a fast covariance type algorithm for sequential least squares filtering and prediction fast implementation of sequential least squares ls algorithms is of great importance in various applications of signal processing estimation system identification and control the purpose of this note is the introduction of an efficient sequential ls algorithm for multichannel unwindowed signals covariance case the new scheme in the single channel case requires 10 m madpr multiplications and divisions per recursion m being the number of estimated parameters this offers a saving of 5 m madpr compared to other existing algorithms

transforming random elements and shifting random fields consider a locally compact second countable topological transformation group acting measurably on an arbitrary space we show that the distributions of two random elements x and x in this space agree on invariant sets if and only if there is a random transformation r such that rx has the same distribution as x applying this to random fields in d dimensions under site shifts we show further that these equivalent claims are also equivalent to site average total variation convergence this convergence result extends to amenable groups

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

comparison of the proportions of affected relatives of cases and controls analysis and minimum sample size formula the problem of familial aggregation has frequently been approached by comparing the proportion of affected relatives of index cases with the proportion of affected relatives of index controls this type of study has an analogy with the case control design and is frequently analysed as if it was one it is however an essentially different design which may involve dependent observations we show that conventional tests for comparing proportions of affected subjects are still valid with this design we give a formula for computing the minimum sample size required to detect a given degree of aggregation measured by the intracluster correlation coefficient which can be estimated very simply by the difference in proportions of affected relatives in the two groups

least squares adaptive lattice and transversal filters a unified geometric theory a unified theory is presented to characterize least squares adaptive filters in either lattice or transversal filter form for nonstationary processes the derivations are based upon a geometric formulation of least squares estimation and on the concept of displacement rank a few basic geometric relations are shown to underlie the various algorithms insights into the fundamental concepts that unify lattice and transversal filter approaches to least squares adaptive filters are also given the general results are illustrated by applications to the so called pre windowed and growing memory covariance formulations of the deterministic least squares problem

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

sample size requirements for stratified cluster randomization designs sample size requirements are provided for designs of studies in which clusters are randomized within each of several strata where cluster size itself may be a stratifying factor the approach generalizes a formula derived by woolson et al which provides sample size requirements for the cochran mantel haenszel statistic issues of data analysis are also discussed

the block processing ftf adaptive algorithm a new block type adaptive filtering algorithm is presented this new block adaptive filter differs from the frequency domain block adaptive filters of ferrara 1980 and of clark mitra and parker 1980 in that the new method applies a deterministic time domain least squares criteria within each of the data blocks information is carried from block to block via a weighted initial condition this new block fast transversal filters bftf algorithm is a numerically stable algorithm and can also be used to perform efficient least squares system identification on any one data block in which case it shows a moderate computational advantage over the previous most efficient single data block algorithms of morf et al 1977 of marple 1981 and of kalouptsidis manolakis and carayannis 1984 1985 mechanisms for tracking and varying block length from block to block are also presented and evaluated finally we indicate how the new algorithm could be pipelined for maximum throughput with delay proportional to the number of parameters after computation of the sample correlation lags

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

comparison of different maximum likelihood estimators in a small sample logistic regression with two independent binary variables in order to examine the bias of the estimate of the log odds ratio in a 2 2 contingency table walter computed the entire distribution of the estimated log odds ratio using various small sample sizes this is equivalent to computing the distribution of the estimated parameter b1 in a logistic regression with one independent binary variable in this paper the distributions of the estimated parameters b1 and b2 for two independent binary variables are computed for some small sample logistic regressions using six different estimation methods based on maximum likelihood these estimates are then compared to the true parameter values the best estimation method depends on the frequency of the outcome of interest and on whether the bias or mean square error is considered more important

efficient least squares fir system identification if finite impulse response fir system identification is performed by minimizing the squared error between the measured system output and an estimate from an fir system output a set of least squares normal equations to be solved for the fir system coefficients is obtained if the assumed fir system is of duration m samples the usual solution for the m least squares simultaneous equations requires a number of computational operations proportional to m3and storage of normal equation coefficients proportional to m2 the set of normal equations has an underlying structure however that can be exploited to yield a solution with computational operations proportional to m2and storage proportional to m such an efficient algorithmic solution is presented here

correlated binomial variates properties of estimator of intraclass correlation and its effect on sample size calculation in group randomized studies the sample size calculations are complicated by within group worksite community etc correlation we compare by simulation the moment method and the more standard anova method of estimating the intraclass correlation we find the former is less biased for a small to moderate number of clusters but the difference disappears when the appropriate degree of freedom is used for the anova estimator we propose a simulation approach for sample size determination and illustrate it with an example

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

sample size considerations for stratified cluster randomization design with binary outcomes and varying cluster size stratified cluster randomization trials crts have been frequently employed in clinical and healthcare research comparing with simple randomized crts stratified crts reduce the imbalance of baseline prognostic factors among different intervention groups due to the popularity there has been a growing interest in methodological development on sample size estimation and power analysis for stratified crts however existing work mostly assumes equal cluster size within each stratum and uses multilevel models clusters are often naturally formed with random sizes in crts with varying cluster size commonly used ad hoc approaches ignore the variability in cluster size which may underestimate overestimate the required number of clusters for each group per stratum and lead to underpowered overpowered clinical trials we propose closed form sample size formulas for estimating the required total number of subjects and for estimating the number of clusters for each group per stratum based on cochran mantel haenszel statistic for stratified cluster randomization design with binary outcomes accounting for both clustering and varying cluster size we investigate the impact of various design parameters on the relative change in the required number of clusters for each group per stratum due to varying cluster size simulation studies are conducted to evaluate the finite sample performance of the proposed sample size method a real application example of a pragmatic stratified crt of a triad of chronic kidney disease diabetes and hypertension is presented for illustration

estimation of a common odds ratio in paired cluster randomization designs we develop two estimators of a common odds ratio for designs in which the investigator randomly assigns each of two clusters to interventions within strata the estimators rely on an empirical adjustment for clustering to provide improved estimators of relative to the standard woolf and mantel haenszel estimators respectively the results of a simulation study show that the suggested adjustment improves the accuracy of both of these well known estimators under conditions likely to arise in practice we find the clustered woolf estimator as particularly effective in terms of mean squared error reduction we also discuss interval estimation

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

bayesian methods of analysis for cluster randomized trials with binary outcome data we explore the potential of bayesian hierarchical modelling for the analysis of cluster randomized trials with binary outcome data and apply the methods to a trial randomized by general practice an approximate relationship is derived between the intracluster correlation coefficient icc and the between cluster variance used in a hierarchical logistic regression model by constructing an informative prior for the icc on the basis of available information we are thus able implicitly to specify an informative prior for the between cluster variance the approach also provides us with a credible interval for the icc for binary outcome data several approaches to constructing informative priors from empirical icc values are described we investigate the sensitivity of results to the prior specified and find that the estimate of intervention effect changes very little in this data set while its interval estimate is more sensitive the bayesian approach allows us to assume distributions other than normality for the random effects used to model the clustering this enables us to gain insight into the robustness of our parameter estimates to the classical normality assumption in a model with a more complex variance structure bayesian methods can provide credible intervals for a difference between two variance components in order for example to investigate whether the effect of intervention varies across clusters we compare our results with those obtained from classical estimation discuss the relative merits of the bayesian framework and conclude that the flexibility of the bayesian approach offers some substantial advantages although selection of prior distributions is not straightforward

sample size and power for mcnemar s test with clustered data mcnemar s test is used to compare the distribution of two paired binary random variables when the data are clustered adjustment is needed to ensure that it is still a valid test this article presents two approximations for calculating the power and sample size for the adjusted mcnemar s test for clustered data working with a particular adjustment a simulation study is conducted to demonstrate the accuracy of these approximations the method is also applied to the design of a study involving positron emission tomography in detecting metastatic colorectal cancer and sensitivity of sample size computations to the design parameters are explored in this context

symmetric exclusion on random sets and a related problem for random walks in random environment we study symmetric exclusion on a random set where the underlying kernelp x y is strictly positive the random set is generated by bernoulli experiments with success probabilityq

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

a new unwindowed lattice filter for rls estimation adaptive lattice algorithms are derived for the solution of unwindowed least squares estimation problems for ar and fir models the basic approach is to embed the unwindowed problem in a larger prewindowed problem and then eliminate superfluous terms in the lattice initializations are given to allow the lattice to use no initial parameter estimates or to include initial parameter estimates with desired weightings in the quadratic criterion for parameter estimation a numerical example is given

beta binomial model for meta analysis of odds ratios in meta analysis of odds ratios ors heterogeneity between the studies is usually modelled via the additive random effects model rem an alternative multiplicative rem for ors uses overdispersion the multiplicative factor in this overdispersion model odm can be interpreted as an intra class correlation icc parameter this model naturally arises when the probabilities of an event in one or both arms of a comparative study are themselves beta distributed resulting in beta binomial distributions we propose two new estimators of the icc for meta analysis in this setting one is based on the inverted breslow day test and the other on the improved gamma approximation by kulinskaya and dollinger 2015 p 26 to the distribution of cochran s q the performance of these and several other estimators of icc on bias and coverage is studied by simulation additionally the mantel haenszel approach to estimation of ors is extended to the beta binomial model and we study performance of various icc estimators when used in the mantel haenszel or the inverse variance method to combine ors in meta analysis the results of the simulations show that the improved gamma based estimator of icc is superior for small sample sizes and the breslow day based estimator is the best for n 100 the mantel haenszel based estimator of or is very biased and is not recommended the inverse variance approach is also somewhat biased for ors 1 but this bias is not very large in practical settings developed methods and r programs provided in the web appendix make the beta binomial model a feasible alternative to the standard rem for meta analysis of ors 2017 the authors statistics in medicine published by john wiley sons ltd

a condition for the equivalence of coupling and shift coupling it is proved in this paper that a weak parabolic harnack inequality for a markov semigroup implies the existence of a coupling and a shift coupling for the corresponding process with equal chances of success this implies equality of the tail and invariant sigma fields for the diffusion as well as equality of the class of bounded parabolic functions and the class of bounded harmonic functions

estimation of a common odds ratio under binary cluster sampling we present results from a simulation study for the estimation of a common odds ratio in multiple 2 x 2 tables when the data are correlated within clusters we model the correlation of the data by the beta binomial distribution through a simulation study we compare the mantel haenszel estimator with rao and scott s estimator in terms of their biases observed variances relative efficiencies of their variances and 95 per cent coverage proportions we limit the simulation study to the case where there are the same number of subjects in each cluster and the same number of observations in each row of each stratum when rho 0 we recommend use of the mantel haenszel estimator gamma mh with an unadjusted variance and rao and scott s estimator gamma rsp with a pooled design effect in general when rho 0 we recommend the mantel haenszel estimator gamma mh with an adjusted variance and rao and scott s estimator gamma rsp with a pooled design effect

on the identification of systems from data measurements using arma lattice models methods for the autoregressive moving average arma modeling of digital systems using a two channel autoregressive ar lattice are presented one method has the advantage that one half of the lattice parameters are zero when the system s excitation signal is white noise

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

couplings of markov chains by randomized stopping times we consider a markov chain on e generated by a markov kernel p we study the question when we can find for two initial distributions and two randomized stopping times t of x n n n and s of x n n n such that the distribution of x t equals the one of x s and t s are both finite

an unwindowed multichannel lattice filter with orthogonal channels an unwindowed or covariance multichannel lattice filter for recursive least squares estimation is derived the channels are orthogonalized to eliminate the need for matrix inversion the channel orthogonalization process leads to forward propagating and backward propagating blocks in both the lattice filter and the model parameter construction algorithm these blocks are particularly suitable for array processing as illustrated by arrays presented in the paper

shift coupling in continuous time the result linking shift coupling to time average total variation convergence and to the invariant field is extended to continuous time and an analogous result established linking e couplings to smooth total variation convergence and to a smooth tail field shift and e coupling inequalities are presented

efficient recursive in order least squares fir filtering and prediction this paper is concerned with the efficient determination of the optimum in the least squares sense fir filter on the basis of data samples of the input and desired response signals by procedures recursive in the filter order this situation typically arises when no a priori statistics are available and the system order is not known the general multiinput multioutput multichannel case is considered here and a fast algorithm is presented requiring for single channel signals approximately 2s 15m multiplications mps per order m s being the number of samples in the special case of linear prediction it calls for about s 12m mps hence it offers a computational reduction of 5m and 2m mps in comparison to the methods of marple 1 and morf et al 2 respectively additionally the proposed scheme is inherently symmetric and is suited very well to initialization of fast sequential algorithms as well as algorithms searching for the optimum lag filter

an order downdating algorithm for tracking system order and parameters in recursive least squares identification a new time and order recursive method for on line tracking of system order and parameters using recursive least squares rls is presented the method consists of two parts a time updating portion that uses existing rls inverse qr decomposition algorithms and a new computationally efficient order downdating portion that calculates the model parameters and residual error energies for an entire set of models with order varying from one to some prespecified maximum model order

estimating the number of clusters for the analysis of correlated binary response variables from unbalanced data dominating the literature on sample size determination are papers concerned with observations collected from independent responses we discuss in this paper under the common correlation model for binary responses the issue of estimating the number of groups when the sampling units are clusters of variable sizes

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

square root covariance ladder algorithms square root normalized ladder algorithms provide an efficient recursive solution to the problem of multichannel autoregressive model fitting a simplified derivation of the general update formulas for such ladder forms is presented and is used to develop the growing memory and sliding memory covariance ladder algorithms new ladder form realizations for the identified models are presented leading to convenient methods for computing the model parameters from estimated reflection coefficients a complete solution to the problem of possible singularity in the ladder update equations is also presented

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

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

intraclass correlation coefficients and bootstrap methods of hierarchical binary outcomes intraclass correlation coefficients are designed to assess consistency or conformity between two or more quantitative measurements when multistage cluster sampling is implemented no methods are readily available to estimate intraclass correlations of binomial distributed outcomes within a cluster because statistical distribution of the intraclass correlation coefficients could be complicated or unspecified we propose using a bootstrap method to estimate the standard error and confidence interval within the framework of a multilevel generalized linear model we compared the results derived from a parametric bootstrap method with those from a non parametric bootstrap method and found that the non parametric method is more robust for non parametric bootstrap sampling we showed that the effectiveness of sampling on the highest level is greater than that on lower levels to illustrate the effectiveness we analyse survey data in china and do simulation studies

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

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

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

finite sample properties of some old and some new estimators of a common odds ratio from multiple 2 2 tables abstract a simulation study was used to determine the finite sample properties of various estimators of a common odds ratio from multiple 2 2 tables the maximum likelihood mantel haenszel and woolf estimators plus four variants of each were considered the original woolf estimator and one of its variants are dismissed on the grounds that they often cannot be calculated in terms of minimum bias maximum likelihood is the recommended procedure after adding 25 to each cell

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

fast recursive least squares transversal filters for adaptive filtering fast transversal filter ftf implementations of recursive least squares rls adaptive filtering algorithms are presented in this paper substantial improvements in transient behavior in comparison to stochastic gradient or lms adaptive algorithms are efficiently achieved by the presented algorithms the true not approximate solution of the rls problem is always obtained by the ftf algorithms even during the critical initialization period first n iterations of the adaptive filter this true solution is recursively calculated at a relatively modest increase in computational requirements in comparison to stochastic gradient algorithms factor of 1 6 to 3 5 depending upon application additionally the fast transversal filter algorithms are shown to offer substantial reductions in computational requirements relative to existing fast rls algorithms such as the fast kalman algorithms of morf ljung and falconer 1976 and the fast ladder lattice algorithms of morf and lee 1977 1981 they are further shown to attain steady state unnormalized or improve upon first n initialization steps the very low computational requirements of the efficient rls solutions of carayannis manolakis and kalouptsidis 1983 finally several efficient procedures are presented by which to ensure the numerical stability of the transversal filter algorithms including the incorporation of soft constraints into the performance criteria internal bounding and rescuing procedures and dynamic range increasing square root normalized variations of the transversal filters

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

jonction maximale en distribution dans le cas markovien une representation des sousmartingales retournees est utilisee pour etablir que le moment de jonction maximale en distribution peut etre choisi comme un temps d arret randomise pour les chaines de markov non homogenes de memes probabilites et de distributions initiales differentes en outre nous illustrons a partir d un exemple la non unicite de la jonction maximale en distribution et ceci malgre des conditions supplementaires

application of the mcnemar test to non independent matched pair data mcnemar s one degree of freedom chi square test for the equality of proportions appears frequently in the analysis of pairs of matched binary outcome data y1i y2i an assumption underlying this test is that the responses from pair to pair are mutually independent in certain applications however the pairs may represent repeated measurements on the same experimental unit and hence this assumption is violated in this paper we suggest an adjustment to the mcnemar test to account for the repeated measures clustering effect and we report on a monte carlo simulation that evaluates the effectiveness of this approach

adjustments to the mantel haenszel test for data from stratified multistage surveys the usual form of the mantel haenszel test statistic assumes independent observations this is inappropriate for data from a stratified multistage survey two alternative adjustments to the test statistic are developed to deal with this a a modification of the effective sample size for each row of each table using the design effects extending a method proposed by donald and donner for familial aggregation studies b a taylor series approximation to the variance of the square root of the numerator of the mantel haenszel statistic both methods are evaluated by application to both simulated and real data the two methods perform equally well and offer a considerable improvement over the unadjusted test statistic when observations from the same cluster are highly correlated a simplified adjustment is also considered as is the need for correction to the variance of the odds ratio estimator

a simple method for the analysis of clustered binary data a simple method for comparing independent groups of clustered binary data with group specific covariates is proposed it is based on the concepts of design effect and effective sample size widely used in sample surveys and assumes no specific models for the intracluster correlations it can be implemented using any standard computer program for the analysis of independent binary data after a small amount of preprocessing the method is applied to a variety of problems involving clustered binary data testing homogeneity of proportions estimating dose response models and testing for trend in proportions and performing the mantel haenszel chi squared test for independence in a series of 2 x 2 tables and estimating the common odds ratio and its variance illustrative applications of the method are also presented

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

a class of least squares filtering and identification algorithms with systolic array architectures a unified approach is presented for deriving a large class of new and previously known time and order recursive least squares algorithms with systolic array architectures suitable for high throughput rate and vlsi implementations of space time filtering and system identification problems the geometrical derivation given is unique in that no assumption is made concerning the rank of the sample data correlation matrix this method utilizes and extends the concept of oblique projections as used previously in the derivations of the least squares lattice algorithms both the growing and sliding memory exponentially weighted least squares criteria are considered

normalized lattice algorithms for least squares fir system identification recently developed algorithms for least squares identification of autoregressive models are extended in this paper so as to facilitate least squares identification of finite impulse response models the algorithms belong to the class of square root normalized lattice algorithms hence they share the computational efficiency and good numerical behavior of the latter two versions are presented one for identifying time invariant models and the other for tracking time varying parameters new lattice form realizations of the identified fir models are given the general framework is then specialized to the important cases of prediction and smoothing

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

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

score test for familial aggregation in probands studies application to alzheimer s disease when studying familial aggregation of a disease the following two stage design is often used first select index subjects cases and controls then record data on their relatives the likelihood corresponding to this design is derived and a score test of homogeneity is proposed for testing the hypothesis of no aggregation this test takes into account the selection procedure and allows adjustment to be made for explanatory variables it appears as the sum of three terms a pure test of homogeneity a test of comparison of observed minus expected cases in the two groups and a term which adjusts for the possible unequal probabilities of disease of the index subjects asymptotic efficiency and a simulation study show that the proposed test is superior to either the pure homogeneity test or tests based on the comparison of numbers of affected in the two groups the test statistic which has an asymptotically standard normal distribution is applied to a study of familial aggregation of early onset alzheimer s disease for which a highly significant value 9 46 is obtained this is the highest value among the three tests compared in agreement with the simulation study a logistic normal model is fitted to the data taking account of the selection procedure it allows to estimate the regression parameters and the variance of the random effect the likelihood ratio test for familial aggregation seems less powerful than the score test

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

the intraclass correlation coefficient distribution free definition and test a definition of the intraclass correlation coefficient is given on the basis of a general class of random effect model the conventional intraclass correlation coefficient and the intracluster correlation coefficient for binary data are both particular cases of the generalized coefficient we derive the score test for the hypothesis of null intraclass correlation in the exponential family the statistic does not depend on the particular distribution in this family and is related to the pairwise correlation coefficient the test can be adjusted for explanatory variables