on the use of concordant pairs in matched case control studies a new estimator of the common odds ratio in one to one matched case control studies is proposed the connection between this estimator and the james stein estimating procedure is highlighted through the argument of estimating functions comparisons are made between this estimator the conditional maximum likelihood estimator and the estimator ignoring the matching in terms of finite sample bias mean squared error coverage probability and length of confidence interval in many situations the new estimator is found to be more efficient than the conditional maximum likelihood estimator without being as biased as the estimator that ignores matching the extension to multiple risk factors is also outlined

confidence interval construction for proportion difference in small sample paired studies paired dichotomous data may arise in clinical trials such as pre post test comparison studies and equivalence trials reporting parameter estimates e g odds ratio rate difference and rate ratio along with their associated confidence interval estimates becomes a necessity in many medical journals various asymptotic confidence interval estimators have long been developed for differences in correlated binary proportions nevertheless the performance of these asymptotic methods may have poor coverage properties in small samples in this article we investigate several alternative confidence interval estimators for the difference between binomial proportions based on small sample paired data specifically we consider exact and approximate unconditional confidence intervals for rate difference via inverting a score test the exact unconditional confidence interval guarantees the coverage probability and it is recommended if strict control of coverage probability is required however the exact method tends to be overly conservative and computationally demanding our empirical results show that the approximate unconditional score confidence interval estimators based on inverting the score test demonstrate reasonably good coverage properties even in small sample designs and yet they are relatively easy to implement computationally we illustrate the methods using real examples from a pain management study and a cancer study

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

weak convergence for random weighting estimation of smoothed quantile processes this paper presents a new random weighting method for smoothed quantile processes a theory is established for random weighting estimation of smoothed quantile processes it proves the weak convergence of the random weighting estimation error experiments and comparison analysis demonstrate that the proposed random weighting method can effectively estimate statistics and the achieved accuracy and convergence speed are much higher than those of the bootstrap method

exact properties of some exact test statistics for comparing two binomial proportions abstract using exact unconditional distributions we evaluated the size and power of four exact test procedures and three versions of the 2 statistic for the two sample binomial problem in small to moderate sample sizes the exact unconditional test suissa and shuster 1985 and fisher s 1935 exact test are the only tests whose size can be guaranteed never to exceed the nominal size though the former is distinctly more powerful it is also computationally difficult we propose an alternative that approximates the exact unconditional test by computing the exact distribution of the 2 statistic at a single point the maximum likelihood estimate of the common success probability this test is a modification of the test of liddell 1978 which considered the exact distribution of the difference in the sample proportions our test is generally more powerful than either the exact unconditional or liddell s test and its true size rarely exceeds the nominal size the uncorrected 2 statistic is frequently a

a practical two step method for testing moment inequalities this paper considers the problem of testing a finite number of moment inequalities we propose a two step approach in the first step a confidence region for the moments is constructed in the second step this set is used to provide information about which moments are negative a bonferonni type correction is used to account for the fact that with some probability the moments may not lie in the confidence region it is shown that the test controls size uniformly over a large class of distributions for the observed data an important feature of the proposal is that it remains computationally feasible even when the number of moments is large the finite sample properties of the procedure are examined via a simulation study which demonstrates among other things that the proposal remains competitive with existing procedures while being computationally more attractive

a comparative study of tests for homogeneity of variances with applications to the outer continental shelf bidding data many of the existing parametric and nonparametric tests for homogeneity of variances and some variations of these tests are examined in this paper comparisons are made under the null hypothesis for robustness and under the alternative for power monte carlo simulations of various symmetric and asymmetric distributions for various sample sizes reveal a few tests that are robust and have good power these tests are further compared using data from outer continental shelf bidding on oil and gas leases

efficient experimental design for binary matched pairs data the analysis of data from matched pairs binary experiments often performed with mcnemar s test presents a unique experimental design challenge in dealing with the effect of the discordance probability p most approaches for determining size and power use point estimates or maximization but this fails to account for the considerable variability across values of the nuisance parameter that occur for all common tests we recommend viewing the size and power functions across the full range of possible discordance probability values which gives a complete picture of the behavior of a test for any given sample size this method also allows us to compare the behavior of different hypothesis tests we present exact power and size functions for several tests including the original mcnemar s test and its most common variants and compare their properties this analysis reveals that in general mcnemar s test comes closest to the nominal size and has the highest power we also demonstrate our technique using the transmission disequilibrium test tdt to check for linkage between schizophrenia and a locus related to the d 3 dopamine receptor and on a hypnosis pain management data set

frequentist performance of bayesian confidence intervals for comparing proportions in 2 2 contingency tables this article investigates the performance in a frequentist sense of bayesian confidence intervals cis for the difference of proportions relative risk and odds ratio in 2 x 2 contingency tables we consider beta priors logit normal priors and related correlated priors for the two binomial parameters the goal was to analyze whether certain settings for prior parameters tend to provide good coverage performance regardless of the true association parameter values for the relative risk and odds ratio we recommend tail intervals over highest posterior density hpd intervals for invariance reasons to protect against potentially very poor coverage probabilities when the effect is large it is best to use a diffuse prior and we recommend the jeffreys prior otherwise with relatively small samples bayesian cis using more informative even uniform priors tend to have poorer performance than the frequentist cis based on inverting score tests which perform uniformly quite well for these parameters

interval estimation of the risk ratio between a secondary infection given a primary infection and the primary infection this paper discusses interval estimation of the risk ratio rr between a secondary infection given a primary infection and the primary infection three asymptotic closed form interval estimators are developed using wald s test statistic the logarithmic transformation and fieller s theorem the performance of these interval estimators is compared with respect to the coverage probability and the expected length of the resulting confidence intervals when the underlying probability of a primary infection is high say 0 80 all three estimators perform reasonably well in fact in this case they are all essentially equivalent when the number of subjects n or 100 when the probability of a primary infection is small say 0 20 or moderate say 0 30 to 0 50 the interval estimator using the logarithmic transformation outperforms the other two estimators when n or 100 in fact the coverage probability of the former estimator is consistently greater than or equal to the desired confidence level in all the situations considered in this paper and hence is recommended for general use

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

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

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

binomial confidence intervals abstract for x with binomial n p distribution section 1 gives a one page table of 95 and 99 confidence intervals for p for n 1 2 30 this interval is equivariant under x n x and p 1 p has approximately equal probability tails is approximately unbiased has crow s property of minimizing the sum of the n 1 possible lengths and each of its ends is increasing in x and decreasing in n with about as regular steps as possible sections 2 and 3 consider the usual approximate confidence intervals calculations and asymptotic results show the need for the continuity correction in these even when n is large because of the nonuniformity of the binomial normal convergence as p 0 these intervals fail to have their stated asymptotic confidence coefficients simple corrections are given for this in the approximate interval x n c n x n 1 x n 1 2n it is shown that the factor c n should be replaced by c n c 2 2c n 1 n

confidence intervals for a ratio of binomial proportions based on paired data four interval estimation methods for the ratio of marginal binomial proportions are compared in terms of expected interval width and exact coverage probability two new methods are proposed that are based on combining two wilson score intervals the new methods are easy to compute and perform as well or better than the method recently proposed by nam and blackwelder two sample size formulas are proposed to approximate the sample size required to achieve an interval estimate with desired confidence level and width

p values maximized over a confidence set for the nuisance parameter abstract for testing problems of the form h 0 v v 0 with unknown nuisance parameter various methods are used to deal with the simplest approach is exemplified by the t test where the unknown variance is replaced by the sample variance and the t distribution accounts for estimation of the variance in other problems such as the 2 2 contingency table one conditions on a sufficient statistic for 0 and proceeds as in fisher s exact test because neither of these standard methods is appropriate for all situations this article suggests a new method for handling the unknown this new method is a simple modification of the formal definition of a p value that involves taking a maximum over the nuisance parameter space of a p value obtained for the case when is known the suggested modification is to restrict the maximization to a confidence set for the nuisance parameter after giving a brief justification we give various examples to show how this new method gives improved results for 2 2 tabl

test based exact confidence intervals for the difference of two binomial proportions summary confidence intervals are often provided to estimate a treatment difference when the sample size is small as is typical in early phases of clinical trials confidence intervals based on large sample approximations may not be reliable in this report we propose test based methods of constructing exact confidence intervals for the difference in two binomial proportions these exact confidence intervals are obtained from the unconditional distribution of two binomial responses and they guarantee the level of coverage we compare the performance of these confidence intervals to ones based on the observed difference alone we show that a large improvement can be achieved by using the standardized z test with a constrained maximum likelihood estimate of the variance

buehler confidence bounds for a reliability maintainability measure this article presents an upper confidence bound for a measure of reliability maintainability of a series system in which component repair is assumed to restore the system to its original status under exponentiality of component repair time and survival time distributions the measure m is the ratio of expected system repair time to expected system survival time moreover under this exponentiality assumption the bound is uniformly minimum among all bounds of specified level that are nondecreasing functions of the maximum likelihood estimator of m as a matter of practical interest the measure m has been incorporated into military standard mil std 470b and is an official statistic of the air force reliability maintainability information system

a polynomial time complexity bound for the computation of the singular part of a puiseux expansion of an algebraic function in this paper we present a refined version of the newton polygon process to compute the puiseux expansions of an algebraic function defined over the rational function field we determine an upper bound for the bit complexity of computing the singular part of a puiseux expansion by this algorithm and use a recent quantitative version of eisenstein s theorem on power series expansions of algebraic functions to show that this computational complexity is polynomial in the degrees and the logarithm of the height of the polynomial defining the algebraic function

strong approximation of density estimators from weakly dependent observations by density estimators from independent observations we derive an approximation of a density estimator based on weakly dependent random vectors by a density estimator built from independent random vectors we construct on a sufficiently rich probability space such a pairing of the random variables of both experiments that the set of observations x 1 x n from the time series model is nearly the same as the set of observations y 1 y n from the i i d model with a high probability all sets of the form x 1 x n delta y 1 y n boolean and a 1 b 1 x x a d b d contain no more than o n 1 2 pi b i a i 1 log n elements respectively although this does not imply very much for parametric problems it has important implications in nonparametric statistics it yields a strong approximation of a kernel estimator of the stationary density by a kernel density estimator in the i i d model moreover it is shown that such a strong approximation is also valid for the standard bootstrap and the smoothed bootstrap using these results we derive simultaneous confidence bands as well as supremum type nonparametric tests based on reasoning for the i i d model

confidence intervals for the binomial parameter some new considerations several methods have been proposed to construct confidence intervals for the binomial parameter some recent papers introduced the mean coverage criterion to evaluate the performance of confidence intervals and suggested that exact methods because of their conservatism are less useful than asymptotic ones in these studies however exact intervals were always represented by the clopper pearson interval c p now we focus on sterne s interval which is also exact and known to be better than the c p in the two sided case introducing a computer intensive level adjustment procedure which allows constructing intervals that are exact in terms of mean coverage we demonstrate that sterne s interval performs better than the best asymptotic intervals even in the mean coverage context level adjustment improves the c p as well which with an appropriate level adjustment becomes equivalent to the mid p interval finally we show that the asymptotic behaviour of the mid p method is far poorer than is generally expected

bootstrapping the distance between smooth bootstrap and sample quantile distribution the normalized kolmogorov smirnov and variational distance between the distribution of the sampleq quantile and the pertaining smooth bootstrap distribution are asymptotically distributed like the absolute value of a normal random variable the distribution functions of these random distances may serve as measures of the accuracy of the bootstrap procedure

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

accounting for within patient correlation in assessing relative sensitivity of an adjunctive diagnostic test application to lung cancer we address the comparison of results between two diagnostic tests applied multiple times to the same subjects the estimand of interest is the sensitivity of the combined test primary and adjunct relative to a primary test analytical methods are first described that assume independence between the multiple observations within a subject in order to account for the within subject correlation introduced by the multiple measurements analytical approaches for correlated categorical response data are described in the discussion of these methods we pay particular attention to the presence of a structural zero which results from the decision rule for the combination of diagnostic tests in a simulation study we compare the finite sample performances of all analytical approaches in terms of confidence interval coverage rates and median lengths our methods are cast in the context of a diagnostic bronchoscopy technology for the detection of lung cancer

unconditional versions of several tests commonly used in the analysis of contingency tables summary by focusing on a confidence interval for a nuisance parameter berger and boos 1994 journal of the american statistical association89 1012 1016 proposed new unconditional tests in particular they showed that for a 2 2 table this procedure generally was more powerful than fisher s exact test this paper utilizes and extends their approach to obtain unconditional tests for combining several 2 2 tables and testing for trend and homogeneity in a 2 k table the unconditional procedures are compared to the conditional ones by reanalyzing some published biomedical data

factoring polynomials with rational coefficients in this paper we present a polynomial time algorithm to solve the following problem given a non zero polynomial fe q x in one variable with rational coefficients find the decomposition of f into irreducible factors in q x it is well known that this is equivalent to factoring primitive polynomials fez x into irreducible factors in z x here we call f z x primitive if the greatest common divisor of its coefficients the content of f is 1 our algorithm performs well in practice cf 8 its running time measured in bit operations is o nl2 n9 log fd3

a cautionary note on exact unconditional inference for a difference between two independent binomial proportions utilise pour la comparaison de proportions dans le cadre d essais randomises le test exact de ficher peut se reveler particulierement conservateur principalement lorsque les echantillons sont de petite taille ou lorsque les proportions observees sont proches de 0 ou de 1 cette propriete indesirable s explique surtout par une distribution de la statistique de test sous hypothese nulle trop discretisee notamment en raison d une inference effectuee conditionnellement au nombre total des repondeurs de ce fait les procedures exactes non conditionnelles ont conquis une popularite fondee sur l idee d une augmentation de la puissance entrainee par des distributions de statistiques de tests sous hypothese nulle necessairement moins discretisees toutefois nous mettons en garde les chercheurs contre le choix hasardeux d un test exact non conditionnel car dans certains cas leur utilisation peut s averer franchement moins puissante que le test de fisher a l appui de nos propos nous traitons d un exemple reel puis nous calculons les risques de type i et les puissances associees a differents tests lors de comparaisons portant sur des groupes de tailles egales ou inegales nos resultats montrent que le test exact de fisher fait generalement mieux que les tests exacts non conditionnels bases sur la difference des proportions mieux aussi dans le cas d echantillons de taille inegales que les tests exacts non conditionnels bases sur la difference des proportions divisee par son ecart type estime sous hypothese alternative a l inverse le test exact non conditionnel base sur la difference des proportions divisee par son ecart type estime sous hypothese nulle il s agit de la statistique du score fait mieux que le test de fisher ce test est recommande tout comme le test de boschloo test dans lequel le test de fisher est utilise comme une statistique de test dans un test exact non conditionnel ce dernier test s avere quant a lui uniformement plus puissant que le test de fisher

improved confidence intervals for the difference between binomial proportions based on paired data by robert g newcombe statistics in medicine 17 2635 2650 1998

welch s approximate solution for the behrens fisher problem the wald likelihood ratio and score statistics have been calculated for the behrens fisher problem these statistics provide asymptotically equivalent and weakly optimal tests the test based on the wald statistic was found to be very similar to the v test discussed by welch 1937 hence the v test was compared with the likelihood ratio and score tests in a power study since the powers were very similar and the v test was more convenient to use from several points of view we recommend this test sizes of the v test as well as a power comparison with the usual pooled t test were also obtained

generalized p values in significance testing of hypotheses in the presence of nuisance parameters abstract this article examines some problems of significance testing for one sided hypotheses of the form h 0 0 versus h 1 0 where is the parameter of interest in the usual setting let x be the observed data and let t x be a test statistic such that the family of distributions of t x is stochastically increasing in define cx as x t x t x 0 the p value is p x sup 0 pr x cx in the presence of a nuisance parameter there may not exist a nontrivial cx with a p value independent of we consider tests based on generalized extreme regions of the form cx x t x x t x x and conditions on t x x are given such that the p value p x sup 0 pr x cx is free of the nuisance parameter where t is stochastically increasing in we provide a solution to the problem of testing hypotheses about the differences in means of two independent exponential distributions a problem for which the fixed level testing approach

confidence interval for rate ratio in a 2 2 table with structural zero an application in assessing false negative rate ratio when combining two diagnostic tests summary in this article we consider problems with correlated data that can be summarized in a 2 2 table with structural zero in one of the off diagonal cells data of this kind sometimes appear in infectious disease studies and two step procedure studies lui 1998 biometrics54 706 711 considered confidence interval estimation of rate ratio based on fieller type wald type and logarithmic transformation statistics we reexamine the same problem under the context of confidence interval construction on false negative rate ratio in diagnostic performance when combining two diagnostic tests we propose a score statistic for testing the null hypothesis of nonunity false negative rate ratio score test based confidence interval construction for false negative rate ratio will also be discussed simulation studies are conducted to compare the performance of the new derived score test statistic and existing statistics for small to moderate sample sizes in terms of confidence interval construction our asymptotic score test based confidence interval estimator possesses significantly shorter expected width with coverage probability being close to the anticipated confidence level in terms of hypothesis testing our asymptotic score test procedure has actual type i error rate close to the pre assigned nominal level we illustrate our methodologies with real examples from a clinical laboratory study and a cancer study

unconditional efficient one sided confidence limits for the odds ratio based on conditional likelihood we compare various one sided confidence limits for the odds ratio in a 2 x 2 table the first group of limits relies on first order asymptotic approximations and includes limits based on the signed likelihood ratio score and wald statistics the second group of limits is based on the conditional tilted hypergeometric distribution with and without mid p correction all these limits have poor unconditional coverage properties and so we apply the general transformation of buehler j am statist assoc 1957 52 482 493 to obtain limits which are unconditionally exact the performance of these competing exact limits is assessed across a range of sample sizes and parameter values by looking at their mean size the results indicate that buehler limits generated from the conditional likelihood have the best performance with a slight preference for the mid p version this confidence limit has not been proposed before and is recommended for general use especially when the underlying probabilities are not extreme

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

on small sample confidence intervals for parameters in discrete distributions summary the traditional definition of a confidence interval requires the coverage probability at any value of the parameter to be at least the nominal confidence level in constructing such intervals for parameters in discrete distributions less conservative behavior results from inverting a single two sided test than inverting two separate one sided tests of half the nominal level each we illustrate for a variety of discrete problems including interval estimation of a binomial parameter the difference and the ratio of two binomial parameters for independent samples and the odds ratio

accurate confidence limits for stratified clinical trials for stratified 2 2 tables standard approximate confidence limits can perform poorly from a strict frequentist perspective even for moderate sized samples yet they are routinely used in this paper i show how to use importance sampling to compute highly accurate limits in reasonable time the methodology is very general and simple to implement and orders of magnitude are faster than existing alternatives copyright 2013 john wiley sons ltd

exact one sided confidence limits for the difference between two correlated proportions we construct exact and optimal one sided upper and lower confidence bounds for the difference between two probabilities based on matched binary pairs using well established optimality theory of buehler starting with five different approximate lower and upper limits we adjust them to have coverage probability exactly equal to the desired nominal level and then compare the resulting exact limits by their mean size exact limits based on the signed root likelihood ratio statistic are preferred and recommended for practical use

the importance of the designated statistic on buehler upper limits on a system failure probability the upper limits introduced by buehler are constructed to be honest confidence limits that are as small as possible subject to the constraint that they are nondecreasing functions of a designated statistics this methodology has largely been developed for applications in reliability that involve finding an upper limit on the probability of failure p1 pk of a system of k components with probabilities of failure pi for mainly computational reasons it is common to choose the designated statistic s p1 pk where pi is an estimator of pi buehler on the other hand suggested the choice s pu1 puk where pui is a so called exact 1 1 k upper limit for pi in this article we draw attention to existing general theory suggesting that s should be chosen to be an approximate upper limit for the interest parameter not an estimator we also give numerical results suggesting that extreme loss in efficiency typically follows if s is chosen poorly our current recommendation is that s should be an a

interval estimation for the difference between independent proportions comparison of eleven methods several existing unconditional methods for setting confidence intervals for the difference between binomial proportions are evaluated computationally simpler methods are prone to a variety of aberrations and poor coverage properties the closely interrelated methods of mee and miettinen and nurminen perform well but require a computer program two new approaches which also avoid aberrations are developed and evaluated a tail area profile likelihood based method produces the best coverage properties but is difficult to calculate for large denominators a method combining wilson score intervals for the two proportions to be compared also performs well and is readily implemented irrespective of sample size

factoring multivariate integral polynomials an algorithm is presented to factorize polynomials in several variables with integral coefficients that is polynomial time in the degrees of the polynomial to be factored for any fixed number of variables the algorithm generalizes the algorithm presented by a k lenstra et al to factorize integral polynomials in one variable

tests for equivalence or non inferiority for paired binary data assessment of therapeutic equivalence or non inferiority between two medical diagnostic procedures often involves comparisons of the response rates between paired binary endpoints the commonly used and accepted approach to assessing equivalence is by comparing the asymptotic confidence interval on the difference of two response rates with some clinical meaningful equivalence limits this paper investigates two asymptotic test statistics a wald type sample based test statistic and a restricted maximum likelihood estimation rmle based test statistic to assess equivalence or non inferiority based on paired binary endpoints the sample size and power functions of the two tests are derived the actual type i error and power of the two tests are computed by enumerating the exact probabilities in the rejection region the results show that the rmle based test controls type i error better than the sample based test to establish an equivalence between two treatments with a symmetric equivalence limit of 0 15 a minimal sample size of 120 is needed the rmle based test without the continuity correction performs well at the boundary point 0 a numerical example illustrates the proposed procedures

on m estimators and normal quantiles this paper explores a class of robust estimators of normal quantiles filling the gap between maximum likelihood estimators and empirical quantiles our estimators are linear combinations of m estimators their asymptotic variances can be arbitrarily close to variances of the maximum likelihood estimators compared with empirical quantiles the new estimators offer considerable reduction of variance at near normal probability distributions

a new exact and more powerful unconditional test of no treatment effect from binary matched pairs we consider the problem of testing for a difference in the probability of success from matched binary pairs starting with three standard inexact tests the nuisance parameter is first estimated and then the residual dependence is eliminated by maximization producing what i call an e m p value the e m p value based on mcnemar s statistic is shown numerically to dominate previous suggestions including partially maximized p values as described in berger and sidik 2003 statistical methods in medical research 12 91 108 the latter method however may have computational advantages for large samples

effects and non effects of paired identical observations in comparing proportions with binary matched pairs data binary matched pairs data occur commonly in longitudinal studies such as in cross over experiments many analyses for comparing the matched probabilities of a particular outcome do not utilize pairs having the same outcome for each observation an example is mcnemar s test some methodologists find this to be counterintuitive we review this issue in the context of subject specific and population averaged models for binary data with various link functions for standard models and inferential methods pairs with identical outcomes may affect the estimated size of the effect and its standard error but they have negligible if any effect on significance we also discuss extension of this result to matched sets

confidence intervals from the difference between two correlated proportions abstract when data arise as matched binary pairs it is often of interest to test whether or not the probabilities of an odd pair of each type are equal construction of a small sample confidence interval for the difference in these probabilities is more difficult and either approximate or conservative methods need be resorted to two methods are suggested in this article one a natural asymptotic method and the other a more generally applicable conservative method the coverage probability and average width are studied for small and moderate sample sizes

exact unconditional tests for testing non inferiority in matched pairs design the problem of testing non inferiority in a 2 2 matched pairs sample is considered two exact unconditional tests based on the standard and the confidence interval p values are proposed although tests of non inferiority have two nuisance parameters under the null hypothesis the exact tests are defined by reducing the dimension of nuisance parameter space from two to one using the monotonicity of the distribution the exact sizes and powers of these tests and the existing asymptotic test are considered the exact tests are found to be accurate in view of their size property in addition the exact test based on the confidence interval p value is more powerful than the other exact test it is shown that the asymptotic test is inaccurate that is its size exceeds the claimed nominal level therefore it recommends a cautious approach in use of the asymptotic test for the problem of testing non inferiority particularly when sample sizes are small or moderately large copyright 2003 john wiley sons ltd

simple improved confidence intervals for comparing matched proportions for binary matched pairs data this article discusses interval estimation of the difference of probabilities and an odds ratio for comparing success probabilities we present simple improvements of the commonly used wald confidence intervals for these parameters the improvement of the interval for the difference of probabilities is to add two observations to each sample before applying it the improvement for estimating an odds ratio transforms a confidence interval for a single proportion

coverage probabilities of bootstrap confidence intervals for quantiles an asymptotic expansion of length 2 is established for the coverage probabilities of confidence intervals for the underlying q quantile which are derived by bootstrapping the sample q quantile the corresponding level error turns out to be of order o n 1 2 which is unexpectedly low a confidence interval of even more practical use is derived by using backward critical points the resulting confidence interval is of the same length as the one derived by ordinary bootstrap but it is distribution free and has higher coverage probability

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

a polynomial time complexity bound for computations on curves in this paper we use a recent quantitative version of eisenstein s theorem on power series expansions of algebraic functions to compute a polynomial time bit complexity bound for the computation of the genus of an algebraic curve over the rationals the result is extendable to any field of characteristic zero which is finitely generated over the rationals

a note on monotonicity assumptions for exact unconditional tests in binary matched pairs designs summary exact unconditional tests have been widely applied to test the difference between two probabilities for 2 2 matched pairs binary data with small sample size in this context lloyd 2008 biometrics64 716 723 proposed an e m p value that showed better performance than the existing m p value and c p value however the analytical calculation of the e m p value requires that the barnard convexity condition be satisfied this can be challenging to prove theoretically in this article by a simple reformulation we show that a weaker condition conditional monotonicity is sufficient to calculate all three p values m c and e m and their corresponding exact sizes moreover this conditional monotonicity condition is applicable to noninferiority tests

two sided confidence intervals for the single proportion comparison of seven methods simple interval estimate methods for proportions exhibit poor coverage and can produce evidently inappropriate intervals criteria appropriate to the evaluation of various proposed methods include closeness of the achieved coverage probability to its nominal value whether intervals are located too close to or too distant from the middle of the scale expected interval width avoidance of aberrations such as limits outside 0 1 or zero width intervals and ease of use whether by tables software or formulae seven methods for the single proportion are evaluated on 96 000 parameter space points intervals based on tail areas and the simpler score methods are recommended for use in each case methods are available that aim to align either the minimum or the mean coverage with the nominal 1 alpha

bootstrap and second order tests of risk difference clinical trials data often come in the form of low dimensional tables of small counts standard approximate tests such as score and likelihood ratio tests are imperfect in several respects first they can give quite different answers from the same data second the actual type 1 error can differ significantly from nominal even for quite large sample sizes third exact inferences based on these can be strongly nonmonotonic functions of the null parameter and lead to confidence sets that are discontiguous there are two modern approaches to small sample inference one is to use so called higher order asymptotics reid 2003 annal of statistics 31 1695 1731 to provide an explicit adjustment to the likelihood ratio statistic the theory for this is complex but the statistic is quick to compute the second approach is to perform an exact calculation of significance assuming the nuisance parameters equal their null estimate lee and young 2005 statistic and probability letters 71 143 153 which is a kind of parametric bootstrap the purpose of this article is to explain and evaluate these two methods for testing whether a difference in probabilities p 2 p 1 exceeds a prechosen noninferiority margin 0 on the basis of an extensive numerical study we recommend bootstrap p values as superior to all other alternatives first they produce practically identical answers regardless of the basic test statistic chosen second they have excellent size accuracy and higher power third they vary much less erratically with the null parameter value 0