rationality problem of three dimensional monomial group actions abstract let k be a field of characteristic not two and k x y z the rational function field over k with three variables x y z let g be a finite group acting on k x y z by monomial k automorphisms we consider the rationality problem of the fixed field k x y z g under the action of g namely whether k x y z g is rational that is purely transcendental over k or not we may assume that g is a subgroup of gl 3 z and the problem is determined up to conjugacy in gl 3 z there are 73 conjugacy classes of g in gl 3 z by results of endo miyata voskresenski lenstra saltman hajja kang and yamasaki 8 conjugacy classes of 2 groups in gl 3 z have negative answers to the problem under certain monomial actions over some base field k and the necessary and sufficient condition for the rationality of k x y z g over k is given in this paper we show that the fixed field k x y z g under monomial action of g is rational over k except for possibly negative 8 cases of 2 groups and unknown one case of the alternating group of degree four moreover we give explicit transcendental bases of the fixed fields over k for the unknown case we obtain an affirmative solution to the problem under some conditions in particular we show that if k is quadratically closed field then k x y z g is rational over k we also give an application of the result to 4 dimensional linear noether s problem

estimating a weighted average of stratum specific parameters this article investigates estimators of a weighted average of stratum specific univariate parameters and compares them in terms of a design based estimate of mean squared error mse the research is motivated by a stratified survey sample of florida medicaid beneficiaries in which the parameters are population stratum means and the weights are known and determined by the population sampling frame assuming heterogeneous parameters it is common to estimate the weighted average with the weighted sum of sample stratum means under homogeneity one ignores the known weights in favor of precision weighting adaptive estimators arise from random effects models for the parameters we propose adaptive estimators motivated from these random effects models but we compare their design based performance we further propose selecting the tuning parameter to minimize a design based estimate of mean squared error this differs from the model based approach of selecting the tuning parameter to accurately represent the heterogeneity of stratum means our design based approach effectively downweights strata with small weights in the assessment of homogeneity which can lead to a smaller mse we compare the standard random effects model with identically distributed parameters to a novel alternative which models the variances of the parameters as inversely proportional to the known weights we also present theoretical and computational details for estimators based on a general class of random effects models the methods are applied to estimate average satisfaction with health plan and care among florida beneficiaries just prior to medicaid reform

test of marginal compatibility and smoothing methods for exchangeable binary data with unequal cluster sizes exchangeable binary data are often collected in developmental toxicity and other studies and a whole host of parametric distributions for fitting this kind of data have been proposed in the literature while these distributions can be matched to have the same marginal probability and intra cluster correlation they can be quite different in terms of shape and higher order quantities of interest such as the litter level risk of having at least one malformed fetus a sensible alternative is to fit a saturated model bowman and george 1995 journal of the american statistical association 90 871 879 using the expectation maximization em algorithm proposed by stefanescu and turnbull 2003 biometrics 59 18 24 the assumption of compatibility of marginal distributions is often made to link up the distributions for different cluster sizes so that estimation can be based on the combined data stefanescu and turnbull proposed a modified trend test to test this assumption their test however fails to take into account the variability of an estimated null expectation and as a result leads to inaccurate p values this drawback is rectified in this article when the data are sparse the probability function estimated using a saturated model can be very jagged and some kind of smoothing is needed we extend the penalized likelihood method simonoff 1983 annals of statistics 11 208 218 to the present case of unequal cluster sizes and implement the method using an em type algorithm in the presence of covariate we propose a penalized kernel method that performs smoothing in both the covariate and response space the proposed methods are illustrated using several data sets and the sampling and robustness properties of the resulting estimators are evaluated by simulations

sample based polynomial approximation of rational bezier curves we present an iteration method for the polynomial approximation of rational bezier curves starting with an initial bezier curve we adjust its control points gradually by the scheme of weighted progressive iteration approximations the l p error calculated by the trapezoidal rule using sampled points is used to guide the iteration approximation we reduce the l p error by a predefined factor at every iteration so as to obtain the best approximation with a minimum error numerical examples demonstrate the fast convergence of our method and indicate that results obtained using the l 1 error criterion are better than those obtained using the l 2 error and l error criteria

estimation of covariate effects in generalized linear mixed models with informative cluster sizes in standard regression analyses of clustered data one typically assumes that the expected value of the response is independent of cluster size however this is often false for example in studies of surgical interventions investigators have frequently found surgery volume and outcomes to be related to the skill level of the surgeons this paper examines the effect of ignoring response dependent informative cluster sizes on standard analytical methods such as mixed effects models and conditional likelihood methods using analytic calculations simulation studies and an example from a study of periodontal disease we consider the case in which cluster sizes and responses share random effects which we assume to be independent of the covariates our focus is on maximum likelihood methods that ignore informative cluster sizes and we show that they exhibit little bias in estimating covariate effects that are uncorrelated with the random effects associated with cluster sizes however estimation of covariate effects that are associated with the random effects can be biased in particular for models with random intercepts only ignoring informative cluster sizes can yield biased estimators of the intercept but little bias in estimation of all covariate effects

weighted logrank tests for interval censored data when assessment times depend on treatment we consider weighted logrank tests for interval censored data when assessment times may depend on treatment and for each individual we only use the two assessment times that bracket the event of interest it is known that treating finite right endpoints as observed events can substantially inflate the type i error rate under assessment treatment dependence atd but the validity of several other implementations of weighted logrank tests score tests permutation tests multiple imputation tests has not been studied in this situation with a bounded number of unique assessment times the score test under the grouped continuous model retains the type i error rate asymptotically under atd however although the approximate permutation test based on the permutation central limit theorem is not asymptotically valid under every atd scenario we show through simulation that in many atd scenarios it retains the type i error rate better than the score test we show a case where the approximate permutation test retains the type i error rate when the exact permutation test does not we study and modify the multiple imputation logrank tests of huang lee and yu 2008 statistics in medicine 27 3217 3226 showing that the distribution of the rank like scores asymptotically does not depend on the assessment times we show through simulations that our modifications of the multiple imputation logrank tests retain the type i error rate in all cases studied even with atd and a small number of individuals in each treatment group simulations were performed using the interval r package us government work in the public domain

mean estimating equation approach to analysing cluster correlated data with nonignorable cluster sizes most methods for analysing cluster correlated biological data implicitly assume the ignorability of cluster sizes when this assumption fails the resulting inferences may be asymptotically invalid hoffman et al 2001 proposed a simple but computationally intensive method based on a large number of within cluster resamples and associated separate estimating equations that leads to asymptotically valid inferences whether the cluster sizes are ignorable or not we study a simple method based on a single inverse cluster size weighted estimating equation that avoids resampling and yet leads to asymptotically valid inferences simulation results are presented to assess the performance of the proposed method we also propose wald tests for ignorability of cluster sizes

augmented weighted estimators dealing with practical positivity violation to causal inferences in a random coefficient model the inverse probability of treatment weighted iptw estimator can be used to make causal inferences under two assumptions 1 no unobserved confounders ignorability and 2 positive probability of treatment and of control at every level of the confounders positivity but is vulnerable to bias if by chance the proportion of the sample assigned to treatment or proportion of control is zero at certain levels of the confounders we propose to deal with this sampling zero problem also known as practical violation of the positivity assumption in a setting where the observed confounder is cluster identity i e treatment assignment is ignorable within clusters specifically based on a random coefficient model assumed for the potential outcome we augment the iptw estimating function with the estimated potential outcomes of treatment or of control for clusters that have no observation of treatment or control if the cluster specific potential outcomes are estimated correctly the augmented estimating function can be shown to converge in expectation to zero and therefore yield consistent causal estimates the proposed method can be implemented in the existing software and it performs well in simulated data as well as with real world data from a teacher preparation evaluation study

weighted rank regression for clustered data analysis we consider ranked based regression models for clustered data analysis a weighted wilcoxon rank method is proposed to take account of within cluster correlations and varying cluster sizes the asymptotic normality of the resulting estimators is established a method to estimate covariance of the estimators is also given which can bypass estimation of the density function simulation studies are carried out to compare different estimators for a number of scenarios on the correlation structure presence absence of outliers and different correlation values the proposed methods appear to perform well in particular the one incorporating the correlation in the weighting achieves the highest efficiency and robustness against misspecification of correlation structure and outliers a real example is provided for illustration

a weighted multivariate sign test for cluster correlated data we consider the multivariate location problem with cluster correlated data a family of multivariate weighted sign tests is introduced for which observations from different clusters can receive different weights under weak assumptions the test statistic is asymptotically distributed as a chi squared random variable as the number of clusters goes to infinity the asymptotic distribution of the test statistic is also given for a local alternative model under multivariate normality optimal weights maximizing pitman asymptotic efficiency are provided these weights depend on the cluster sizes and on the intracluster correlation several approaches for estimating these weights are presented using pitman asymptotic efficiency we show that appropriate weighting can increase substantially the efficiency compared to a test that gives the same weight to each cluster a multivariate weighted t test is also introduced the finite sample performance of the weighted sign test is explored through a simulation study which shows that the proposed approach is very competitive a real data example illustrates the practical application of the methodology

letter to the editor on the conditions for the coincidence of two cubic bezier curves in a recent article wang et al 2 derive a necessary and sufficient condition for the coincidence of two cubic bezier curves with non collinear control points the condition reads that their control points must be either coincident or in reverse order we point out that this uniqueness of the control points for polynomial cubics is a straightforward consequence of a previous and more general result of barry and patterson namely the uniqueness of the control points for rational bezier curves moreover this uniqueness applies to properly parameterized polynomial curves of arbitrary degree

modeling survival data with informative cluster size analysis of clustered data focusing on inference of the marginal distribution may be problematic when the risk of the outcome is related to the cluster size termed as informative cluster size in the absence of censoring hoffman et al proposed a within cluster resampling method which is asymptotically equivalent to a weighted generalized estimating equations score equation we investigate the estimation of the marginal distribution for multivariate survival data with informative cluster size using cluster weighted weibull and cox proportional hazards models the cluster weighted cox model can be implemented using standard software simulation results demonstrate that the proposed methods produce unbiased parameter estimation in the presence of informative cluster size to illustrate the proposed approach we analyze survival data from a lymphatic filariasis study in recife brazil

interactive shape preserving interpolation by curvature continuous rational cubic splines abstract a scheme is described for interactively modifying the shape of convexity preserving planar interpolating curves an initial curve is obtained by patching together rational cubic and straight line segments this scheme has in general geometric continuity of order 2 g2 continuity and preserves the local convexity of the data a method for interactively modifying such curves while maintaining their desirable properties is discussed in detail in particular attention is focused upon local changes to the curve while retaining g2 continuity and shape preserving properties this is achieved by interactive adjustment of the bezier control points followed by automatic adjustment of the values of weights and curvatures in a prescribed manner a number of examples are presented

a c 1 rational spline in range restricted interpolation of scattered data a range restricted c1 interpolation local scheme to scattered data is developed c rational spline function classes over triangles and quadrilaterals have been investigated by the first author in this paper we concentrate on the c1 rational spline over triangles and represent it as piecewise a convex combination of three cubic bezier triangular patches further with such an equivalent form of c1 rational spline the construction of a range restricted c1 interpolant subject to polynomial constraint surface of degree up to three is considered in the end of this paper some numerical examples are illustrated

doubly robust estimation optimally truncated inverse intensity weighting and increment based methods for the analysis of irregularly observed longitudinal data longitudinal data arising from routine follow up of patients will often have irregular measurement times existing methods for analysis include joint modelling of the outcome and measurement processes and inverse intensity weighting iiw this work extends previously proposed analysis of increments to the case of irregular follow up yielding a model for the increments that can be used as a stand alone method furthermore we propose two ways of combining the increments and iiw estimators first we use the increment model to select the truncation point for the inverse intensity weights that minimises the mean squared error of the iiw estimator second we use the increment model to augment the usual iiw estimating equations to form a doubly robust estimator we evaluate the methods through simulation and apply these to a recent study of juvenile dermatomyositis

likelihood methods for binary responses of present components in a cluster in some biomedical studies involving clustered binary responses say disease status the cluster sizes can vary because some components of the cluster can be absent when both the presence of a cluster component as well as the binary disease status of a present component are treated as responses of interest we propose a novel two stage random effects logistic regression framework for the ease of interpretation of regression effects both the marginal probability of presence absence of a component as well as the conditional probability of disease status of a present component preserve the approximate logistic regression forms we present a maximum likelihood method of estimation implementable using standard statistical software we compare our models and the physical interpretation of regression effects with competing methods from literature we also present a simulation study to assess the robustness of our procedure to wrong specification of the random effects distribution and to compare finite sample performances of estimates with existing methods the methodology is illustrated via analyzing a study of the periodontal health status in a diabetic gullah population

marginal analyses of clustered data when cluster size is informative we propose a new approach to fitting marginal models to clustered data when cluster size is informative this approach uses a generalized estimating equation gee that is weighted inversely with the cluster size we show that our approach is asymptotically equivalent to within cluster resampling hoffman sen and weinberg 2001 biometrika 73 13 22 a computationally intensive approach in which replicate data sets containing a randomly selected observation from each cluster are analyzed and the resulting estimates averaged using simulated data and an example involving dental health we show the superior performance of our approach compared to unweighted gee the equivalence of our approach with wcr for large sample sizes and the superior performance of our approach compared with wcr when sample sizes are small

marginal analyses of longitudinal data with an informative pattern of observations we consider solutions to generalized estimating equations with singular working correlation matrices of which the estimator of diggle et al 2007 is a special case we give explicit conditions for consistent estimation when the pattern of observations may be informative in such cases simulations reveal reduced bias and reduced mean squared error compared with existing alternatives a study of peritoneal dialysis is used to illustrate the methodology

range restricted scattered data interpolation using convex combination of cubic bezier triangles abstract the construction of range restricted bivariate c 1 interpolants to scattered data is considered sufficient nonnegativity conditions on the bezier ordinates are derived to ensure that the nonnegativity of a cubic bezier triangular patch the gradients at the data sites are modified if necessary to ensure that the nonnegativity conditions are fulfilled the interpolating surface is piecewise a convex combination of three cubic bezier triangular patches with the same set of boundary bezier ordinates its construction is local and is easily extended to include as upper and lower constraints to the interpolant surfaces of the form z c x y where c x y is a constant linear quadratic or cubic polynomial moreover c 1 piecewise polynomial surfaces consisting of polynomial pieces of the form z c x y on the triangulation of the data sites are also admissible constraints a number of numerical examples are presented graphically

two sample tests for comparing intra individual genetic sequence diversity between populations gilbert rossini and shankarappa 2005 biometrics 61 106 117 present four u statistic based tests to compare genetic diversity between different samples the proposed tests improved upon previously used methods by accounting for the correlations in the data we find however that the same correlations introduce an unacceptable bias in the sample estimators used for the variance and covariance of the inter sequence genetic distances for modest sample sizes here we compute unbiased estimators for these and test the resulting improvement using simulated data we also show that contrary to the claims in gilbert et al it is not always possible to apply the welch satterthwaite approximate t test and we provide explicit formulas for the degrees of freedom to be used when on the other hand such approximation is indeed possible

regression analysis of clustered interval censored data with informative cluster size interval censored data are commonly found in studies of diseases that progress without symptoms which require clinical evaluation for detection several techniques have been suggested with independent assumption however the assumption will not be valid if observations come from clusters furthermore when the cluster size relates to response variables commonly used methods can bring biased results for example in a study on lymphatic filariasis a parasitic disease where worms make several nests in the infected person s lymphatic vessels and reside until adulthood the response variable of interest is the nest extinction times as the extinction times of nests are checked by repeated ultrasound examinations exact extinction times are not observed instead data are composed of two examination points the last examination time with living worms and the first examination time with dead worms furthermore as williamson et al statistics in medicine 2008 27 543 555 pointed out larger nests show a tendency for low clearance rates this association has been denoted as an informative cluster size to analyze the relationship between the numbers of nests and interval censored nest extinction times this study proposes a joint model for the relationship between cluster size and clustered interval censored failure data a proportional hazard model with random effect and a mixed ordinal regression model are applied to failure times and cluster size respectively the joint model approach addresses both the association among failure times from the same cluster and the dependency of failure times on cluster size simulation studies are performed to assess the finite sample properties of the estimators and lymphatic filariasis data are analyzed as an illustration

marginal analysis of correlated failure time data with informative cluster sizes we consider modeling correlated survival data when cluster sizes may be informative to the outcome of interest based on a within cluster resampling wcr approach and a weighted score function wsf method we derive the large sample properties for the wcr estimators under the cox proportional hazards model we establish consistency and asymptotic normality of the regression coefficient estimators and the weak convergence property of the estimated baseline cumulative hazard function the wsf method is to incorporate the inverse of cluster sizes as weights in the score function we conduct simulation studies to assess and compare the finite sample behaviors of the estimators and apply the proposed methods to a dental study as an illustration

constrained polynomial approximation of rational bezier curves using reparameterization abstract this paper proposes a novel method for polynomial approximation of rational bezier curves with constraints different from the previous techniques for a given rational bezier curve r t a polynomial curve q s with a parameter transformation s t such that q t is the closest point to the point r t is considered to approximate it to minimize the distance between these two curves in the l 2 norm produces a similar effect as that of the hausdorff distance we use a rational function s t of a mobius parameter transformation to approximate the function t the method can preserve parametric continuity or geometric continuity of any u v u v 0 orders at two endpoints respectively and applying the least squares method we deduce a matrix based representation of the control points of the approximation curve finally numerical examples show that the reparameterization based method is feasible and effective and has a smaller approximation error under the hausdorff distance than the previous methods

a log rank test for clustered data with informative within cluster group size the log rank test is a popular nonparametric test for comparing survival distributions among groups when data are organized in clusters of potentially correlated observations adjustments can be made to account for within cluster dependencies among observations eg tests derived from frailty models tests for clustered data can be further biased when the number of observations within each cluster and the distribution of groups within cluster are correlated with survival times phenomena known as informative cluster size and informative within cluster group size in this manuscript we develop a log rank test for clustered data that adjusts for the potentially biasing effect of informative cluster size and within cluster group size we provide the results of a simulation study demonstrating that our proposed test remains unbiased under cluster based informativeness while other candidate tests not accounting for the clustering structure do not properly maintain size furthermore our test exhibits power advantages under scenarios in which traditional tests are appropriate we demonstrate an application of our test by comparing time to functional progression between groups defined initial functional status in a spinal cord injury data set

a signed rank test for clustered data we consider the problem of comparing two outcome measures when the pairs are clustered using the general principle of within cluster resampling we obtain a novel signed rank test for clustered paired data we show by a simple informative cluster size simulation model that only our test maintains the correct size under a null hypothesis of marginal symmetry compared to four other existing signed rank tests further our test has adequate power when cluster size is noninformative in general cluster size is informative if the distribution of pair wise differences within a cluster depends on the cluster size an application of our method to testing radiation toxicity trend is presented

tests for informative cluster size using a novel balanced bootstrap scheme clustered data are often encountered in biomedical studies and to date a number of approaches have been proposed to analyze such data however the phenomenon of informative cluster size ics is a challenging problem and its presence has an impact on the choice of a correct analysis methodology for example dutta and datta 2015 biometrics presented a number of marginal distributions that could be tested depending on the nature and degree of informativeness of the cluster size these marginal distributions may differ as do the choices of the appropriate test in particular they applied their new test to a periodontal data set where the plausibility of the informativeness was mentioned but no formal test for the same was conducted we propose bootstrap tests for testing the presence of ics a balanced bootstrap method is developed to successfully estimate the null distribution by merging the re sampled observations with closely matching counterparts relying on the assumption of exchangeability within clusters the proposed procedure performs well in simulations even with a small number of clusters at different distributions and against different alternative hypotheses thus making it an omnibus test we also explain how to extend the ics test to a regression setting and thereby enhancing its practical utility the methodologies are illustrated using the periodontal data set mentioned earlier copyright 2017 john wiley sons ltd

rank sum tests for clustered data the wilcoxon rank sum test is widely used to test the equality of two populations because it makes fewer distributional assumptions than parametric procedures such as the t test however the wilcoxon rank sum test can be used only if data are independent when data are clustered tests based on generalized estimating equations gees that generalize the t test have been proposed here we develop a rank sum test that can be used when data are clustered as an application we use our rank sum test to develop a nonparametric test of association between a genetic marker and a quantitative trait locus we also give a rank sum test for equivalence of three or more populations that generalizes the kruskal wallis test to situations with clustered data unlike previous rank tests for clustered data our proposal is valid when members of the same cluster belong to different groups or when the correlation between cluster members differs across groups

an application of harrell s c index to ph frailty models frailty models are encountered in many medical applications yet little research has been devoted to develop measures that quantify the predictive ability of these models in this paper we elaborate on the concept of the concordance probability to clustered data resulting in an overall conditional c index or bfc o c and an overall marginal c index or c o m both overall c indices can be split up into a between conditional or c b c and a between marginal c index or c b m and into a within conditional or c w c and a within marginal c index or c w m for ph frailty models of the power variance family c w c and c w m are equivalent resulting in one within c index c w we propose an application of harrell s c index to estimate the proposed indices within a likelihood and a bayesian context and the performances of their point estimates and confidence credible intervals are compared in an extensive simulation study this simulation study shows that the point estimates of c w and c b m perform good within both a likelihood and bayesian context but that the point estimates of c b c show less bias for the bayesian approach than for the likelihood approach the 95 per cent confidence credible intervals also possess good coverage properties given that the point estimates perform good the performance of the c indices is evaluated on a real data set

informative cluster sizes for subcluster level covariates and weighted generalized estimating equations williamson et al 2003 s cluster weighted generalized estimating equations cwgee are effective at adjusting for bias due to informative cluster sizes for cluster level covariates we show that cwgee may not perform well however for covariates that can take different values within a cluster if the numbers of observations at each covariate level are informative on the other hand inverse probability of treatment weighting accounts for informative treatment propensity but not for informative cluster size motivated by evaluating the effect of a binary exposure in presence of such types of informativeness we propose several weighted generalized estimating equation estimators with weights related to the size of a cluster as well as the distribution of the binary exposure within the cluster choice of the weights depends on the population of interest and the nature of the exposure through simulation studies we demonstrate the superior performance of the new estimators compared to existing estimators such as from gee cwgee and inverse probability of treatment weighted gee we demonstrate the use of our method using an example examining covariate effects on the risk of dental caries among small children

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

bootstrapping robust estimates for clustered data in mixed models the use of robust estimates raises several interesting inferential challenges one of these challenges arises from the realization that the effect of contamination is to increase the variability in the data but robust estimates of variance components are usually smaller than their nonrobust counterparts the robust estimates reflect the variability of the bulk of the data which is not the same as the variability in the data generating process this means that the naive implementation of bootstrap procedures might not work in this article we consider several bootstrap procedures including random effect transformation and weighted bootstraps we give conditions for the asymptotic validity of the bootstraps and assess their performance via a small simulation study both the transformation and generalized cluster bootstrap perform well and are asymptotically valid under reasonable conditions

nurbs for curve and surface design from the publisher nurbs nonuniform rational b splines promises to be the future geometry standard for free form curves and surfaces this volume contains recent results and new nurbs techniques and developments the most important being curve surface from the cad cam industry the book has been carefully refereed researchers system programmers and graduate students in cagd cad cam and computer graphics will find this book uniquely suited to their field of work

closed natural splines an effective solution an algorithm for construction closed curvature continuous splines named as closed natural splines or cn splines based on cubic bezier representation along with supporting fuz zui theorem which provides an effective solution for the inversion of fuz zu a special case of almost three diagonal circulant matrix in explicit form is presented characteristics of fuz zui matrices examined exponentially relaxing oscillations for single point disturbance of cn spline demonstrated

a resampling procedure for complex survey data abstract in complex survey data often the sampling design induces a non iid structure to the data e g without replacement sampling stratification multistage or unequal probability of selection though techniques for variance estimation and confidence intervals do exist they often are cumbersome to implement or do not extend to complex designs it would be desirable to have resampling methods that reuse the existing estimation system repeatedly using computing power to avoid theoretical work and that can be applied to such data in recognition of this need various resampling procedures for variance estimation and confidence intervals in sample survey data where the sampling is without replacement have been proposed in the literature these include the jackknife the with replacement bootstrap bwr the without replacement bootstrap bwo and the rescaling bootstrap the bwr and bwo are applicable only to simple sampling designs others have shown the asymptotic consistency of jackknife vari

within cluster resampling for multilevel models under informative cluster size a within cluster resampling method is proposed for fitting a multilevel model in the presence of informative cluster size our method is based on the idea of removing the information in the cluster sizes by drawing bootstrap samples which contain a fixed number of observations from each cluster we then estimate the parameters by maximising an average over the bootstrap samples of a suitable composite log likelihood the consistency of the proposed estimator is shown 15 and does not require that the correct model for cluster size is specified we give an estimator of the covariance matrix of the proposed estimator and a test for the non informativeness of the cluster sizes a simulation study shows as in neuhaus mcculloch 2011 that the standard maximum likelihood estimator exhibits little bias for some regression coefficients however for those parameters which exhibit non negligible bias the proposed method is successful in cor 20 recting for this bias

correlated binary regression with covariates specific to each binary observation regression methods are considered for the analysis of correlated binary data when each binary observation may have its own covariates it is argued that binary response models that condition on some or all binary responses in a given block are useful for studying certain types of dependencies but not for the estimation of marginal response probabilities or pairwise correlations fully parametric approaches to these latter problems appear to be unduly complicated except in such special cases as the analysis of paired binary data hence a generalized estimating equation approach is advocated for inference on response probabilities and correlations illustrations involving both small and large block sizes are provided

necessary and sufficient conditions for rational quartic representation of conic sections conic section is one of the geometric elements most commonly used for shape expression and mechanical accessory cartography a rational quadratic bezier curve is just a conic section it cannot represent an elliptic segment whose center angle is not less than p however conics represented in rational quartic format when compared to rational quadratic format enjoy better properties such as being able to represent conics up to 2 p but not including 2 p without resorting to negative weights and possessing better parameterization therefore it is actually worth studying the necessary and sufficient conditions for the rational quartic bezier representation of conics this paper attributes the rational quartic conic sections to two special kinds that is degree reducible and improperly parameterized on this basis the necessary and sufficient conditions for the rational quartic bezier representation of conics are derived they are divided into two parts bezier control points and weights these conditions can be used to judge whether a rational quartic bezier curve is a conic section or for a given conic section present positions of the control points and values of the weights of the conic section in form of a rational quartic bezier curve many examples are given to show the use of our results

efficient estimation for rank based regression with clustered data rank based inference is widely used because of its robustness this article provides optimal rank based estimating functions in analysis of clustered data with random cluster effects the extensive simulation studies carried out to evaluate the performance of the proposed method demonstrate that it is robust to outliers and is highly efficient given the existence of strong cluster correlations the performance of the proposed method is satisfactory even when the correlation structure is misspecified or when heteroscedasticity in variance is present finally a real dataset is analyzed for illustration

symmetric functions and the phase problem in crystallography the calculation of crystal structure from x ray diffraction data requires that the phases of the structure factors fourier coefficients determined by scattering be deduced from the absolute values of those structure factors motivated by a question of herbert hauptman we consider the problem of determining phases by direct algebraic means in the case of crystal structures with n equal atoms in the unit cell with n small we rephrase the problem as a question about multiplicative invariants for a particular finite group action we show that the absolute values form a generating set for the field of invariants of this action and consider the problem of making this theorem constructive and practical the most promising approach for deriving explicit formulas uses sagbi bases

some actions of symmetrical groups abstract let k be any field v the n dimensional vector space over k on which the symmetric group sn acts by permuting a basis then the fixed fields k skv sn and k k v sn are rational over k where skv and k v are the kth symmetric power and exterior power of v respectively the rationality of some other fixed fields are established also

design and recovery of 2 d and 3 d shapes using rational gaussian curves and surfaces a new representation for parametric curves and surfaces is introduced here it is in rational form and uses rational gaussian bases this representation allows design of 2 d and 3 d shapes and makes recovery of shapes from noisy image data possible the standard deviations of gaussians in a curve or surface control the smoothness of a recovered shape the control points of a surface in this representation are not required to form a regular grid and a scattered set of control points is sufficient to reconstruct a surface examples of shape design shape recovery and image segmentation using the proposed representation are given

resampling inference with complex survey data abstract methods for standard errors and confidence intervals for nonlinear statistics such as ratios regression and correlation coefficients have been extensively studied for stratified multistage designs in which the clusters are sampled with replacement in particular the important special case of two sampled clusters per stratum these methods include the customary linearization or taylor method and resampling methods based on the jackknife and balanced repeated replication brr unlike the jackknife or the brr the linearization method is applicable to general sampling designs but it involves a separate variance formula for each nonlinear statistic thereby requiring additional programming efforts both the jackknife and the brr use a single variance formula for all nonlinear statistics but they are more computing intensive the resampling methods developed here retain these features of the jackknife and the brr yet permit extension to more complex designs involving sampling without replace

high order parametric polynomial approximation of quadrics in rd abstract in this paper an approximation of implicitly defined quadrics in r d by parametric polynomial hypersurfaces is considered the construction of the approximants provides the polynomial hypersurface in a closed form and it is based on the minimization of the error term arising from the implicit equation of a quadric it is shown that this approach also minimizes the normal distance between the quadric and the polynomial hypersurface furthermore the asymptotic analysis confirms that the distance decreases at least exponentially as the polynomial degree grows numerical experiments for spatial quadrics illustrate the obtained theoretical results

twisted actions of symmetric groups abstract let k be any field and the symmetric group s n act on the rational function field k x 1 x n by x i x i if a n and x i x i 1 if a n we shall show that the fixed field k x 1 x n s n is rational over k similar results for actions of s n on the symmetric powers and exterior powers of v n i 1 k x i are valid

hybrid polynomial approximation to higher derivatives of rational curves abstract in this paper we extend the results published in jcam volume 214 pp 163 174 in 2008 based on the bound estimates of higher derivatives of both bernstein basis functions and rational bezier curves we prove that for any given rational bezier curve if the convergence condition of the corresponding hybrid polynomial approximation is satisfied then not only the l th l 1 2 3 derivatives of its hybrid polynomial approximation curve uniformly converge to the corresponding derivatives of the rational bezier curve but also this conclusion is tenable in the case of any order derivative this result can expand the area of applications of hybrid polynomial approximation to rational curves in geometric design and geometric computation

a covariate specific time dependent receiver operating characteristic curve for correlated survival data several studies for the clinical validity of circulating tumor cells ctcs in metastatic breast cancer were conducted showing that it is a prognostic biomarker of overall survival in this work we consider an individual patient data meta analysis for nonmetastatic breast cancer to assess the discrimination of ctcs regarding the risk of death data are collected in several centers and present correlated failure times for subjects of the same center however although the covariate specific time dependent receiver operating characteristic roc curve has been widely used for assessing the performance of a biomarker there is no methodology yet that can handle this specific setting with clustered censored failure times we propose an estimator for the covariate specific time dependent roc curves and area under the roc curve when clustered failure times are detected we discuss the assumptions under which the estimators are consistent and their interpretations we assume a shared frailty model for modeling the effect of the covariates and the biomarker on the outcome in order to account for the cluster effect a simulation study was conducted and it shows negligible bias for the proposed estimator and a nonparametric one based on inverse probability censoring weighting while a semiparametric estimator ignoring the clustering is markedly biased finally in our application to breast cancer data the estimation of the covariate specific area under the curves illustrates that the ctcs discriminate better patients with inflammatory tumor than patients with noninflammatory tumor with respect to their risk of death

detecting case control expression quantitative trait loci using locally most powerful or maximin robust rank tests in testing genome wide gene expression quantitative trait loci efficiency robust statistical methods and their computational convenience are most relevant for this purpose we propose to use a modified locally most powerful rank test for the analysis of case control expression data this modified rank test statistic is computationally simple robust for non normally distributed expression data and asymptotically locally most powerful it depends on the specification of a location distribution form for data but is not sensitive to misspecifications when such a location distribution form cannot be specified we apply gastwirth s maximin efficiency robust rank test to gene expression data to maximize the worst pitman asymptotic relative efficiency among a family of location distributions we conduct simulation studies to assess their performance and use an application to real data for illustration copyright 2011 john wiley sons ltd

rank based inference for covariate and group effects in clustered data in presence of informative intra cluster group size there have been numerous attempts to extend the wilcoxon rank sum test to clustered data recently one such rank sum test dutta datta 2016 biometrics 72 432 440 was developed to compare the group specific marginal distributions of outcomes in clustered data where the conditional distributions of outcomes depend on the number of observations from that group in a given cluster a phenomenon referred to as informative intra cluster group icg size however comparison of group specific marginal distributions may not be sufficient in presence of some potentially useful covariables that are observed in the study in addition not accounting for the effect of these covariates can lead to biased and misleading inference for the group comparisons thus the purpose of this article is twofold first we develop a method to estimate the covariate effects using rank based weighted estimating equations that are appropriate when the icg size is informative second we construct an aligned rank sum test based on the covariate adjusted outcomes asymptotic distributions of the r estimators and the test statistic are provided through simulation studies we show the importance of selecting proper weights in constructing the estimating equations when informativeness is present through the cluster or icg sizes we also demonstrate the superiority and the robustness of our method in comparison to regular parametric linear mixed models in clustered data we apply our method to analyze different real life data sets including a data on birthweights of rat pups in different litters and a dental data on tooth attachment loss

bayesian modeling of multivariate spatial binary data with applications to dental caries dental research gives rise to data with potentially complex correlation structure assessments of dental caries yield a binary outcome indicating the presence or absence of caries experience for each surface of each tooth in a subject s mouth in addition to this nesting caries outcome exhibit spatial structure among neighboring teeth we develop a bayesian multivariate model for spatial binary data using random effects autologistic regression that controls for the correlation within tooth surfaces and spatial correlation among neighboring teeth using a sample from a clinical study conducted at the medical university of south carolina we compare this autologistic model with covariates to alternative models to demonstrate the improvement in predictions and also to assess the effects of covariates on caries experience

efficiency of regression estimates for clustered data statistical methods for clustered data such as generalized estimating equations gee and generalized least squares gls require selecting a correlation or convariance structure to specify the dependence between observations within a cluster valid regression estimates can be obtained that do not depend on correct specification of the true correlation but inappropriate specifications can result in a loss of efficiency we derive general expressions for the asymptotic relative efficiency of gee and gls estimators under nested correlation structures efficiency is shown to depend on the covariate distribution the cluster sizes the response variable correlation and the regression parameters the results demonstrate that efficiency is quite sensitive to the between and within cluster variation of the covariates and provide useful characterizations of models for which upper and lower efficiency bounds are attained efficiency losses for simple working correlation matrices such as independence can be large even for small to moderate correlations and cluster sizes

analysis of semiparametric regression models for repeated outcomes in the presence of missing data abstract we propose a class of inverse probability of censoring weighted estimators for the parameters of models for the dependence of the mean of a vector of correlated response variables on a vector of explanatory variables in the presence of missing response data the proposed estimators do not require full specification of the likelihood they can be viewed as an extension of generalized estimating equations estimators that allow for the data to be missing at random but not missing completely at random these estimators can be used to correct for dependent censoring and nonrandom noncompliance in randomized clinical trials studying the effect of a treatment on the evolution over time of the mean of a response variable the likelihood based parametric g computation algorithm estimator may also be used to attempt to correct for dependent censoring and nonrandom noncompliance but because of possible model misspecification the parametric g computation algorithm estimator in contrast with the proposed w

on the degree elevation of bernstein polynomial representation the polynomials determined in the bernstein bezier basis enjoy considerable popularity in computer aided design cad applications the common situation in these applications is that polynomials given in the basis of degree n have to be represented in the basis of higher degree the corresponding transformation algorithms are called algorithms for degree elevation of bernstein polynomial representations these algorithms are only then of practical importance if they do not require the ill conditioned conversion between the bernstein and the power basis we discuss all the algorithms of this kind known in the literature and compare them to the new ones we establish some among the latter are better conditioned and not more expensive than the currently used ones all these algorithms can be applied componentwise to vector valued polynomial bezier representations of curves or surfaces

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

on the convergence of hybrid polynomial approximation to higher derivatives of rational curves in this paper we derive the bounds on the magnitude of lth l 2 3 order derivatives of rational bezier curves estimate the error in the l norm sense for the hybrid polynomial approximation of the lth l 1 2 3 order derivatives of rational bezier curves we then prove that when the hybrid polynomial approximation converges to a given rational bezier curve the lth l 1 2 3 derivatives of the hybrid polynomial approximation curve also uniformly converge to the corresponding derivatives of the rational curve these results are useful for designing simpler algorithms for computing tangent vector curvature vector and torsion vector of rational bezier curves

nonparametric analysis of clustered multivariate data there is wide interest in extending univariate and multivariate nonparametric procedures to clustered and hierarchical data traditionally parametric mixed models have been used to account for the correlation structures among the dependent observational units in this work we extend multivariate nonparametric procedures for one sample and several sample location problems to clustered data settings the results are given for a general score function but with an emphasis on spatial sign and rank methods mixed models notation involving design matrices for fixed and random effects is used throughout the asymptotic variance formulas and limiting distributions of the test statistics under the null hypothesis and under a sequence of alternatives are derived as are the limiting distributions for the corresponding estimates the approach based on a general score function also shows for example how m estimates behave with clustered data efficiency studies demonstrate the practical advantages and disadvantag

new formulae for higher order derivatives and applications we present new formulae the slevinsky safouhi formulae i and ii for the analytical development of higher order derivatives these formulae which are analytic and exact represent the kth derivative as a discrete sum of only k 1 terms involved in the expression for the kth derivative are coefficients of the terms in the summation these coefficients can be computed recursively and they are not subject to any computational instability as examples of applications we develop higher order derivatives of legendre functions chebyshev polynomials of the first kind hermite functions and bessel functions we also show the general classes of functions to which our new formula is applicable and show how our formula can be applied to certain classes of differential equations we also presented an application of the formulae of higher order derivatives combined with extrapolation methods in the numerical integration of spherical bessel integral functions

cluster adjusted regression for displaced subject data cards marginal inference under potentially informative temporal cluster size profiles ignorance of the mechanisms responsible for the availability of information presents an unusual problem for analysts it is often the case that the availability of information is dependent on the outcome in the analysis of cluster data we say that a condition for informative cluster size ics exists when the inference drawn from analysis of hypothetical balanced data varies from that of inference drawn on observed data much work has been done in order to address the analysis of clustered data with informative cluster size examples include inverse probability weighting ipw cluster weighted generalized estimating equations cwgee and doubly weighted generalized estimating equations dwgee when cluster size changes with time i e the data set possess temporally varying cluster sizes tvcs these methods may produce biased inference for the underlying marginal distribution of interest we propose a new marginalization that may be appropriate for addressing clustered longitudinal data with tvcs the principal motivation for our present work is to analyze the periodontal data collected by beck et al 1997 journal of periodontal research 6 497 505 longitudinal periodontal data often exhibits both ics and tvcs as the number of teeth possessed by participants at the onset of study is not constant and teeth as well as individuals may be displaced throughout the study

bootstrapping clustered data summary various bootstraps have been proposed for bootstrapping clustered data from one way arrays the simulation results in the literature suggest that some of these methods work quite well in practice the theoretical results are limited and more mixed in their conclusions for example mccullagh reached negative conclusions about the use of non parametric bootstraps for one way arrays the purpose of this paper is to extend our understanding of the issues by discussing the effect of different ways of modelling clustered data the criteria for successful bootstraps used in the literature and extending the theory from functions of the sample mean to include functions of the between and within sums of squares and non parametric bootstraps to include model based bootstraps we determine that the consistency of variance estimates for a bootstrap method depends on the choice of model with the residual bootstrap giving consistency under the transformation model whereas the cluster bootstrap gives consistent estimates under both the transformation and the random effect model in addition we note that the criteria based on the distribution of the bootstrap observations are not really useful in assessing consistency

consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models generalized linear models are used for regression analysis in a number of cases including categorical responses where the classical assumptions are violated the statistical analysis of such models is based on the asymptotic properties of the maximum likelihood estimator we present mild general conditions which respectively assure weak or strong consistency or asymptotic normality most of the previous work has been concerned with natural link functions in this case our normality condition though obtained by a different approach is closely related to a condition of haberman 1977a examples show how the general conditions reduce to weak requirements for special exponential families further for regressors with a compact range sufficient conditions are given which do not involve the unknown parameter and are therefore easy to check in practice responses with a bounded range e g categorical responses and stochastic regressors also are treated

pearson s chi square test and rank correlation inferences for clustered data pearson s chi square test has been widely used in testing for association between two categorical responses spearman rank correlation and kendall s tau are often used for measuring and testing association between two continuous or ordered categorical responses however the established statistical properties of these tests are only valid when each pair of responses are independent where each sampling unit has only one pair of responses when each sampling unit consists of a cluster of paired responses the assumption of independent pairs is violated in this article we apply the within cluster resampling technique to u statistics to form new tests and rank based correlation estimators for possibly tied clustered data we develop large sample properties of the new proposed tests and estimators and evaluate their performance by simulations the proposed methods are applied to a data set collected from a pet ct imaging study for illustration

scattered data interpolation subject to piecewise quadratic range restrictions abstract the constriction of range restricted univariate and bivariate c1 interpolants to scattered data is considered in particular we deal with quadratic spline interpolation on a refined univariate grid respectively on a powell sabin refinement of a triangulation of the data sites subject to piecewise quadratic lower and upper obstacles to the values of the interpolant the derived sufficient conditions for the fulfillment of the range restrictions result in a system of linear inequalities for the slopes respectively gradients as parameters which is separated with respect to the data sites this system is shown to be always solvable for important special forms of the obstacles if at all in general there exist an infinite number of spline interpolants meeting the constraints the selection of a visually pleasant one is based on the minimization of a suitable choice functional

analysis of clustered binary outcomes using within cluster paired resampling summary conditional logistic regression clr is useful for analyzing clustered binary outcome data when interest lies in estimating a cluster specific exposure parameter while treating the dependency arising from random cluster effects as a nuisance clr aggregates unmeasured cluster specific factors into a cluster specific baseline risk and is invalid in the presence of unmodeled heterogeneous covariate effects or within cluster dependency we propose an alternative resampling based method for analyzing clustered binary outcome data within cluster paired resampling wcpr which allows for within cluster dependency not solely due to baseline heterogeneity for example dependency may be in part caused by heterogeneity in response to an exposure across clusters due to unmeasured cofactors when both clr and wcpr are valid our simulations suggest that the two methods perform comparably when clr is invalid wcpr continues to have good operating characteristics for illustration we apply both wcpr and clr to a periodontal data set where there is heterogeneity in response to exposure across clusters

event weighted proportional hazards modelling for recurrent gap time data the analysis of gap times in recurrent events requires an adjustment to standard marginal models one can perform this adjustment with a modified within cluster resampling technique however this method is computationally intensive in this paper we describe a simple adjustment to the standard cox proportional hazards model analysis that mimics the intent of within cluster resampling and results in similar parameter estimates this method essentially weights the partial likelihood contributions by the inverse of the number of gap times observed within the individual while assuming a working independence correlation matrix we provide an example involving recurrent mammary tumours in female rats to illustrate the methods considered in this paper copyright 2012 john wiley sons ltd

range restricted interpolation using gregory s rational cubic splines abstract the construction of range restricted univariate and bivariate interpolants to gridded data is considered we apply gregory s rational cubic c1 splines as well as related rational quintic c2 splines assume that the lower and upper obstacles are compatible with the data set then the tension parameters occurring in the mentioned spline classes can be always determined in such a way that range restricted interpolation is successful

marginal association measures for clustered data the use of correlation coefficients in measuring the association between two continuous variables is common but regular methods of calculating correlations have not been extended to the clustered data framework for clustered data in which observations within a cluster may be correlated regular inferential procedures for calculating marginal association between two variables can be biased this is particularly true for data in which the number of observations in a given cluster is informative for the association being measured in this paper we apply the principle of inverse cluster size reweighting to develop estimators of marginal correlation that remain valid in the clustered data framework when cluster size is informative for the correlation being measured these correlations are derived as analogs to regular correlation estimators for continuous independent data namely pearson s and kendall s we present the results of a simple simulation study demonstrating the appropriateness of our proposed estimators and the inherent bias of other inferential procedures for clustered data we illustrate their use through an application to data from patients with incomplete spinal cord injury in the usa

a rank sum test for clustered data when the number of subjects in a group within a cluster is informative the wilcoxon rank sum test is a popular nonparametric test for comparing two independent populations groups in recent years there have been renewed attempts in extending the wilcoxon rank sum test for clustered data one of which datta and satten 2005 journal of the american statistical association 100 908 915 addresses the issue of informative cluster size i e when the outcomes and the cluster size are correlated we are faced with a situation where the group specific marginal distribution in a cluster depends on the number of observations in that group i e the intra cluster group size we develop a novel extension of the rank sum test for handling this situation we compare the performance of our test with the datta satten test as well as the naive wilcoxon rank sum test using a naturally occurring simulation model of informative intra cluster group size we show that only our test maintains the correct size we also compare our test with a classical signed rank test based on averages of the outcome values in each group paired by the cluster membership while this test maintains the size it has lower power than our test extensions to multiple group comparisons and the case of clusters not having samples from all groups are also discussed we apply our test to determine whether there are differences in the attachment loss between the upper and lower teeth and between mesial and buccal sites of periodontal patients

analysis of failure time data with multilevel clustering with application to the child vitamin a intervention trial in nepal we consider the problem of estimating covariate effects in the marginal cox proportional hazard model and multilevel associations for child mortality data collected from a vitamin a supplementation trial in nepal where the data are clustered within households and villages for this purpose a class of multivariate survival models that can be represented by a functional of marginal survival functions and accounts for hierarchical structure of clustering is exploited based on this class of models an estimation strategy involving a within cluster resampling procedure is proposed and a model assessment approach is presented the asymptotic theory for the proposed estimators and lack of fit test is established the simulation study shows that the estimates are approximately unbiased and the proposed test statistic is conservative under extremely heavy censoring but approaches the size otherwise the analysis of the nepal study data shows that the association of mortality is much greater within households than within villages

finite group actions on rational function fields is an invertible n x n matrix with integer entries and where a a e k o if a c 1 vi then cj is called purely monomial it is proved in 6 theorem that if g is any finite group of monomial k automorphisms of k x x2 then its fixed held k x x2 is rational purely transcendental over k this does not generalize to the three variable case since the fixed field of the order 4 cyclic group generated by the monomial q automorphism o defined on q x x2 x3 by is not rational s last paragraph however we prove here that the fixed field of every finite abeliun group of purely monomial k automorphisms of

within cluster resampling within cluster resampling is proposed as a new method for analysing clustered data although the focus of this paper is clustered binary data the within cluster resampling asymptotic theory is general for many types of clustered data within cluster resampling is a simple but computationally intensive estimation method its main advantage over other marginal analysis methods such as generalised estimating equations liang zeger 1986 zeger liang 1986 is that it remains valid when the risk for the outcome of interest is related to the cluster size which we term nonignorable cluster size we present theory for the asymptotic normality and provide a consistent variance estimator for the within cluster resampling estimator simulations and an example are developed that assess the finite sample behaviour of the new method and show that when both methods are valid its performance is similar to that of generalised estimating equations

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

model selection for semiparametric marginal mean regression accounting for within cluster subsampling variability and informative cluster size we propose a model selection criterion for semiparametric marginal mean regression based on generalized estimating equations the work is motivated by a longitudinal study on the physical frailty outcome in the elderly where the cluster size that is the number of the observed outcomes in each subject is informative in the sense that it is related to the frailty outcome itself the new proposal called resampling cluster information criterion rcic is based on the resampling idea utilized in the within cluster resampling method hoffman sen and weinberg 2001 biometrika 88 1121 1134 and accommodates informative cluster size the implementation of rcic however is free of performing actual resampling of the data and hence is computationally convenient compared with the existing model selection methods for marginal mean regression the rcic method incorporates an additional component accounting for variability of the model over within cluster subsampling and leads to remarkable improvements in selecting the correct model regardless of whether the cluster size is informative or not applying the rcic method to the longitudinal frailty study we identify being female old age low income and life satisfaction and chronic health conditions as significant risk factors for physical frailty in the elderly

separating between and within cluster covariate effects by using conditional and partitioning methods summary we consider the situation where the random effects in a generalized linear mixed model may be correlated with one of the predictors which leads to inconsistent estimators we show that conditional maximum likelihood can eliminate this bias conditional likelihood leads naturally to the partitioning of the covariate into between and within cluster components and models that include separate terms for these components also eliminate the source of the bias another viewpoint that we develop is the idea that many violations of the assumptions including correlation between the random effects and a covariate in a generalized linear mixed model may be cast as misspecified mixing distributions we illustrate the results with two examples and simulations

marginal analysis of ordinal clustered longitudinal data with informative cluster size the issue of informative cluster size ics often arises in the analysis of dental data ics describes a situation where the outcome of interest is related to cluster size much of the work on modeling marginal inference in longitudinal studies with potential ics has focused on continuous outcomes however periodontal disease outcomes including clinical attachment loss are often assessed using ordinal scoring systems in addition participants may lose teeth over the course of the study due to advancing disease status here we develop longitudinal cluster weighted generalized estimating equations cwgee to model the association of ordinal clustered longitudinal outcomes with participant level health related covariates including metabolic syndrome and smoking status and potentially decreasing cluster size due to tooth loss by fitting a proportional odds logistic regression model the within teeth correlation coefficient over time is estimated using the two stage quasi least squares method the motivation for our work stems from the department of veterans affairs dental longitudinal study in which participants regularly received general and oral health examinations in an extensive simulation study we compare results obtained from cwgee with various working correlation structures to those obtained from conventional gee which does not account for ics our proposed method yields results with very low bias and excellent coverage probability in contrast to a conventional generalized estimating equations approach