive error rate is greater than specified score method and normal deviate based on a restricted maximum likelihood estimation are presented these two test statistics are shown to be algebraically equal their actual type i error probabilities are satisfactorily close to a nominal level numerical examinations demonstrate that the sample size formulas using these alternative methods are reasonable while that by lu and bean is not the efficiency of matching in equivalence studies is positively related to intercorrelation or the kappa coefficient of agreements we recommend the score or ml methods to establish equivalence of two treatments for individually matched samples

fusion systems and amalgams we study reduced fusion systems from the point of view of their essential subgroups using the classification by goldschmidt and fan of amalgams of prime index to analyze certain pairs of such subgroups our results are applied here to study reduced fusion systems over 2 groups of order at most 64 and also reduced fusion systems over 2 groups having abelian subgroups of index two more applications are given in later papers

more powerful exact noninferiority and equivalence tests based on binary matched pairs assessing the therapeutic noninferiority or equivalence of one medical treatment compared to another is often based on the difference of response rates from a matched binary pairs design this paper develops new exact unconditional tests for noninferiority and equivalence that are more powerful than available alternatives there are three new elements presented in this paper first we introduce the lr statistic as an alternative to the previously proposed score statistic of nam 1997 second we eliminate the nuisance parameter by estimation followed by maximization as an alternative to the partial maximization of berger and boos 1994 or traditional full maximization third for testing equivalence it is standard to combine two one sided tests tost we point out that even if the one sided tests are exact and efficient the tost will be conservative and requires a further adjustment to remove this conservatism based on an extensive numerical study we recommend tests based on the score statistic the nuisance parameter being controlled by estimation followed by maximization

improving an interior point approach for large block angular problems by hybrid preconditioners abstract the computational time required by interior point methods is often dominated by the solution of linear systems of equations an efficient specialized interior point algorithm for primal block angular problems has been used to solve these systems by combining cholesky factorizations for the block constraints and a conjugate gradient based on a power series preconditioner for the linking constraints in some problems this power series preconditioner resulted to be inefficient on the last interior point iterations when the systems became ill conditioned in this work this approach is combined with a splitting preconditioner based on lu factorization which works well for the last interior point iterations computational results are provided for three classes of problems multicommodity flows oriented and nonoriented minimum distance controlled tabular adjustment for statistical data protection and the minimum congestion problem the results show that in most cases the hybrid preconditioner improves the performance and robustness of the interior point solver in particular for some block angular problems the solution time is reduced by a factor of 10

extensions of p local finite groups a p local finite group consists of a finite p group s together with a pair of categories which encode conjugacy relations among subgroups of s and which are modelled on the fusion in a sylow p subgroup of a finite group it contains enough information to define a classifying space which has many of the same properties as p completed classifying spaces of finite groups in this paper we study and classify extensions of p local finite groups and also compute the fundamental group of the classifying space of a p local finite group

analysis of the ratio of marginal probabilities in a matched pair setting statistical methods for testing and interval estimation of the ratio of marginal probabilities in the matched pair setting are considered in this paper we are especially interested in the situation where the null value is not one as in one sided equivalence trials we propose a fieller type statistic based on constrained maximum likelihood cml estimation of nuisance parameters for a series of examples the significance level of the cml test is satisfactorily close to the nominal level while a wald type test is anticonservative for reasonable sample sizes we present formulae for approximate power and sample size for the cml and wald tests the matched design is seen to have a clear advantage over the unmatched design in terms of asymptotic efficiency when the two responses of the pair are highly positively correlated we recommend the cml method over the wald method especially for small or moderate sample sizes

the maximal subgroups of the chevalley groups g2 q with q odd the ree groups 2g2 q and their automorphism groups

homotopy fixed point methods for lie groups and finite loop spaces a loop space x is by definition a triple x bx e in which x is a space bx is a connected pointed space and e x qbx is a homotopy equivalence from x to the space qbx of based loops in bx we will say that a loop space x is finite if the integral homology h x z is finitely generated as a graded abelian group i e if x appears at least homologically to be a finite complex in this paper we prove the following theorem

sample size determination for establishing equivalence noninferiority via ratio of two proportions in matched pair design summary in this article we propose approximate sample size formulas for establishing equivalence or noninferiority of two treatments in match pairs design using the ratio of two proportions as the equivalence measure we derive sample size formulas based on a score statistic for two types of analyses hypothesis testing and confidence interval estimation depending on the purpose of a study these formulas can be used to provide a sample size estimate that guarantees a prespecified power of a hypothesis test at a certain significance level or controls the width of a confidence interval with a certain confidence level our empirical results confirm that these score methods are reliable in terms of true size coverage probability and skewness a liver scan detection study is used to illustrate the proposed methods

non inferiority test and confidence interval for the difference in correlated proportions in diagnostic procedures based on multiple raters the efficacy of diagnostic procedures is generally evaluated on the basis of the results from multiple raters however there are few adequate methods of performing non inferiority tests with confidence intervals to compare the accuracies sensitivities or specificities when multiple raters are considered we propose new statistical methods for comparing the accuracies of two diagnostic procedures in a non inferiority trial on the basis of the results from multiple independent raters who are also independent of the study centers we consider a study design in which each patient is subjected to two diagnostic procedures and all images are read by all raters by assuming a multinomial distribution for matched pair categorical data arising from the study design we derive a score based full menu that is a non inferiority test confidence interval and sample size formula for inference of the difference in correlated proportions between the two diagnostic procedures we conduct monte carlo simulation studies to examine the validity of the proposed methods which showed that the proposed test has a size closer to the nominal significance level than a wald type test and that the proposed confidence interval has better empirical coverage probability than a wald type confidence interval we illustrate the proposed methods with data from a study of diagnostic procedures for the diagnosis of oesophageal carcinoma infiltrating the tracheobronchial tree copyright 2011 john wiley sons ltd

quadratic regularizations in an interior point method for primal block angular problems one of the most efficient interior point methods for some classes of primal block angular problems solves the normal equations by a combination of cholesky factorizations and preconditioned conjugate gradient for respectively the block and linking constraints its efficiency depends on the spectral radius in 0 1 of a certain matrix in the definition of the preconditioner spectral radius close to 1 degrade the performance of the approach the purpose of this work is twofold first to show that a separable quadratic regularization term in the objective reduces the spectral radius significantly improving the overall performance in some classes of instances second to consider a regularization term which decreases with the barrier function thus with no need for an extra parameter computational experience with some primal block angular problems confirms the efficiency of the regularized approach in particular for some difficult problems the solution time is reduced by a factor of two to ten by the regularization term outperforming state of the art commercial solvers

reducing cost in sequential testing a limit of indifference approach in noninferiority studies a limit of indifference is used to express a tolerance in results such that the clinician would regard such results as being acceptable or not worse we applied this concept to a measure of accuracy the receiver operating characteristic roc curve for a sequence of tests we expressed a limit of indifference for the range of acceptable sensitivity values and examined the associated cost of testing within this range in doing so we generated the minimum cost maximum roc mcmroc curve which reflects the reduced sensitivity and cost of testing we compared the mcmroc and its associated cost curve between limits of indifference set to 0 999 a 0 1 reduction in true positive rate tpr 0 95 a 5 reduction in tpr and 1 no reduction in tpr the limit of indifference tended to have less of an effect on the mcmroc curves than on the associated cost curves that were greatly affected cost was reduced at high false positive rates fprs at higher limit of indifference 0 999 and at small fprs as the limit of indifference decreased 0 95 these patterns were also observed as applied to sequential strategies used to diagnose diabetes in the pima indians copyright 2013 john wiley sons ltd

asymptotic analysis of the flow deviation method for the maximum concurrent flow problem we analyze the asymptotic behavior of the flow deviation method first presented in 1971 by fratta gerla and kleinrock and show that when applied to packing linear programs such as the maximum concurrent flow problem it yields a fully polynomial time approximation scheme

the 2 x 2 matched pairs trial exact unconditional design and analysis an exact unconditional method for the design and analysis of the 2 x 2 matched pairs trial is presented unlike the exact conditional method which is based on only the number of discordant pairs the exact unconditional method uses the total number n of sampled pairs this unconditional test based on a simple z statistic yields sample sizes that are generally smaller than those produced by the exact conditional test for the cases tabulated herein namely one sided alpha 01 025 and 05 along with 80 and 90 power moreover it is found to be uniformly more powerful than the latter for all the combinations of parameters considered in this paper namely alpha 01 025 and 05 and n 10 1 200 the method is illustrated by assessing various design options of an in vitro study of the effectiveness of antimicrobial agents some numerical examples of matching efficiency are also given

on the sample size for one sided equivalence of sensitivities based upon mcnemar s test in this paper we formalize the problem of testing the one sided equivalence in the sensitivities of two medical diagnostic tests under a matched pair study design we derive conditional and unconditional sample size formulae which are decreasing functions of the probability of being diagnosed by both tests we calculate upper boundary and midpoint sample sizes results of a monte carlo simulation study that compares the proposed sample size formulae with that of lachenbruch suggest that our midpoint conditional sample size is the best choice to obtain the desired power for the type of equivalence studies discussed in the paper