robust estimation of the variance in moment methods for extra binomial and extra poisson variation when faced with data in the form of overdispersed counts or proportions moment methods allow consistent parameter estimation when only the form of the mean and variance is specified if the variance form is misspecified these methods still yield consistent parameter estimates though with lower efficiency and the variances of the estimates will be inconsistent a variance correction is available that yields consistent variance estimates in these circumstances the asymptotic and small sample efficiencies of this correction are calculated and its performance under variance misspecification is studied a group randomized breast self examination prevention study that is now underway serves as a focal point for the study of these properties the use of the variance correction in modelling is illustrated on a teratology data set

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

bootstrap j tests of nonnested linear regression models the j test for nonnested regression models often overrejects very severely as an asymptotic test we provide a theoretical analysis which explains why and when it performs badly this analysis implies that except in certain extreme cases the j test will perform very well when bootstrapped using several methods to speed up the simulations we obtain extremely accurate monte carlo results on the finite sample performance of the bootstrapped j test these results fully support the predictions of our theoretical analysis even in contexts where the analysis is not strictly applicable

a simple test for regression specification with non nested alternatives abstract in this paper i introduce a simple test for the presence of the data generating process among several non nested alternatives the test is an extension of the classical j test for non nested regression models i also provide a bootstrap version of the test that avoids possible size distortions inherited from the j test

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

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

sample size estimation for stratified individual and cluster randomized trials with binary outcomes individual randomized trials irts and cluster randomized trials crts with binary outcomes arise in a variety of settings and are often analyzed by logistic regression fitted using generalized estimating equations for crts the effect of stratification on the required sample size is less well understood for trials with binary outcomes than for continuous outcomes we propose easy to use methods for sample size estimation for stratified irts and crts and demonstrate the use of these methods for a tuberculosis prevention crt currently being planned for both irts and crts we also identify the ratio of the sample size for a stratified trial vs a comparably powered unstratified trial allowing investigators to evaluate how stratification will affect the required sample size when planning a trial for crts these can be used when the investigator has estimates of the within stratum intracluster correlation coefficients iccs or by assuming a common within stratum icc using these methods we describe scenarios where stratification may have a practically important impact on the required sample size we find that in the two stratum case for both irts and for crts with very small cluster sizes there are unlikely to be plausible scenarios in which an important sample size reduction is achieved when the overall probability of a subject experiencing the event of interest is low when the probability of events is not small or when cluster sizes are large however there are scenarios where practically important reductions in sample size result from stratification

a comparison of confidence interval methods for the intraclass correlation coefficient in cluster randomized trials a correction has been published for this article in statistics in medicine 23 18 2004 2935 this study compared different methods for assigning confidence intervals to the analysis of variance estimator of the intraclass correlation coefficient the context of the comparison was the use of to estimate the variance inflation factor when planning cluster randomized trials the methods were compared using monte carlo simulations of unbalanced clustered data and data from a cluster randomized trial of an intervention to improve the management of asthma in a general practice setting the coverage and precision of the intervals were compared for data with different numbers of clusters mean numbers of subjects per cluster and underlying values of the performance of the methods was also compared for data with normal and non normally distributed cluster specific effects results of the simulations showed that methods based upon the variance ratio statistic provided greater coverage levels than those based upon large sample approximations to the standard error of searle s method provided close to nominal coverage for data with normally distributed random effects adjusted versions of searle s method to allow for lack of balance in the data generally did not improve upon it either in terms of coverage or precision analyses of the trial data however showed that limits provided by thomas and hultquist s method may differ from those of the other variance ratio statistic methods when the arithmetic mean differs markedly from the harmonic mean cluster size the simulation results demonstrated that marked non normality in the cluster level random effects compromised the performance of all methods confidence intervals for the methods were generally wide relative to the underlying size of suggesting that there may be great uncertainty associated with sample size calculations for cluster trials where large clusters are randomized data from cluster based studies with sample sizes much larger than those typical of cluster randomized trials are required to estimate with a reasonable degree of precision copyright 2002 john wiley sons ltd

sample size requirements for reliability studies this paper provides exact power contours to guide the planning of reliability studies where the parameter of interest is the coefficient of intraclass correlation rho derived from a one way analysis of variance model the contours display the required numbers of subjects k and number of repeated measurements n that provide 80 per cent power for testing ho rho less than or equal to rho 0 versus h1 rho greater than rho 0 at the 5 per cent level of significance for selected values of rho o we discuss the design considerations of these results

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

testing the effect of treatment in experiments with correlated binary outcomes this paper considers the problem of testing for treatment effect in a randomized experiment with correlated binary outcomes representing success or failure for different parts of a randomized unit attention is restricted to tests that are based on a summary score for each individual randomized and thus are valid regardless of the precise nature of the correlation among parts the focus is on the efficiency of such tests under various correlation structures with special emphasis on the case in which the correlation among parts within an individual differs across treatment groups a class of summary score statistics is defined and optimal testing is discussed for some simple situations three potential general purpose tests also are described 1 the ratio estimate test discussed by henderson et al 1988 controlled clinical trials 9 189 205 2 a modified ratio estimate test with adjusted weighting based on the within individual correlation between parts 3 a test defined by applying the mantel haenszel procedure to the proportion of individuals with at least one failure stratifying by the number of parts for these general purpose tests numerical calculations of asymptotic efficiency are presented under a wide range of designs and correlation structures on the basis of these results some practical recommendations for choosing a test are made

sample size determination for hierarchical longitudinal designs with differential attrition rates we consider the problem of sample size determination for three level mixed effects linear regression models for the analysis of clustered longitudinal data three level designs are used in many areas but in particular multicenter randomized longitudinal clinical trials in medical or health related research in this case level 1 represents measurement occasion level 2 represents subject and level 3 represents center the model we consider involves random effects of the time trends at both the subject level and the center level in the most common case we have two random effects constant and a single trend at both subject and center levels the approach presented here is general with respect to sampling proportions number of groups and attrition rates over time in addition we also develop a cost model as an aid in selecting the most parsimonious of several possible competing models i e different combinations of centers subjects within centers and measurement occasions we derive sample size requirements i e power characteristics for a test of treatment by time interaction s for designs based on either subject level or cluster level randomization the general methodology is illustrated using two characteristic examples

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

small sample performance of bias corrected sandwich estimators for cluster randomized trials with binary outcomes the sandwich estimator in generalized estimating equations gee approach underestimates the true variance in small samples and consequently results in inflated type i error rates in hypothesis testing this fact limits the application of the gee in cluster randomized trials crts with few clusters under various crt scenarios with correlated binary outcomes we evaluate the small sample properties of the gee wald tests using bias corrected sandwich estimators our results suggest that the gee wald z test should be avoided in the analyses of crts with few clusters even when bias corrected sandwich estimators are used with t distribution approximation the kauermann and carroll kc correction can keep the test size to nominal levels even when the number of clusters is as low as 10 and is robust to the moderate variation of the cluster sizes however in cases with large variations in cluster sizes the fay and graubard fg correction should be used instead furthermore we derive a formula to calculate the power and minimum total number of clusters one needs using the t test and kc correction for the crts with binary outcomes the power levels as predicted by the proposed formula agree well with the empirical powers from the simulations the proposed methods are illustrated using real crt data we conclude that with appropriate control of type i error rates under small sample sizes we recommend the use of gee approach in crts with binary outcomes because of fewer assumptions and robustness to the misspecification of the covariance structure copyright 2014 john wiley sons ltd

power analyses for longitudinal study designs with missing data existing methods for power analysis for longitudinal study designs are limited in that they do not adequately address random missing data patterns although the pattern of missing data can be assessed during data analysis it is unknown during the design phase of a study the random nature of the missing data pattern adds another layer of complexity in addressing missing data for power analysis in this paper we model the occurrence of missing data with a two state first order markov process and integrate the modelling information into the power function to account for random missing data patterns the markov model is easily specified to accommodate different anticipated missing data processes we develop this approach for the two most popular longitudinal models the generalized estimating equations gee and the linear mixed effects model under the missing completely at random mcar assumption for gee we also limit our consideration to the working independence correlation model the proposed methodology is illustrated with numerous examples that are motivated by real study designs

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 formulae for intervention studies with the cluster as unit of randomization this paper presents sample size formulae for both continuous and dichotomous endpoints obtained from intervention studies that use the cluster as the unit of randomization the formulae provide the required number of clusters or the required number of individuals per cluster when the other number is given the proposed formulae derive from student s t test with use of cluster summary measures and a variance that consists of within and between cluster components power contours are provided to help in the design of intervention studies that use cluster randomization sample size formulae for designs with and without stratification of clusters appear separately

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

on the user selection for mimo broadcast channels in this paper a downlink communication system in which a base station bs equipped with antennas communicates with users each equipped with receive antennas is considered an efficient suboptimum algorithm is proposed for selecting a set of users in order to maximize the sum rate throughput of the system in a rayleigh fading environment for the asymptotic case when tends to infinity the necessary and sufficient conditions in order to achieve the maximum sum rate throughput such that the difference between the achievable sum rate and the maximum value approaches zero is derived the complexity of our algorithm is investigated in terms of the required amount of feedback from the users to the bs as well as the number of searches required for selecting the users it is shown that the proposed method is capable of achieving a large portion of the sum rate capacity with a very low complexity

far field multicast beamforming for uniform linear antenna arrays the problem of transmit beamforming to multiple cochannel multicast groups is considered for the important special case when the channel vectors are vandermonde this arises when a uniform linear antenna antenna ula array is used at the transmitter under far field line of sight propagation conditions as provisioned in 802 16e and related wireless backhaul scenarios two design approaches are pursued i minimizing the total transmitted power subject to providing at least a prescribed received signal to interference plus noise ratio sinr to each intended receiver and ii maximizing the minimum received sinr under a total transmit power budget whereas these problems have been recently shown to be np hard in general it is proven here that for vandermonde channel vectors it is possible to recast the optimization in terms of the autocorrelation sequences of the sought beam vectors yielding an equivalent convex reformulation this affords efficient optimal solution using modern interior point methods the optimal beam vectors can then be recovered using spectral factorization robust extensions for the case of partial channel state information where the direction of each receiver is known to lie in an interval are also developed interestingly these also admit convex reformulation the various optimal designs are illustrated and contrasted in a suite of pertinent numerical experiments

an efficient global algorithm for single group multicast beamforming consider the single group multicast beamforming problem where multiple users receive the same data stream simultaneously from a single transmitter the problem is np hard and all existing algorithms for the problem either find suboptimal approximate or local stationary solutions in this paper we propose an efficient branch and bound algorithm for the problem that is guaranteed to find its global solution to the best of our knowledge our proposed algorithm is the first tailored global algorithm for the single group multicast beamforming problem simulation results show that our proposed algorithm is computationally efficient albeit its theoretical worst case iteration complexity is exponential with respect to the number of receivers and it significantly outperforms a state of the art general purpose global optimization solver called baron our proposed algorithm provides an important benchmark for performance evaluation of existing algorithms for the same problem by using it as the benchmark we show that two state of the art algorithms semidefinite relaxation algorithm and successive linear approximation algorithm work well when the problem dimension i e the number of antennas at the transmitter and the number of receivers is small but their performance deteriorates quickly as the problem dimension increases

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

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

precoder design for physical layer multicasting this paper studies the instantaneous rate maximization and the weighted sum delay minimization problems over a k user multicast channel where multiple antennas are available at the transmitter as well as at all the receivers motivated by the degree of freedom optimality and the simplicity offered by linear precoding schemes we consider the design of linear precoders using the aforementioned two criteria we first consider the scenario wherein the linear precoder can be any complex valued matrix subject to rank and power constraints we propose cyclic alternating ascent based precoder design algorithms and establish their convergence to respective stationary points simulation results reveal that our proposed algorithms considerably outperform known competing solutions we then consider a scenario in which the linear precoder can be formed by selecting and concatenating precoders from a given finite codebook of precoding matrices subject to rank and power constraints we show that under this scenario the instantaneous rate maximization problem is equivalent to a robust submodular maximization problem which is strongly np hard we propose a deterministic approximation algorithm and show that it yields a bicriteria approximation for the weighted sum delay minimization problem we propose a simple deterministic greedy algorithm which at each step entails approximately maximizing a submodular set function subject to multiple knapsack constraints and establish its performance guarantee

estimating intraclass correlation for binary data summary this paper reviews many different estimators of intraclass correlation that have been proposed for binary data and compares them in an extensive simulation study some of the estimators are very specific while others result from general methods such as pseudo likelihood and extended quasi likelihood estimation the simulation study identifies several useful estimators one of which does not seem to have been considered previously for binary data estimators based on extended quasi likelihood are found to have a substantial bias in some circumstances

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 comparison of generalized linear mixed model procedures with estimating equations for variance and covariance parameter estimation in longitudinal studies and group randomized trials response data in longitudinal studies and group randomized trials are gathered on units that belong to clusters within which data are usually positively correlated therefore estimates and confidence intervals for intraclass correlation or variance components are helpful when designing a longitudinal study or group randomized trial data simulated from both study designs are used to investigate the estimation of variance and covariance parameters from the following procedures for continuous outcomes restricted maximum likelihood reml and estimating equations ee for binary outcomes restricted pseudo likelihood repl and estimating equations ee we evaluate these procedures to see which provide valid and precise estimates as well as correct standard errors for the intraclass correlation coefficient or variance components reml seems the better choice for estimating terms related to correlation for models with normal outcomes especially in group randomized trial situations results for reml and ee are mixed when outcomes are continuous and non normal with binary outcomes neither repl nor ee provides satisfactory estimation or inference in longitudinal study situations while repl is preferable for group randomized trials

non parametric bootstrap confidence intervals for the intraclass correlation coefficient the intraclass correlation coefficient rho plays a key role in the design of cluster randomized trials estimates of rho obtained from previous cluster trials and used to inform sample size calculation in planned trials may be imprecise due to the typically small numbers of clusters in such studies it may be useful to quantify this imprecision this study used simulation to compare different methods for assigning bootstrap confidence intervals to rho for continuous outcomes from a balanced design data were simulated for combinations of numbers of clusters 10 30 50 intraclass correlation coefficients 0 001 0 01 0 05 0 3 and outcome distributions normal non normal continuous the basic bootstrap t percentile bias corrected and bias corrected accelerated bootstrap intervals were compared with new methods using the basic and bootstrap t intervals applied to a variance stabilizing transformation of rho the standard bootstrap methods provided coverage levels for 95 per cent intervals that were markedly lower than the nominal level for data sets with only 10 clusters and only provided close to 95 per cent coverage when there were 50 clusters application of the bootstrap t method to the variance stabilizing transformation of rho improved upon the performance of the standard bootstrap methods providing close to nominal coverage

logistic regression for dependent binary observations summary the likelihood of a set of binary dependent outcomes with or without explanatory variables is expressed as a product of conditional probabilities each of which is assumed to be logistic the models are called regressive logistic models they provide a simple but relatively unknown parametrization of the multivariate distribution they have the theoretical and practical advantage that they can be analyzed and fitted as in logistic regression for independent outcomes and with the same computer programs the paper is largely expository and is intended to motivate the development and usage of the regressive logistic models the discussion includes serially dependent outcomes equally predictive outcomes more specialized patterns of dependence multidimensional tables and three examples this paper seeks to promote the development and usage of a simple but relatively unknown approach to the specification of models for dependent binary outcomes that are useful in situations where it is apt to describe the dependence in terms of conditional probabilities the joint probability is decomposed into a product of successive conditional probabilities each of which is assumed to be univariate logistic since the probability of an observation is conditioned on all preceding observations the models will be referred to as regressive logistic models two broad situations are distinguished in this paper the first concerning sequences of binary outcomes possibly with measures on associated explanatory variables can usually be supported by simple patterns of dependence these will be discussed in sections 2 5 the second broad situation concerns dependent binary outcomes crossclassified into multidimensional tables that admit a fuller parametrization this is discussed in section 6 for all the regressive logistic models discussed here the parametrization is such that jointly dependent binary observations with or without explanatory variables can be fitted with existing computer programs for the standard logistic regression for independent observations some of the possibilities of the approach are illustrated with real data in section 8

estimation of the design effect in community intervention studies this paper considers the estimation of the variance of a mortality rate in community intervention studies with little or no replication of intervention regimens our approach in estimation of this cluster sampling variance is to determine the variance for simple random sampling and multiply it by a design effect which we calculate with use of information obtained from other sources when the county is the unit of randomization and the outcome is mortality we calculate the design effect as the ratio of the age adjusted mortality rates for single stage cluster sampling relative to simple random sampling we use information from all counties in a state in the calculations we apply this approach empirically for breast cancer mortality we found that these design effects were dependent on length of time for accumulation of deaths 1 1 for one year up to 3 5 for eight years and were quite consistent for the three states and nine years considered in the investigation we present a model that accounts for the time dependence of the design effect and we show it provides a good representation of the observed relationship

optimal and successive approaches to signal design for multiple antenna physical layer multicasting in modern wireless communications systems that send a common information stream called multicasting systems are widely needed for distributing content such as television or radio in this paper the multiple antenna physical layer multicasting channel is considered in which a common message is simultaneously transmitted to multiple single antenna users to achieve the capacity of this multicasting set up the covariance matrix of the transmit signal vector needs to be determined to maximize the smallest maximum achievable rate among all the users in this paper we develop a simple successive algorithm to determine the covariance matrix of the signal vector under the assumption that channel state information csi is perfectly available at the transmitter we first characterize properties of the capacity achieving covariance matrix and derive a closed form expression for the matrix in the two user case we then derive a closed form expression for the rate maximizing beamformer in the case of two users and propose a successive beamforming algorithm that generates the beamforming vector with low computational complexity in the proposed precoding design scheme the covariance matrix is successively constructed by orthogonalizing the subspace spanned by each user s channel vector until the maximum number of recursions which is the same as the minimum of the number of transmit antennas and the number of users is reached the achievable rate of the proposed scheme is compared with the capacity of optimal transmission transmit beamforming antenna subset selection and open loop transmission which does not require csi at the transmitter as the number of users and or antennas grows large it is shown that the average achievable rate of the proposed scheme achieves the same average achievable rate scaling as the true capacity while reducing the computational complexity

two sample comparison for large groups of correlated binary responses although there is much literature on testing the treatment effect in experiments with correlated binary outcomes the existing methodologies only work well when the cluster size is small in this paper i propose a simple method to test the treatment effect in experiments with large groups of correlated binary outcomes i use the weighted estimating equations approach to estimate the treatment effect the proposal is appropriate under any correlation structure power comparisons show the advantage of the new procedure

exact permutation tests for non nested non linear regression models abstract this paper proposes exact distribution free permutation tests for the specification of a non linear regression model against one or more possibly non nested alternatives the new tests may be validly applied to a wide class of models including models with endogenous regressors and lag structures these tests build on the well known j test developed by davidson and mackinnon 1981 several tests for model specification in the presence of alternative hypotheses econometrica 49 781 793 and their exactness holds under broader assumptions than those underlying the conventional j test the j type test statistics are used with a randomization or monte carlo resampling technique which yields an exact and computationally inexpensive inference procedure a simulation experiment confirms the theoretical results and also shows the performance of the new procedure under violations of the maintained assumptions the test procedure developed is illustrated by an application to inflation dynamics

incorporation of clustering effects for the wilcoxon rank sum test a large sample approach the wilcoxon rank sum test is frequently used in statistical practice for the comparison of measures of location when the underlying distributions are far from normal or not known in advance an assumption of the ordinary rank sum test is that individual sampling units are independent in many ophthalmologic clinical trials the early treatment for diabetic retinopathy scale etdrs is a principal endpoint used for measuring the level of diabetic retinopathy this is an ordinal scale and it is natural to consider the wilcoxon rank sum test for the comparison of the level of diabetic retinopathy between treatment groups however under this design unlike the usual wilcoxon rank sum test the subject is the unit of randomization but the eye is the unit of analysis furthermore a person will tend to have different but correlated etdrs scores for fellow eyes thus we propose a correction to the variance of the wilcoxon rank sum statistic that accounts for clustering effects and that can be used for both balanced same number of subunits per cluster or unbalanced different number of subunits per cluster data both in the presence or absence of ties with p value adjusted accordingly in this article we present large sample theory and simulation results for this test procedure and apply it to diabetic retinopathy data from type i diabetics in the sorbinil retinopathy trial

sample size calculations for clustered binary data in this paper we propose a sample size calculation method for testing on a binomial proportion when binary observations are dependent within clusters in estimating the binomial proportion in clustered binary data two weighting systems have been popular equal weights to clusters and equal weights to units within clusters when the number of units varies cluster by cluster performance of these two weighting systems depends on the extent of correlation among units within each cluster in addition to them we will also use an optimal weighting method that minimizes the variance of the estimator a sample size formula is derived for each of the estimators with different weighting schemes we apply these methods to the sample size calculation for the sensitivity of a periodontal diagnostic test simulation studies are conducted to evaluate a finite sample performance of the three estimators we also assess the influence of misspecified input parameter values on the calculated sample size the optimal estimator requires equal or smaller sample sizes and is more robust to the misspecification of an input parameter than those assigning equal weights to units or clusters

power and sample size for a collection of 2 x 2 tables a simple approximation is presented for the asymptotic power of the mantel haenszel procedure for testing the hypothesis that the common odds ratio in a collection of 2 x 2 tables is unity this approximation is particularly useful in evaluating the power of a study with several strata which reaches negative conclusions the corresponding formula is also provided for estimating the sample size before such a study has begun by approximating the margins of the stratum specific tables with estimates obtained from pre existing data the approximations are good for moderate odds ratios not greater than 6 and provide estimates which can differ by 10 to 30 from the traditional power estimates based on the overall table of totals obtained by collapsing the stratum specific subtables

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

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

bootstrap based critical values for the information matrix test abstract in finite samples the true size of white s information matrix test often differs greatly from its nominal size based on asymptotic critical values this paper shows how the bootstrap can be used to obtain improved finite sample critical values the results of monte carlo experiments show that for the cases investigated the bootstrap largely eliminates the problem of incorrect finite sample size moreover when size corrected critical values are used forms of the test that have small size distortions with asymptotic critical values can have much lower power than forms that have large size distortions with asymptotic critical values

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

a simple sample size formula for analysis of covariance in cluster randomized trials for cluster randomized trials with a continuous outcome the sample size is often calculated as if an analysis of the outcomes at the end of the treatment period follow up scores would be performed however often a baseline measurement of the outcome is available or feasible to obtain an analysis of covariance ancova using both the baseline and follow up score of the outcome will then have more power we calculate the efficiency of an ancova analysis using the baseline scores compared with an analysis on follow up scores only the sample size for such an ancova analysis is a factor r 2 smaller where r is the correlation of the cluster means between baseline and follow up this correlation can be expressed in clinically interpretable parameters the correlation between baseline and follow up of subjects subject autocorrelation and that of clusters cluster autocorrelation because of this subject matter knowledge can be used to provide range of plausible values for these correlations when estimates from previous studies are lacking depending on how large the subject and cluster autocorrelations are analysis of covariance can substantially reduce the number of clusters needed copyright c 2012 john wiley sons ltd

tests of non nested regression models small sample adjustments and monte carlo evidence abstract it is known that the small sample significance levels of cox type tests of non nested regression models can be much greater than the nominal level adjustments designed to overcome this problem are discussed and two tests are proposed monte carlo evidence on the performance of the tests derived in this paper the davidson mackinnon j test and the fisher mcaleer test is presented the f test applied to the comprehensive model is also included in the simulation experiments

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

sample size for case control studies using cochran s statistic sample size determination for case control studies of chronic disease are often based on the simple 2 x 2 tabular cross classification of exposure and disease thereby ignoring stratification which may be considered in the analysis one consequence of this approach is that the sample size may be inadequate to attain a specified power and size when performing a statistical analysis on j 2 x 2 tables using cochran s 1954 biometrics 10 417 451 statistic or the mantel haenszel 1959 journal of the national cancer institute 22 719 748 statistic a sample size formula is derived from cochran s statistic and it is compared with the corresponding one derived when the data are treated as unstratified and also with two other formulas proposed for stratified data analysis the formula developed yields values slightly higher than one recently proposed by munoz and rosner 1984 biometrics 40 995 1004 which assumes that both margins of each 2 x 2 table are fixed while the present study considers only the case control margin to be fixed

binary regression using an extended beta binomial distribution with discussion of correlation induced by covariate measurement errors abstract the beta binomial distribution is extended to allow negative correlations among binary variates within an experimental unit regression models are proposed for both the binary variate response rate and for the pairwise correlation between binary variates and corresponding likelihood estimation procedures are described binary regression problems are also considered in which measurement errors in the regression variables represent the sole source of overdispersion some corresponding response rate estimation procedures are described and illustrated

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

on determination of sample size in hierarchical binomial models we consider a two and a three stage hierarchical design containing the effects of k clusters with n units per cluster in the two stage model the conditional distribution of the discrete response y i is assumed to be independent binomial with mean n straight theta i i 1 k the success probabilities straight theta i s are assumed exchangeable across the k clusters each arising from a beta distribution in the three stage model the parameters in the beta distribution are assumed to have independent gamma distributions the size of each cluster n is determined for functions of straight theta i lengths of central posterior intervals are computed for various functions of the straight theta i s using markov chain monte carlo and monte carlo simulations several prior distributions are characterized and tables are provided for n with given k methods for sample size calculations under the two and three stage models are illustrated and compared for the design of a multi institutional study to evaluate the appropriateness of discharge planning rates for a cohort of patients with congestive heart failure

tests of non nested regression models some results on small sample behaviour and the bootstrap the most popular procedures for testing a regression model against a single non nested alternative can be substantially oversized in small samples also when a regression model is to be tested in the presence of several non nested alternatives the null model is sometimes accepted only if testing against each alternative in turn produces no significant outcomes this approach leads to an implicit overall test with a significance level that is not known even asymptotically it is shown that the bootstrap can be used to control significance levels in both types of situation power estimates for various tests using bootstrap critical values are also obtained and compared

high performance adaptive algorithms for single group multicast beamforming the single group multicast beamforming problem is np hard and the available approximations do not always achieve favorable performance complexity tradeoffs this paper introduces a new class of adaptive multicast beamforming algorithms that features guaranteed convergence and state of the art performance at low complexity each update takes a step in the direction of an inverse signal to noise ratio snr weighted linear combination of the snr gradient vectors of all the users convergence of this update to a karush kuhn tucker kkt point of proportionally fair beamforming is established simulations show that the proposed approach can enable better performance than the prior state of art in terms of multicast rate at considerably lower complexity this reveals an interesting link between max min fair and proportionally fair multicast beamforming formulations for cases where there is no initial channel state information at the transmitter an online algorithm is developed that simultaneously learns the user channel correlation matrices and adapts the beamforming vector to maximize the minimum long term average snr among the users using only periodic binary snr feedback from each receiver the online algorithm uses the analytic center cutting plane method to quickly learn the user correlation matrices with limited signaling overhead

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

comparison of operational characteristics for binary tests with clustered data although statistical methodology is well developed for comparing diagnostic tests in terms of their sensitivity and specificity comparative inference about predictive values is not in this paper we consider the analysis of studies comparing operating characteristics of two diagnostic tests that are measured on all subjects and have test outcomes from multiple sites with varying number of sites among subjects we have developed a new approach for comparing sensitivity specificity positive predictive value and negative predictive value with simple variance calculation and in particular focus on comparing tests using difference of positive and negative predictive values simulation studies are conducted to show the performance of our approach we analyze real data on patients with lung cancer diagnostic tests to illustrate the methodology

confidence interval estimation of the intraclass correlation coefficient for binary outcome data we obtain closed form asymptotic variance formulae for three point estimators of the intraclass correlation coefficient that may be applied to binary outcome data arising in clusters of variable size our results include as special cases those that have previously appeared in the literature fleiss and cuzick 1979 applied psychological measurement 3 537 542 bloch and kraemer 1989 biometrics 45 269 287 altaye donner and klar 2001 biometrics 57 584 588 simulation results indicate that confidence intervals based on the estimator proposed by fleiss and cuzick provide coverage levels close to nominal over a wide range of parameter combinations two examples are presented

the power of the mantel haenszel test abstract the mantel haenszel mh test mantel and haenszel 1959 is a widely used method for analyzing sets of two by two tables that compare the outcome of two treatments in several strata bailar and anthony 1977 the procedure tests the null hypothesis of no partial association between treatment and outcome in any of the strata or tables against the alternative that the partial association as measured by the common odds ratio differs from 1 birch 1964 showed that for a fixed number of tables both the mh test and an earlier version due to cochran 1954 are asymptotically identical to the uniformly most powerful unbiased test of this hypothesis this article is concerned with calculating the power of the mh test as a prelude to embarking upon a study we consider versions of the test with and without corrections for continuity the spirit behind the approximations is that although the odds ratio is the appropriate parameter for computing asymptotic power under local alternatives in practice

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

alternative procedures and associated tests of significance for non nested hypotheses this paper attempts to synthesize various procedures for testing non nested hypotheses within the framework of artificial nesting and establishes the result that different tests correspond to different treatments of its identification problem numerical and a priori identification methods are distinguished we derive two modified likelihood ratio tests that are asymptotically equivalent to the cox test and explain the relationship between them the tests are consistent this abstract was borrowed from another version of this item

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

optimal permutation tests for the analysis of group randomized trials two facts complicate the comparison of interventions in group randomized trials grt s a family of clinical trials in which each member of a particular group receives the same treatment assignment first individual outcomes within each group are often correlated second the number of groups in a grt is often not sufficient to make asymptotic approximations possible therefore the tests used with methods such as generalized estimating equations gee and penalized quasi likelihood pql originally developed for longitudinal studies may not be valid as an alternative a class of permutation tests is derived to maximize the power of testing for an intervention effect in a grt while maintaining a nominal test size the test uses a statistic that is a weighted sum of residuals with the weights based on the group sizes and the variability of each individual outcome through simulation we demonstrate the importance of weights to a permutation test s power and compare the power of permutation tests ge

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

the distributions of the j and cox non nested tests in regression models with weakly correlated regressors abstract this paper examines the asymptotic null distributions of the j and cox non nested tests in the framework of two linear regression models with nearly orthogonal non nested regressors the analysis is based on the concept of near population orthogonality npo according to which the non nested regressors in the two models are nearly uncorrelated in the population distribution from which they are drawn new distributional results emerge under npo the j and cox tests tend to two different random variables asymptotically each of which is expressible as a function of a nuisance parameter c a n 0 1 variate and a 2 q variate where q is the number of non nested regressors in the alternative model the monte carlo method is used to show the relevance of the new results in finite samples and to compute alternative critical values for the two tests under npo by plugging consistent estimates of c into the relevant asymptotic expressions an empirical example illustrates the plug in procedure

prepivoting test statistics a bootstrap view of asymptotic refinements abstract approximate tests for a composite null hypothesis about a parameter may be obtained by referring a test statistic to an estimated critical value either asymptotic theory or bootstrap methods can be used to estimate the desired quantile the simple asymptotic test a refers the test statistic to a quantile of its asymptotic null distribution after unknown parameters have been estimated the bootstrap approach used here is based on the concept of prepivoting prepivoting is the transformation of a test statistic by the cdf of its bootstrap null distribution the simple bootstrap test b refers the prepivoted test statistic to a quantile of the uniform 0 1 distribution under regularity conditions the bootstrap test b has a smaller asymptotic order of error in level than does the asymptotic test a provided that the asymptotic null distribution of the test statistic does not depend on unknown parameters in the contrary case both a and b have the same order of level error certain class

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

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures