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

analysis of an optimal control problem for the three dimensional coupled modified navier stokes and maxwell equations the mathematical formulation and analysis of an optimal control problem associated with a viscous incompressible electrically conducting fluid in a bounded three dimensional domain with fixed perfectly conducting boundaries is considered the objective of control is the matching of the velocity and magnetic fields to given target fields control is effected through distributed mechanical force and current controls the existence of optimal solutions is shown the g teaux differentiability for the magnetohydrodynamic system with respect to controls is proved and the optimality system is obtained

a penalized neumann control approach for solving an optimal dirichlet control problem for the navier stokes equations we introduce a penalized neumann boundary control approach for solving an optimal dirichlet boundary control problem associated with the two or three dimensional steady state navier stokes equations we prove the convergence of the solutions of the penalized neumann control problem the suboptimality of the limit and the optimality of the limit under further restrictions on the data we describe the numerical algorithm for solving the penalized neumann control problem and report some numerical results

the foundations of confounding in epidemiology abstract a statistically coherent view of confounding motivated by the over controversy over the proper control of confounding in the presence of prior knowledge is presented confounding by a covariate c in the presence of data on c is distinguished from confounding in the absence of data on c a covariate c is defined to be a nonconfounder in the absence of data on c if the population parameter of interest can be unbiasedly estimated asymptotically absent data on c under this definition c may be a confounder for some parameters of interest and a nonconfounder for others if c is a confounder for a parameter of interest that has a causal interpretation we call c a causal confounder when data on c are available c is defined to be a nonconfounder for a particular parameter of interest if and only if inference on the parameter of interest does not depend on the data through c bayesians frequentists and pure likelihoodists will in general agree on the prior knowledge necessary to render c a non confounder in particular c will in general be a nonconfounder precisely when the crude data ignoring c are s sufficient for the parameter of interest the intuitive view held by many practicing epidemiologists that confounding by c represents a bias of the unadjusted crude estimator is in a sense correct provided inference is performed conditional on approximate ancillary statistics that measure the degree to which associations in the data differ due to sampling variability from those population associations known a priori

real time computational algorithm for optimal control of an mhd flow system the flow of weakly electrically conducting fluids can be controlled by electromagnetic forces originating from electrodes and permanent magnets we consider the possibility of separation control for an electrically conducting bluff body flow with reduced order modeling the reduced order model is derived using the proper orthogonal decomposition pod and galerkin projection the pod allows one to extract the dominant modes in the observed physical phenomena and to define the smallest possible solution space this can be exploited in a galerkin framework to reduce break the nonlinear infinite dimensional model to a small finite dimensional model we investigate the design of a reduced order nonlinear optimal controller for flow separation in a channel we present numerical experiments with an applied spanwise magnetic field distribution and a boundary electric potential actuation on a part of the boundary our methods are found to be efficient and fast and our methods demonstrate a significant reduction in computational time

a generalisation of the mantel haenszel test to bivariate failure time data summary this paper presents a class of mantel haenszel 1959 type statistics for testing independence between pairs of failure times this class is extended to include a weight function in order to enhance test power large sample distributions of these statistics are given under the null hypothesis of independence the paper also presents a simplified test the covariance test which is asymptotically equivalent to the mantel haenszel type test in order to account for heterogeneity among subjects both tests are generalised to include subject specific covariates in a simulation study the weighted mantel haenszel and covariance tests are shown to lead to an increase in power for detecting dependence compared to unweighted tests and to a score test commenges andersen 1995 that is based on a random effects model an example is used to illustrate the methodology

adjustments to the mantel haenszel chi square statistic and odds ratio variance estimator when the data are clustered dependence between observations on a dichotomous variable renders invalid the usual chi square tests of independence and inflates the variances of parameter estimates such a situation occurs for example when subjects consist of members of the same family or with repeated observations on the same person in this paper we describe methods of measuring the extent of correlation or clustering we also develop methods of adjusting the mantel haenszel chi square test statistic and the variance of the mantel haenszel estimate of a common odds ratio in sets of 2 2 contingency tables

homogeneity test with a generalized mantel haenszel estimator for l2 k contingency tables abstract a conditional test for the homogeneity of the odds ratios in l2 k k 2 tables is developed based on a multiple hypergeometric distribution the test is a generalization of the breslow day test 1980 and is useful in sparse tables for computational feasibility the conditional maximum likelihood estimator is replaced by a consistent but inefficient estimator in the test statistic if this is the case it is shown that the asymptotic distribution is not chi squared as has been noticed by tarone 1985 in the case of 2 2 tables following tarone we develop a correction method so that the statistic follows an asymptotic chi squared distribution an algorithm is developed for calculating the homogeneity test with a generalized mantel haenszel estimator

a comparison of two simple hazard ratio estimators based on the logrank test two hazard ratio estimators based on the logrank test are investigated using a simulation study the pike estimator ratio of relative death rates was shown to be consistently less biased than the peto 1 step estimator the latter has recently been advocated as the method of choice for point and interval estimation both estimators exhibited bias with increasing hazard ratios although the bias was minimal for effects less than 3 the confidence intervals also did not achieve the nominal coverage with increasing hazard ratios but again the pike estimator was superior the coverage could be improved by recalculation of the variance incorporating the point estimate for a hazard ratio of less than 3 we recommend the use of the pike estimator otherwise it is necessary to use a more complex method of estimation

a new variance estimator for the mantel haenszel odds ratio many asymptotic formulas for estimating the variance of and confidence intervals for odds ratios in case control studies are available but most have limitations the method suggested by cornfield 1956 proceedings of the third berkeley symposium 4 135 148 for example is iterative and requires calculation of exact variances if the number of subjects within each stratum is small this paper presents a new asymptotic noniterative variance estimate for the mantel haenszel odds ratio which based on a series of monte carlo experiments compares favorably with other noniterative estimates when used for confidence interval estimation

marginal likelihood conditional likelihood and empirical likelihood connections and applications marginal likelihood and conditional likelihood are often used for eliminating nuisance parameters for a parametric model it is well known that the full likelihood can be decomposed into the product of a conditional likelihood and a marginal likelihood this property is less transparent in a nonparametric or semiparametric likelihood setting in this paper we show that this nice parametric likelihood property can be carried over to the empirical likelihood world we discuss applications in case control studies genetical linkage analysis genetical quantitative traits analysis tuberculosis infection data and unordered paired data all of which can be treated as semiparametric finite mixture models we consider the estimation problem in detail in the simplest case of unordered paired data where we can only observe the minimum and maximum values of two random variables the identities of the minimum and maximum values are lost the profile empirical likelihood approach is used for maximum semiparametric likelihood estimation we present some large sample results along with a simulation study

goodness of fit tests for log linear models in sparse contingency tables abstract the asymptotic normality of the likelihood ratio goodness of fit statistic is demonstrated for testing the fit of log linear models with closed form maximum likelihood estimates in sparse contingency tables unlike the traditional chi squared theory the number of categories in the table increases as the sample size increases but not all of the expected frequencies are required to become large some results of a small monte carlo study are presented the traditional chi squared approximation is reasonably accurate for the pearson statistic for many sparse tables but cases are presented for which it fails the normal approximation can be much more accurate than the chi squared approximation for the likelihood ratio statistic but the bias of estimated moments is a potential problem for very sparse tables

interval estimation of the common odds ratio from k 2 x 2 tables under cluster sampling we propose a simple correction factor for the variance of the logarithm of the common odds ratio estimated by the method of mantel and haenszel from a series of 2 2 tables when data are cluster correlated the adjustment is applied to the variance estimators proposed by hauck and by robins breslow and greenland for the log of the mantel haenszel common odds ratio and its performance is evaluated in a simulation study the key features of the proposed adjustment are i it has closed form ii it can accommodate covariates defined at the cluster specific level the site specific level or both and iii it does not require the user to specify a particular correlation structure for the response data the correction derives from liang and zeger s generalized estimating equations gee technique for logistic regression modelling via simulation we examine empirical versus nominal coverage probabilities for interval estimation of the common odds ratio using adjusted and unadjusted variance estimates and we present ratios of observed to estimated variances results are compared to those obtained from the fully iterated gee analysis the characteristics of the simulation study mimic scenarios common in the periodontal research setting with small numbers of subjects n 25 50 moderate numbers of sites per cluster m 4 16 32 and modest intracluster correlation levels 0 0 0 1 0 2 0 3 results show that adjusted confidence intervals applied to the hauck or the robins breslow greenland variance estimate provide coverage probabilities close to the nominal level for the mantel haenszel common odds ratio over a variety of cluster sizes and levels of correlation copyright 1999 john wiley sons ltd

bias corrected maximum likelihood estimator of a log common odds ratio summary a bias correction factor for the maximum likelihood estimator of the log common odds ratio for sparse data is derived which is applicable when the design is balanced and or when the number of strata is large the corrected maximum likelihood estimator is practically unbiased and its mean squared error is smaller than that of the uncorrected maximum likelihood estimator the correction factor for the maximum likelihood estimator approaches one as strata sizes increase examples demonstrate that the corrected maximum likelihood estimator and the exact conditional maximum likelihood estimator are essentially identical although the standard error of the former tends to be slightly smaller than that of the latter it is also demonstrated that a simple version of the correction factor is a satisfactory approximation the bias corrected maximum likelihood estimator proposed in this paper is the extension of breslow s 1981 and it can be useful particularly when the computational burden of the exact conditional method is excessive

generalization of the mantel haenszel estimator to nonconstant odds ratios nouvel estimateur issu de la generalisation de l estimateur de mantel haenszel etude de ses proprietes asymptotiques en fonction du nombre de tables fixe et du comptage des cellules

tests for homogeneity of odds ratio when the data are sparse summary three tests for homogeneity of odds ratio for a series of 2 x 2 tables when the data are sparse are studied by means of monte carlo experiments a score test based on the assumption that the log odds ratios are generated from some unknown distribution is shown to be more powerful than the other two the original test of zelen 1971 later corrected by halperin ware byar et al 1977 is also examined it tends to be too liberal under the sparse data situation however it has approximately the nominal size when there are as many as ten tables with as few as ten observations per table

generalized mantel haenszel estimators for k 2 x j tables mickey and elashoff 1985 biometrics 41 623 635 gave an extension of mantel haenszel estimation to log linear models for 2 x j x k tables their extension yields two generalizations of the mantel haenszel odds ratio estimator to k 2 x j tables this paper provides variance and covariance estimators for these generalized mantel haenszel estimators that are dually consistent i e consistent in both large strata and sparse data and presents comparisons of the efficiency of the generalized mantel haenszel estimators

summary attributable risk estimation from unmatched case control data abstract we propose an alternative method to obtain summary estimators variances and confidence intervals for attributable risk measures this method combines weighted exposure prevalences for cases and controls across strata formed by the cross classification of relevant covariates to form estimates of attributable risk among the exposed and attributable risk in the target population the major benefit of this approach over those previously proposed in the literature is that it operates on data summed across strata rather than on estimation of statistics within each stratum this alternative method for attributable risk measures utilizes the mantel haenszel estimate of an average odds ratio and can be implemented using the matrix procedure in sas this method is appropriate even when the within stratum sample sizes are too small for other methods to be valid simulation results indicate that this method is superior to others with respect to bias and coverage probability for confidence intervals

a generalization of the mantel haenszel estimator of partial association for 2 x j x k tables summary a generalization of the mantel haenszel estimator of a common odds ratio for a series of 2 x 2 tables is proposed for the estimation of log linear partial association parameters for a series of 2 x j j 2 tables the assumption of no three way interaction among row column and stratifying variables is made two approximate covariance estimators are presented small sample properties of these estimators are investigated by simulation studies the results indicate that use of the proposed partial association technique produces estimates with negligible bias both covariance estimation techniques provide confidence intervals for functions of partial association parameters for example odds ratios or adjusted rates a test of no three way interaction results from these procedures

estimators of the variance of the mantel haenszel log odds ratio estimate summary a new approach to large sample studies of the variance of the log odds ratio estimate of mantel and haenszel is developed and used to derive formulas that lead to useful standard error formulas for the mantel haenszel estimate the variance estimator of robins breslow and greenland 1986 biometrics 42 311 324 is derived in a new way and a new variance estimator valid only for the case of 1 m matching is also derived using the new approach

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

the asymptotic efficiency of conditional likelihood methods summary this paper concerns the efficiency of the conditional likelihood method for inference in models which include nuisance parameters a new concept of ancillarity asymptotic weak ancillarity is introduced it is shown that the conditional maximum likelihood estimator and the conditional score test of 0 the parameter of interest are asymptotically equivalent to their unconditional counterparts and hence are asymptotically efficient provided that the conditioning statistic is asymptotically weakly ancillary the key assumption that the conditioning statistic is asymptotically weakly ancillary is verified when the underlying distribution is from exponential families some illustrative examples are given

odds ratio inference with dependent data summary when data can be presented as a series of k 2 x 2 tables with cell counts xi ni xi yi mi yi it is often assumed that xi and yi are binomially distributed this paper deals with inference for the common odds ratio i l when the binomial assumption is invalid when k increases the consistency and asymptotic normality of the mantel haenszel 1959 estimator is derived the conditional maximum likelihood estimator is shown to be inconsistent and the asymptotic bias is computed when either the first order markov chain or beta binomial model is assumed the mantel haenszel test for testing f 1 is also shown to be inappropriate through some simulation studies two consistent test statistics are proposed and shown to be comparable to each other in terms of size and efficiency some possible further work is described

a conditional composite likelihood ratio test with boundary constraints summary composite likelihood has been widely used in applications the asymptotic distribution of the composite likelihood ratio statistic at the boundary of the parameter space is a complicated mixture of weighted chi 2 distributions in this paper we propose a conditional test with data dependent degrees of freedom we consider a modification of the composite likelihood which satisfies the second order bartlett identity we show that the modified composite likelihood ratio statistic given the number of estimated parameters lying on the boundary converges to a simple chi 2 distribution this conditional testing procedure is validated through simulation studies

computations of boundary optimal control problems for an electrically conducting fluid we study four optimal control problems for an electrically conducting fluid the control is the normal electrical current on the boundary of the flow domain the objectives are to match a desired velocity field or to match a desired electrical potential field or to minimize the potential gradient or to minimize the vorticity in the flow domain we develop a systematic way to use the lagrange multiplier rules to derive an optimality system of equations from which an optimal solution can be computed mixed finite element methods are used to find approximate solutions for the optimality systems of equations that characterize the optimal controls a direct method and an iterative method are proposed for solving the discrete nonlinear optimality systems of equations numerical results for several examples are presented

on heterogeneity tests based on efficient scores summary for cases in which a parameter may be estimated from several independent data sets mather 1935 proposed a heterogeneity test based on the efficient scores for the individual data sets evaluated at the overall maximum likelihood estimator following fisher 1946 a modification of the heterogeneity score test is presented wherein a consistent but inefficient estimator of the parameter of interest is substituted for the overall maximum likelihood estimator the modified test is also derived using the c q theory of neyman 1959 using the modified procedure we derive a test for a common odds ratio in several 2 x 2 tables based on the mantel haenszel estimator

composite conditional likelihood for sparse clustered data summary sparse clustered data arise in finely stratified genetic and epidemiologic studies and pose at least two challenges to inference first it is difficult to model and interpret the full joint probability of dependent discrete data which limits the utility of full likelihood methods second standard methods for clustered data such as pairwise likelihood and the generalized estimating function approach are unsuitable when the data are sparse owing to the presence of many nuisance parameters we present a composite conditional likelihood for use with sparse clustered data that provides valid inferences about covariate effects on both the marginal response probabilities and the intracluster pairwise association our primary focus is on sparse clustered binary data in which case the method proposed utilizes doubly discordant quadruplets drawn from each stratum to conduct inference about the intracluster pairwise odds ratios

analyzing k 2 x 2 tables under cluster sampling summary in many data analytic applications such as ophthalmologic longitudinal or periodontal studies multiple observations are recorded over several sites or timepoints within the same subject bringing about dependence between measurements this correlation in turn precludes the use of standard statistical methods that assume independence between outcome measurements for example the mantel haenszel statistic used to assess association between a binary outcome and a binary exposure while adjusting for a categorical covariate does not follow the usual chi squared distribution under the null hypothesis when there is correlation between observations a modified mantel haenszel procedure which makes adjustment for dependence is proposed no particular correlation structure is assumed for responses within a cluster this closed form adjustment stems from liang and zeger s 1986 biometrika73 13 22 generalized estimating equations approach for clustered data the difference between this tabular i e noniterative technique and many earlier tabular methods is that the current method allows for consideration of site specific exposure and covariate information an example from a periodontal research study illustrates application of the method

numerical approximation of optimal flow control problems by a penalty method error estimates and numerical results the purpose of this paper is to present numerically convenient approaches to solve optimal dirichlet control problems governed by the steady navier stokes equations we will examine a penalized neumann control approach for solving dirichlet control problems from numerical and computational points of view the control is affected by the suction or injection of fluid through the boundary or by boundary surface movements in the tangential direction the control objective is to minimize the vorticity in the flow or to drive the velocity field to a desired one we develop sequential quadratic programming methods to solve these optimal control problems the effectiveness of the optimal control techniques in flow controls and the feasibility of the proposed penalized neumann control approaches for flow control problems are demonstrated by numerical experiments for a viscous incompressible fluid flow in a two dimensional channel and in a cavity geometry

statistical methods for estimating attributable risk from retrospective data this paper extends levin s measure of attributable risk to adjust for confounding by aetiologic factors other than the exposure of interest one can estimate this extended measure from case control data provided either i from the control data one can estimate exposure prevalence within each stratum of the confounding factor or ii one has additional information available concerning the confounder distribution and the stratum specific disease rates in both cases we give maximum likelihood estimates and their estimated asymptotic variances and show them to be independent of the sampling design matched vs random computer simulations investigate the behaviour of these estimates and of three types of confidence intervals when sample size is small relative to the number of confounder strata the simulations indicate that attributable risk estimates tend to be too low the bias is not serious except when exposure prevalence is high among controls in this case the estimates and their standard error estimates are also highly unstable in general the asymptotic standard error estimates performed quite well even in small samples and even when the true asymptotic standard error was too small by contrast the bootstrap estimate tended to be too large none of the three confidence intervals proved superior in accuracy to the other two thus there appears no advantage in using the log based interval suggested by walter which is always longer than the simpler symmetric interval

a two sample censored data rank test for acceleration a score test for the null hypothesis of proportional hazards against rank regression alternatives is proposed as a complement to the logrank test for comparing censored survival curves the test statistic has an asymptotic normal distribution that is independent of the logrank distribution under the null hypothesis and its power is good against acceleration alternatives i e with crossing hazards where the logrank test fails monte carlo studies indicate that its small sample properties are comparable to those of the logrank and ranksum procedures

conditional association and unidimensionality in monotone latent variable models latent variable models represent the joint distribution of observable variables in terms of a simple structure involving unobserved or latent variables usually assuming the conditional independence of the observable variables given the latent variables these models play an important role in educational measurement and psychometrics in sociology and in population genetics and are implicit in some work on systems reliability we study a broad class of latent variable models namely the monotone unidimensional models in which the latent variable is a scalar the observable variables are conditionally independent given the latent variable and the conditional distribution of the observables given the latent variable is stochastically increasing in the latent variable all models in this class imply a new strong form of positive dependence among the observable variables namely conditional positive association this positive dependence condition may be used to test whether any model in this class can provide an adequate fit to observed data various applications generalizations and a numerical example are discussed

attributable risk estimation from matched case control data a methodology is proposed for obtaining summary estimators variances and confidence intervals for attributable risk measures from data obtained through a case control study design where one or more controls have been matched to each case the sampling design for obtaining these data is conceptualized as a simple random sample of cases being equivalent to a simple random sample of matched sets by combining information across the strata determined by the matched sets this approach provides all of the benefits associated with the mantel haenszel procedure for the estimators of attributable risk among the exposed and population attributable risk asymptotic variances are derived under the assumption that the frequencies of the unique response patterns follow the multinomial distribution simulation results indicate that these methods fare very well with respect to bias and coverage probability

testing the conditional independence and monotonicity assumptions of item response theory when item characteristic curves are nondecreasing functions of a latent variable the conditional or local independence of item responses given the latent variable implies nonnegative conditional covariances between all monotone increasing functions of a set of item responses given any function of the remaining item responses this general result provides a basis for testing the conditional independence assumption without first specifying a parametric form for the nondecreasing item characteristic curves the proposed tests are simple have known asymptotic null distributions and possess certain optimal properties in an example the conditional independence hypothesis is rejected for all possible forms of monotone item characteristic curves

a comparison of tests of homogeneity of odds ratios in k 2 2 tables we conducted a simulation study to determine the performance of nine procedures for testing the homogeneity of odds ratios in k 2 2 contingency tables we recommend tarone s approximate score test based on the mantel haenszel estimator of the common odds ratio for use in practice we also recommend a non iterative statistic developed by gart and based on the modified woolf estimator of the common odds ratio for very large samples in balanced or mildly unbalanced designs we base our recommendation of a statistic on its performance in terms of size and power in comparison with the other statistics considered

an evaluation of methods for the stratified analysis of clustered binary data in community intervention trials a simulation study is conducted in a community intervention setting several methods of stratified analysis of clustered binary data are compared in terms of empirical significance and empirical power levels they are the mantel haenszel test statistic chi 2 mh the adjusted mantel haenszel test statistic of donald donner chi 2 dd rao scott chi 2 rsn and chi 2 rsp and zhang boos chi 2 zbn and chi 2 zbp wald chi 2 w robust wald chi 2 rw score chi 2 s robust score chi 2 rs and the test statistic based on generalized linear mixed model glmm chi 2 glmm when rho not equal 0 chi 2 mh has inflated type i error and it should not be used when observations are correlated the results also warn of the use of chi 2 rsn and chi 2 rw due to their poor performance in terms of empirical significance level chi 2 zbp and chi 2 glmm have better empirical significance levels as compared to other statistics however chi 2 zbp tends to have lower empirical powers than other statistics when the number of clusters n is less than 24 chi 2 rsp provides the highest empirical powers when rho or 0 1 and n or 12 when rho or 0 01 we recommend the use of chi 2 rs and chi 2 glmm since they have better overall performance in terms of empirical significance levels and empirical power levels

the relation between score tests and approximate umpu tests in exponential models common in biometry in several recent papers both published and unpublished the theory of score tests rao 1973 pp 415 420 or the equivalent c a test neyman 1959 has been used to derive tests involving likelihoods based on exponential families which yield sufficient statistics a recently published example is a paper by day and byar 1979 in which the test for combined 2 x 2 tables due to cochran 1954 sometimes called the mantel haenszel 1959 statistic is shown to be a logit score test day and byar also considered a second multiparameter test for a more general logistic model we shall show that in such cases score tests can ordinarily be written down directly upon examination of the structure of the likelihood neither differentiation of the likelihood nor matrix inversion is usually needed furthermore for the case in which a single parameter is tested in the presence of nuisance parameters the score test is simply the normal approximation to the uniformly most powerful unbiased umpu test obviously for one parameter exponential families the score test is not only asymptotically locally most powerful but is also an approximation to the umpu test efron 1975

inference for odds ratio regression models with sparse dependent data suppose the number of 2 x 2 tables is large relative to the average table size and the observations within a given table are dependent as occurs in longitudinal or family based case control studies we consider fitting regression models to the odds ratios using table level covariates the focus is on methods to obtain valid inferences for the regression parameters beta when the dependence structure is unknown in this setting liang 1985 biometrika 72 678 682 has shown that inference based on the noncentral hypergeometric likelihood is sensitive to misspecification of the dependence structure in contrast estimating functions based on the mantel haenszel method yield consistent estimators of beta we show here that under the estimating function approach wald s confidence interval for beta performs well in multiplicative regression models but unfortunately has poor coverage probabilities when an additive regression model is adopted as an alternative to wald inference we present a mantel haenszel quasi likelihood function based on integrating the mantel haenszel estimating function a simulation study demonstrates that in medium sized samples the mantel haenszel quasi likelihood approach yields better inferences than other methods under an additive regression model and inferences comparable to wald s method under a multiplicative model we illustrate the use of this quasi likelihood method in a study of the familial risk of schizophrenia

stability criteria for linear systems with uncertain delays new delay independent and delay dependent stability criteria for linear systems with multiple uncertain delays are established by using both the time domain and the frequency domain methods the results are derived based on the established new preliminary lemmas and by using new type stability theorems for general retarded dynamical systems and new analysis techniques in the time domain and the frequency domain all the established stability criteria depend only on the eigenvalues related to the coefficient matrices of the systems and do not involve any free tuning parameters in addition some remarks are given to explain in detail the obtained results and to point out the limitations of the existing results in the literature

generalization of the mantel haenszel estimating function for sparse clustered binary data we extend the mantel haenszel estimating function to estimate both the intra cluster pairwise correlation and the main effects for sparse clustered binary data we propose both a composite likelihood approach and an estimating function approach for the analysis of such data the proposed estimators are consistent and asymptotically normally distributed simulation results demonstrate that the two approaches are comparable in terms of bias and efficiency however the estimating equation approach is computationally simpler analysis of the georgia high blood pressure survey is used for illustration

mantel haenszel type inference for cumulative odds ratios with a stratified ordinal response this article proposes a mantel haenszel type estimator of an assumed common cumulative odds ratio in a proportional odds model for an ordinal response with several 2 x c contingency tables it is useful for instance for comparing two treatments on an ordinal response for data from several centers when the data are highly sparse the estimator has behavior similar to the mantel haenszel estimator of a common odds ratio for several 2 x 2 tables it is consistent under the ordinary asymptotic framework in which the number of tables is fixed and unlike the maximum likelihood ml estimator also under sparse asymptotics in which the number of tables grows with the sample size simulations reveal a considerable difference between it and the ml estimator when each table has few observations efficiency comparisons suggest that little efficiency loss occurs compared to the ml estimator when the data are not sparse tests and estimators are presented for detecting and handling heterogeneity in the odds ratios and generalizations are available for stratified r x c contingency tables

the large sample relative efficiency of the mantel haenszel estimator in the fixed strata case the large sample relative efficiency of the mantel haenszel estimator psi mh of an odds ratio is investigated for the case in which the number of strata is fixed and the sample sizes within each stratum increase indefinitely the results show that psi mh is very efficient over a wide range of designs likely to occur in practice however conditions are identified under which the relative efficiency of this widely used estimator can be unusually low

an estimating equation approach for the analysis of case control studies with exposure measured at several levels liang gave an extension of the mantel haenszel estimating procedure for a common odds ratio to logistic regression models it is applicable to case control studies with multiple exposure levels which yield k 2 j tables this paper provides variance and covariance estimators which are consistent in both sparse data and large strata for liang s estimating functions in the k 2 j tables case and proposes an approximate confidence interval method for the common odds ratios

a semiparametric odds ratio model for measuring association we propose a semiparametric odds ratio model to measure the association between two variables taking discrete values continuous values or a mixture of both methods for estimation and inference with varying degrees of robustness to model assumptions are studied semiparametric efficient estimation and inference procedures are also considered the estimation methods are compared in a simulation study and applied to the study of associations among genital tract bacterial counts in hiv infected women

confidence limits for the common odds ratio based on the asymptotic distribution of the mantel haenszel estimator this paper proposes a new approximate confidence limit method for the common odds ratio based on the asymptotic distribution of the mantel haenszel estimator the proposed method provides easily computed limits and is applicable to both sparse data and large strata cases monte carlo experiments compare its performance with that of a method based on the asymptotic distribution of the log mantel haenszel odds ratio applications of the proposed method to the common risk and rate ratio cases are given

methods of estimation in log odds ratio regression models mccullagh s 1984 journal of the royal statistical society series b 46 250 256 approximation to the conditional maximum likelihood estimator in log odds ratio regression models is shown to have negligible asymptotic bias unless the odds ratios are large and the sample sizes in individual 2 x 2 tables are very small in application to two sets of case control data it yields results virtually indistinguishable from those of the conditional analysis a generalization of the mantel haenszel estimator proposed by davis 1985 biometrics 41 487 495 does not approximate the conditional results nearly as well

median bias reduction of maximum likelihood estimates for regular parametric problems we show how median centring of the maximum likelihood estimate can be achieved by a simple modification of the score equation for a scalar parameter of interest the estimator is equivariant under interest respecting reparameterizations and is third order median unbiased with a vector parameter of interest componentwise equivariance and third order median centring are obtained like the implicit method of firth 1993 for bias reduction the new method does not require finiteness of the maximum likelihood estimate and is effective in preventing infinite estimates simulation results for continuous and discrete models including binary and beta regression confirm that the method succeeds in achieving componentwise median centring and in solving the boundary estimate problem while keeping comparable dispersion and the same approximate distribution as its main competitors

on the asymptotic inefficiency of certain noniterative estimators of a common relative risk or odds ratio nurminen 1981 gives conditions for the asymptotic efficiency of general weighted mean estimators his application is a noniterative estimator of a common relative risk for binomial variates this summary estimator and by implication the mantel haenszel summary odds ratio estimator are asserted to be asymptotically efficient we examine conditions for the asymptotic efficiency in the unconditional sample space of the mantelhaenszel estimator for a common odds ratio the estimator of a common relative risk considered by nurminen and tarone s 1981 estimator of a common relative risk for binomial variables contrary to nurminen we find that except for a few degenerate cases these estimators are inefficient whenever the common odds ratio or common relative risk is not equal to 1

projection method mantel haenszel estimator for k 2 j tables abstract a projection method is introduced to generalize the mantel haenszel estimator for estimating the common odds ratios in k 2 j j 2 tables the method provides estimators in an explicit form and needs no iterative computation it is shown that the generalized mantel haenszel estimator proposed by greenland and yanagawa and fujii is obtained by this method as a special case furthermore selecting appropriate weight it is shown that the method leads to an estimator that is asymptotically equivalent to the generalized mantel haenszel estimator proposed by liang a dually consistent estimator of the variance of the estimator is proposed the characteristics of these estimators have been evaluated by monte carlo means

a note on the covariance of the mantel haenszel log odds ratio estimator and the sample marginal rates a simple technique developed in phillips unpublished ph d dissertation university of windsor windsor ontario 1987 is used to approximate cov theta mh pi i 1 2 where theta mh is the mantel haenszel log odds ratio estimator for a 2 x 2 x k table and the pi are the sample marginal proportions these results are then applied to obtain an approximate variance estimate of an adjusted risk difference based on the mantel haenszel odds ratio estimator

estimators of the mantel haenszel variance consistent in both sparse data and large strata limiting models summary this paper proposes a new estimator of the variance of the mantel haenszel estimator of common odds ratio that is easily computed and consistent in both sparse data and large strata limiting models monte carlo experiments compare its performance to that of previously proposed variance estimators

effects of cluster sampling on epidemiologic analysis in population based case control studies we consider population based case control designs in which controls are selected by one of three cluster sampling plans from the entire population at risk the effects of cluster sampling on classical epidemiologic procedures are investigated and appropriately modified procedures are developed in particular modified procedures for testing the homogeneity of odds ratios across strata and for estimating and testing a common odds ratio are presented simulations that use the data from the 1970 health interview survey as a population suggest that classical procedures may be fairly robust in the presence of cluster sampling a more extreme example based on a mixed multinomial model clearly demonstrates that the classical mantel haenszel 1959 journal of the national cancer institute 22 719 748 and woolf haldane tests of no exposure effect may have sizes exceeding nominal levels and confidence intervals with less than nominal coverage under an alternative hypothesis classical estimates of odds ratios may also be biased with non self weighting cluster samples the modified procedures we propose remedy these defects

modelling marginal hazards in multivariate failure time data we consider the problem of estimating relative risk parameters in the marginal distribution of failure times from a sample in which individuals are grouped into clusters and failure times for individuals within clusters may be dependent we assume that the marginal hazard of failure for individuals within a cluster is specified by a relative risk regression model and the structure of dependence between individuals within a cluster is left unspecified estimating equations for the regression parameters and an estimator for the cumulative base line marginal hazard are described

a signal reconstruction approach for control systems with unknown time varying delays abstract this work addresses the problem of time varying delays in systems and control in the first part of the paper we propose a processing scheme that allows reconstruction of a signal subject to time varying delays we show robustness of the scheme with respect to sensing and actuation noise we obtain a necessary and sufficient result for stability of compensated scalar linear systems under constant time delay then we apply the scheme to a general n dimensional linear system subject to time varying delay in the state feedback we present sufficient conditions for stability of the closed loop system these conditions provide a constructive procedure to design the compensation parameter to maximize the delay that the system can support while remaining stable finally we extend the scheme to delayed nonlinear systems and prove stability of the closed loop system for proper values of the control parameter

optimal control for a stationary mhd system in velocity current formulation an optimal control problem for the equations governing the stationary problem of magnetohydrodynamics mhd is considered control mechanisms by external and injected currents and magnetic fields are treated an optimal control problem is formulated first order necessary and second order sufficient conditions are developed an operator splitting scheme for the numerical solution of the mhd state equations is analyzed

a unified framework for studying parameter identifiability and estimation in biased sampling designs summary based on the odds ratio representation of a joint density we propose a unified framework to study parameter identifiability in biased sampling designs it is shown that most of these designs encountered in practice can be reformulated within the proposed framework and as a result the question of parameter identifiability can be largely clarified estimation of the identifiable parameters is considered and traditional results on the equivalence of the prospective and retrospective likelihoods are extended information contained in data on certain identifiable parameters is often very limited such parameters can be poorly estimated by the likelihood approach with practically attainable sample sizes which can substantially affect the estimates of parameters of primary interest a partially penalized likelihood approach is proposed to address this simulation results suggest that the proposed approach has good performance

a simulation study of the analysis of sets of 2 2 contingency tables under cluster sampling estimation of a common odds ratio abstract this article presents the results of a simulation study of the estimation of a common odds ratio in multiple contingency tables when the data are correlated within clusters the correlation is modeled by the beta binomial distribution the three objectives of the study were to determine a the variances biases and relative efficiencies of the beta binomial maximum likelihood estimator mle the binomial mle and the mantel haenszel estimator of the common odds ratio b the variances and biases of two estimators of the intracluster correlation coefficient and c the effectiveness of adjusting variance estimates of the binomial and mantel haenszel estimators using the two estimators of the simulation shows that increasing the size of the intracluster correlation coefficient increases the variance and the positive bias of all three estimators of the odds ratio the mantel haenszel estimator displays less variance and bias than the mle except for large values of and an unexpected b

extended mantel haenszel estimating procedure for multivariate logistic regression models a class of estimating functions is proposed for the estimation of multivariate relative risk in stratified case control studies it reduces to the well known mantel haenszel estimator when there is a single binary risk factor large sample properties of the solutions to the proposed estimating equations are established for two distinct situations efficiency calculations suggest that the proposed estimators are nearly fully efficient relative to the conditional maximum likelihood estimator for the parameters considered application of the proposed method to family data and longitudinal data where the conditional likelihood approach fails is discussed two examples from case control studies and one example from a study on familial aggregation are presented

analysis of data arising from a stratified design with the cluster as unit of randomization this paper discusses statistical techniques for the analysis of dichotomous data arising from a design in which the investigator randomly assigns each of two clusters of possibly varying size to interventions within strata the problem addressed is that of assessing the statistical significance of the intervention effect over all strata we propose a weighted paired t test based on the empirical logistic transform for designs that randomize large aggregate clusters in each of several strata

saddlepoint approximations for small sample logistic regression problems double saddlepoint approximations provide quick and accurate approximations to exact conditional tail probabilities in a variety of situations this paper describes the use of these approximations in two logistic regression problems an investigation of regression analysis of the log odds ratio in a sequence or set of 2 2 tables via simulation studies shows that in practical settings the saddlepoint methods closely approximate exact conditional inference the double saddlepoint approximation in the test for trend in a sequence of binomial random variates is also shown via simulation studies to be an effective approximation to exact conditional inference copyright 2000 john wiley sons ltd

estimation of a common odds ratio in case control studies of familial aggregation a new estimator of a common odds ratio is proposed for case control studies of familial aggregation the proposed estimator is a modification to the usual mantel haenszel estimator that relies on an empirical adjustment for the within family clustering which is typical of such designs a simulation study shows that the estimator tends to have smaller mean squared error than the unmodified mantel haenszel estimator under conditions likely to arise in practice the construction of confidence intervals is also discussed

conditional logistic regression with sandwich estimators application to a meta analysis motivated by a meta analysis of animal experiments on the effect of dietary fat and total caloric intake on mammary tumorigenesis we explore the use of sandwich estimators of variance with conditional logistic regression classical conditional logistic regression assumes that the parameters are fixed effects across all clusters while the sandwich estimator gives appropriate inferences for either fixed effects or random effects however inference using the standard wald test with the sandwich estimator requires that each parameter is estimated using information from a large number of clusters since our example violates this condition we introduce two modifications to the standard wald test first we reduce the bias of the empirical variance estimator the middle of the sandwich by using standardized residuals second we approximately account for the variance of these estimators by using the t distribution instead of the normal distribution where the degrees of freedom are estimated using satterthwaite s approximation through simulations we show that these sandwich estimators perform almost as well as classical estimators when the true effects are fixed and much better than the classical estimators when the true effects are random we achieve simulated nominal coverage for these sandwich estimators even when some parameters are estimated from a small number of clusters

the asymptotic relative efficiency of the mantel haenszel estimator in the increasing number of strata case the asymptotic relative efficiency are of the mantel haenszel estimator of a common odds ratio at is determined for the case in which the number of strata increases indefinitely for fixed withinstratum sample sizes the are remains above 90 over a very wide range of cases and above 93 for 2 a 5 these results support consideration of the relatively easily calculated mantel haenszel estimator rather than the conditional maximum likelihood estimator in these increasing strata cases

elementary methods of cohort analysis with several exposure levels this paper proposes an extension of the mantel haenszel rate ratio for the dichotomous exposure to the multiple exposure levels this extension is based on the unbiased estimating function approach and yields closed form mantel haenszel rate ratio estimators dually consistent variance and covariance estimators of the estimating functions are given and a quasi score based confidence interval for individual common rate ratio is provided a similar extension to the common rate difference case is also given

comments on an improved razumikhin type theorem and its applications with reply xu and liu see ibid vol 39 no 4 p 839 41 1994 tried to improve the well known razumikhin theorem on the stability of differential functional equations the commenter states that the proof of their main result contains an error so the results may not be correct in reply bugong xu gives a corrected result

interpretation and estimation of summary ratios under heterogeneity of the several types of summary odds ratios in use in epidemiology only those proposed by mantel and haenszel and miettinen do not assume homogeneity constancy of stratum specific parameters under heterogeneity miettinen s estimators consistently estimate meaningful epidemiologic parameters whereas the asymptotic expectation of the mantel haenszel odds ratio varies according to irrelevant features of the sampling design although one can modify the mantel haenszel summary to overcome the latter problem one can also extend the miettinen estimators to sparse data and thus limit the use of mantel haenszel summaries to situations in which the homogeneity hypothesis is reasonable this paper provides formulae for the extended miettinen estimators and large sample variances and confidence limits for summary ratios under heterogeneity