analysis of rank measures of association for ordinal data from longitudinal studies abstract consideration is given to longitudinal data settings in which an ordinal response variable is observed at two or more visits for each subject in two or more ordered groups with at least moderately large sample sizes e g overall n 40 rank measures of association between group and response are constructed at each time and the covariance matrix of these measures is also estimated variation among the rank measures of association is then analyzed through weighted least squares methods with weights based on the estimated covariance matrix such methods permit evaluation of group visit interaction as well as other effects of interest extensions of this type of analysis to situations with stratification or concomitant variables or missing data are also considered examples are provided for illustrative purposes

multivariate non parametric methods for mann whitney statistics to analyse cross over studies with two treatment sequences a non parametric strategy for the analysis of ordinal data from cross over studies with two treatment sequences and d or 2 periods is examined through mann whitney rank measures of association for each period these statistics estimate the probability of larger response for a randomly selected patient in one group relative to a randomly selected patient in the other group such estimates are as well formed for comparisons between groups for u pairs of periods with the same treatment methods for u statistics are used to produce a consistent estimate of the covariance matrix for the d u mann whitney estimates the effects of periods and treatments on the respective mann whitney estimates are evaluated through linear or log linear models for estimation of the parameters in these models a modified weighted least squares method is applied through a 2d 1 or d u dimensional basis which effectively addresses potentially near singularities in the estimated covariance matrix of the mann whitney estimates the proposed methods are applicable to response variables with an interval or an ordered categorical scale their scope additionally has capabilities for controlling strata in the design of a cross over study or concomitant variables for which covariance adjustment is of interest for reduction of variance applications of the methods are illustrated through three cross over studies with different specifications for the two sequences of two treatments during two to four periods

pair correlation of torsion points on elliptic curves we prove the existence of the pair correlation measure associated to torsion points on the real locus e r of an elliptic curve e and provide an explicit formula for the limiting pair correlation function

recovery of inter block information in cross over trials for cross over designs we show that one can recover information on direct and or residual treatment effects from an inter block patients as blocks analysis as is done in an incomplete block design 1 by combining the intra and inter block estimates we obtain the generalized least squares estimate in analysing cross over trials we recommended this approach provided the between patient variance component can be estimated efficiently

clique descriptor of affine invariant regions for robust wide baseline image matching assuming that the image distortion between corresponding regions of a stereo pair of images with wide baseline can be approximated as an affine transformation if the regions are reasonably small recent image matching algorithms have focused on affine invariant region ir detection and its description to increase the robustness in matching however the distinctiveness of an intensity based region descriptor tends to deteriorate when an image includes homogeneous texture or repetitive pattern to address this problem we investigated the geometry of a local ir cluster also called a clique and propose a new clique based image matching method in the proposed method the clique of an ir is estimated by delaunay triangulation in a local affine frame and the hausdorff distance is adopted for matching an inexact number of multiple descriptor vectors we also introduce two adaptively weighted clique distances where the neighbour distance in a clique is appropriately weighted according to characteristics of the local feature distribution experimental results show the clique based matching method produces more tentative correspondences than variants of the sift based method

using the maximum test statistic in the two period crossover clinical trial in a two period crossover trial where residual carryover is suspected it is often advised that first period data only be used in an analysis appropriate for a parallel design however it has been shown willan and pater 1986 biometrics 42 593 599 that the crossover analysis is more powerful than the parallel analysis if the residual carryover expressed as a proportion of treatment effect is less than 2 square root of 2 1 rho where rho is the intrasubject correlation coefficient choosing between the analyses based on the empirical evaluation of this condition is equivalent to choosing the analysis with the larger corresponding test statistic approximate nominal significance levels are presented that maintain the desired level when basing the analysis on the maximum test statistic furthermore the power and precision of the analysis based on the maximum test statistic are compared to the crossover and parallel analyses

small sample inference for fixed effects from restricted maximum likelihood restricted maximum likelihood reml is now well established as a method for estimating the parameters of the general gaussian linear model with a structured covariance matrix in particular for mixed linear models conventionally estimates of precision and inference for fixed effects are based on their asymptotic distribution which is known to be inadequate for some small sample problems in this paper we present a scaled wald statistic together with an f approximation to its sampling distribution that is shown to perform well in a range of small sample settings the statistic uses an adjusted estimator of the covariance matrix that has reduced small sample bias this approach has the advantage that it reproduces both the statistics and f distributions in those settings where the latter is exact namely for hotelling t2 type statistics and for analysis of variance f ratios the performance of the modified statistics is assessed through simulation studies of four different reml analyses and the methods are illustrated using three examples

a conditional analysis for two treatment multiple period crossover designs with binomial or poisson outcomes and subjects who drop out we propose a conditional analysis for outcome data on numbers of recurrent symptoms arising in a two treatment multiple period crossover trial conditioning on subject specific totals removes any dependence on mean subject specific symptom rates and permits the use of standard software to perform regression analysis to examine treatment period carryover and interaction effects the addition of offsets to the regression equations allows the incorporation of data from subjects who do not complete all period in the trial we apply the proposed method to data from a crossover trial and discuss its advantages and disadvantages

determination of optimal designs using linear models in crossover trials this study determines the optimal designs for crossover trials with fixed size of population in order to estimate contrasts between two treatment effects for various numbers of periods the problem is approached in the framework of a linear model taking into consideration the structure of a variance matrix constructed from two random sources linked to subject random effect and linked to measurement random error different models as well as different optimality criteria are considered for example when two periods are planned for the criterion of the minimization of the variance of the treatment effect estimator in the presence of residual effect the optimal design corresponds to four groups of sequences t1 t2 t2 t1 t1 t1 t2 t2 without residual effect it corresponds to two groups t1 t2 t2 t1 optimal designs are given for the comparison of two treatments when using three or four periods

an analysis of two period crossover designs with carry over effects the crossover design is a type of longitudinal study with subjects receiving different treatments in different time periods when carry over effects are absent the usual crossover design is structured so that all the information about treatment effects is contained in the within subject contrasts standard analyses are based on these within subject contrasts and ignore any between subject information with carry over effects present these standard analyses can be very inefficient especially for suboptimal designs we describe alternative approaches based on methods for the analysis of longitudinal data

comparing treatment variances in repeated measures bioavailability trials in repeated measures bioavailability bioequivalence studies involving two formulations the underlying measurements such as the area under the plasma concentration time curve auc and the maximum plasma concentration cmax typically have a block compound symmetric covariance matrix to test the equality of the variances in such a covariance matrix we derive in this paper an exact test and four asymptotic tests we compare these tests using simulation to determine those that have good performance in terms of controlling the type i error rate as well as providing good power we provide an example to demonstrate the proposed method copyright 1999 john wiley sons ltd

the desirability of adjusting for residual effects in a crossover design summary crossover experiments in which treatments are applied in sequence to the same experimental unit may give misleading results if there are carryover effects from previous treatments in each sequence and these effects are not allowed for in the analysis this paper is concerned with how to decide whether or not to allow for carryover effects the general conclusion is that despite the increased variance resulting from adjustment the safest policy is always to allow for these effects in a crossover design different treatments are applied in turn to the same experimental unit kershner and federer 1981 patterson 1951 the commonest applications are in nutritional trials on animals and in clinical trials of drugs however one difficulty associated with this design is that from the second period onwards a residual or carryover effect may be present due to the treatment applied in the previous period this problem can be mitigated by ensuring that each treatment is preceded equally often by every other treatment williams 1949 has shown how latin squares can be chosen to achieve this balance even with this balance the straightforward comparison of any two treatment means will be biased if their residual effects differ because no treatment is preceded by itself the repetition of one of the periods in order to achieve a complete balance of the residual effects and hence remove the bias is often impossible because of the time that would be required for the extended experiment when crossover designs are used for treatment comparisons the usual procedure is to test for residual effects and only if they are significantly different from zero adjust for them in the estimation of treatment effects the decision whether to adjust or not is therefore based on a significance test applied at an arbitrarily specified significance level if however the precise estimation of treatment effects is of prime interest procedures which lead to estimators that have smallest mean square errors mses are more appropriate the purpose of this paper is to investigate the effectiveness of such a procedure attention is restricted to the case in which it is reasonable to suppose that the duration of residual effects is limited to the period immediately following the direct application of the treatment we shall assume that the major interest is in the effect of the treatments during the period of their application some combination of direct and residual effects would merit consideration if in practice the treatment is to be applied for a longer period

stereo matching using genetic algorithm with adaptive chromosomes abstract a new stereo matching scheme using a genetic algorithm is presented to improve the depth reconstruction method of stereo vision systems genetic algorithms are efficient search methods based on principles of population genetics i e mating chromosome crossover gene mutation and natural selection the proposed approach considers the matching environment as an optimization problem and finds the optimal solution by using an evolutionary strategy accordingly genetic operators are adapted for the circumstances of stereo matching 1 an individual is a disparity set 2 a chromosome has a 2d structure for handling image signals efficiently and 3 a fitness function is composed of certain constraints which are commonly used in stereo matching since the fitness function consists of intensity similarity and disparity smoothness the matching and relaxation processes are considered at the same time in each generation in order to acquire a disparity map consistent with the image appearance a region of the input image divided by zero crossing points is extracted and used in the determination of the chromosome shape as a result all chromosomes contain the external image form and the disparity output coincides with the input image without any modification of the matching algorithm in addition an informed gene generation based on intensity difference is applied to reduce the searching space of the genetic operations

scale affine invariant interest point detectors in this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations our scale and affine invariant detectors are based on the following recent results 1 interest points extracted with the harris detector can be adapted to affine transformations and give repeatable results geometrically stable 2 the characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives the laplacian 3 the affine shape of a point neighborhood is estimated based on the second moment matrix our scale invariant detector computes a multi scale representation for the harris interest point detector and then selects points at which a local measure the laplacian is maximal over scales this provides a set of distinctive points which are invariant to scale rotation and translation as well as robust to illumination changes and limited changes of viewpoint the characteristic scale determines a scale invariant region for each point we extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood an iterative algorithm modifies location scale and neighborhood of each point and converges to affine invariant points this method can deal with significant affine transformations including large scale changes the characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point we present a comparative evaluation of different detectors and show that our approach provides better results than existing methods the performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale affine invariant descriptors computed on the regions associated with our points

optimal two period repeated measurement designs with two or more treatments summary for two period repeated measurement designs for comparing t 2 treatments we discuss universally optimal designs when the number of subjects n is a multiple of t2 and some cases when n is a multiple of t we examine efficiencies of balanced designs and other symmetric designs relative to strongly balanced designs in addition efficiencies of the universally optimal designs obtained by hedayat zhao 1990 are examined under both fixed subject and random subject effect model assumptions

exact logistic regression theory and examples we provide an alternative to the maximum likelihood method for making inferences about the parameters of the logistic regression model the method is based appropriate permutational distributions of sufficient statistics it is useful for analysing small or unbalanced binary data with covariates it also applies to small sample clustered binary data we illustrate the method by analysing several biomedical data sets

analysis of repeated categorical data using generalized estimating equations moment methods for analysing repeated binary responses have been proposed by liang and zeger and extended by prentice and zhao and prentice in these estimating equations models are proposed for the correlation between the repeated binary responses we extend liang and zeger s method to models for the correlation between repeated nominal or ordinal categorical responses in particular when the repeated responses are binary our methods reduce to liang and zeger s method our method is illustrated with two datasets one dataset contains repeated observations of self assessment of arthritis an ordered variable with three categories collected during a randomized comparative study of alternative treatments of patients with rheumatoid arthritis the second dataset is a longitudinal study of the health effects of air pollution in which the repeated ordered multinomial response is the wheezing status no wheeze wheeze with cold wheeze apart from cold of a child at ages 9 10 11 and 12 years

a nonparametric approach to the analysis of the two treatment two period four sequence crossover model owing to the estimability problems in the two treatment two period two sequence crossover model the four sequence design ab ba aa bb has gained popularity this paper presents a nonparametric approach to the analysis of the two treatment two period four sequence crossover model using an approach similar to that of koch 1972 biometrics 28 577 584 after forming differences within an experimental unit the benard van elteren test benard and van elteren 1953 proc konink nederlandse akad van wetenshappen series a 56 358 369 uses the transformed data to construct a test of the equality of the direct effects of the treatment a numerical example is presented to illustrate the methodology

computing for incomplete repeated measures summary repeated measures experiments involve two or more intended measurements per subject if the within subjects design is the same for each subject and no data are missing then the analysis is relatively simple and there are readily available programs that do the analysis automatically however if the data are incomplete and do not have the same arrangement for each subject then the analysis becomes much more difficult beginning with procedures that are not optimal but are comparatively simple we discuss unbalanced linear model analysis and then normal maximum likelihood ml procedures included are ml and reml restricted maximum likelihood estimators for the mixed model and also estimators for a model that allows arbitrary within subject covariance matrices the objective is to give procedures that can be implemented with available software

analysis of crossover designs with multivariate response crossover designs involve observing the same response variate under different experimental conditions for each subject univariate methods are commonly used for analysis of data arising in these designs but multivariate procedures offer a more general approach the general multivariate linear model provides a natural framework for the simplest data structure as well as more complex settings with two or more response variates and measurements repeated over time multivariate models for crossover designs provide a unified approach that clarifies specification of hypotheses assumptions required and testing procedures in a wide class of applications that include longitudinal data as a special case we focus on the 2 2 crossover design but also describe models for analysing more complex crossover designs

estimation of denominator degrees of freedom of f distributions for assessing wald statistics for fixed effect factors in unbalanced mixed models summary tests for fixed effect factors in unbalanced mixed models have previously used t tests on a contrastby contrast basis or wald statistics without a universally accepted method of calculating the denominator degrees of freedom this situation has arisen because the variances of different contrasts are differently weighted sums of the variance components with associated degrees of freedom that are not necessarily equal a simultaneous f test for differences between all levels of a fixed effect factor can be derived by forming new contrasts by rotation of the original contrasts with variances that are close to being the same weighted sum of variance components the associated degrees of freedom for these new contrasts are nearly equal a small simulation study shows the appropriateness of a x2 approximation to the distribution of the weighted sums of variance components three simple examples are used to demonstrate the effects of rotation the last of these examples is also used to compare the proposed simultaneous f test with the distribution of the wald statistic obtained by numerical simulation the method of rotations is then applied to data on the range size of mountain hares lepus timidus to assess the evidence for a two way interaction between season and habitat analysis of data from balanced experiments is traditionally performed by an analysis of variance in which the total sum of squared deviations of observations about their mean is partitioned into sums of squares attributable to either the different treatment effects or the different random effects under standard distributional assumptions each random effect sum of squares follows a multiple of a x2 distribution this multiple being the product of the degrees of freedom the number of independent error contrasts whose square has the required expectation and a linear combination of the different variance components the coefficients in this linear combination being fixed by the design under any null hypothesis concerning the absence of treatment effects the corresponding treatment sum of squares also follows such a multiple of a x2 distribution furthermore the linear combination of variance components in the multiple for the treatment sum of squares is identical to the linear combination for one of the random effect sum of squares hence hypotheses about the treatment effects can be tested by dividing treatment mean squares by the appropriate error mean square to form a variance ratio with an f distribution the benefits of experimental design accrue first through the variance of all contrasts for any given treatment factor or interaction having the same expectation under the null hypothesis second through this variance being as small as possible and third through there being as many error contrasts as possible whose variance is the same as that for the treatment factor or interaction analysis of data that lacks these properties of balance is much less straightforward yet there are many areas in which due to the nature of experimental material the treatment effects cannot be applied in a balanced fashion and so such unbalanced data are the norm rather than the

one stage individual participant data meta analysis models for continuous and binary outcomes comparison of treatment coding options and estimation methods a one stage individual participant data ipd meta analysis synthesizes ipd from multiple studies using a general or generalized linear mixed model this produces summary results eg about treatment effect in a single step whilst accounting for clustering of participants within studies via a stratified study intercept or random study intercepts and between study heterogeneity via random treatment effects we use simulation to evaluate the performance of restricted maximum likelihood reml and maximum likelihood ml estimation of one stage ipd meta analysis models for synthesizing randomized trials with continuous or binary outcomes three key findings are identified first for ml or reml estimation of stratified intercept or random intercepts models a t distribution based approach generally improves coverage of confidence intervals for the summary treatment effect compared with a z based approach second when using ml estimation of a one stage model with a stratified intercept the treatment variable should be coded using study specific centering ie 1 0 minus the study specific proportion of participants in the treatment group as this reduces the bias in the between study variance estimate compared with 1 0 and other coding options third reml estimation reduces downward bias in between study variance estimates compared with ml estimation and does not depend on the treatment variable coding for binary outcomes this requires reml estimation of the pseudo likelihood although this may not be stable in some situations eg when data are sparse two applied examples are used to illustrate the findings

local spacings along curves we investigate local spacing problems along curves via smooth maps moreover we provide explicit formulas for the nearest neighbor spacing distribution function of torsion points on elliptic curves over r and of rational points on the unit circle

optimal crossover designs for the comparison of two treatments in the presence of carryover effects and autocorrelated errors summary a model for responses in a crossover experiment that includes direct and first order carryover treatment effects together with an autocorrelated error term is considered when there are two treatments a method for generating designs that minimize the variance of the estimated treatment effects is proposed and explicit results are given for the three and four period cases efficiencies of some practical designs are calculated

meta analysis for 2 2 tables a bayesian approach this paper develops and implements a fully bayesian approach to meta analysis in which uncertainty about effects in distinct but comparable studies is represented by an exchangeable prior distribution specifically hierarchical normal models are used along with a parametrization that allows a unified approach to deal easily with both clinical trial and case control study data monte carlo methods are used to obtain posterior distributions for parameters of interest integrating out the unknown parameters of the exchangeable prior or random effects distribution the approach is illustrated with two examples the first involving a data set on the effect of beta blockers after myocardial infarction and the second based on a classic data set comprising 14 case control studies on the effects of smoking on lung cancer in both examples rather different conclusions from those previously published are obtained in particular it is claimed that widely used methods for meta analysis which involve complete pooling of o e values lead to understatement of uncertainty in the estimation of overall or typical effect size

unbalanced repeated measures models with structured covariance matrices the question of how to analyze unbalanced or incomplete repeated measures data is a common problem facing analysts we address this problem through maximum likelihood analysis using a general linear model for expected responses and arbitrary structural models for the within subject covariances models that can be fit include standard univariate and multivariate models with incomplete data random effects models and models with time series and factor analytic error structures we describe newton raphson and fisher scoring algorithms for computing maximum likelihood estimates and generalized em algorithms for computing restricted and unrestricted maximum likelihood estimates an example fitting several models to a set of growth data is included

the application of reml in clinical trials residual maximum likelihood reml is a technique for estimating variance components in multi classified data in contrast to analysis of variance it can be routinely applied to unbalanced data and avoids some of the problems of biased variance estimates found with standard maximum likelihood estimation the full reml method is of particular value for the analysis of unbalanced clinical trials as it allows recovery of all the available information on treatment effects which can lead to significant improvements in their precision the use of reml has until recently been limited by heavy computational requirements and lack of readily available software this is no longer such a restriction however as reml procedures are now available in several widely used statistical packages including bmdp genstat and sas this paper describes the reml technique and discusses its application to three common types of clinical trial crossover repeated measures and multicentre

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

use of two stage test statistic in the two period crossover trials for two period crossover trials where the residual carryover can only exist in the presence of treatment effect willan 1988 biometrics 44 211 218 recommended use of the maximum test statistic that chooses the analysis with the larger test statistic corresponding to the parallel analysis and the crossover analysis we construct two alternative two stage test procedures based on grizzle s approach that maintain the actual type i error rate at the desirable level the power accuracy and precision of the analysis based on the modified two stage procedures are compared to those based on the parallel analysis crossover analysis and the maximum test statistic

is the simple carry over model useful it is argued that the models usually employed for carry over effects in cross over trials are not reasonable the example of a non linear dose response for a dose finding trial arranged in a williams square is developed to show that if carry over is present to any appreciable degree the usual statistical models provide no guaranteed protection against its effects it is concluded that the most reasonably defended assumption about carry over effects is that no important carry over has taken place and that where this assumption cannot be defended statistical models provide no satisfactory substitute for it

distribution free fitting of logit models with random effects for repeated categorical responses this article discusses random effects models for within subject comparisons of repeated responses on the same categorical scale the models account for the correlation that normally occurs between repeated responses the standard way of fitting such models maximizes the marginal likelihood after integrating with respect to a distribution for the random effect an alternative non parametric approach does not assume a distributional form for the random effects recent literature shows that for certain simple logit models this approach yields essentially the same model parameter estimates as conditional maximum likelihood moreover these estimates also result from fitting corresponding quasi symmetric log linear models for simple data sets in which primary interest relates to subject specific comparisons of the repeated responses one can easily obtain the estimates with standard software for log linear models examples include data from crossover designs and from comparisons of treatment and control groups regarding the change between baseline and follow up observations

the analysis of data from 2 2 cross over trials with baseline measurements an account is given of the analysis of data from 2 x 2 cross over trials which include baseline measurements we show that most of the previously proposed methods can be incorporated into a general framework of least squares estimation with a simple linear model a simple analysis based on ordinary least squares estimators is described which can be used with either two sample t tests and confidence intervals or with the corresponding non parametric procedures it is shown how the use of generalized least squares estimators is equivalent to the use of covariance adjustment these methods require no assumptions about the covariance structure of the measurements from each subject the results of assessing the covariance structure present in examples of data from a number of trials are summarized these results suggest that previously proposed simple covariance structures are unlikely to be appropriate in general

a quasi dense approach to surface reconstruction from uncalibrated images this paper proposes a quasi dense approach to 3d surface model acquisition from uncalibrated images first correspondence information and geometry are computed based on new quasi dense point features that are resampled subpixel points from a disparity map the quasi dense approach gives more robust and accurate geometry estimations than the standard sparse approach the robustness is measured as the success rate of full automatic geometry estimation with all involved parameters fixed the accuracy is measured by a fast gauge free uncertainty estimation algorithm the quasi dense approach also works for more largely separated images than the sparse approach therefore it requires fewer images for modeling more importantly the quasi dense approach delivers a high density of reconstructed 3d points on which a surface representation can be reconstructed this fills the gap of insufficiency of the sparse approach for surface reconstruction essential for modeling and visualization applications second surface reconstruction methods from the given quasi dense geometry are also developed the algorithm optimizes new unified functionals integrating both 3d quasi dense points and 2d image information including silhouettes combining both 3d data and 2d images is more robust than the existing methods using only 2d information or only 3d data an efficient bounded regularization method is proposed to implement the surface evolution by level set methods its properties are discussed and proven for some cases as a whole a complete automatic and practical system of 3d modeling from raw images captured by hand held cameras to surface representation is proposed extensive experiments demonstrate the superior performance of the quasi dense approach with respect to the standard sparse approach in robustness accuracy and applicability

a variational approach to optimal two treatment crossover designs application to carryover effect models abstract a variational method is used to obtain sufficient conditions for an optimal two treatment p period design given a repeated measures model with arbitrary within subject covariance the design minimizes the variance of the estimator of treatment differences over all possible allocations of n subjects to the 2 p possible treatment sequences the method is applied to a model that includes carryover effects when subject effects are random with equicorrelated observations designs are optimal if they are a strongly balanced b uniform on the rows and c either uniform on the subjects p is even and greater than 2 or uniform on the first p 1 periods if p is odd for two periods the optimal design is ab ba aa bb the same designs are optimal when baseline measurements are obtained in each period baseline observations improve efficiency considerably for p 2 only slightly for p odd and are of no help for p even and greater than 2 a second model of errors in which a subject s response ha

interference between units in randomized experiments in a randomized experiment comparing two treatments there is interference between units if applying the treatment to one unit may affect other units interference implies that treatment effects are not comparisons of two potential responses that a unit may exhibit one under treatment and the other under control but instead are inherently more complex interference is common in social settings where people communicate compete or spread disease in studies that treat one part of an organism using a symmetrical part as control in studies that apply different treatments to the same organism at different times and in many other situations available statistical tools are limited for instance fisher s sharp null hypothesis of no treatment effect implicitly entails no interference and so his randomization test may be used to test no effect but conventional ways of inverting the test to obtain confidence intervals say for an additive effect are not applicable with interference another commonly used

optimal and efficient repeated measurements designs for uncorrelated observations abstract in repeated measurements crossover or changeover designs experimental subjects units are repeatedly exposed to treatments effects of treatments from one period that extend into the next are called carryover or residual effects in exact design theory designs that are universally optimal in the presence of carryover effects have been found when a subject s responses are uncorrelated however the results are valid only for restricted values of t the number of treatments p the number of periods and n the number of subjects in other optimality results the competing class of designs is a subset of the full class of repeated measurements designs these restrictions hinder applicability in the setting of approximate design theory kushner 1997b developed a new approach valid even for correlated responses here the results are specialized to the case of uncorrelated responses linear equations are given that determine all universally or a and d optimal repeated measurements desig

two treatment crossover designs for estimating a variety of effects abstract the variances of contrasts among direct residual and cumulative treatment effects are compared for a variety of two treatment crossover designs estimation of contrasts among second order residual effects and among direct by period and direct by first order residual interaction effects is also considered

some analysis strategies for three period changeover designs with two treatments alternative analysis strategies for the three period crossover design with two treatments are discussed in this paper one analysis strategy involves a parametric model that incorporates the effects of interest to implement this method one usually assumes that the covariance structure for the data has the sphericity or circularity property alternative approaches that do not require this assumption are described they are based on the parametric and non parametric analysis of appropriate within subject linear functions of the data the advantage of these methods is that one only needs the assumption that the resulting linear functions for the respective subjects are independent and have a common distribution the parametric approach also requires normality of the resulting within subject linear functions for small sample situations an extension of the non parametric method is considered for cases in which the treatment sequences are randomly assigned within strata the various methods are illustrated for a three period crossover design involving two strata with randomly assigned treatment sequences of the form a b a and b a b

stochastic stereo matching over scale a stochastic optimization approach to stereo matching is presented unlike conventional correlation matching and feature matching the method provides a dense array of disparities eliminating the need for interpolation first the stereo matching problem is defined in terms of finding a disparity map that satisfies two competing constraints 1 matched points should have similar image intensity and 2 the disparity map should vary as slowly as possible these constraints are interpreted as specifying the potential energy of a system of oscillators ground states are approximated by a new variant of simulated annealing which has two important features first the microcanonical ensemble is simulated using a new algorithm that is more efficient and more easily implemented than the familiar metropolis algorithm which simulates the canonical ensemble secondly it uses a hierarchical coarse to fine control structure employing gaussian or laplacian pyramids of the stereo images in this way quickly computed results at low resolutions are used to initialize the system at higher resolutions

a bayesian analysis of the two period crossover design for clinical trials statisticians have been critical of the use of the two period crossover designs for clinical trials because the estimate of the treatment difference is biased when the carryover effects of the two treatments are not equal in the standard approach if the null hypothesis of equal carryover effects is not rejected data from both periods are used to estimate and test for treatment differences if the null hypothesis is rejected data from the first period alone are used a bayesian analysis based on the bayes factor against unequal carryover effects is given although this bayesian approach avoids the all or nothing decision inherent in the standard approach it recognizes that with small trials it is difficult to provide unequivocal evidence that the carryover effects of the two treatments are equal and thus that the interpretation of the difference between treatment effects is highly dependent on a subjective assessment of the reality or not of equal carryover effects

modelling the covariance structure of repeated measurements models for repeated measurements used by wilson hebel and sherwin 1981 biometrics 37 553565 and mansour nordheim and rutledge 1985 biometrics 41 287 294 are considered these two models are generalized by the a p e k model obtained by introducing an extra parameter k a more general class of models described by kenward unpublished ph d thesis university of reading 1981 is briefly discussed simulation results are presented in which model parameters are estimated by maximum likelihood and likelihood ratios are used as criteria for choosing between models a set of blood pressure data is used to illustrate model fitting

progressively weighted affine adaptive correlation matching for quasi dense 3d reconstruction correlation matching has been widely accepted as a rudimentary similarity measure to obtain dense 3d reconstruction from a stereo pair in particular given a large overlapping area between images with minimal scale differences the correlation results followed by a geometrically constrained global optimisation delivers adequately dense and accurate reconstruction results in order to achieve greater reliability however correlation matching should correctly account for the geometrical distortion introduced by the different viewing angles of the stereo or multi view sensors conventional adaptive least squares correlation alsc matching addresses this by modifying the shape of a matching window iteratively assuming that the distortion can be approximated by an affine transform nevertheless since an image captured from different viewing angle is often not practically identical due to scene occlusions the matching confidence normally deteriorates subsequently it affects the density of the reconstruction results from alsc based stereo region growing algorithms to address this we propose an advanced alsc matching method that can progressively update matching weight for each pixel in an aggregating window using a relaxation labelling technique the experimental results show that the proposed method can improve matching performance which consequently enhances the quality of stereo reconstruction also the results demonstrate its ability to refine a scale invariant conjugate point pair to an affine and scale invariant point pair

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

the performance of the two stage analysis of two treatment two period crossover trials in the two treatment two period crossover trial patients are randomly allocated either to one group that receives treatment a followed by treatment b or to another group that receives the treatments in the reverse order grizzle first proposed a two stage procedure for analysing the data from such a trial this paper examines the long run sampling properties of this procedure in terms of mean square error of point estimates coverage probability of confidence intervals and actual significance level of hypothesis tests for the differences between the effects of the two treatments the advantages of incorporating baseline observations into the analysis are also explored because the preliminary test for carryover is highly correlated with the analysis of data from the first period only actual significance levels are higher than nominal levels even when there is no differential carryover when carryover is present the nominal level very seriously understates the actual level and this becomes even worse when baseline observations are ignored increasing sample size only exacerbates the problem since this adverse behaviour then occurs at smaller values of the carryover effect it is concluded that the two stage analysis is too potentially misleading to be of practical use

extending a bayesian analysis of the two period crossover to allow for baseline measurements in the context of a two period crossover study with baseline measurements a graphical method is developed for displaying the dependence of posterior inferences concerning the treatment effect on unavoidable prior beliefs about the correct model the method is a generalization of the approach developed by grieve for the corresponding case without baselines

optimal crossover designs in the presence of carryover effects under either the random patient effect model with sequence effects or the fixed patient effect model the usual two period two treatment crossover design ab ba cannot be used to estimate the contrast between direct treatment effects when unequal carryover effects are present if baseline observations are available the design ab ba can validly be used to estimate a treatment contrast however the design ab ba aa bb with baseline observations is more efficient in fact we show that this design is optimal whether or not baseline observations are available for experiments with more than two periods universally optimal designs are found for both models with and without carryover effects it is shown that uncertainty about the presence of carryover effects is of little or no consequence and the addition of baseline observations is of little or no added value for designs with three or more periods however if the experiment is limited to only two periods the investigator pays a heavy penalty

issues for covariance analysis of dichotomous and ordered categorical data from randomized clinical trials and non parametric strategies for addressing them analysis of covariance is an effective method for addressing two considerations for randomized clinical trials one is reduction of variance for estimates of treatment effects and thereby the production of narrower confidence intervals and more powerful statistical tests the other is the clarification of the magnitude of treatment effects through adjustment of corresponding estimates for any random imbalances between the treatment groups with respect to the covariables the statistical basis of covariance analysis can be either non parametric with reliance only on the randomization in the study design or parametric through a statistical model for a postulated sampling process for non parametric methods there are no formal assumptions for how a response variable is related to the covariables but strong correlation between response and covariables is necessary for variance reduction computations for these methods are straightforward through the application of weighted least squares to fit linear models to the differences between treatment groups for the means of the response variable and the covariables jointly with a specification that has null values for the differences that correspond to the covariables moreover such analysis is similarly applicable to dichotomous indicators ranks or integers for ordered categories and continuous measurements since non parametric covariance analysis can have many forms the ones which are planned for a clinical trial need careful specification in its protocol a limitation of non parametric analysis is that it does not directly address the magnitude of treatment effects within subgroups based on the covariables or the homogeneity of such effects for this purpose a statistical model is needed when the response criterion is dichotomous or has ordered categories such a model may have a non linear nature which determines how covariance adjustment modifies results for treatment effects insight concerning such modifications can be gained through their evaluation relative to non parametric counterparts such evaluation usually indicates that alternative ways to compare treatments for a response criterion with adjustment for a set of covariables mutually support the same conclusion about the strength of treatment effects this robustness is noteworthy since the alternative methods for covariance analysis have substantially different rationales and assumptions since findings can differ in important ways across alternative choices for covariables as opposed to methods for covariance adjustment the critical consideration for studies with covariance analyses planned as the primary method for comparing treatments is the specification of the covariables in the protocol or in an amendment or formal plan prior to any unmasking of the study

large occlusion stereo a method for solving the stereo matching problem in the presence of large occlusion is presented a data structure the disparity space image is defined to facilitate the description of the effects of occlusion on the stereo matching process and in particular on dynamic programming dp solutions that find matches and occlusions simultaneously we significantly improve upon existing dp stereo matching methods by showing that while some cost must be assigned to unmatched pixels sensitivity to occlusion cost and algorithmic complexity can be significantly reduced when highly reliable matches or ground control points are incorporated into the matching process the use of ground control points eliminates both the need for biasing the process towards a smooth solution and the task of selecting critical prior probabilities describing image formation finally we describe how the detection of intensity edges can be used to bias the recovered solution such that occlusion boundaries will tend to be proposed along such edges reflecting the observation that occlusion boundaries usually cause intensity discontinuities

using empirical bayes methods in biopharmaceutical research a compound sampling model where a unit specific parameter is sampled from a prior distribution and then observed are generated by a sampling distribution depending on the parameter underlies a wide variety of biopharmaceutical data for example in a multi centre clinical trial the true treatment effect varies from centre to centre observed treatment effects deviate from these true effects through sampling variation knowledge of the prior distribution allows use of bayesian analysis to compute the posterior distribution of clinic specific treatment effects frequently summarized by the posterior mean and variance more commonly with the prior not completely specified observed data can be used to estimate the prior and use it to produce the posterior distribution an empirical bayes or variance component analysis in the empirical bayes model the estimated prior mean gives the typical treatment effect and the estimated prior standard deviation indicates the heterogeneity of treatment effects in both the bayes and empirical bayes approaches estimated clinic effects are shrunken towards a common value from estimates based on single clinics this shrinkage produces more efficient estimates in addition the compound model helps structure approaches to ranking and selection provides adjustments for multiplicity allows estimation of the histogram of clinic specific effects and structures incorporation of external information this paper outlines the empirical bayes approach coverage will include development and comparison of approaches based on parametric priors for example a gaussian prior with unknown mean and variance and non parametric priors discussion of the importance of accounting for uncertainty in the estimated prior comparison of the output and interpretation of fixed and random effects approaches to estimating population values estimating histograms and identification of key considerations in the use and interpretation of empirical bayes methods

stability in the absence of treatment when subjects are measured twice once at each of two symmetrical locations or times stability of responses in the absence of treatment within subjects together with comparability of untreated responses between subjects is often viewed as supporting a conclusion that differences between treated and control responses reflect effects actually caused by the treatment the degree to which this intuitive argument is formally correct is explored in several related models a multivariate normal model a nonparametric model defined by symmetries an analogous randomized experiment and a sensitivity analysis model for observational studies in which treatments are not randomly assigned to subjects nor to locations within subjects card and kreuger s study of the employment effects of the minimum wage is used to illustrate the methods

optimality and efficiency of two treatment repeated measurements designs for an arbitrary covariance matrix and any number of treatments and periods necessary and sufficient conditions for the optimality of a repeated measurements i e crossover or changeover design were given in the as yet unpublished report by h b kushner optimal repeated measurements designs the linear optimality equations kushner report here we specialise the results to the two treatment case we give linear equations whose solutions are the proportions of subjects allocated to each treatment sequence in the most general optimal design the treatment effects information matrix of an optimal design is also presented the results are applied to several situations for arbitrary covariance matrices we show that designs consisting of at most two treatment sequences and their duals must necessarily be dual balanced to be optimal for autoregressive covariance matrices we confirm that designs of matthews 1987 for three and four periods are optimal and we derive new optimal designs for five and six periods some optimality results of laska meisner 1985 are extended a simple formula for the efficiency of a dual balanced nonoptimal design is provided and used to compute the exact efficiencies of some of kunert s 1991 designs

analysis of incomplete multivariate data using linear models with structured covariance matrices incomplete and unbalanced multivariate data often arise in longitudinal studies due to missing or unequally timed repeated measurements and or the presence of time varying covariates a general approach to analysing such data is through maximum likelihood analysis using a linear model for the expected responses and structural models for the within subject covariances two important advantages of this approach are 1 the generality of the model allows the analyst to consider a wider range of models than were previously possible using classical methods developed for balanced and complete data and 2 maximum likelihood estimates obtained from incomplete data are often preferable to other estimates such as those obtained from complete cases from the standpoint of bias and efficiency a variety of applications of the model are discussed including univariate and multivariate analysis of incomplete repeated measures data analysis of growth curves with missing data using random effects and time series models and applications to unbalanced longitudinal data

the analysis of continuous outcomes in multi centre trials with small centre sizes the standard analysis of clinical trials stratified by centre is to include centres as fixed effects but if many centres contribute small numbers of patients this approach results in a loss of power assuming no treatment by centre interaction we used simulation to examine power and coverage of confidence intervals from three approaches to the analysis of continuous outcome in multi centre trials ignoring centres including centres as fixed effects and including them as random effects the simulation incorporated eight sizes of centre effects randomization in blocks of size 2 or 4 and two sample sizes namely 100 and 200 patients per treatment arm in a parallel groups design all simulated data sets included many centres with few subjects the three different approaches were unbiased and had similar coverage fixed effects analysis was less powerful particularly when centre effects were small incorporating block randomization with larger block size increased non orthogonality in the design contributing to loss of power where centre effects are small and recruitment in many centres is low the approaches of ignoring centres or incorporating them as random effects have better performance than the traditional fixed effects analysis

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

switch back designs summary switch back designs originally proposed for cow lactation experiments are repeated measurement designs appropriate for experiments in which the responses of experimental units vary with time according to different rates a method for constructing such designs to compare an arbitrary number of treatments is presented together with their analysis of variance robustness of the switch back design when the treatments have residual as well as main effects is considered switch back and balanced residual designs are compared when the treatment has three levels in repeated measurement designs also referred to as before and after reversal crossover change over and multiple time series designs each experimental unit is assigned more than once to a treatment we consider a particular such design the switch back design originally proposed by brandt 1938 for comparing the effects of two different feeds on the milk yields of dairy cattle this design adjusts for the natural decline at rates which vary widely from cow to cow in milk yield during successive periods of lactation by switching the feeds given to the cows in a balanced manner lucas 1956 extended this design to cover up to nine treatments and computed the analysis of variance for treatment and possibly block effects for ease of exposition our discussion is couched in terms of lactation experiments although clearly our results are applicable in other contexts as well in 2 we construct switch back designs for an arbitrary number of treatments applied in three consecutive time periods section 3 provides the complete analysis of variance for treatment period lactation curve slope cow and block effects lucas s 1956 f statistic for treatment effects is identical to ours if no block effects are assumed however when block effects are assumed his error sum of squares has fewer degrees of freedom since his analysis is based on a singular transformation of the data so that the sum of squares for blocks must be partitioned from the error sum of squares also he defines the block effect using the curvatures of the lactation curves of the cows in the block while we more appropriately we believe use the cows average milk yields in 4 we consider the robustness of switch back designs to residual effects which occur when each treatment has a main effect on the experimental unit when it is applied and a residual effect during the immediately following time period in this case we derive the distribution of the switch back test statistic for treatment effects when residual effects are present

stereo matching with nonlinear diffusion one of the central problems in stereo matching and other image registration tasks is the selection of optimal window sizes for comparing image regions this paper addresses this problem with some novel algorithms based on iteratively diffusing support at different disparity hypotheses and locally controlling the amount of diffusion based on the current quality of the disparity estimate it also develops a novel bayesian estimation technique which significantly outperforms techniques based on area based matching ssd and regular diffusion we provide experimental results on both synthetic and real stereo image pairs