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

homogeneous linear predictor models for contingency tables maximum likelihood ml inference for the class of homogeneous linear predictor hlp models for contingency tables is described hlp models constrain the expected table counts m through l m x where the link l is allowed to be a many to one nonlinear function generalized log linear association trend marginal cumulative probit and conditional marginal homogeneity models are given as specific examples ml fit results which include point estimates goodness of fit statistics and asymptotic based approximate distributions are described and compared for equivalent hlp models the results are valid for a wide variety of sampling plans including combinations of product multinomial and poisson sampling an important practical implication of this article is that the implementation of ml fitting and theory is straightforward and an attractive alternative to weighted least squares estimation for hlp models

combined signal setting design and traffic assignment problem abstract the paper provides a comprehensive discussion about the global signal settings problem subject to the user equilibrium constraint for traffic flows a new algorithm that applies the armijo rule for step size estimation to usual projected gradient algorithm is presented and compared to other usual solution procedures moreover numerical experiments are performed on a test network in order to investigate the shape of the objective function and then obtain further information about mathematical properties of the problem issues concerning multiplicity of solutions algorithm convergence and sensitivity to demand patterns are also discussed

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

confidence intervals for differnces in correlated binary proportions by w l may and w d johnson statistics in medicine 16 2127 2136 1997

a comparison of methods for the construction of confidence interval for relative risk in stratified matched pair designs a stratified matched pair study is often designed for adjusting a confounding effect or effect of different trails centers groups in modern medical studies the relative risk is one of the most frequently used indices in comparing efficiency of two treatments in clinical trials in this paper we propose seven confidence interval estimators for the common relative risk and three simultaneous confidence interval estimators for the relative risks in stratified matched pair designs the performance of the proposed methods is evaluated with respect to their type i error rates powers coverage probabilities and expected widths our empirical results show that the percentile bootstrap confidence interval and bootstrap resampling based bonferroni simultaneous confidence interval behave satisfactorily for small to large sample sizes in the sense that i their empirical coverage probabilities can be well controlled around the pre specified nominal confidence level with reasonably shorter confidence widths and ii the empirical type i error rates of their associated test statistics are generally closer to the pre specified nominal level with larger powers they are hence recommended two real examples from clinical laboratory studies are used to illustrate the proposed methodologies

profile likelihood inference for highly accurate diagnostic tests nous envisageons une inference sur la vraisemblance de profil basee sur la distribution multinomiale pour evaluer la precision d un test diagnostic la methode s applique a des donnees ordinales quand la precision est evaluee au moyen de l aire sous la courbe caracteristique du receveur courbe roc des resultats de simulation suggerent que les intervalles de confiance derives ont vies probabilites de couverture acceptables meme lorsque les tailles d echantillons sont petites et que le test diagnostic a une haute precision les methodes s etendent a des contextes stratifies et a des situations ou les evaluations sont correlees nous illustrons les methodes sur des donnees provenant d un essai clinique sur la detection du cancer de l ovaire

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

multiple imputation for the comparison of two screening tests in two phase alzheimer studies two phase designs are common in epidemiological studies of dementia and especially in alzheimer research in the first phase all subjects are screened using a common screening test s while in the second phase only a subset of these subjects is tested using a more definitive verification assessment i e golden standard test when comparing the accuracy of two screening tests in a two phase study of dementia inferences are commonly made using only the verified sample it is well documented that in that case there is a risk for bias called verification bias when the two screening tests have only two values e g positive and negative and we are trying to estimate the differences in sensitivities and specificities of the tests one is actually estimating a confidence interval for differences of binomial proportions estimating this difference is not trivial even with complete data it is well documented that it is a tricky task in this paper we suggest ways to apply imputation procedures in order to correct the verification bias this procedure allows us to use well established complete data methods to deal with the difficulty of the estimation of the difference of two binomial proportions in addition to dealing with incomplete data we compare different methods of estimation and evaluate the use of multiple imputation in this case our simulation results show that the use of multiple imputation is superior to other commonly used methods we demonstrate our finding using alzheimer data

optimization of limited network capacity with toll settings a non smooth optimization model is established for determining reserve capacity of a road network with toll settings optimization of limited network capacity with toll settings can be formulated as a mathematical program with equilibrium constraints mpec a quasi newton subgradient projection and contractive method qspc with global convergence is proposed numerical calculations are conducted using an example network where good results are obtained

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

moyennes de certaines fonctions multiplicatives sur les entiers friables 2 nous evaluons les moyennes indiquees dans le titre sous des hypotheses analytiques concernant la serie de dirichlet associee

on polynomial selection for the general number field sieve the general number field sieve gnfs is the asymptotically fastest algorithm for factoring large integers its runtime depends on a good choice of a polynomial pair in this article we present an improvement of the polynomial selection method of montgomery and murphy which has been used in recent gnfs records

moyennes de certaines fonctions multiplicatives sur les entiers friables 4 we provide two generic applications of previously established estimates for friable mean values of non negative multiplicative functions

multinomial poisson homogeneous models for contingency tables a unified approach to maximum likelihood inference for a broad new class of contingency table models is presented the model class comprises multinomial poisson homogeneous mph models which can be characterized by an independent sampling plan and a system of homogeneous constraints h m 0 where m is the vector of expected table counts maximum likelihood ml fitting and large sample inference for mph models are described the mph models are partitioned into well defined equivalence classes and explicit comparisons of the large sample behaviors of ml estimators of equivalent models are given the equivalence theory not only unifies a large collection of previously known results it also leads to useful generalizations and many new results the practical computational implication is that ml fit results for any particular mph model can be obtained directly from the ml fit results for any conveniently chosen equivalent model issues of hypothesis testability and parameter estimability are also addressed to illustrate an example based on statistics journal citation patterns is given for which the data can be used to test the hypothesis that a certain model holds but they cannot be used to estimate any of that model s parameters

confidence intervals for differences in correlated binary proportions an experiment to assess the efficacy of a particular treatment or process often produces dichotomous responses either favourable or unfavourable when we administer the treatment on two occasions to the same subjects we often use mcnemar s test to investigate the hypothesis of no difference in the proportions on the two occasions that is the hypothesis of marginal homogeneity a disadvantage in using mcnemar s statistic is that we estimate the variance of the sample difference under the restriction that the marginal proportions are equal a competitor to mcnemar s statistic is a wald statistic that uses an unrestricted estimator of the variance because the wald statistic tends to reject too often in small samples we investigate an adjusted form that is useful for constructing confidence intervals quesenberry and hurst and goodman discussed methods of construction that we adapt for constructing confidence intervals for the differences in correlated proportions we empirically compare the coverage probabilities and average interval lengths for the competing methods through simulation and give recommendations based on the simulation results

confidence intervals for the mean of a variable taking the values 0 1 and 2 the problem of setting a confidence interval for the mean of a variable on 0 1 2 arises in three contexts paired organ procedure rates estimation of gene frequency and three point likert scales an effective approach to its estimation may be based on a good interval for a paired difference of proportions four good methods due to newcombe and tango are shown to have much better performance than more naive methods over regions of the parameter space corresponding to the above applications

a globally convergent iterative scheme for toll design network with signal settings a toll design network for urban traffic roads with signal settings is considered subject to the underlying behavior of users route choice such problem can be formulated as an optimization problem by taking traffic assignment as a constraint due to the non differentiability of the perturbed solutions in equilibrium constraints a non smooth optimization model is established a globally convergent iterative scheme designed to heuristically search for a local optimum is proposed numerical illustrations are conducted through a hypothetical network from the literature as it shows from numerical calculations the proposed algorithm achieved substantially better performance than did the previous for a toll design network with signal settings

a family of confidence intervals for the ratio of two binomial proportions the power divergence family of statistics introduced by cressie and read 1984 journal of the royal statistical society series b 46 440 464 is used to obtain approximate confidence intervals for the ratio of two proportions intervals based on inverting the pearson likelihood ratio and freeman tukey statistics are included in this family small sample comparisons of the intervals are presented

some mathematical remarks on the polynomial selection in nfs in this work we consider the proportion of smooth free of large prime factors values of a binary form f x 1 x 2 in mathbf z x 1 x 2 in a particular case we give an asymptotic equivalent for this proportion which depends on f this is related to murphy s alpha function which is known in the cryptographic community but which has not been studied before from a mathematical point of view our result proves that when alpha f is small f has a high proportion of smooth values this has consequences on the first step called polynomial selection of the number field sieve the fastest algorithm of integer factorization

interval estimation of the difference in proportions under m to one matching when the number of potential controls is large relative to the number of available cases or when little effort needs to be expended in collecting the relevant information on the controls we often apply multiple matching to attain the validity or increase the efficiency of our inference in epidemiological studies in this paper we focus interval estimation on the difference in proportions for m to one matching we consider four asymptotic interval estimators including the estimator directly using the mantel haenszel mh point estimator the estimator using the tanh 1 x transformation the estimator derived from the cochran mantel haenszel cmh test statistic and the estimator derived from the quadratic inequality developed in this paper to evaluate and compare the performance of these estimators we employ monte carlo simulation we find that the estimator directly using the mh estimator can have the coverage probability less than the desired confidence level when the number of matched sets is small we note that the estimator derived from the quadratic inequality can perform well when the underlying difference is close to 0 even for a small number of matched sets however this estimator tends to have the coverage probability less than the desired confidence level as well when the underlying difference in proportions is large by contrast the estimator using the cmh statistic tends to have the coverage probability larger than the desired confidence level when the underlying difference is small we also find that the estimator using the tanh 1 x transformation consistently outperforms the interval estimator directly using the mh estimator we use the data regarding the association between induced abortions and ectopic pregnancy to illustrate the use of these estimators copyright 2005 john wiley sons ltd

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

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

standard errors and confidence intervals of norm statistics for educational and psychological tests norm statistics allow for the interpretation of scores on psychological and educational tests by relating the test score of an individual test taker to the test scores of individuals belonging to the same gender age or education groups et cetera given the uncertainty due to sampling error one would expect researchers to report standard errors for norm statistics in practice standard errors are seldom reported they are either unavailable or derived under strong distributional assumptions that may not be realistic for test scores we derived standard errors for four norm statistics standard deviation percentile ranks stanine boundaries and z scores under the mild assumption that the test scores are multinomially distributed a simulation study showed that the standard errors were unbiased and that corresponding wald based confidence intervals had good coverage finally we discuss the possibilities for applying the standard errors in practical test use in education and psychology the procedure is provided via the r function check norms which is available in the mokken package

an mpec approach to second best toll pricing this paper addresses two second best toll pricing problems one with fixed and the other with elastic travel demands as mathematical programs with equilibrium constraints several equivalent nonlinear programming formulations for the two problems are discussed one formulation leads to properties that are of interest to transportation economists another produces an algorithm that is capable of solving large problems and easy to implement with existing software for linear and nonlinear programming problems numerical results using transportation networks from the literature are also presented

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

simultaneously modeling joint and marginal distributions of multivariate categorical responses abstract we discuss model fitting methods for analyzing simultaneously the joint and marginal distributions of multivariate categorical responses the models are members of a broad class of generalized logit and loglinear models we fit them by improving a maximum likelihood algorithm that uses lagrange s method of undetermined multipliers and a newton raphson iterative scheme we also discuss goodness of fit tests and adjusted residuals and give asymptotic distributions of model parameter estimators for this class of models inferences are equivalent for poisson and multinomial sampling assumptions simultaneous models for joint and marginal distributions may be useful in a variety of applications including studies dealing with longitudinal data multiple indicators in opinion research cross over designs social mobility and inter rater agreement the models are illustrated for one such application using data from a recent general social survey regarding opinions about various types of government s

score and profile likelihood confidence intervals for contingency table parameters a straightforward approach to computing score and profile likelihood confidence intervals for contingency table parameters is described the computational approach herein avoids two main limitations of existing methods 1 compared with existing methods this paper s approach is applicable to a much broader class of parameters 2 unlike existing methods this paper s approach is not case specific and hence lends itself to a general yet very simple computational algorithm this paper describes the sliding quadratic computational algorithm and illustrates its use on examples that have not been previously considered in the literature a small scale simulation study highlights the advantage of using score and profile likelihood intervals rather than wald intervals

approximate interval estimation of the ratio of binomial parameters a review and corrections for skewness various methods for finding confidence intervals for the ratio of binomial parameters are reviewed and evaluated numerically it is found that the method based on likelihood scores koopman 1984 biometrics 40 513 517 miettinen and nurminen 1985 statistics in medicine 4 213 226 performs best in achieving the nominal confidence coefficient but it may distribute the tail probabilities quite disparately using general theory of bartlett 1953 biometrika 40 306 317 1955 biometrika 42 201 203 we correct this method for asymptotic skewness following gart 1985 biometrika 72 673 677 we extend this correction to the case of estimating the common ratio in a series of two by two tables computing algorithms are given and applied to numerical examples parallel methods for the odds ratio and the ratio of poisson parameters are noted

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

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

selecting polynomials for the function field sieve the function field sieve ffs algorithm is dedicated to computing discrete logarithms in a finite field fqn where q is a prime power small compared to q n introduced by adleman in adl94 and inspired by the number field sieve nfs the algorithm collects pairs of polynomials a b 2 fq t such that the norms of a bx in two function fields are both smooth the sieving stage i e having only irreducible divisors of small degree it then solves a sparse linear system the linear algebra stage whose solutions called virtual logarithms allow to compute the discrete algorithm of any element during a final stage individual logarithm stage the choice of the defining polynomials f and g for the two function fields can be seen as a preliminary stage of the algorithm it takes a small amount of time but it can greatly influence the sieving stage by slightly changing the probabilities of smoothness in order to solve the discrete logarithm in fqn the main required property of f g2 fq t x is that their resultant resx f g has an irreducible factor t of degree n various methods have been proposed to build such polynomials but the best results in practice correspond to the method of joux and lercier jl02 its particularity is that one of the two polynomials say g is linear moreover for any polynomial f in fq t x and any input fqn one can associate a linear polynomialg satisfying the requirements of the ffs this allows us to precompute some polynomials f which have good properties for the sieving stage for this we define and measure the size property and the so called root and cancellation properties in short the cancellation property is measured by a function related to the size of the coecients of f as well as to the cardinality of the set of pairs a b to be sieved the root property is measured by which is inspired by the function used for the factorization algorithms it is related to the number of roots of f when reduced modulo small irreducible polynomials of fq t finally 1 measures the cancellation property by evaluating the average loss of degree due to the cancellation of the terms of f r when r is a random rational fraction of fq t we present a sieving procedure which computes the most costly to evaluate of the three functions we next combine the dierent criteria in order to compare arbitrary polynomials in particular we show experimental evidence that defined as 1 predicts the eciency of any polynomial our methods were used in two records of discrete logarithm in f2n with prime values of n in the last couple of weeks new algorithms were proposed which are particularly well adapted for the fields f2n for composite values of n in the case when n is prime the crossing point is to be computed this latter being determined by the practical improvement of the ffs see bar13 for a broader presentation of our work

a nonsmooth version of newton s method newton s method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized jacobian instead of the derivative this extension includes the b derivative version of newton s method as a special case convergence theorems are proved under the condition of semismoothness it is shown that the gradient function of the augmented lagrangian forc2 nonlinear programming is semismooth thus the extended newton s method can be used in the augmented lagrangian method for solving nonlinear programs

pseudo score confidence intervals for parameters in discrete statistical models we propose pseudo score confidence intervals for parameters in models for discrete data the confidence interval is obtained by inverting a test that uses a pearson chi squared statistic to compare fitted values for the working model with fitted values of the model when a parameter of interest takes various fixed values for multinomial models the pseudo score method simplifies to the score method when the model is saturated and otherwise it is asymptotically equivalent to score and likelihood ratio test based inferences for cases in which ordinary score methods are impractical such as when the likelihood function is not an explicit function of model parameters the pseudo score method is feasible we illustrate the method for four such examples generalizations of the method are also presented for future research including inference for complex sampling designs using a quasilikelihood pearson statistic that compares fitted values for two models relative to the variance of the observations under the simpler model

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

improvements to the general number field sieve for discrete logarithms in prime fields a comparison with the gaussian integer method in this paper we describe many improvements to the number field sieve our main contribution consists of a new way to compute individual logarithms with the number field sieve without solving a very large linear system for each logarithm we show that with these improvements the number field sieve outperforms the gaussian integer method in the hundred digit range we also illustrate our results by successfully computing discrete logarithms with gnfs in a large prime field