misunderstandings about q and cochran s q test in meta analysis many meta analyses report using cochran s q test to assess heterogeneity of effect size estimates from the individual studies some authors cite work by w g cochran without realizing that cochran deliberately did not use q itself to test for heterogeneity further when heterogeneity is absent the actual null distribution of q is not the chi squared distribution assumed for cochran s q test this paper reviews work by cochran related to q it then discusses derivations of the asymptotic approximation for the null distribution of q as well as work that has derived finite sample moments and corresponding approximations for the cases of specific measures of effect size those results complicate implementation and interpretation of the popular heterogeneity index i 2 also it turns out that the test based confidence intervals used with i 2 are based on a fallacious approach software that outputs q and i 2 should use the appropriate reference value of q for the particular measure of effect size and the current meta analysis q is a key element of the popular dersimonian laird procedure for random effects meta analysis but the assumptions of that procedure and related procedures do not reflect the actual behavior of q and may introduce bias the dersimonian laird procedure should be regarded as unreliable

exact inference on the random effects model for meta analyses with few studies we describe an exact unconditional non randomized procedure for producing confidence intervals for the grand mean in a normal normal random effects meta analysis the procedure targets meta analyses based on too few primary studies 7 say to allow for the conventional asymptotic estimators e g dersimonian and laird 1986 or non parametric resampling based procedures e g liu et al 2017 meta analyses with such few studies are common with one recent sample of 22 453 heath related meta analyses finding a median of 3 primary studies per meta analysis davey et al 2011 reliable and efficient inference procedures are therefore needed to address this setting the coverage level of the resulting ci is guaranteed to be above the nominal level up to monte carlo error provided the meta analysis contains more than 1 study and the model assumptions are met after employing several techniques to accelerate computation the new ci can be easily constructed on a personal computer simulations suggest that the proposed ci typically is not overly conservative we illustrate the approach on several contrasting examples of meta analyses investigating the effect of calcium intake on bone mineral density

twisted fourier mukai functors due to a theorem by orlov every exact fully faithful functor between the bounded derived categories of coherent sheaves on smooth projective varieties is of fourier mukai type we extend this result to the case of bounded derived categories of twisted coherent sheaves and at the same time we weaken the hypotheses on the functor as an application we get a complete description of the exact functors between the abelian categories of twisted coherent sheaves on smooth projective varieties

on the 0 dimensional cusps of the kahler moduli of a k3 surface let s be a complex algebraic k3 surface it is proved that the 0 dimensional cusps of the kahler moduli of s are in one to one correspondence with the twisted fourier mukai partners of s as a result a counting formula for the 0 dimensional cusps of the kahler moduli is obtained applications to rational maps between k3 surfaces are given when the picard number of s is 1 the bijective correspondence is calculated explicitly by using the fricke modular curve

generalized linear mixed models for meta analysis we examine two strategies for meta analysis of a series of 2 x 2 tables with the odds ratio modelled as a linear combination of study level covariates and random effects representing between study variation penalized quasi likelihood pql an approximate inference technique for generalized linear mixed models and a linear model fitted by weighted least squares to the observed log odds ratios are used to estimate regression coefficients and dispersion parameters simulation results demonstrate that both methods perform adequate approximate inference under many conditions but that neither method works well in the presence of highly sparse data under certain conditions with small cell frequencies the pql method provides better inference

a random effects model for binary data from dependent samples a model is proposed for the binary data analog of the paired t situation in this model the success probabilities vary across strata and have a specified probability distribution the parameters can be estimated by moments or likelihood methods various large sample tests are proposed the estimates and tests do not require fixed sample sizes the model can be applied to case control studies in which at least some cases have multiple controls and to other nested designs that have two treatments per stratum and small samples in each treatment stratum combination

a mixed effects model for categorical data a mixed model for categorical data from unbalanced designs which is directly analogous to a two way anova model for quantitative data is proposed an extension of the fitting constants method is developed to estimate model variance components based on appropriate reductions in sums of squares the resulting variance component estimators are incorporated into the covariance structure of a general linear models wald statistic to test for treatment differences these procedures are illustrated with data obtained from a multicenter clinical trial in which the treatments are regarded as fixed effects and the clinics are regarded as random effects

generalization of the mantel haenszel estimator to nonconstant odds ratios nouvel estimateur issu de la generalisation de l estimateur de mantel haenszel etude de ses proprietes asymptotiques en fonction du nombre de tables fixe et du comptage des cellules

valid inference in random effects meta analysis the standard approach to inference for random effects meta analysis relies on approximating the null distribution of a test statistic by a standard normal distribution this approximation is asymptotic on k the number of studies and can be substantially in error in medical meta analyses which often have only a few studies this paper proposes permutation and ad hoc methods for testing with the random effects model under the group permutation method we randomly switch the treatment and control group labels in each trial this idea is similar to using a permutation distribution for a community intervention trial where communities are randomized in pairs the permutation method theoretically controls the type i error rate for typical meta analyses scenarios we also suggest two ad hoc procedures our first suggestion is to use a t reference distribution with k 1 degrees of freedom rather than a standard normal distribution for the usual random effects test statistic we also investigate the use of a simple t statistic on the reported treatment effects

estimation in generalized linear models with random effects summary a conceptually very simple but general algorithm for the estimation of the fixed effects random effects and components of dispersion in generalized linear models with random effects is proposed conditions are described under which the algorithm yields approximate maximum likelihood or quasi maximum likelihood estimates of the fixed effects and dispersion components and approximate empirical bayes estimates of the random effects the algorithm is applied to two data sets to illustrate the estimation of components of dispersion and the modelling of overdispersion

random effects models for serial observations with binary response this paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants each subject s serial responses are assumed to arise from a logistic model but with regression coefficients that vary between subjects the logistic regression parameters are assumed to be normally distributed in the population inference is based upon maximum likelihood estimation of fixed effects and variance components and empirical bayes estimation of random effects exact solutions are analytically and computationally infeasible but an approximation based on the mode of the posterior distribution of the random parameters is proposed and is implemented by means of the em algorithm this approximate method is compared with a simpler two step method proposed by korn and whittemore using data from a panel study of asthmatics originally described in that paper one advantage of the estimation strategy described here is the ability to use all of the data including that from subjects with insufficient data to permit fitting of a separate logistic regression model as required by the korn and whittemore method however the new method is computationally intensive

a random effects regression model for meta analysis many meta analyses use a random effects model to account for heterogeneity among study results beyond the variation associated with fixed effects a random effects regression approach for the synthesis of 2 x 2 tables allows the inclusion of covariates that may explain heterogeneity a simulation study found that the random effects regression method performs well in the context of a meta analysis of the efficacy of a vaccine for the prevention of tuberculosis where certain factors are thought to modify vaccine efficacy a smoothed estimator of the within study variances produced less bias in the estimated regression coefficients the method provided very good power for detecting a non zero intercept term representing overall treatment efficacy but low power for detecting a weak covariate in a meta analysis of 10 studies we illustrate the model by exploring the relationship between vaccine efficacy and one factor thought to modify efficacy the model also applies to the meta analysis of continuous outcomes when covariates are present

computing an exact confidence interval for the common odds ratio in several 2 2 contingency tables abstract a quadratic time network algorithm is provided for computing an exact confidence interval for the common odds ratio in several 2 2 independent contingency tables the algorithm is shown to be a considerable improvement on an existing algorithm developed by thomas 1975 which relies on exhaustive enumeration problems that would formerly have consumed several cpu hours can now be solved in a few cpu seconds the algorithm can easily handle sparse data sets where asymptotic results are suspect the network approach on which the algorithm is based is also a powerful tool for exact statistical inference in other settings

nonparametric methods for stratified two sample designs with application to multiclinic trials abstract motivated by some problems arising from multiclinic trials we consider stratified two sample designs nonparametric effects are defined and nonparametric hypotheses are formulated in a design where treatment centers strata and interactions are assumed to be fixed factors the interpretation of the nonparametric effects and hypotheses is analyzed in two classes of semiparametric models the linear models and models with lehmann alternatives the case where centers and interactions are assumed to be random factors the so called mixed model is also considered nonparametric effects and hypotheses are defined for general models and their properties are analyzed in corresponding linear models and in models with lehmann alternatives the nonparametric effects are estimated by linear rank statistics where the ranks over all centers are used the mixed model for repeated baseline and endpoint observations is briefly considered and rank procedures are also proposed for this model all procedure

the moment problem on compact semi algebraic sets in this chapter we begin the study of the multidimensional moment problem the passage to dimensions d 2 brings new difficulties and unexpected phenomena in sect 3 2 we derived solvability criteria of the moment problem on intervals in terms of positivity conditions it seems to be natural to look for similar characterizations in higher dimensions as well this leads us immediately into the realm of real algebraic geometry and to descriptions of positive polynomials on semi algebraic sets in this chapter we treat this approach for basic closed compact semi algebraic subsets of mathbb r d it turns out that for such sets there is a close interaction between the moment problem and positivstellensatze for strictly positive polynomials

equivalences of twisted k3 surfaces we prove that two derived equivalent twisted k3 surfaces have isomorphic periods the converse is shown for k3 surfaces with large picard number it is also shown that all possible twisted derived equivalences between arbitrary twisted k3 surfaces form a subgroup of the group of all orthogonal transformations of the cohomology of a k3 surface

analysis of binary data from a multicentre clinical trial summary we develop several methods for estimating the treatment effect difference defined as the overall log odds ratio of favourable response in a multicentre clinical trial comparing two treatments with binary response a simulation study compares the bias and mean squared error of the point estimates and the exact coverage probabilities of confidence intervals obtained distributions multicentre randomized clinical trials are frequently used to test the efficacy of new medical regimens these trials are attractive due to the ease of getting the desired sample size in a short period of time and the broad coverage of the patient population and medical practitioners the analysis of data from such trials requires combining information from the centres in a way that properly accounts for the variation due to the centres and the differential efficacy of treatments between the centres in this paper we investigate several approaches to pooling the data across centres and for handling the effects associated with the centres chakravarthi grizzle 1975 and beitler landis 1985 argue for treating these effects as random and fleiss 1986 argues against because the centres are seldom chosen at random from a well defined population of clinics and therefore the effects cannot be associated with any population we prefer the random effect model approach for the following reasons the goal of a trial is to extend the results of the study to the general population duly accounting for variation in the patient population and the medical skills of practitioners hence if we believe that the variability between centres as estimated by the data is typical of the variability in the population of centres then the inference based on the random effects model is more appropriate than the one based on the fixed effects model furthermore the variation among the centres may be more than that predicted from samples from a binomial distribution treating the centre effects as random introduces this intra class correlation into our model assumptions let the outcome variable from each centre be a pair of binomial random variables xaj

models for longitudinal data a generalized estimating equation approach this article discusses extensions of generalized linear models for the analysis of longitudinal data two approaches are considered subject specific ss models in which heterogeneity in regression parameters is explicitly modelled and population averaged pa models in which the aggregate response for the population is the focus we use a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes when the subject specific parameters are assumed to follow a gaussian distribution simple relationships between the pa and ss parameters are available the methods are illustrated with an analysis of data on mother s smoking and children s respiratory disease

twisted fourier mukai number of a k3 surface we give a counting formula for the twisted fourier mukai partners of a projective k3 surface as an application we describe all twisted fourier mukai partners of a projective k3 surface of picard number 1