maximum of the weighted kaplan meier tests with application to cancer prevention and screening trials summary a class of maximum weighted kaplan meier test statistics is described where the weight functions are chosen from a family of smooth functions the investigated test statistic is robust and sensitive to a variety of alternatives that are often observed in cancer prevention and screening trials a simulation study is performed to compare the size and power properties between the proposed test statistics and some existing ones we illustrate the procedure using data from a clinical trial of a breast cancer screening program

a generalized estimating equations approach for testing ordered group effects with repeated measurements in repeated measures studies we are often interested in comparing group effects in which groups are associated with a certain order relation we propose testing procedures for ordered group effects using the generalized estimating equations gee approach of liang and zeger 1986 biometrika 73 13 22 the order constrained gee estimators of group effects are approximated by the isotonic regression of the unconstrained gee estimators based on these constrained estimators we construct test statistics for detecting ordered group effects the limiting distributions of the test statistics are mixtures of chi square distributions a monte carlo experiment shows improved performances of the proposed tests over the usual chi square tests in detecting ordered group effects the proposed test procedures are illustrated by familial polyposis supplementation trial data

power of the mantel haenszel and other tests for discrete or grouped time to event data under a chained binomial model power for time to event analyses is usually assessed under continuous time models often however times are discrete or grouped as when the event is only observed when a procedure is performed wallenstein and wittes biometrics 1993 describe the power of the mantel haenszel test for discrete life tables under their chained binomial model for specified vectors of event probabilities over intervals of time herein the expressions for these probabilities are derived under a piecewise exponential model allowing for staggered entry and losses to follow up radhakrishna biometrics 1965 showed that the mantel haenszel test is maximally efficient under the alternative of a constant odds ratio and derived the optimal weighted test under other alternatives lachin biostatistical methods the assessment of relative risks 2011 describes the power function of this family of weighted mantel haenszel tests prentice and gloeckler biometrics 1978 describe a generalization of the proportional hazards model for grouped time data and the corresponding maximally efficient score test their test is also shown to be a weighted mantel haenszel test and its power function is likewise obtained there is trivial loss in power under the discrete chained binomial model relative to the continuous time case provided that there is a modest number of periodic evaluations relative to the case of homogeneity of odds ratios there can be substantial loss in power when there is substantial heterogeneity of odds ratios especially when heterogeneity occurs early in a study when most subjects are at risk but little loss in power when there is heterogeneity late in a study

estimators and tests in the analysis of multiple nonindependent 2 x 2 tables with partially missing observations we present methods for the analysis of a k variate binary measure for two independent groups where some observations may be incomplete as in the case of k repeated measures in a comparative trial for the k 2 x 2 tables let theta theta 1 theta k be a vector of association parameters where theta k is a measure of association that is a continuous function of the probabilities pi ik in each group i 1 2 k 1 k such as the log odds ratio or log relative risk the asymptotic distribution of the estimates theta theta 1 theta k is derived under the assumption that theta k theta for all k we describe the maximally efficient linear estimator theta of the common parameter theta tests of contrasts on the theta are presented which provide a test of homogeneity ha theta k theta l for all k not equal to l we then present maximally efficient tests of aggregate association hb theta theta 0 where theta 0 is a given value it is shown that the test of aggregate association hb is asymptotically independent of the preliminary test of homogeneity ha these methods generalize the efficient estimators of gart 1962 biometrics 18 601 610 and the cochran 1954 biometrics 10 417 451 mantel haenszel 1959 journal of the national cancer institute 22 719 748 and radhakrishna 1965 biometrics 21 86 98 tests to nonindependent tables the methods are illustrated with an analysis of repeated morphologic evaluations of liver biopsies obtained in the national cooperative gallstone study

testing for ordered group effects with repeated measurements summary in the repeated measures experiment testing procedures for ordered group effects are proposed using the likelihood ratio principle the constrained maximum likelihood estimators of ordered group effects are approximated by the isotonic regression of the unconstrained maximum likelihood estimators based on these constrained maximum likelihood estimators test statistics are constructed and are used for detecting ordered group effects the limiting distributions of the proposed test statistics are shown to be mixtures of chi squared distributions a simulation study shows that the proposed tests have improved powers over the usual chi squared statistic for testing equality of group effects a real data set is analysed to illustrate the proposed statistics

rank based inference for the accelerated failure time model summary a broad class of rank based monotone estimating functions is developed for the semiparametric accelerated failure time model with censored observations the corresponding estimators can be obtained via linear programming and are shown to be consistent and asymptotically normal the limiting covariance matrices can be estimated by a resampling technique which does not involve nonparametric density estimation or numerical derivatives the new estimators represent consistent roots of the non monotone estimating equations based on the familiar weighted log rank statistics simulation studies demonstrate that the proposed methods perform well in practical settings two real examples are provided

statistical spectrum of the non markovity parameter for simple model systems the spectra of the non markovity parameter for three model systems are found an ideal gas weakly non ideal gas and a medium in hydrodynamic limits it is shown that the non markovian effects play the dominant role in all three above mentioned cases the effects of molecular memory are connected with the statistical appearance of intermolecular interactions in statistical systems

statistical mechanics of neocortical interactions canonical momenta indicatorsof electroencephalography a series of papers has developed a statistical mechanics of neocortical interactions smni deriving aggregate behavior of experimentally observed columns of neurons from statistical electrical chemical properties of synaptic interactions while not useful to yield insights at the single neuron level smni has demonstrated its capability in describing large scale properties of short term memory and electroencephalographic eeg systematics the necessity of including nonlinear and stochastic structures in this development has been stressed sets of eeg and evoked potential data were fit collected to investigate genetic predispositions to alcoholism and to extract brain signatures of short term memory adaptive simulated annealing asa a global optimization algorithm was used to perform maximum likelihood fits of lagrangians defined by path integrals of multivariate conditional probabilities canonical momenta indicators cmi are thereby derived for an individual s eeg data the cmi give better signal recognition than the raw data and can be used to advantage as correlates of behavioral states these results give strong quantitative support for an accurate intuitive picture portraying neocortical interactions as having common algebraic or physics mechanisms that scale across quite disparate spatial scales and functional or behavioral phenomena i e describing interactions among neurons columns of neurons and regional masses of neurons

synchronous oscillations in the cerebral cortex the dynamics of a cortex driven by a finite number of white noise point sources is studied using a recently developed wave equation formulation green s functions power spectra fluctuation levels and two point correlation functions are computed analytically and numerically it is shown that a range of observed properties of so called synchronous oscillations in the cerebral cortex can be correctly reproduced using the wave equation that involves only excitatory interactions between neurons in particular the observed existence of a maximal correlation at zero temporal lag between spatially separated points is reproduced and explained for a cortex driven by two white noise sources

signed rank tests for censored matched pairs abstract i consider the problem of testing bivariate symmetry in matched pair experiments where the observations are subject to univariate censoring thus the observable random variables are given by y 1 y 2 and 1 2 where y j min x j c and j i x j c j 1 2 here x 1 x 2 is a random pair of partially observable lifetimes and c is a fixed or random censoring variable the hypothesis to be tested is that x 1 x 2 and x 2 x 1 have the same distribution following woolson and lachenbruch 1980 i consider censored data generalizations of signed rank tests such as the sign signed wilcoxon and signed normal scores tests i derive the asymptotic distribution of these test statistics under fixed and contiguous alternatives the efficiencies of the signed rank tests are considered in a log linear model and compared with efficiencies of the paired prentice wilcoxon and log rank tests

the sine gordon model perturbation theory and cluster monte carlo abstract we study the expansion of the surface thickness in the 2 dimensional lattice sine gordon model in powers of the fugacity z using the expansion to order z 2 we derive lines of constant physics in the rough phase we describe and test a vmr cluster algorithm for the monte carlo simulation of the model the algorithm shows nearly no critical slowing down we apply the algorithm in a comparison of our perturbative results with monte carlo data

two sample tests and one way manova for multivariate biomarker data with nondetects testing whether the mean vector of a multivariate set of biomarkers differs between several populations is an increasingly common problem in medical research biomarker data is often left censored because some measurements fall below the laboratory s detection limit we investigate how such censoring affects multivariate two sample and one way multivariate analysis of variance tests type i error rates power and robustness to increasing censoring are studied under both normality and non normality parametric tests are found to perform better than non parametric alternatives indicating that the current recommendations for analysis of censored multivariate data may have to be revised copyright 2016 john wiley sons ltd

asymptotic properties of censored linear rank tests a conjecture of prentice is established which states that for censored linear rank test exact scores based on conditional expectations can be replaced by approximate scores obtained by evaluating the score function at an estimate of the survival function we show that under minimal conditions asymptotically equivalent tests are obtained when either the kaplan meier altshuler or moment estimator of the survival function is used asymptotic normality is also established for a general random censorship model under the null hypothesis and for contiguous alternatives this is used to calculate efficacies and when the censoring times are i i d an expression for the asymptotic relative efficiency is given which is a natural generalization of the one for classical uncensored linear rank tests 1 introduction prentice 1978 has constructed a general class of linear rank tests for a regression model with censored data his approach was to specify a score function for a classical linear rank test in the absence of censoring chernoff and savage 1958 hajek and sidak 1967 to construct all possible rankings of the unobserved uncensored values which were consistent with observed censored sample and then to assign to each observation the average of all possible scores it could have received in the absence of censoring giving equal weighting to each possible uncensored ranking except for a few special scoring functions notably logarithmic or power law scores these averages are unwieldy when there is appreciable censoring and prentice suggested that asymptotically equivalent tests might arise if the score function was evaluated at some suitable estimate of the survivor function this is well known to be true for uncensored data but requires further justification when censoring is present because the estimate of the survivor function is more complicated in this work we show that prentice s conjecture is true under minimal conditions and also we show that it remains true if prentice s moment estimator of the survivor function is replaced by either the kaplan meier estimator or altshuler s estimator asymptotic normality of these tests is established under a random censorship model for the null hypothesis and contiguous alternatives by martingale methods this is used to compute efficacies for a general random censorship model and asymptotic relative efficiencies for i i d potential censoring times where fully efficient linear rank tests exist asymptotic normality for general alternatives has been established in cuzick 1982 by more complicated methods

computing the roughening transition of ising and solid on solid models by bcsos model matching we study the roughening transition of the dual of the two dimensional 2d xy model of the discrete gaussian model of the absolute value solid on solid model and of the interface in an ising model on a three dimensional 3d simple cubic lattice the investigation relies on a renormalization group finite size scaling method that was proposed and successfully tested a few years ago the basic idea is to match the renormalization group flow of the interface observables with that of the exactly solvable body centred solid on solid bcsos model our estimates for the critical couplings are and for the xy model the discrete gaussian model and the absolute value solid on solid model respectively for the inverse roughening temperature of the ising interface we find to the best of our knowledge these are the most precise estimates for these parameters published so far

high precision renormalization group study of the roughening transition abstract we confirm the kosterlitz thouless scenario of the roughening transition for three different solid on solid models the discrete gaussian model the absolute value solid on solid model and the dual transform of the xy model with standard cosine action the method is based on a matching of the renormalization group flow of the candidate models with the flow of a bona fide kt model the exactly solvable bcsos model the monte carlo simulations are performed using efficient cluster algorithms we obtain high precision estimates for the critical couplings and other non universal quantities for the xy model with cosine action our critical coupling estimate is xyr 1 1197 5 for the roughening coupling of the discrete gaussian and the absolute value solid on solid model we find kdgr 0 6645 6 and kasosr 0 8061 3 respectively

rank tests and a one sample logrank test for comparing observed survival data to a standard population for cox s proportional hazards model test procedures are described for the comparison of randomly right censored observed and expected standard population survival data it is observed that the class of linear rank tests proposed by prentice 1978 biometrika 65 167 179 may be employed to test regression hypotheses in this one sample setting in order to compare globally the observed and expected survival data the one sample limit of mantel s logrank test is formally derived the statistic derived is identical to one proposed from a diflerent viewpoint by breslow 1975 intemational statistical review 43 45 58 throughout it is assumed that the standard population survival function is a continuous function of time and that the survival or censoring time for each study sample individual is exact and is not grouped into categories

combining dependent tests with incomplete repeated measurements summary in comparing the effectiveness of two treatments repeated measurements of the same characteristic are often taken under two or more distinct conditions for each experimental subject a locally best linear combination of individual test statistics obtained under different conditions is proposed to test the equality of the two treatments the test procedure allows different patterns of missing observations for the two groups to be compared special cases such as combining wilcoxon tests t tests and 2 x 2 tables are discussed in detail with real examples

markov and non markov processes in complex systems by the dynamical information entropy abstract we consider the markov and non markov processes in complex systems by the dynamical information shannon entropy dise method the influence and important role of the two mutually dependent channels of entropy alternation creation or generation of correlation and anti correlation destroying or annihilation of correlation have been discussed the developed method has been used for the analysis of the complex systems of various natures slow neutron scattering in liquid cesium psychology short time numeral and pattern human memory and effect of stress on the dynamical taping test random dynamics of rr intervals in human ecg problem of diagnosis of various disease of the human cardio vascular systems chaotic dynamics of the parameters of financial markets and ecological systems

1 f α noise from self organized critical models with uniform driving using the well known olami feder christensen model as our paradigm we show how to modify uniform driven self organized critical models to generate 1 f ensuremath alpha noise this model can reproduce all the main features of 1 f ensuremath alpha noise 1 ensuremath alpha is close to one and does not depend on the dimension of the system 2 the 1 f ensuremath alpha behavior is found for very low frequencies 3 the spatial correlations do not obey a power law that proves that spatially extended systems based on activation deactivation processes do not have to be point driven to produce 1 f ensuremath alpha noise the essential ingredient is a local memory of the activation deactivation process

regression analysis of multivariate incomplete failure time data by modeling marginal distributions abstract many survival studies record the times to two or more distinct failures on each subject the failures may be events of different natures or may be repetitions of the same kind of event in this article we consider the regression analysis of such multivariate failure time observations each marginal distribution of the failure times is formulated by a cox proportional hazards model no specific structure of dependence among the distinct failure times on each subject is imposed the regression parameters in the cox models are estimated by maximizing the failure specific partial likelihoods the resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated simultaneous inferential procedures are then proposed extensive monte carlo studies indicate that the normal approximation is adequate for practical use the new methods allow time dependent covariates missing observations and arbitrary patterns of censorship they are illustrat

rank based regression with repeated measurements data summary a rank based regression method is proposed for repeated measurements data it is a generalisation of the classical wilcoxon mann whitney rank statistic for independent observations the method is valid under a weak condition on the error terms that can accommodate certain heteroscedasticity and within subject dependency the asymptotic normality of the proposed estimator is proved using empirical process theory a variance estimator shown to be consistent is also constructed the proposed method is illustrated using data from a clinical trial on treating labour pain robustness and efficiency of the estimator is demonstrated in simulation studies

the solid on solid surface width around the roughening transition abstract we investigate the surface width w of solid on solid surfaces in the vicinity of the roughening temperature t r above t r w 2 is expected to diverge with the system size l like ln l however close to t r a clean ln l behavior can only be seen on extremely large lattices starting from the kosterlitz thouless renormalization group we derive an improved formula that describes the small l behavior on both sides of t r for the discrete gaussian model we used the valleys to mountains reflections cluster algorithm in order to simulate the fluctuating solid on solid surface the base plane above which the surface is defined is an l l square lattice in the simulation we took 8 l 256 the improved formula fits the numerical results very well from the analysis we estimate the roughening temperature to be t r 0 755 3

long range memory and non markov statistical effects in human sensorimotor coordination in this paper the non markov statistical processes and long range memory e ects in human sensorimotor coordination are investigated the theoretical basis of this study is the statistical theory of non stationary discrete non markov processes in complex systems phys rev e 62 6178 2000 the human sensorimotor coordination was experimentally studied by means of standard dynamical tappingtest on the g roup of 32 youngpeoples with tap numbers up to 400 this test was carried out separately for the right and the left hand according to the degree of domination of each brain hemisphere the numerical analysis of the experimental results was made with the help of power spectra of the initial time correlation function the memory functions of low orders and the 7rst three points of the statistical spectrum of non markovity parameter our observations demonstrate that with the regard to results of the standard dynamic tapping test it is possible to divide all examinees into 7ve di erent dynamic types we have introduced the con ict coe cient to estimate quantitatively the order disorder e ects underlying life systems the last one re ects the existence of disbalance between the nervous and the motor human coordination the suggested classi7cation of the neurophysiological activity represents the dynamic generalization of the well known neuropsychological types and provides the new approach in a modern neuropsychology c

balanced risk set matching a new form of matching optimal balanced risk set matching is applied in an observational study of a treatment cystoscopy and hydrodistention given in response to the symptoms of the chronic nonlethal disease interstitial cystitis when a patient receives the treatment at time t that patient is matched to another patient with a similar history of symptoms up to time t who has not received the treatment up to time t this is risk set matching by using a penalty function in integer programming in a new way we force the marginal distributions of symptoms to be balanced in the matched treated and control groups among all balanced matchings we pick the one that is optimal in the sense of minimizing the multivariate pretreatment covariate distance within matched pairs under a simple model for the treatment assignment mechanism we study the sensitivity of the findings to hidden biases in particular we show that a simple conventional sensitivity analysis is appropriate with risk set matching when the

rank based estimating equations with general weight for accelerated failure time models an induced smoothing approach the induced smoothing technique overcomes the difficulties caused by the non smoothness in rank based estimating functions for accelerated failure time models but it is only natural when the estimating function has gehan s weight for a general weight the induced smoothing method does not provide smooth estimating functions that can be easily evaluated we propose an iterative induced smoothing procedure for general weights with the estimator from gehan s weight initial value the resulting estimators have the same asymptotic properties as those from the non smooth estimating equations with the same weight their variances are estimated with an efficient resampling approach that avoids solving estimating equations repeatedly the methodology is generalized to incorporate an additional weight to accommodate missing data and various sampling schemes in a numerical study the proposed estimators were obtained much faster without losing accuracy in comparison to those from non smooth estimating equations and the variance estimators provided good approximation of the variation in estimation the methodology was applied to two real datasets the first one from an adolescent depression study and the second one from a cancer study with missing covariates by design the implementation is available in an r package aftgee

maximum weighted partial likelihood estimators for the cox model new estimators for cox regression that maximize a weighted version of the partial likelihood are considered their asymptotic properties on the model are sketched estimators with bounded influence curves are identified and shown to have good asymptotic relative efficiency the results of a small simulation study are included the estimators are applied to a well known data set the possible influence of an outlying observation on the cox estimator can be of any magnitude individuals who survive longest have a high potential of being influential in analogy with weighted linear rank tests we introduce estimators of the regression coefficients that maximize a weighted partial likelihood for instance by using weights proportional to the number at risk one obtains a wilcoxon type estimator this estimator has bounded influence provided the covariate space is compact and in a wide variety of situations its asymptotic relative efficiency is at least as good as that of the wilcoxon test asymptotic prop

using surrogate failure time data to increase cost effectiveness in clinical trials summary in clinical trials with failure time outcomes the cost of follow up for the endpoint of primary interest is sometimes expensive in many of these settings one or more secondary or surrogate failure time outcomes are also available which either occur much earlier or are much less expensive to follow than the primary outcome this paper presents a method for using these secondary outcomes to increase the power of detecting a treatment effect on the primary outcome only without introducing bias the proposed method requires that patients be randomized to either extended or limited follow up a test statistic is constructed by forming a minimum variance linear combination of a linear rank statistic based on the primary outcome and a mean zero weighted sum of linear rank statistics based on secondary outcomes from both follow up arms large sample distribution theory for this statistic is developed while moderate sample behaviour is explored through a simulation study

some test statistics for use in multistate survival analysis summary some current nonparametric methods related to the log rank test are extended to cover ordered categories of response e g response no change progression and to incorporate information on duration of response as an example data from a protocol for the treatment of advanced breast cancer are analysed the powers of several tests for this special case of multistate survival data are compared by monte carlo simulation for both small and moderate samples from exponential and weibull distributions

comparison of monte carlo results for the 3d ising interface tension and interface energy with extrapolated series expansions abstract we compare monte carlo results for the interface tension and interface energy of the 3 dimensional ising model with pade and inhomogeneous differential approximants of the low temperature series that was recently extended by arisue to 17th order in u exp 4 the series is expected to suffer from the roughening singularity at u 0 196 the comparison with the monte carlo data shows that the pade and inhomogeneous differential approximants fail to improve the truncated series result of the interface tension and the interface energy in the region around the roughening transition the monte carlo data show that the specific heat displays a peak in the smooth phase neither the truncated series nor the pade approximants find this peak we also compared monte carlo data for the energy of the asos model with the corresponding low temperatures series that we extended to order u12

sample size calculation for cluster randomization trials with a time to event endpoint cluster randomization trials randomize groups called clusters of subjects called subunits between intervention arms and observations are collected from each subject in this case subunits within each cluster share common frailties so that the observations from subunits of each cluster tend to be correlated oftentimes the outcome of a cluster randomization trial is a time to event endpoint with censoring in this article we propose a closed form sample size formula for weighted rank tests to compare the marginal survival distributions between intervention arms under cluster randomization with possibly variable cluster sizes extensive simulation studies are conducted to evaluate the performance of our sample size formula under various design settings real study examples are taken to demonstrate our method

estimation and testing in a two sample generalized odds rate model abstract the generalized odds ratio for a survival variable t is defined as t t c c 1 1 sc t sc t for c 0 and log s t for c 0 where s t pr t t this ratio coincides with the integrated hazard for c 0 and the odds ratio for c 1 when the distribution of t depends on a covariate vector we assume that conditionally on the covariates log t t c is linear in the covariates this model is a generalization of the proportional hazard model phm which has an interpretation both as a phm with random nuisance effects clayton and cuzick 1986 and as a proportional odds rate model with the odds rate defined from the response times of series systems harrington and fleming 1982 and bickel 1986a considered rank tests for this semiparametric model clayton and cuzick 1986 considered estimation we use the odds rate representation to define a class of estimates of the proportionality parameter in the two sample case we show that the estimates are consistent and asymptotica

testing for differences in changes in the presence of censoring parametric and non parametric methods some commonly used parametric and non parametric methods for analysing repeated measures with incomplete observations are briefly reviewed the performances of these methods in the presence of completely random as well as informative censoring are compared in simulated experiments generated under the linear random effects model with parameter values derived from realistic examples the effects of some moderate model deviations are also compared the results indicate that in the presence of informative censoring the usual parametric and nonparametric methods derived under the assumption of random censoring could either suffer severe loss of power or provide false positive results the conditional linear model for informative censoring when used in conjunction with the bootstrap variance estimation procedure performed well under both random and informative censoring mechanisms the non parametric procedure obtained by ranking the individual summary statistics although not as efficient as the conditional linear model with robust variance also performed relatively well in most situations therefore in situations in which informative censoring is likely to occur it is important to select the proper method of analysis to test for the informativeness of censoring and to account for its effects

a comparison of estimated proportional hazards models and regression trees we present examples of the usage of regression trees for censored response via two real world datasets one a rheumatoid arthritis survival study and the other a hip replacement study and draw comparisons with the results of cox proportional hazards modelling the two methods pursue different goals motivation of the tree techniques is the desire to extract meaningful prognostic groups while the proportional hazards model enables assessment of the impact of risk factors the methods are thus complementary for the arthritis study the two techniques corroborate one another although the flavour of the conclusions derived differ for the hip replacement study however the regression tree approach reveals structure that would not emerge from a routine proportional hazards analysis we also discuss the treatment of data analytic issues such as the handling of missing values and influence in the presence of non uniform censoring

variance and sample size calculations in quality of life adjusted survival analysis q twist the quality adjusted time without symptoms or toxicity q twist statistic previously introduced by glasziou simes and gelber 1990 statistics in medicine 9 1259 1276 combines toxicity disease free survival and overall survival information in assessing the impact of treatments on the lives of patients this methodology has received positive reviews from clinicians as intuitive and useful but to date the variance of this statistic has remained unspecified we review aspects of the q twist method for analyzing clinical trial data extend the method to accommodate multiple treatment arms and provide closed form asymptotic variance formulas we also provide a framework for designing q twist clinical trials with sample sizes determined using the derived asymptotic variance formulas trials currently collecting quality of life data did not have the benefit of these sample size calculation techniques in designing their studies

stochastic dynamics of time correlation in complex systems with discrete time in this paper we present the concept of description of random processes in complex systems with discrete time it involves the description of kinetics of discrete processes by means of the chain of finite difference non markov equations for time correlation functions tcfs we have introduced the dynamic time dependent information shannon entropy s i t where i 0 1 2 3 ellipsis as an information measure of stochastic dynamics of time correlation i 0 and time memory i 1 2 3 ellipsis the set of functions s i t constitute the quantitative measure of time correlation disorder i 0 and time memory disorder i 1 2 3 ellipsis in complex system the theory developed started from the careful analysis of time correlation involving dynamics of vectors set of various chaotic states we examine two stochastic processes involving the creation and annihilation of time correlation or time memory in details we carry out the analysis of vectors dynamics employing finite difference equations for random variables and the evolution operator describing their natural motion the existence of tcf results in the construction of the set of projection operators by the usage of scalar product operation harnessing the infinite set of orthogonal dynamic random variables on a basis of gram shmidt orthogonalization procedure tends to creation of infinite chain of finite difference non markov kinetic equations for discrete tcfs and memory functions mfs the solution of the equations above thereof brings to the recurrence relations between the tcf and mf of senior and junior orders this offers new opportunities for detecting the frequency spectra of power of entropy function s i t for time correlation i 0 and time memory i 1 2 3 ellipsis the results obtained offer considerable scope for attack on stochastic dynamics of discrete random processes in a complex systems application of this technique on the analysis of stochastic dynamics of rr intervals from human ecg s shows convincing evidence for a non markovian phenomemena associated with a peculiarities in short and long range scaling this method may be of use in distinguishing healthy from pathologic data sets based in differences in these non markovian properties

non markov stochastic dynamics of real epidemic process of respiratory infections abstract the study of social networks and especially of stochastic dynamics of diseases spread in human population has recently attracted considerable attention in statistical physics in this work we present a new statistical method of analyzing the spread of epidemic processes of grippe and acute respiratory track infections arti by means of the theory of discrete non markov stochastic processes we use the results of our last theory phys rev e 65 2002 046107 to study statistical memory effects long range correlation and discreteness in real data series describing the epidemic dynamics of human arti infections and grippe we have carried out the comparative analysis of the data of the two infections grippe and arti in one of the industrial districts of kazan one of the largest cities of russia the experimental data are analyzed by the power spectra of the initial time correlation function and the memory functions of junior orders the phase portraits of the four first dynamic variables the three first points of the statistical non markov parameter and the locally averaged kinetic and relaxation parameters the received results give an opportunity to provide a strict quantitative description of regular and stochastic components in epidemic dynamics of social networks taking into account their time discreteness and effects of statistical memory they also allow to reveal the degree of randomness and predictability of the real epidemic process in the specific social network

exact two sample inference with missing data when comparing follow up measurements from two independent populations missing records may arise due to censoring by events whose occurrence is associated with baseline covariates in these situations inferences based only on the completely followed observations may be biased if the follow up measurements and the covariates are correlated this article describes exact inference for a class of modified u statistics under covariate dependent dropouts the method involves weighing each permutation according to the retention probabilities and thus requires estimation of the missing data mechanism the proposed procedure is nonparametric in that no distributional assumption is necessary for the outcome variables and the missingness patterns monte carlo approximation by the gibbs sampler is proposed and is shown to be fast and accurate via simulation the method is illustrated in two small data sets for which asymptotic inferential procedures may not be appropriate

propagation and stability of waves of electrical activity in the cerebral cortex nonlinear equations are introduced to model the behavior of the waves of cortical electrical activity that are responsible for signals observed in electroencephalography these equations incorporate nonlinearities axonal and dendritic lags excitatory and inhibitory neuronal populations and the two dimensional nature of the cortex while rendering nonlinear features far more tractable than previous formulations both analytically and numerically the model equations are first used to calculate steady state levels of cortical activity for various levels of stimulation dispersion equations for linear waves are then derived analytically and an analytic expression is found for the linear stability boundary beyond which a seizure will occur the effects of boundary conditions in determining global eigenmodes are also studied in various geometries and the corresponding eigenfrequencies are found numerical results confirm the analytic ones which are also found to reproduce existing results in the relevant limits thereby elucidating the limits of validity of previous approximations

two sample asymptotically distribution free tests for incomplete multivariate observations abstract asymptotically distribution free tests for equality of two multivariate distributions based on censored observations are proposed by choosing appropriate test scores we obtain the multivariate versions of the gehan and log rank tests an important application of the proposed tests is in the area in which multiple observations are collected on study subjects some of whom may have missing observations the patterns of missing observations are allowed to differ for the two groups to be compared these tests are particularly useful for longitudinal studies for example the analysis of repeated measurements and growth curves real examples are also provided for illustration

the square lattice f model revisited a loop cluster update scaling study the six vertex f model on the square lattice constitutes the unique example of an exactly solved model exhibiting an infinite order phase transition of the kosterlitz thouless type as one of the few non trivial exactly solved models it provides a welcome gauge for new numerical simulation methods and scaling techniques in view of the notorious problems of clearly resolving the kosterlitz thouless scenario in the two dimensional xy model numerically the f model in particular constitutes an instructive reference case for the simulational description of this type of phase transition we present a loop cluster update monte carlo study of the square lattice f model with a focus on the properties not exactly known such as the polarizability or the scaling dimension in the critical phase for the analysis of the simulation data finite size scaling is explicitly derived from the exact solution and plausible assumptions guided by the available exact results the careful inclusion of correction terms in the scaling formulae allows for a reliable determination of the asymptotic behaviour

isotropy properties of the multi step markov symbolic sequences abstract a new object of the probability theory the two sided chain of symbols introduced in ref arxiv physics 0306170 is used to study isotropy properties of binary multi step markov chains with the long range correlations established statistical correspondence between the markov chains and certain two sided sequences allows us to prove the isotropy properties of three classes of the markov chains one of them is the important class of weakly correlated additive markov chains which turned out to be equivalent to the additive two sided sequences

a generalization of the weibull distribution with application to the analysis of survival data abstract the weibull distribution which is frequently used for modeling survival data is embedded in a larger family obtained by introducing an additional shape parameter this generalized family not only contains distributions with unimodal and bathtub hazard shapes but also allows for a broader class of monotone hazard rates furthermore the distributions in this family are analytically tractable and computationally manageable the modeling and analysis of survival data using this family is discussed and illustrated in terms of a lifetime dataset and the results of a two arm clinical trial

dynamics of the information entropy in random processes abstract the problem of the description of temporal evolution of the random variables in terms of the information shannon entropy of correlation processes has been considered the influence and important role of the two mutually dependent channels of the entropy alternation correlation creation or the generation of correlations and anti correlation decay or the annihilation of correlation have been discussed the method developed is used for the analysis of chaotic dynamics of the long range fluctuation in the short time human memory

a class of rank test procedures for censored survival data summary a class of linear rank statistics is proposed for the k sample problem with rightcensored survival data the class contains as special cases the log rank test mantel 1966 cox 1972 and a test essentially equivalent to peto peto s 1972 generalization of the wilcoxon test martingale theory is used to establish asymptotic normality of test statistics under the null hypotheses considered and to derive expressions for asymptotic relative efficiencies under contiguous sequences of alternative hypotheses a class of distributions is presented which corresponds to the class of rank statistics in the sense that for each distribution there is a statistic with some optimal properties for detecting location alternatives from that distribution some monte carlo results are displayed which present small sample behaviour

a method for determining groups in multiple survival curves survival analysis includes a wide variety of methods for analyzing time to event data one basic but important goal in survival analysis is the comparison of survival curves between groups several nonparametric methods have been proposed in the literature to test for the equality of survival curves for censored data when the null hypothesis of equality of curves is rejected leading to the clear conclusion that at least one curve is different it can be interesting to ascertain whether curves can be grouped or if all these curves are different from each other a method is proposed that allows determining groups with an automatic selection of their number the validity and behavior of the proposed method was evaluated through simulation studies the applicability of the proposed method is illustrated using real data software in the form of an r package has been developed implementing the proposed method

repeated significance testing for a general class of statistics used in censored survival analysis abstract the asymptotic joint distribution of a class of sequentially computed statistics used in survival analysis is derived when the individuals under study enter serially and are subject to random loss to follow up these results are used for constructing repeated significance tests over real time

some large sample distribution free estimators and tests for multivariate partially incomplete data from two populations the most common instance of multivariate observations is the case of repeated measures over time the two most widely used methods for the analysis of k repeated measures for two groups are the k degrees of freedom d f t2 manova f test and the within subjects 1 degree of freedom anova f test both require complete samples from normally distributed populations in this paper i describe alternative k and 1 d f distribution free procedures which allow for randomly missing observations these include a large sample analysis of means the wei and lachin multivariate wilcoxon test with estimates of the mann whitney parameter and a multivariate hodges lehmann location shift estimator based on the multivariate u statistic of wei and johnson each of these methods provides a distribution free k variate estimate of the magnitude of group differences which can be used as the basis for an overall test of group differences these tests include the k d f omnibus t2 like test 1 d f tests of restricted hypotheses such as the wei lachin multivariate one sided test of stochastic ordering and the test of general association based on a minimum variance generalized least squares gls estimate of the average group difference i then describe covariate stratified adjusted gls estimates and tests of group differences this approach also provides tests of homogeneity interaction for within subjects and between subjects effects i illustrate these analyses with an analysis of repeated cholesterol measurements in two groups of patients stratified by sex such analyses provide an overall distribution free summary estimate and test of the treatment effect obtained by combining the group differences over both time repeated measures and strata

a composite design for transition from a preliminary to a full scale study in drug development a sequence of studies are conducted to evaluate effectiveness or efficacy and safety such as a phase ii study to assess pharmacological activity or safety that is then followed by a definitive phase iii study to assess clinical effectiveness rather than conducting separate successive studies we describe a design in which the patients enrolled in a preliminary e g phase ii study are continued into a subsequent full scale e g phase iii study this design also applies to a study that uses an internal pilot with a preliminary assessment of efficacy or safety the combined preliminary to full scale design potentially reduces the total numbers of patients required and the total duration of the program the design allows a futility or safety stopping boundary for the preliminary study result that is specified in terms of a lower critical z value z l and the pursuant type ii error probability incurred under a specified alternative hypothesis of a beneficial effect or no toxicity at that stage this boundary also leads to a deflation of the type i error probability for the final test at the completion of the full scale study such that a critical value for the final test z f can be determined that provides the desired level of the type i error probability exactly thus it is possible to determine sample sizes at the two stages and critical values z l and z f that provide specified type i and ii error probabilities for the combined study we describe the design using large sample normally distributed z tests at the two phases including a test for means or proportions or survival times or combinations thereof such as a test for means at phase ii followed by a test for proportions at phase iii we compare the properties of this design versus the conduct of two successive studies and explore the factors that influence the operating characteristics of the design we also discuss the practical considerations in the implementation of the design

competition between two kinds of correlations in literary texts a theory of additive markov chains with long range memory is used to describe the correlation properties of coarse grained literary texts the complex structure of the correlations in the texts is revealed anti persistent correlations at small distances l approximately 300 define this non trivial structure for some concrete examples of literary texts the memory functions are obtained and their power law behavior at long distances is disclosed this property is shown to be a cause of self similarity of texts with respect to the decimation procedure

learning dynamics from nonstationary time series analysis of electroencephalograms we propose an empirical modeling technique for a nonstationary time series analysis proposed methods include a high dimensional n 3 dynamical model construction in the form of delay differential equations a nonparametric method of respective time delay calculation the detection of quasistationary regions of the process by recurrence analysis in the space of model coefficients and final fitting of the model to quasistationary segments of observed time series we also demonstrate the effectiveness of our approach for nonstationary signal classification in the space of model coefficients applying the empirical modeling technique to electroencephalogram eeg records analysis we find evidence of high dimensional nonlinear dynamics in quasistationary eeg segments recurrence analysis of model parameters reveals long term correlations in nonstationary eeg records using the dynamical model as a nonlinear filter we find that different emotional states of subjects can be clearly distinguished in the space of model coefficients

parametric inference in a multiple renewal process with time dependent covariates our particular problem arises from a survey of acute respiratory tract infection ari in which 1 312 kindergarten children in beijing have been followed day by day for 1 year six types of infection are considered upper respiratory tract infection including influenza pyogenic tonsillitis laryngitis otitis media bronchitis and pneumonia the record of each child consists of not only the types of diseases and the times of illness but also age sex some indices of health family history and personal history of respiratory diseases during the data analysis in addition we considered several basic meteorological variables kindly provided by the beijing meteorological observatory a parametric statistical model based on a renewal process with competing risks and time dependent covariates is used to analyse these data similar models have been considered by several authors including kalbfleisch and prentice 1980 prentice williams and peterson 1981 and hsieh crowley and tormey 1983 these authors use reordering of the time scale in order to modify the partial likelihood techniques of the semiparametric proportional hazards model in contrast to this our parametric model allows a direct approach avoiding the complicated conditioning argument in the model with time dependent covariates enjoying full efficiency since inference is based on the full likelihood and performing the analysis directly in chronological time as opposed to the reordered time scales of the above authors the asymptotic statistical properties are standard for our fully parametric model the statistical model was proposed in j q fang s unpublished ph d dissertation university of california at berkeley 1985 the history of each individual can make several contributions to the full likelihood in the sense of a renewal process the proportional hazards model is assumed with a general parametric underlying hazard log polynomial

weighted log rank type statistics for comparing survival curves when there is a time lag in the effectiveness of treatment summary in certain long term treatment trials one expects some lag period before the treatment is fully effective this paper presents two weighted log rank type statistics designed to have good efficiency over a wide range of lags a maximin efficiency robust statistic and a simplified version of this statistic both statistics can be computed as easily as the log rank statistic asymptotic efficiency calculations supported by small sample simulations show that the two proposed statistics are substantially more efficient than the conventional log rank statistic in certain lag situations with comparatively little efficiency loss relative to the log rank statistic when no lag exists we recommend the maximin statistic for situations where a lag is expected but cannot be specified precisely in advance

dynamical shannon entropy and information tsallis entropy in complex systems abstract in this work we offer a new approach to the concept of the information entropy for the description of the dynamic behaviour of complex systems on the basis of the unification of the known information approach to the shannon entropy submitted in works of authors phys rev e 62 5 2000 6178 physica a 303 2002 427 and generalization of the boltzman gibbs entropy offered by tsallis braz j phys 29 1 1999 1 we have received a new representation of the dynamic information entropy here we present concrete applications of the received equations to the study of complex systems related to the electric signals of ecgs of healthy people and patients with myocardial infarction mi as an example various modifications of the non markovity parameter are also submitted they were received with the help of the new approach to the information entropy we have received detailed information about markov quasi markov and non markov characteristics of the rr interval fluctuations of the ecgs with the help of the chain of zwanzig mori s discrete kinetic equations and dynamical tsallis entropy

group sequential large sample t2 like chi2 tests for multivariate observations in many studies a k degree of freedom large sample 2 test is used to assess the effect of treatment on a multivariate response such as an omnibus t2 like test of a difference between two treatment groups in any of k repeated measures alternately a k df 2 test may be used to test the equality of k 1 groups in a single outcome measure jennison and turnbull biometrika 1991 78 133 141 describe group sequential 2 and f tests for normal errors linear models and proschan follmann and geller statist med 1994 13 1441 1452 describe group sequential tests for k 1 group comparisons these methods apply to sequences of statistics that can be characterized as having an independent increments variance covariance structure thus simplifying the computation of the sequential variance covariance matrix and the resulting sequential test boundaries however many commonly used statistics do not share this structure including a liang zeger biometrika 1986 73 13 22 gee longitudinal analysis with an independence working correlation structure and a wei lachin j amer statist assoc 1984 79 653 661 multivariate wilcoxon rank test among others for such analyses this paper describes the computation of group sequential boundaries for the interim analysis of emerging results using k df tests that are expressed as quadratic forms in a statistics vector that is distributed as multivariate normal at least asymptotically we derive the elements of the covariance matrix of multiple successive k df 2 statistics based on established theorems on the distribution of quadratic forms this covariance matrix is estimated by augmenting the data from the successive interim analyses into a single analysis from which the component sequential tests and their variance covariance matrix can then be extracted boundary values for the sequential statistics can then be computed using the method of slud and wei j amer statist assoc 1982 77 862 868 or using the spending function of lan and demets biometrika 1983 70 659 663 with a surrogate measure of information an example is presented using the analysis of repeated cholesterol measurements in a clinical trial copyright 2003 john wiley sons ltd

biometrika centenary survival analysis although papers relating to survival analysis have appeared in biometrika since the very first issue the current emphasis on the topic in this journal is fairly new especially as it relates to applications in biostatistics this survey traces the development of survival analysis throughout the twentieth century as reflected in the pages of biometrika focusing primarily on work published since 1980

sensitivity analysis of longitudinal binary quality of life data with drop out an example using the eortc qlq c30 analysing quality of life data qol may be complicated for several reasons quality of life data not only involves repeated measures but is also usually collected on ordered categorical responses in addition it is evident that not all patients provide the same number of assessments due to attrition caused by death or other medical reasons in the recent statistical literature increasing attention is given to methods which can handle non continuous outcomes in the presence of missing data the aim of this paper is to investigate the effect on statistical conclusions of applying different modelling techniques to qol data generated from an eortc phase iii trial treatment effects and treatment differences are of major concern first a random effects model is fitted relating a binary longitudinal response derived from the physical functioning scale of the qlq c30 to several covariates in a second approach marginal models are fitted retaining the response variable and the mean structure used before the fitted marginal models only differ with respect to the considered estimation procedure generalized estimating equations gee weighted generalized estimating equations wgee and maximum likelihood ml copyright c 2001 john wiley sons ltd

interim analyses with repeated measurements in a sequential clinical trial summary in comparing two treatments suppose that patients are available for the study sequentially repeated measurements of the same characteristic are collected serially over time for each study patient sequential procedures are proposed to monitor the trial for early evidence of treatment difference or harmful side effects based on such repeated measurements all the methods are illustrated with a real life example

rank tests for clustered survival data when dependent subunits are randomized in clustered survival data subunits within each cluster share similar characteristics so that observations made from them tend to be positively correlated in clinical trials the correlated subunits from the same cluster are often randomized to different treatment groups in this case the variance formulas of the standard rank tests such as the logrank gehan wilcoxon or prentice wilcoxon proposed for independent samples need to be adjusted for intracluster correlations both within and between treatment groups for testing equality of marginal survival distributions in this paper we derive a general form of simple variance formulas of the rank tests when subunits from the same cluster are randomized into different treatment groups extensive simulation studies are conducted to investigate small sample performance of the variance formulas we compare our non parametric rank tests based on the adjusted variances with one from a shared frailty model which is an optimal semi parametric testing procedure when the intracluster correlations within and between groups are the same

rank estimation of treatment differences based on repeated measurements subject to dependent censoring abstract in comparing the effectiveness of two treatments suppose that for each patient repeated measurements of an outcome variable are taken at prespecified time points but some observations may be missing due to the patient s dependent right censoring in this article a simple rank estimation procedure constructed based on an artificial censoring technique is proposed for the treatment differences over time without imposing a parametric structure on the dependence between the outcome measures and the censoring variable our method can be easily implemented and is illustrated by a dataset from an aids clinical trial

stratification of summary statistic tests according to missing data patterns summary statistics such as slope or area under the time response curve reduce the dimensionality of repeated measures data and can thereby simplify the comparison of groups in longitudinal studies since summary statistic distributions vary according to the amount timing and type of any missingness that occurs one must choose between analysing the data unconditionally or conditionally on the missingness patterns this paper uses simulations to compare such unstratified and stratified summary statistic analyses with respect to their size and power under models that allow for both non informative and informative missingness mechanisms of particular interest is the robustness of these methods to violations of the assumptions that one must make if they are to have proper test size it is found that stratification of the analysis tends to result in an increase of power and improves the robustness to violations of missing data assumptions

the problem of a covariate time qualitative interaction in a survival study we introduce a test for the equality of two survival distributions against the specific alternative of crossing hazards although this kind of alternative is somewhat rare designing a test specifically aimed at detecting such departures from the null hypothesis in this direction leads to powerful procedures upon which we can call in those few cases where such departures are suspected furthermore the proposed test and an approximate version of the test are seen to suffer only moderate losses in power when compared with their optimal counterparts should the alternative be one of proportional hazards our interest in the problem is motivated by clinical studies on the role of acute graft versus host disease as a risk factor in leukemic children and we discuss the analysis of this study in detail the model we use in this work is a special case of the one introduced by anderson and senthilselvan 1982 applied statistics 31 44 51 we propose overcoming an inferential problem stemming from their model by using the methods of davies 1977 biometrika 64 247 254 1987 biometrika 74 33 43 backed up by resampling techniques we also look at an approach relying directly on resampling techniques the distributional aspects of this approach under the null hypothesis are interesting but practically its behaviour is such that its use cannot be generally recommended outlines of the necessary asymptotic theory are presented and for this we use the tools of martingale theory

monotone estimating equations for censored data the monotone class rank test based estimating equations for regression models with right censored data is considered we introduce an estimator which is a solution of a monotone estimating equation that is an extension of the gehan test the estimator is easy to derive sqrt n consistent and asymptotically normal under minimal conditions all monotone estimating equations are characterized and a simulation study which shows that our suggested procedure performs well is included

on the regression analysis of multivariate failure time data summary the paper is concerned with the analysis of regression effects when individual study subjects may experience multiple failures the proposed methods are most likely to be useful when there are a fairly large number of study subjects two general classes of regression models are considered in order to relate the hazard or intensity function to covariates and to preceding failure time history both models are of a stratified proportional hazards type one model includes baseline intensity functions that are arbitrary as a function of time from the beginning of study while the other includes baseline intensity functions that are arbitrary as a function of time from the study subject s immediately preceding failure partial likelihood functions are derived for the regression coefficients generalizations and illustrations are given

nonparametric methods for analyzing incomplete nondecreasing repeated measurements in comparing the effectiveness of two treatments suppose that nondecreasing repeated measurements of the same characteristic are scheduled to be taken over a common set of time points for each study subject a class of univariate one sided global asymptotically distribution free tests is proposed to test the equality of the two treatments the test procedures allow different patterns of missing observations in the two groups to be compared although the missing data mechanism is required to be independent of the observations in each treatment group test based point and interval estimators of the global treatment difference are given multiple inference procedures are also provided to examine the time trend of treatment differences over the entire study the proposed methods are illustrated by an example from a bladder cancer study

nonparametric models and methods for designs with dependent censored data part i we consider a nonparametric np approach to the analysis of repeated measures designs with censored data using the np model of akritas and arnold 1994 journal of the american statistical association 89 336 343 for marginal distributions we present test procedures for the np hypotheses of no main effects no interaction and no simple effects this extends the existing np methodology for such designs wei and lachin 1984 journal of the american statistical association 79 653 661 the procedures do not require any modeling assumptions and should be useful in cases where the assumptions of proportional hazards or location shift fail to be satisfied the large sample distribution of the test statistics is based on an i i d representation for kaplan meier integrals the testing procedures apply also to ordinal data and to data with ties useful small sample approximations are presented and their performance is examined in a simulation study finally the methodology is illustrated with two real life examples one with censored and one with missing data it is indicated that one of the data sets does not conform to any set of assumptions underlying the available methods and also that the present method provides a useful additional analysis even when data sets conform to modeling assumptions

testing for order restricted hypotheses in longitudinal data an inherent ordering we propose a quadratic score test qst based on a quadratic inference function for detecting an order in treatment effects for correlated data the quadratic inference function is similar to the negative of a log likelihood and it provides test statistics in the spirit of a x2 test for testing nested hypotheses as well as for assessing the goodness of fit of model assumptions under the null hypothesis of no order restriction it is shown that the qst statistic has a wald type asymptotic representation and that the asymptotic distribution of the qst statistic is a weighted x2 distribution furthermore an asymptotic distribution of the qst statistic under an arbitrary convex cone alternative is provided the performance of the qst is investigated through monte carlo simulation experiments analysis of the polyposis data demonstrates that the qst outperforms the wald test when data are highly correlated with a small sample size and there is a significant amount of missing data with a small number of clusters the proposed test statistic accommodates both time dependent and time independent covariates in a model

semi parametric and non parametric methods for the analysis of repeated measurements with applications to clinical trials techniques applicable for the analysis of longitudinal data when the response variable is non normal are not nearly as comprehensive as for normally distributed outcomes however there have been several recent developments semi parametric and non parametric methodology for the analysis of repeated measurements is reviewed the commonly encountered design in which for each subject one assesses a univariate response variable at multiple fixed time points is considered the types of outcomes considered include binary ordered categorical and continuous but extremely non normal response variables all of the methods considered allow for incomplete data due to the occurrence of missing observations in addition discrete and or continuous covariates which may be time dependent are accommodated by some of the approaches the methods are demonstrated using data from three clinical trials

cox regression analysis of multivariate failure time data the marginal approach multivariate failure time data are commonly encountered in scientific investigations because each study subject may experience multiple events or because there exists clustering of subjects such that failure times within the same cluster are correlated in this paper i present a general methodology for analysing such data which is analogous to that of liang and zeger for longitudinal data analysis this approach formulates the marginal distributions of multivariate failure times with the familiar cox proportional hazards models while leaving the nature of dependence among related failure times completely unspecified the baseline hazard functions for the marginal models may be identical or different simple estimating equations for the regression parameters are developed which yield consistent and asymptotically normal estimators and robust variance covarinace estimators are constructed to account for the intra class correlation simulation results demonstrate that the large sample approximations are adequate for practical use and that ignoring the intra class correlation could yield rather misleading variance estimators the proposed methodology has been fully implemented in a simple computer program which also incorporates several alternative approaches detailed illustrations with data from four clinical or epidemiologic studies are provided