extended vikor method in comparison with outranking methods the vikor method was developed to solve mcdm problems with conflicting and noncommensurable different units criteria assuming that compromising is acceptable for conflict resolution the decision maker wants a solution that is the closest to the ideal and the alternatives are evaluated according to all established criteria this method focuses on ranking and selecting from a set of alternatives in the presence of conflicting criteria and on proposing compromise solution one or more the vikor method is extended with a stability analysis determining the weight stability intervals and with trade offs analysis the extended vikor method is compared with three multicriteria decision making methods topsis promethee and electre a numerical example illustrates an application of the vikor method and the results by all four considered methods are compared

choice of column scores for testing independence in ordered 2 x k contingency tables the numerous statistical methods for testing no association between a binary response rows and k ordered categories columns group naturally into two classes those that require preassigned numerical column scores and those that do not an example of the former would be a logistic regression analysis and of the latter would be a wilcoxon rank sum test in this paper we demonstrate that the perceived advantage of not preassigning scores is illusory we do this by presenting an example from our consulting experience in which the midrank scores used by the rank tests that do not require preassigned scores are clearly inappropriate our recommendations are to assign reasonable column scores whenever possible and to consider equally spaced scores when the choice is not apparent midranks as scores should always be examined for their appropriateness before a rank test is applied

multicriteria sorting using a valued indifference relation under a preference disaggregation paradigm abstract most multicriteria decision methods need the definition of a significant amount of preferential information from a decision agent the preference disaggregation analysis paradigm infers the model s parameter values from holistic judgments provided by a decision agent here a new method for inferring the parameters of a fuzzy outranking model for multicriteria sorting is proposed this approach allows us to use most of the preferential information contained in a reference set the central idea is to characterize the quality of the model by measuring discrepancies and concordances amongst i the preference relations derived from the outranking model and ii the preferential information contained in the reference set the model s parameters are inferred from a multiobjective optimization problem according to some additional preferential information from a decision agent once the model has been fitted sorting decisions about new objects are performed by using a fuzzy indifference relation this proposal performs very well in some examples

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

homogeneous linear predictor models for contingency tables maximum likelihood ml inference for the class of homogeneous linear predictor hlp models for contingency tables is described hlp models constrain the expected table counts m through l m x where the link l is allowed to be a many to one nonlinear function generalized log linear association trend marginal cumulative probit and conditional marginal homogeneity models are given as specific examples ml fit results which include point estimates goodness of fit statistics and asymptotic based approximate distributions are described and compared for equivalent hlp models the results are valid for a wide variety of sampling plans including combinations of product multinomial and poisson sampling an important practical implication of this article is that the implementation of ml fitting and theory is straightforward and an attractive alternative to weighted least squares estimation for hlp models

evolutionary induction of global model trees with specialized operators and memetic extensions metaheuristics such as evolutionary algorithms ea s have been successfully applied to the problem of decision tree induction recently an ea was proposed to evolve model trees which are a particular type of decision tree that is employed to solve regression problems however there is a need to specialize the ea s in order to exploit the full potential of evolutionary induction the main contribution of this paper is a set of solutions and techniques that incorporates knowledge about the inducing problem for the global model tree into the evolutionary search the objective of this paper is to demonstrate that specialized ea can find more accurate and less complex solutions to the traditional greedy induced counterparts and the straightforward application of ea this paper proposes a novel solution for each step of the evolutionary process and presents a new specialized ea for model tree induction called the global model tree gmt an empirical investigation shows that trees induced by the gmt are one order of magnitude less complex than trees induced by popular greedy algorithms and they are equivalent in terms of predictive accuracy with output models from straightforward implementations of evolutionary induction and state of the art methods

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

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

a hybrid multi objective immune algorithm for a flow shop scheduling problem with bi objectives weighted mean completion time and weighted mean tardiness this paper investigates a novel multi objective model for a no wait flow shop scheduling problem that minimizes both the weighted mean completion time c w and weighted mean tardiness t w obtaining an optimal solution for this type of complex large sized problem in reasonable computational time by using traditional approaches and optimization tools is extremely difficult this paper presents a new hybrid multi objective algorithm based on the features of a biological immune system is and bacterial optimization bo to find pareto optimal solutions for the given problem to validate the performance of the proposed hybrid multi objective immune algorithm hmoia in terms of solution quality and diversity level various test problems are examined further the efficiency of the proposed algorithm based on various metrics is compared against five prominent multi objective evolutionary algorithms ps nc ga nsga ii spea ii moia and misa our computational results suggest that our proposed hmoia outperforms the five foregoing algorithms especially for large sized problems

non local length estimators and concave functions abstract in a previous work 1 the authors introduced the non local estimators nle a wide class of polygonal length estimators including the sparse estimators and a part of the dss ones nle are studied here under concavity assumption and it is shown that concavity almost doubles the multigrid converge rate w r t the general case moreover an example is given that proves that the obtained convergence rate is optimal besides the notion of biconcavity relative to a nle is proposed to describe the case where the digital polygon is also concave thanks to a counterexample it is shown that concavity does not imply biconcavity then an improved error bound is computed under the biconcavity assumption

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

approximating pareto frontier using a hybrid line search approach the aggregation of objectives in multiple criteria programming is one of the simplest and widely used approach but it is well known that this technique sometimes fail in different aspects for determining the pareto frontier this paper proposes a new approach for multicriteria optimization which aggregates the objective functions and uses a line search method in order to locate an approximate efficient point once the first pareto solution is obtained a simplified version of the former one is used in the context of pareto dominance to obtain a set of efficient points which will assure a thorough distribution of solutions on the pareto frontier in the current form the proposed technique is well suitable for problems having multiple objectives it is not limited to bi objective problems and require the functions to be continuous twice differentiable in order to assess the effectiveness of this approach some experiments were performed and compared with two recent well known population based metaheuristics namely parego and nsga ii when compared to parego and nsga ii the proposed approach not only assures a better convergence to the pareto frontier but also illustrates a good distribution of solutions from a computational point of view both stages of the line search converge within a short time average about 150ms for the first stage and about 20ms for the second stage apart from this the proposed technique is very simple easy to implement and use to solve multiobjective problems

estimating a common relative risk application in equal employment abstract to analyze hiring data in equal employment cases the available positions should be stratified in accordance with the qualifications needed for the jobs it is then necessary to combine the results of each stratum to obtain an overall test of equal hiring rates furthermore a summary measure which compares the hiring rate of a minority applicant to that of a majority one is then estimated indeed the relative risk measure is used by the government in assessing an employment practice for possible discriminatory impact sometimes reliable data on the applicants is unavailable but an accurate estimate of the minority fraction i of qualified persons in the appropriate labor market is obtainable from census or other external data usually the number of hires t i in each occupation is small relative to the number of applicants which itself is a small fraction of the large external pool of qualified persons then the number of minority hires x i in each occupation can be regarded as a binom

patterns for multigrid equidistributed functions application to general parabolas and length estimation we show that for some special functions called k multigrid equidistributed functions we can compute the limit of the frequency of patterns in the discretization of their graph when the resolution tends to zero this result is applied to parabolas we deduce also that local length estimators almost never converge to the length for the parabolas

exact meta analysis approach for discrete data and its application to 2 2 tables with rare events this article proposes a general exact meta analysis approach for synthesizing inferences from multiple studies of discrete data the approach combines the p value functions also known as significance functions associated with the exact tests from individual studies it encompasses a broad class of exact meta analysis methods as it permits broad choices for the combining elements such as tests used in individual studies and any parameter of interest the approach yields statements that explicitly account for the impact of individual studies on the overall inference in terms of efficiency power and the type i error rate those statements also give rises to empirical methods for further enhancing the combined inference although the proposed approach is for general discrete settings for convenience it is illustrated throughout using the setting of meta analysis of multiple 2 2 tables in the context of rare events data such as observing few zero or zero total i e zero events in both arms out

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

evolutionary algorithms with preference polyhedron for interval multi objective optimization problems multi objective optimization problems mops with interval parameters are ubiquitous in real world applications existing evolutionary optimization methods however aim to obtain a set of well converged and evenly distributed pareto optimal solutions in this paper we presented a novel evolutionary algorithm ea that interacts with a decision maker dm during the optimization process to obtain the most preferred solution the theory of preference polyhedron for the optimization problem with interval parameters was developed first an interactive evolutionary algorithm iea for mops with interval parameters was then proposed based on the theory of preference polyhedron the algorithm periodically provides a set of non dominated solutions to the dm a preference polyhedron is constructed in the objective space by taking the worst solution chosen by the dm as the vertex the solutions with the same rank are sorted based on the polyhedron constructed finally our method was empirically evaluated on several mops with interval parameters where the value functions were used to simulate the dm s responses the numerical results indicated that our method is simpler and more efficient than the a posteriori method

c psa constrained pareto simulated annealing for constrained multi objective optimization in recent years evolutionary algorithms eas have been extensively developed and utilized to solve multi objective optimization problems however some previous studies have shown that for certain problems an approach which allows for non greedy or uphill moves unlike eas can be more beneficial one such approach is simulated annealing sa sa is a proven heuristic for solving numerical optimization problems but owing to its point to point nature of search limited efforts has been made to explore its potential for solving multi objective problems the focus of the presented work is to develop a simulated annealing algorithm for constrained multi objective problems the performance of the proposed algorithm is reported on a number of difficult constrained benchmark problems a comparison with other established multi objective optimization algorithms such as infeasibility driven evolutionary algorithm idea non dominated sorting genetic algorithm ii nsga ii and multi objective scatter search ii moss ii has been included to highlight the benefits of the proposed approach

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

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

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

an evolutionary approach to construction of outranking models for multicriteria classification the case of the electre tri method outranking methods constitute an important class of multicriteria classification models often however their implementation is cumbersome due to the large number of parameters that the decision maker must specify past studies tried to address this issue using linear and nonlinear programming to elicit the necessary preferential information from assignment examples in this study an evolutionary approach based on the differential evolution algorithm is proposed in the context of the electre tri method computational results are given to test the effectiveness of the methodology and the quality of the obtained models

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

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

a comparison of several point estimators of the odds ratio in a single 2 x 2 contingency table the relative performance of the unconditioned maximum likelihood estimators umles conditional mles cmles and jewell type estimators of the odds ratio or and its logarithm were investigated in sets of single 2 x 2 contingency tables the tables were generated by complete enumeration of all possible cell frequencies consistent with a single fixed margin the bias mean squared error mse and average absolute error aae were computed for all estimators using the individual table probabilities as weights the results showed that for the or jewell s estimator usually had smaller bias mse and aae than either of the mles while the differences were often slight for mse and aae for bias it was sometimes substantial for the log or the umle usually had the lowest bias and its mse and aae were only slightly greater than those for the other estimators overall we recommend estimation on the log scale using the umle if or is to be estimated jewell s method had strong merit although it is nonsymmetric with respect to the table orientation in view of this the umle may again be favoured in some situations

memetic multiobjective particle swarm optimization based radial basis function network for classification problems this paper presents a new multiobjective evolutionary algorithm applied to a radial basis function rbf network design based on multiobjective particle swarm optimization augmented with local search features the algorithm is named the memetic multiobjective particle swarm optimization rbf network mpson because it integrates the accuracy and structure of an rbf network the proposed algorithm is implemented on two class and multiclass pattern classification problems with one complex real problem the experimental results indicate that the proposed algorithm is viable and provides an effective means to design multiobjective rbf networks with good generalization capability and compact network structure the accuracy and complexity of the network obtained by the proposed algorithm are compared with the memetic non dominated sorting genetic algorithm based rbf network mgan through statistical tests this study shows that mpson generates rbf networks coming with an appropriate balance between accuracy and simplicity outperforming the other algorithms considered

randomization model methods for evaluating treatment efficacy in multicenter clinical trials summary this paper studies randomization model methods for analyzing data from a multicenter study comparing the effectiveness of two treatments the mantel haenszel mean score statistic which can be used for continuous or ordered categorical response variables is shown to be a useful nonparametric alternative to standard linear model methods for testing the significance of the average treatment difference in an extensive simulation study the mean score test performs nearly as well as the optimal linear model methods when the normal theory assumptions are satisfied a related estimator of the average treatment difference is also studied this estimator which is a weighted average of the center specific mean differences is analogous to the commonly used mantel haenszel estimator of the average odds ratio in stratified 2 x 2 contingency tables the proposed estimator is equivalent to the fixed effects analysis of variance estimator from the main effects model and valid estimation of its variance is feasible under very general assumptions a frequently occurring problem in medical research is evaluation of the effectiveness of a new treatment in patients with a specified disease or condition one commonly used design involves selection of eligible patients randomization to one of two groups new therapy standard treatment measurement of an appropriate outcome variable following treatment and statistical comparison of the distribution of the outcome in the two groups since the number of eligible patients at any one center may be relatively small such clinical trials often involve the participation of multiple investigators in this case patients are randomized within each center the objectives of the data analysis are to test if there is a statistically significant difference between the two treatments and to estimate the magnitude of the average treatment difference for both objectives it is important to control for the fact that the data are from multiple centers if the outcome variable is normally distributed standard linear model methods are often used to test and estimate the treatment difference one issue that arises in such an analysis however concerns whether the center effect should be treated as fixed or random in the fixed effects model both treatment group and center are considered to be fixed effects and the assumption is made that subjects are randomly selected from the center specific patient populations this model permits statistical inferences to the patient populations associated with the participating centers the mixed model approach treats the treatment group as a fixed effect and the center as a random effect although statistical inferences to a larger population of centers are permitted it makes the strong assumption that centers are selected at random in practice very few if any study protocols incorporate either random selection of centers or random selection of patients within centers thus neither the mixed model nor the fixed effects linear model can be strictly justified in addition although the fixed effects two way analysis of variance anova model with effects for center and treatment is commonly used there is no consensus among statisticians as to whether the model should include the center by treatment interaction this is partially due to the fact that patient enrollment often varies considerably among centers whereas the estimator of the average treatment difference from the main effects model

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

a review of some statistical methods for covariance analysis of categorical data three general methods for covariance analysis of categorical data are reviewed and applied to an example from a clinical trial in rheumatoid arthritis the three methods considered are randomization model nonparametric procedures maximum likelihood logistic regression and weighted least squares analysis of correlated marginal functions a fourth heuristic approach the unweighted linear model analysis is an approximate procedure but it is easy to implement the assumptions and statistical issues for each method are discussed so as to emphasize philosophical differences between their rationales attention is given to computational differences but it is shown that the methods lead to similar results for analogous problems it is argued that the essential differences between the methods lie in their underlying assumptions and the generality of the conclusions which may be drawn

non local estimators an interesting property for curve length digital estimators is the convergence toward the continuous length and the associate convergence speed when the grid spacing tends to zero on the one hand dss based estimators were proved to converge but only under some convexity and smoothness or polygonal assumptions on the other hand the sparse estimators were introduced in a previous paper by the authors and their convergence for lipschitz functions was proved without convexity assumption here a wider class of estimators the non local estimators is defined that intends to gather sparse estimators and dss based estimators their convergence is proved and an error upper bound for a large class of functions is given

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

analysis of repeated ordered categorical outcomes with possibly missing observations and time dependent covariates abstract this article describes a method for comparing responses in two groups of subjects observed repeatedly at a common set of observation times when the response is an ordered categorical outcome the method which allows both time dependent covariates and missing observations consists of two analytic steps in the first step the data are analyzed separately at each occasion using a regression model chosen from the class of models for ordinal data proposed by mccullagh 1980 the joint asymptotic distribution of the estimates of these occasion specific regression coefficients and a consistent estimator of their asymptotic covariance matrix are obtained without imposing any parametric model of dependence on the repeated observations in the second step this asymptotic distribution together with appropriate simultaneous inference procedures is used to characterize the overall difference between groups and the variation in group differences over time the missing data process may differ between gro

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

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

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

increasing selective pressure towards the best compromise in evolutionary multiobjective optimization the extended nosga method most current approaches in the evolutionary multiobjective optimization literature concentrate on adapting an evolutionary algorithm to generate an approximation of the pareto frontier however finding this set does not solve the problem the decision maker still has to choose the best compromise solution out of that set here we introduce a new characterization of the best compromise solution of a multiobjective optimization problem by using a relational system of preferences based on a multicriteria decision aid way of thinking and an outranked based dominance generalization we derive some necessary and sufficient conditions which describe satisfactory approximations to the best compromise such conditions define a lexicographic minimum of a bi objective optimization problem which is a map of the original one the nosga ii method is a nsga ii inspired efficient way of solving the resulting mapped problem

some general methods for the analysis of categorical data in longitudinal studies this paper is concerned with the analysis of multivariate categorical data from epidemiologic and clinical studies with longitudinal designs an expository discussion of pertinent hypotheses for such situations is provided within the context of two relevant data sets appropriate large sample tests of these hypotheses are developed through the application of weighted least squares to generate wald statistics these procedures are illustrated with extensive analyses of one of these data sets in some situations the resulting cross classification of the response variables leads to extremely sparse frequency data especially when the number of subjects is not large for such repeated measurement designs in which a single variable is measured repeatedly over time this paper considers the use of a generalized mantel haenszel strategy for tests of marginal homogeneity symmetry these randomization model methods are illustrated for data in which the repeated measurement variable is reported on an ordinal scale this paper also focuses on the available computing software to implement these methods within the version 5 release of the sas system the randomization model approach can be implemented within the freq procedure and a broad range of models and hypotheses can be investigated within the catmod procedure

an optimal image watermarking approach based on a multi objective genetic algorithm in accordance with the multi objective nature of image watermarking an optimal image watermarking approach using a multi objective genetic algorithm is presented in this paper both watermarking parameters and embedding positions are often important factors affecting the performance of watermarking systems the proposed multi objective watermarking method can automatically optimize system parameters and a variable length mechanism is specially designed to search the most suitable positions for embedding watermarks the method can also remove the difficult issue of determining optimal watermarking parameters from previous watermarking algorithms the proposed multi objective watermarking method directly deals with the problem of optimizing watermarking under non dominated meaning thus it can effectively avoid the difficulty of determining the optimally weighted factor in existing single objective watermarking schemes in addition a pareto optimal set generated by multi objective optimization can provide flexibility in selecting the most suitable watermarking parameters according to practical requirements

nonparametric analysis of covariance by matching the basic problem under consideration is the comparison of treatments with respect to a response y when a covariable x is taken into account various methods involving matching may be regarded as compromises between the standard analysis of covariance and the standard analysis of independent matched pairs first there is no need to restrict attention to independent matched pairs but rather all matched pairs may be incorporated then if x is concomitant that is if its distribution is the same regardless of treatment methods may be used which are based ultimately on randomization although in practice they are based on analysis of variance when x is not concomitant methods related to partial correlation between y and treatment given x are applicable all methods considered may use either the actual magnitudes of y or analogues of their ranks

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

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

covariance adjustment of relative risk estimates in matched studies the matched sample case control study is widely used by epidemiologists to estimate the relative incidence of disease among persons exposed to different levels of one or more risk factors an apparent limitation of such designs has been the necessity to control the effects of all potential confounding variables in the matching process conditional likelihood analyses based on the linear logistic equation enable one to model the effects of covariates while preserving the original matching this paper reviews the logical basis for this methodology and illustrates its value by application to a case control study of esophageal cancer

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

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

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

a repeated measures concordance correlation coefficient the concordance correlation coefficient is commonly used to assess agreement between two raters or two methods of measuring a response when the data are measured on a continuous scale however the situation may arise in which repeated measurements are taken for each rater or method e g longitudinal studies in clinical trials or bioassay data with subsamples this paper proposes a coefficient for measuring agreement between two raters or two methods of measuring a response in the presence of repeated measurements we illustrate the methodology with examples comparing 1 1 hr versus 2 hr blood draws for measuring cortisol in an asthma clinical trial and 2 two measurements of percentage body fat from skinfold calipers and dual energy x ray absorptiometry

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

goodman and kruskal s gamma coefficient for ordinalized bivariate normal distributions we consider a bivariate normal distribution with linear correlation formula see text whose random components are discretized according to two assigned sets of thresholds on the resulting bivariate ordinal random variable one can compute goodman and kruskal s gamma coefficient formula see text which is a common measure of ordinal association given the known analytical monotonic relationship between pearson s formula see text and kendall s rank correlation formula see text for the bivariate normal distribution and since in the continuous case kendall s formula see text coincides with goodman and kruskal s formula see text the change of this association measure before and after discretization is worth studying we consider several experimental settings obtained by varying the two sets of thresholds or equivalently the marginal distributions of the final ordinal variables this study confirming previous findings shows how the gamma coefficient is always larger in absolute value than kendall s rank correlation this discrepancy lessens when the number of categories increases or given the same number of categories when using equally probable categories based on these results a proposal is suggested to build a bivariate ordinal variable with assigned margins and goodman and kruskal s formula see text by ordinalizing a bivariate normal distribution illustrative examples employing artificial and real data are provided

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

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

a new nonparametric approach for baseline covariate adjustment for two group comparative studies we consider two armed clinical trials in which the response and or the covariates are observed on either a binary ordinal or continuous scale a new general nonparametric np approach for covariate adjustment is presented using the notion of a relative effect to describe treatment effects the relative effect is defined by the probability of observing a higher response in the experimental than in the control arm the notion is invariant under monotone transformations of the data and is therefore especially suitable for ordinal data for a normal or binary distributed response the relative effect is the transformed effect size or the difference of response probability respectively an unbiased and consistent np estimator for the relative effect is presented further we suggest a np procedure for correcting the relative effect for covariate imbalance and random covariate imbalance yielding a consistent estimator for the adjusted relative effect asymptotic theory has been developed to derive test statistics and confidence intervals the test statistic is based on the joint behavior of the estimated relative effect for the response and the covariates it is shown that the test statistic can be used to evaluate the treatment effect in the presence of random covariate imbalance approximations for small sample sizes are considered as well the sampling behavior of the estimator of the adjusted relative effect is examined we also compare the probability of a type i error and the power of our approach to standard covariate adjustment methods by means of a simulation study finally our approach is illustrated on three studies involving ordinal responses and covariates

multi objective decision making model under fuzzy random environment and its application to inventory problems in this paper we concentrate on developing a fuzzy random multi objective model about inventory problems by giving some definitions and discussing some properties of fuzzy random variable we design a method of solving solution sets of fuzzy random multi objective programming problems these are applied to numerical inventory problems in which all inventory costs purchasing and selling prices in the objectives and constraints are assumed to be fuzzy random variables in nature and then the impreciseness of fuzzy random variables in the above objectives and constraints are transformed into fuzzy variables which are similar trapezoidal fuzzy numbers the exact parameters of fuzzy membership function and probability density function can be obtained through fuzzy random simulating the past dates by comparing the results with those from the fuzzy multi objective models we believe that the proposed fuzzy random multi objective model and hybrid intelligent algorithm provide significant solutions to construct other inventory models with fuzzy random variables in real life

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

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

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

comparison of design concepts in multi criteria decision making using level diagrams in this work we address the evaluation of design concepts and the analysis of multiple pareto fronts in multi criteria decision making using level diagrams such analysis is relevant when two or more design concepts with different design alternatives lie in the same objective space but describe different pareto fronts therefore the problem can be stated as a pareto front comparison between two or more design concepts that only differ in their relative complexity implementation issues or the theory applied to solve the problem at hand such analysis will help the decision maker obtain a better insight of a conceptual solution and be able to decide if the use of a complex concept is justified instead of a simple concept the approach is validated in a set of multi criteria decision making benchmark problems

application of the non outranked sorting genetic algorithm to public project portfolio selection this paper proposes the application of multi criteria analysis to the problem of allocating public funds to competing programs projects or policies with a subjective approach applied to define the concept of highest portfolio social return this portfolio corresponds to an attainable non strictly outranked state of the social object under consideration its existence requires a decision maker dm to establish a relational preference system of minimal consistency as the number of feasible portfolios increases exponentially the dm s asymmetric preference relation should be computable to perform an exploration of the portfolio space the complexity of many real situations requires evolutionary algorithms but in presence of many objectives evolutionary algorithms are inefficient we overcome this problem by using the extended non outranked sorting genetic algorithm nosga ii which handles multi criteria preferences through a robust model based on a binary fuzzy outranking relation expressing the truth value of the predicate portfolio x is at least as good as portfolio y the dm is assumed to be capable of assigning the parameters for constructing the outranking relation in case of collective decision making we first assume that the possible differing values of the group members are not strongly conflicting so that a consensus can be achieved on the model s parameters otherwise we propose a method in which each member of the heterogeneous group gets his her own best portfolio these individual solutions are then aggregated in a group s best acceptable portfolio which maximizes a measure of group satisfaction and minimizes regret the proposal is examined through two real size problems in which good solutions are reached the first example is useful to illustrate the case of social action program selection the second illustrates the case of basic research project portfolios

large scale evolutionary optimization using cooperative coevolution evolutionary algorithms eas have been applied with success to many numerical and combinatorial optimization problems in recent years however they often lose their effectiveness and advantages when applied to large and complex problems e g those with high dimensions although cooperative coevolution has been proposed as a promising framework for tackling high dimensional optimization problems only limited studies were reported by decomposing a high dimensional problem into single variables dimensions such methods of decomposition often failed to solve nonseparable problems for which tight interactions exist among different decision variables in this paper we propose a new cooperative coevolution framework that is capable of optimizing large scale nonseparable problems a random grouping scheme and adaptive weighting are introduced in problem decomposition and coevolution instead of conventional evolutionary algorithms a novel differential evolution algorithm is adopted theoretical analysis is presented in this paper to show why and how the new framework can be effective for optimizing large nonseparable problems extensive computational studies are also carried out to evaluate the performance of newly proposed algorithm on a large number of benchmark functions with up to 1000 dimensions the results show clearly that our framework and algorithm are effective as well as efficient for large scale evolutionary optimisation problems we are unaware of any other evolutionary algorithms that can optimize 1000 dimension nonseparable problems as effectively and efficiently as we have done

multi objective evolutionary algorithms based on the summation of normalized objectives and diversified selection most multi objective evolutionary algorithms moeas use the concept of dominance in the search process to select the top solutions as parents in an elitist manner however as moeas are probabilistic search methods some useful information may be wasted if the dominated solutions are completely disregarded in addition the diversity may be lost during the early stages of the search process leading to a locally optimal or partial pareto front beside this the non domination sorting process is complex and time consuming to overcome these problems this paper proposes multi objective evolutionary algorithms based on summation of normalized objective values and diversified selection snov ds the performance of this algorithm is tested on a set of benchmark problems using both multi objective evolutionary programming moep and multi objective differential evolution mode with the proposed method the performance metric has improved significantly and the speed of the parent selection process has also increased when compared with the non domination sorting in addition the proposed algorithm also outperforms ten other algorithms

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

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

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

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

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

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