cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

regularized outcome weighted subgroup identification for differential treatment effects summary to facilitate comparative treatment selection when there is substantial heterogeneity of treatment effectiveness it is important to identify subgroups that exhibit differential treatment effects existing approaches model outcomes directly and then define subgroups according to interactions between treatment and covariates because outcomes are affected by both the covariate treatment interactions and covariate main effects direct modeling outcomes can be hard due to model misspecification especially in presence of many covariates alternatively one can directly work with differential treatment effect estimation we propose such a method that approximates a target function whose value directly reflects correct treatment assignment for patients the function uses patient outcomes as weights rather than modeling targets consequently our method can deal with binary continuous time to event and possibly contaminated outcomes in the same fashion we first focus on identifying only directional estimates from linear rules that characterize important subgroups we further consider estimation of comparative treatment effects for identified subgroups we demonstrate the advantages of our method in simulation studies and in analyses of two real data sets

constructing nested bases approximations from the entries of non local operators in this article a method for constructing nested bases approximations to large scale fully populated discretizations of integral operators is introduced the scheme uses only few of the matrix entries for approximating the whole matrix in this sense it is similar to the adaptive cross approximation method however its computational complexity is improved

hierarchical matrix approximation for kernel based scattered data interpolation scattered data interpolation by radial kernel functions leads to linear equation systems with large fully populated ill conditioned interpolation matrices a successful iterative solution of such a system requires an efficient matrix vector multiplication as well as an efficient preconditioner while multipole approaches provide a fast matrix vector multiplication they avoid the explicit setup of the system matrix which hinders the construction of preconditioners such as approximate inverses or factorizations which typically require the explicit system matrix for their construction in this paper we propose an approach that allows both an efficient matrix vector multiplication as well as an explicit matrix representation which can then be used to construct a preconditioner in particular the interpolation matrix will be represented in hierarchical matrix format and several approaches for the blockwise low rank approximation are proposed and compared of both analytical nature separable expansions

subgroup identification based on differential effect search a recursive partitioning method for establishing response to treatment in patient subpopulations we propose a novel recursive partitioning method for identifying subgroups of subjects with enhanced treatment effects based on a differential effect search algorithm the idea is to build a collection of subgroups by recursively partitioning a database into two subgroups at each parent group such that the treatment effect within one of the two subgroups is maximized compared with the other subgroup the process of data splitting continues until a predefined stopping condition has been satisfied the method is similar to interaction tree approaches that allow incorporation of a treatment by split interaction in the splitting criterion however unlike other tree based methods this method searches only within specific regions of the covariate space and generates multiple subgroups of potential interest we develop this method and provide guidance on key topics of interest that include generating multiple promising subgroups using different splitting criteria choosing optimal values of complexity parameters via cross validation and addressing type i error rate inflation inherent in data mining applications using a resampling based method we evaluate the operating characteristics of the procedure using a simulation study and illustrate the method with a clinical trial example copyright 2011 john wiley sons ltd

testing in normal mixture models when the proportions are known summary the aim of this paper is to study the behaviour of the likelihood ratio test statistic in mixture models when the proportions of the distributions are known a priori the results depend on the value of the proportion the dimensionality of the problem and whether or not the variance of the distributions is known

a flexible strategy for testing subgroups and overall population subgroup analyses in addition to the total study population analysis are common in clinical trials however it is well recognized that findings from subgroup analyses do not provide confirmatory evidence for subgroup treatment effects without placing a priori criteria for ensuring that their findings are scientifically sound in this paper we address some of the common pitfalls of subgroup analyses subgroups analyses inherently have low power for detecting treatment effects we investigate the power interplay for a subgroup analysis and that for the total study population and list factors that impact the power of a subgroup analysis then we introduce a flexible statistical strategy for testing a pre specified sequence of hypotheses for both the overall and a subgroup the proposed method strongly controls the familywise type i error rate and enjoys higher power than other traditional methods this testing strategy allows testing for a subgroup once a pre specified degree of consistency in the efficacy findings between the subgroup and the overall study population is met in addition it accounts for the dependency between test statistics for the subgroup and the overall study population we discuss the power performance of this new method and provide significance levels for subgroup analysis finally we illustrate its application through retrospective analysis of data from three published clinical trials

factorization theory from commutative to noncommutative settings abstract we study the non uniqueness of factorizations of non zero divisors into atoms irreducibles in noncommutative rings to do so we extend concepts from the commutative theory of non unique factorizations to a noncommutative setting several notions of factorizations as well as distances between them are introduced in addition arithmetical invariants characterizing the non uniqueness of factorizations such as the catenary degree the invariant and the tame degree are extended from commutative to noncommutative settings we introduce the concept of a cancellative semigroup being permutably factorial and characterize this property by means of corresponding catenary and tame degrees also we give necessary and sufficient conditions for there to be a weak transfer homomorphism from a cancellative semigroup to its reduced abelianization applying the abstract machinery we develop we determine various catenary degrees for classical maximal orders in central simple algebras over global fields by using a natural transfer homomorphism to a monoid of zero sum sequences over a ray class group we also determine catenary degrees and the permutable tame degree for the semigroup of non zero divisors of the ring of n n upper triangular matrices over a commutative domain using a weak transfer homomorphism to a commutative semigroup

hybrid cross approximation of integral operators the efficient treatment of dense matrices arising e g from the finite element discretisation of integral operators requires special compression techniques in this article we use the matrix representation that approximates the dense stiffness matrix in admissible blocks corresponding to subdomains where the underlying kernel function is smooth by low rank matrices the low rank matrices are assembled by a new hybrid algorithm hca that has the same proven convergence as standard interpolation but also the same efficiency as the heuristic adaptive cross approximation aca

hypothesis test for normal mixture models the em approach normal mixture distributions are arguably the most important mixture models and also the most technically challenging the likelihood function of the normal mixture model is unbounded based on a set of random samples unless an artificial bound is placed on its component variance parameter moreover the model is not strongly identifiable so it is hard to differentiate between over dispersion caused by the presence of a mixture and that caused by a large variance and it has infinite fisher information with respect to mixing proportions there has been extensive research on finite normal mixture models but much of it addresses merely consistency of the point estimation or useful practical procedures and many results require undesirable restrictions on the parameter space we show that an em test for homogeneity is effective at overcoming many challenges in the context of finite normal mixtures we find that the limiting distribution of the em test is a simple function of the 0 5 2 0 5 2 and 2 distributions when the mixing variances are equal but unknown and the 2 when variances are unequal and unknown simulations show that the limiting distributions approximate the finite sample distribution satisfactorily two genetic examples are used to illustrate the application of the em test

an improved bonferroni procedure for multiple tests of significance summary a modification of the bonferroni procedure for testing multiple hypotheses is presented the method based on the ordered p values of the individual tests is less conservative than the classical bonferroni procedure but is still simple to apply a simulation study shows that the probability of a type i error of the procedure does not exceed the nominal significance level a for a variety of multivariate normal and multivariate gamma test statistics for independent tests the procedure has type i error probability equal to a the method appears particularly advantageous over the classical bonferroni procedure when several highly correlated test statistics are involved

on elasticities of locally finitely generated monoids abstract let h be a commutative and cancellative monoid the elasticity a of a non unit a h is the supremum of m n over all m n for which there are factorizations of the form a u 1 u m v 1 v n where all u i and v j are irreducibles the elasticity h of h is the supremum over all a we establish a characterization valid for finitely generated monoids when every rational number q with 1 q h can be realized as the elasticity of some element a h furthermore we derive results of a similar flavor for locally finitely generated monoids they include all krull domains and orders in dedekind domains satisfying certain algebraic finiteness conditions and for weakly krull domains

hierarchical mixtures of experts and the em algorithm we present a tree structured architecture for supervised learning the statistical model underlying the architecture is a hierarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models glim s learning is treated as a maximum likelihood problem in particular we present an expectation maximization em algorithm for adjusting the parameters of the architecture we also develop an on line learning algorithm in which the parameters are updated incrementally comparative simulation results are presented in the robot dynamics domain

number theory of matrix semigroups abstract unlike factorization theory of commutative semigroups which are well studied very little literature exists describing factorization properties in noncommutative semigroups perhaps the most ubiquitous noncommutative semigroups are semigroups of square matrices and this article investigates the factorization properties within certain subsemigroups of m n z the semigroup of n n matrices with integer entries certain important invariants are calculated to give a sense of how unique or non unique factorization is in each of these semigroups

bayesian inference in mixtures of experts and hierarchical mixtures of experts models with an application to speech recognition abstract machine classification of acoustic waveforms as speech events is often difficult due to context dependencies here a vowel recognition task with multiple speakers is studied via the use of a class of modular and hierarchical systems referred to as mixtures of experts and hierarchical mixtures of experts models the statistical model underlying the systems is a mixture model in which both the mixture coefficients and the mixture components are generalized linear models a full bayesian approach is used as a basis of inference and prediction computations are performed using markov chain monte carlo methods a key benefit of this approach is the ability to obtain a sample from the posterior distribution of any functional of the parameters of the given model in this way more information is obtained than can be provided by a point estimate also avoided is the need to rely on a normal approximation to the posterior as the basis of inference this is particularly important in cases where the posteri

likelihood ratio test for multi sample mixture model and its application to genetic imprinting genomic imprinting is a known aspect of the etiology of many diseases the imprinting phenomenon depicts differential expression levels of the allele depending on its parental origin when the parental origin is unknown the expression level has a finite normal mixture distribution in such applications a random sample of expression levels consists of three subsamples according to the number of minor alleles an individual possesses of which one is the mixture and the other two are homogeneous this understanding leads to a likelihood ratio test lrt for the presence of imprinting because of the nonregularity of the finite mixture model the classical asymptotic conclusions on likelihood based inference are not applicable we show that the maximum likelihood estimator of the mixing distribution remains consistent more interestingly thanks to the homogeneous subsamples the lrt statistic has an elegant and rather distinct 0 5 21 0 5 22 null limiting distribution simulation studies confirm that the

factorizations in upper triangular matrices over information semialgebras abstract an integral domain or a commutative cancellative monoid is atomic if every nonzero nonunit element factors into atoms and it satisfies the accp if every ascending chain of principal ideals eventually stabilizes the interplay between these two properties has been investigated since the 1970s an atomic domain or monoid satisfies the finite factorization property ffp if every element has only finitely many factorizations and it satisfies the bounded factorization property bfp if for each element there is a bound for the number of atoms in each of its factorizations these two properties have been systematically studied since they were introduced by anderson anderson and zafrullah in 1990 noetherian domains satisfy the bfp while dedekind domains satisfy the ffp it is well known that for commutative cancellative monoids and in particular for multiplicative monoids of integral domains ffp bfp accp atomic for n 2 we show that each of these four properties transfers back and forth between an information semialgebra s certain commutative cancellative semiring and the multiplicative monoid t n s consisting of n n upper triangular matrices over s we also show that a similar transfer behavior takes place if one replaces t n s by its submonoid u n s consisting of upper triangular matrices with units along their main diagonals as a consequence we find that the atomic chain ffp bfp accp atomic also holds for the two classes comprising the noncommutative monoids t n s and u n s finally we construct various rational information semialgebras to verify that in general none of the established implications is reversible

validating effectiveness of subgroup identification for longitudinal data in clinical trials and biomedical studies treatments are compared to determine which one is effective against illness however individuals can react to the same treatment very differently we propose a complete process for longitudinal data that identifies subgroups of the population that would benefit from a specific treatment a random effects linear model is used to evaluate individual treatment effects longitudinally where the random effects identify a positive or negative reaction to the treatment over time with the individual treatment effects and characteristics of the patients various classification algorithms are applied to build prediction models for subgrouping while many subgrouping approaches have been developed recently most of them do not check its validity in this paper we further propose a simple validation approach which not only determines if the subgroups used are appropriate and beneficial but also compares methods to predict individual treatment effects this entire procedure is readily implemented by existing packages in statistical software the effectiveness of the proposed method is confirmed with simulation studies and analysis of data from the women entering care study on depression

detecting treatment covariate interactions using permutation methods the primary objective of a randomized clinical trial usually is to investigate whether one treatment is better than its alternatives on average however treatment effects may vary across different patient subpopulations in contrast to demonstrating one treatment is superior to another on the average sense one is often more concerned with the question that for a particular patient or a group of patients with similar characteristics which treatment strategy is most appropriate to achieve a desired outcome various interaction tests have been proposed to detect treatment effect heterogeneity however they typically examine covariates one at a time do not offer an integrated approach that incorporates all available information and can greatly increase the chance of a false positive finding when the number of covariates is large we propose a new permutation test for the null hypothesis of no interaction effects for any covariate the proposed test allows us to consider the interaction effects of many covariates simultaneously without having to group subjects into subsets based on pre specified criteria and applies generally to randomized clinical trials of multiple treatments the test provides an attractive alternative to the standard likelihood ratio test especially when the number of covariates is large we illustrate the proposed methods using a dataset from the treatment of adolescents with depression study

inference for subgroup analysis with a structured logistic normal mixture model in this article we propose a statistical model for the purpose of identifying a subgroup that has an enhanced treatment effect as well as the variables that are predictive of the subgroup membership the need for such subgroup identification arises in clinical trials and in market segmentation analysis by using a structured logistic normal mixture model our proposed framework enables us to perform a confirmatory statistical test for the existence of subgroups and at the same time to construct predictive scores for the subgroup membership the inferential procedure proposed in the article is built on the recent literature on hypothesis testing for gaussian mixtures but the structured logistic normal mixture model enjoys some distinctive properties that are unavailable to the simpler gaussian mixture models with the bootstrap approximations the proposed tests are shown to be powerful and equally importantly insensitive to the choice of tuning parameters as an illustration we analyze a dataset fr

testing the order of a finite mixture the order is an important parameter in applications of finite mixture models yet designing a valid and easy to use statistical test for the order is challenging to date most results on hypothesis tests have focused on homogeneity a special case where the null model has order 1 in this work we designed an em test for the general problem of testing the null hypothesis of order m0 versus an alternative hypothesis of order larger than m0 for any positive integer m0 the null limiting distribution of the em test is a mixture of 2 distributions the weights in this mixture limiting distribution can be conveniently computed compared with related results the new result is obtained under much less strict requirements on the component distribution and the parameter space extensive simulation studies show that the limiting distributions closely match the finite sample distributions of the em test when m0 2 the new em test has more accurate type i errors and matches the power of the modified likelihood

tree based methods for individualized treatment regimes individualized treatment rules recommend treatments on the basis of individual patient characteristics a high quality treatment rule can produce better patient outcomes lower costs and less treatment burden if a treatment rule learned from data is to be used to inform clinical practice or provide scientific insight it is crucial that it be interpretable clinicians may be unwilling to implement models they do not understand and black box models may not be useful for guiding future research the canonical example of an interpretable prediction model is a decision tree we propose a method for estimating an optimal individualized treatment rule within the class of rules that are representable as decision trees the class of rules we consider is interpretable but expressive a novel feature of this problem is that the learning task is unsupervised as the optimal treatment for each patient is unknown and must be estimated the proposed method applies to both categorical and continuous treatments and produces favourable marginal mean outcomes in simulation experiments we illustrate it using data from a study of major depressive disorder

adaptive group sequential designs for clinical trials combining the advantages of adaptive and of classical group sequential approaches a general method is presented integrating the concept of adaptive interim analyses into classical group sequential testing this allows the researcher to represent every group sequential plan as an adaptive trial design and to make design changes during the course of the trial after every interim analysis in the same way as with adaptive designs the concept of adaptive trial designing is thereby generalized to a large variety of possible sequential plans

factorizations of upper triangular matrices if d is an integral domain in which every element can be factored as a product of irreducible elements then every element a tn d the semigroup of upper triangular matrices with nonzero determinant can be factored as a product of irreducible elements we classify both the irreducible elements and units of this cancellative semigroup having achieved this we provide a means of measuring the uniqueness or non uniqueness of these factorizations in terms of the uniqueness or non uniqueness of factorizations in d in addition to using well studied invariants from factorization theory of commutative semigroups we introduce a new tool weak transfer homomorphisms which are more appropriate for noncommutative settings

a concave pairwise fusion approach to subgroup analysis abstractan important step in developing individualized treatment strategies is correct identification of subgroups of a heterogeneous population to allow specific treatment for each subgroup this article considers the problem using samples drawn from a population consisting of subgroups with different mean values along with certain covariates we propose a penalized approach for subgroup analysis based on a regression model in which heterogeneity is driven by unobserved latent factors and thus can be represented by using subject specific intercepts we apply concave penalty functions to pairwise differences of the intercepts this procedure automatically divides the observations into subgroups to implement the proposed approach we develop an alternating direction method of multipliers algorithm with concave penalties and demonstrate its convergence we also establish the theoretical properties of our proposed estimator and determine the order requirement of the minimal difference of signals between g

evaluation of experiments with adaptive interim analyses summary a general method for statistical testing in experiments with an adaptive interim analysis is proposed the method is based on the observed error probabilities from the disjoint subsamples before and after the interim analysis formally an intersection of individual null hypotheses is tested by combining the twop values into a global test statistic stopping rules for fisher s product criterion in terms of critical limits for the p value in the first subsample are introduced including early stopping in the case of missing effects the control of qualitative treatment stage interactions is considered a generalization to three stages is outlined the loss of power when using the product criterion instead of the optimal classical test on the whole sample is calculated for the test of the mean of a normal distribution depending on increasing proportions of the first subsample in relation to the total sample size an upper bound on the loss of power due to early stopping is derived a general example is presented and rules for assessing the sample size in the second stage of the trial are given the problems of interpretation and precautions to be taken for applications are discussed finally the sources of bias for estimation in such designs are described

point estimation in adaptive enrichment designs adaptive enrichment designs are an attractive option for clinical trials that aim at demonstrating efficacy of therapies which may show different benefit for the full patient population and a prespecified subgroup in these designs based on interim data either the subgroup or the full population is selected for further exploration when selection is based on efficacy data this introduces bias to the commonly used maximum likelihood estimator for the situation of two stage designs with a single prespecified subgroup we present six alternative estimators and investigate their performance in a simulation study the most consistent reduction of bias over the range of scenarios considered was achieved by a method combining the uniformly minimum variance conditionally unbiased estimator with a conditional moment estimator application of the methods is illustrated by a clinical trial example

upper triangular matrices over information algebras abstract factorization in matrix rings has been investigated in a wide variety of contexts recently this study has provided a wealth of information about how factorization works in noncommutative settings it is often the case that when s is a ring of matrices over a base ring r multiplicative factorization in r drives the multiplicative factorization in s that is the additive structure of r is largely irrelevant to how elements of s factor multiplicatively recently chen et al studied factorization of the semiring of upper triangular matrices with entries in n 0 the semiring of nonnegative integers in this work we show that their results fit within the larger context of factorization in upper triangular matrices over reduced information algebras we illustrate that factorization in t n h 0 depends on both the multiplicative and additive structure of h 0 if h 0 is such an information algebra we classify the irreducible elements of t n h 0 and describe the degree to which factorization in t n h 0 is nonunique by considering elasticities delta sets and unions of sets in addition we show that unlike many important classes of semigroups whose arithmetic has been studied t n h 0 is not transfer krull for h 0 n 0 we extend previously known results and give explicit descriptions of nonunique factorization in t n n 0

a conditional error function approach for subgroup selection in adaptive clinical trials growing interest in personalised medicine and targeted therapies is leading to an increase in the importance of subgroup analyses if it is planned to view treatment comparisons in both a predefined subgroup and the full population as co primary analyses it is important that the statistical analysis controls the familywise type i error rate spiessens and debois cont clin trials 2010 31 647 656 recently proposed an approach specific for this setting which incorporates an assumption about the correlation based on the known sizes of the different groups and showed that this is more powerful than generic multiple comparisons procedures such as the bonferroni correction if recruitment is slow relative to the length of time taken to observe the outcome it may be efficient to conduct an interim analysis in this paper we propose a new method for an adaptive clinical trial with co primary analyses in a predefined subgroup and the full population based on the conditional error function principle the methodology is generic in that we assume test statistics can be taken to be normally distributed rather than making any specific distributional assumptions about individual patient data in a simulation study we demonstrate that the new method is more powerful than previously suggested analysis strategies furthermore we show how the method can be extended to situations when the selection is not based on the final but on an early outcome we use a case study in a targeted therapy in oncology to illustrate the use of the proposed methodology with non normal outcomes copyright 2012 john wiley sons ltd

hierarchical mixtures of experts for exponential family regression models approximation and maximum likelihood estimation we consider hierarchical mixtures of experts hme models where exponential family regression models with generalized linear mean functions of the form x t are mixed here is the inverse link function suppose the true response y follows an exponential family regression model with mean function belonging to a class of smooth functions of the form h x where h w 2 k0 a sobolev class over 0 1 s it is shown that the hme probability density functions can approximate the true density at a rate of o m 2 s in hellinger distance and at a rate of o m 4 s in kullback leibler divergence where m is the number of experts and s is the dimension of the predictor x we also provide conditions under which the mean square error of the estimated mean response obtained from the maximum likelihood method converges to zero as the sample size and the number of experts both increase

finite mixture modeling with mixture outcomes using the em algorithm summary this paper discusses the analysis of an extended finite mixture model where the latent classes corresponding to the mixture components for one set of observed variables influence a second set of observed variables the research is motivated by a repeated measurement study using a random coefficient model to assess the influence of latent growth trajectory class membership on the probability of a binary disease outcome more generally this model can be seen as a combination of latent class modeling and conventional mixture modeling the em algorithm is used for estimation as an illustration a random coefficient growth model for the prediction of alcohol dependence from three latent classes of heavy alcohol use trajectories among young adults is analyzed

a modified likelihood ratio test for homogeneity in finite mixture models summary testing for homogeneity in finite mixture models has been investigated by many researchers the asymptotic null distribution of the likelihood ratio test lrt is very complex and difficult to use in practice we propose a modified lrt for homogeneity in finite mixture models with a general parametric kernel distribution family the modified lrt has a x2 type of null limiting distribution and is asymptotically most powerful under local alternatives simulations show that it performs better than competing tests they also reveal that the limiting distribution with some adjustment can satisfactorily approximate the quantiles of the test statistic even for moderate sample sizes

factorizations of block triangular matrices abstract transfer homomorphisms have long been used as tools in factorization theory the idea is to transfer information about factorizations in a semigroup of interest from simpler easier to understand semigroups unfortunately there exist noncommutative semigroups which admit no transfer homomorphism to any commutative semigroup the weak transfer homomorphism was introduced to study such semigroups in particular these weak transfer homomorphisms were used to study factorizations of semigroups of upper triangular matrices with entries coming from a commutative integral domain in this work we extend this study finding weak transfer homomorphisms to both commutative and noncommutative semigroups from upper triangular matrices with entries coming from noncommutative rings in particular we study factorizations of block triangular matrices

testing for observation dependent regime switching in mixture autoregressive models abstract testing for regime switching when the regime switching probabilities are specified either as constants mixture models or are governed by a finite state markov chain markov switching models are long standing problems that have also attracted recent interest this paper considers testing for regime switching when the regime switching probabilities are time varying and depend on observed data observation dependent regime switching specifically we consider the likelihood ratio test for observation dependent regime switching in mixture autoregressive models the testing problem is highly nonstandard involving unidentified nuisance parameters under the null parameters on the boundary singular information matrices and higher order approximations of the log likelihood we derive the asymptotic null distribution of the likelihood ratio test statistic in a general mixture autoregressive setting using high level conditions that allow for various forms of dependence of the regime switching probabilities on past observations and we illustrate the theory using two particular mixture autoregressive models the likelihood ratio test has a nonstandard asymptotic distribution that can easily be simulated and monte carlo studies show the test to have good finite sample size and power properties

identification of subgroups with differential treatment effects for longitudinal and multiresponse variables we describe and evaluate a regression tree algorithm for finding subgroups with differential treatments effects in randomized trials with multivariate outcomes the data may contain missing values in the outcomes and covariates and the treatment variable is not limited to two levels simulation results show that the regression tree models have unbiased variable selection and the estimates of subgroup treatment effects are approximately unbiased a bootstrap calibration technique is proposed for constructing confidence intervals for the treatment effects the method is illustrated with data from a longitudinal study comparing two diabetes drugs and a mammography screening trial comparing two treatments and a control copyright 2016 john wiley sons ltd

fast evaluation of radial basis functions moment based methods this paper presents a new method for the fast evaluation of univariate radial basis functions of the form s x sum n 1 n d n phi x x n to within accuracy epsilon the method can be viewed as a generalization of the fast multipole method in which calculations with far field expansions are replaced by calculations involving moments of the data the method has the advantage of being adaptive to changes in phi that is with this method changing to a new phi requires only coding a one or two line function for the slow evaluation of phi in contrast adapting the usual fast multipole method to a new phi involves much mathematical analysis of appropriate series expansions and corresponding translation operators followed by a substantial amount of work expressing this mathematics in code

testing the number of components in normal mixture regression models testing the number of components in finite normal mixture models is a long standing challenge because of its nonregularity this article studies likelihood based testing of the number of components in normal mixture regression models with heteroscedastic components we construct a likelihood based test of the null hypothesis of m0 components against the alternative hypothesis of m0 1 components for any m0 the null asymptotic distribution of the proposed modified em test statistic is the maximum of m0 random variables that can be easily simulated the simulations show that the proposed test has very good finite sample size and power properties supplementary materials for this article are available online

subgroups from regression trees with adjustment for prognostic effects and postselection inference identification of subgroups with differential treatment effects in randomized trials is attracting much attention many methods use regression tree algorithms this article addresses 2 important questions arising from the subgroups how to ensure that treatment effects in subgroups are not confounded with effects of prognostic variables and how to determine the statistical significance of treatment effects in the subgroups we address the first question by selectively including linear prognostic effects in the subgroups in a regression tree model the second question is more difficult because it falls within the subject of postselection inference we use a bootstrap technique to calibrate normal theory t intervals so that their expected coverage probability averaged over all the subgroups in a fitted model approximates the desired confidence level it can also provide simultaneous confidence intervals for all subgroups the first solution is implemented in the guide algorithm and is applicable to data with missing covariate values 2 or more treatment arms and outcomes subject to right censoring bootstrap calibration is applicable to any subgroup identification method it is not restricted to regression tree models two real examples are used for illustration a diabetes trial where the outcomes are completely observed but some covariate values are missing and a breast cancer trial where the outcome is right censored

subgroup detection and sample size calculation with proportional hazards regression for survival data in this paper we propose a testing procedure for detecting and estimating the subgroup with an enhanced treatment effect in survival data analysis here we consider a new proportional hazard model that includes a nonparametric component for the covariate effect in the control group and a subgroup treatment interaction effect defined by a change plane we develop a score type test for detecting the existence of the subgroup which is doubly robust against misspecification of the baseline effect model or the propensity score but not both under mild assumptions for censoring when the null hypothesis of no subgroup is rejected the change plane parameters that define the subgroup can be estimated on the basis of supremum of the normalized score statistic the asymptotic distributions of the proposed test statistic under the null and local alternative hypotheses are established on the basis of established asymptotic distributions we further propose a sample size calculation formula for detecting a given subgroup effect and derive a numerical algorithm for implementing the sample size calculation in clinical trial designs the performance of the proposed approach is evaluated by simulation studies an application to an aids clinical trial data is also given for illustration

evaluating markers for selecting a patient s treatment selecting the best treatment for a patient s disease may be facilitated by evaluating clinical characteristics or biomarker measurements at diagnosis we consider how to evaluate the potential impact of such measurements on treatment selection algorithms for example magnetic resonance neurographic imaging is potentially useful for deciding whether a patient should be treated surgically for carpal tunnel syndrome or should receive less invasive conservative therapy we propose a graphical display the selection impact si curve that shows the population response rate as a function of treatment selection criteria based on the marker the curve can be useful for choosing a treatment policy that incorporates information on the patient s marker value exceeding a threshold the si curve can be estimated using data from a comparative randomized trial conducted in the population as long as treatment assignment in the trial is independent of the predictive marker estimating the si curve is therefore part of a post hoc analysis to determine whether the marker identifies patients that are more likely to benefit from one treatment over another nonparametric and parametric estimates of the si curve are proposed in this article asymptotic distribution theory is used to evaluate the relative efficiencies of the estimators simulation studies show that inference is straightforward with realistic sample sizes we illustrate the si curve and statistical inference for it with data motivated by an ongoing trial of surgery versus conservative therapy for carpal tunnel syndrome

adaptive sample size calculations in group sequential trials a method for group sequential trials that is based on the inverse normal method for combining the results of the separate stages is proposed without exaggerating the type i error rate this method enables data driven sample size reassessments during the course of the study it uses the stopping boundaries of the classical group sequential tests furthermore exact test procedures may be derived for a wide range of applications the procedure is compared with the classical designs in terms of power and expected sample size

on the approximation rate of hierarchical mixtures of experts for generalized linear models we investigate a class of hierarchical mixtures of experts hme models where generalized linear models with nonlinear mean functions of the form xt are mixed here is the inverse link function it is shown that mixtures of such mean functions can approximate a class of smooth functions of the form h x where h e w 2 k a sobolev class over 0 1 s as the number of experts m in the network increases an upper bound of the approximation rate is given as o m 2 s in lp norm this rate can be achieved within the family of hme structures with no more than s layers where s is the dimension of the predictor x

change plane analysis for subgroup detection and sample size calculation abstractwe propose a systematic method for testing and identifying a subgroup with an enhanced treatment effect we adopts a change plane technique to first test the existence of a subgroup and then identify the subgroup if the null hypothesis on nonexistence of such a subgroup is rejected a semiparametric model is considered for the response with an unspecified baseline function and an interaction between a subgroup indicator and treatment a doubly robust test statistic is constructed based on this model and asymptotic distributions of the test statistic under both null and local alternative hypotheses are derived moreover a sample size calculation method for subgroup detection is developed based on the proposed statistic the finite sample performance of the proposed test is evaluated via simulations finally the proposed methods for subgroup identification and sample size calculation are applied to a data from an aids study

on a logistic mixture autoregressive model summary we generalise the mixture autoregressive mar model to the logistic mixture autoregressive with exogenous variables lmarx model for the modelling of nonlinear time series the models consist of a mixture of two gaussian transfer function models with the mixing proportions changing over time the model can also be considered as a generalisation of the self exciting threshold autoregressive setar model and the open loop threshold autoregressive tarso model the advantages of the lmarx model over other nonlinear time series models include a wider range of shape changing predictive distributions the ability to handle cycles and conditional heteroscedasticity in the time series and better point prediction estimation is easily done via a simple em algorithm and the model selection problem is addressed the models are applied to two real datasets and compared with other competing models

a subgroup cluster based bayesian adaptive design for precision medicine in precision medicine a patient is treated with targeted therapies that are predicted to be effective based on the patient s baseline characteristics such as biomarker profiles oftentimes patient subgroups are unknown and must be learned through inference using observed data we present scuba a subgroup cluster based bayesian adaptive design aiming to fulfill two simultaneous goals in a clinical trial 1 to treatments enrich the allocation of each subgroup of patients to their precision and desirable treatments and 2 to report multiple subgroup treatment pairs stps using random partitions and semiparametric bayesian models scuba provides coherent and probabilistic assessment of potential patient subgroups and their associated targeted therapies each stp can then be used for future confirmatory studies for regulatory approval through extensive simulation studies we present an application of scuba to an innovative clinical trial in gastroesphogeal cancer

statistics and causal inference abstract problems involving causal inference have dogged at the heels of statistics since its earliest days correlation does not imply causation and yet causal conclusions drawn from a carefully designed experiment are often valid what can a statistical model say about causation this question is addressed by using a particular model for causal inference holland and rubin 1983 rubin 1974 to critique the discussions of other writers on causation and causal inference these include selected philosophers medical researchers statisticians econometricians and proponents of causal modeling

subgroup analysis via recursive partitioning subgroup analysis is an integral part of comparative analysis where assessing the treatment effect on a response is of central interest its goal is to determine the heterogeneity of the treatment effect across subpopulations in this paper we adapt the idea of recursive partitioning and introduce an interaction tree it procedure to conduct subgroup analysis the it procedure automatically facilitates a number of objectively defined subgroups in some of which the treatment effect is found prominent while in others the treatment has a negligible or even negative effect the standard cart breiman et al 1984 methodology is inherited to construct the tree structure also in order to extract factors that contribute to the heterogeneity of the treatment effect variable importance measure is made available via random forests of the interaction trees both simulated experiments and analysis of census wage data are presented for illustration

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

testing the number of components in a normal mixture we demonstrate that under a theorem proposed by vuong the likelihood ratio statistic based on the kullback leibler information criterion of the null hypothesis that a random sample is drawn from a k 0 component normal mixture distribution against the alternative hypothesis that the sample is drawn from a k 1 component normal mixture distribution is asymptotically distributed as a weighted sum of independent chi squared random variables with one degree of freedom under general regularity conditions we report simulation studies of two cases where we are testing a single normal versus a two component normal mixture and a two component normal mixture versus a three component normal mixture an empirical adjustment to the likelihood ratio statistic is proposed that appears to improve the rate of convergence to the limiting distribution

hypothesis testing in mixture regression models summary we establish asymptotic theory for both the maximum likelihood and the maximum modified likelihood estimators in mixture regression models moreover under specific and reasonable conditions we show that the optimal convergence rate of n 1 4 for estimating the mixing distribution is achievable for both the maximum likelihood and the maximum modified likelihood estimators we also derive the asymptotic distributions of two log likelihood ratio test statistics for testing homogeneity and we propose a resampling procedure for approximating the p value simulation studies are conducted to investigate the empirical performance of the two test statistics finally two real data sets are analysed to illustrate the application of our theoretical results

a regression tree approach to identifying subgroups with differential treatment effects in the fight against hard to treat diseases such as cancer it is often difficult to discover new treatments that benefit all subjects for regulatory agency approval it is more practical to identify subgroups of subjects for whom the treatment has an enhanced effect regression trees are natural for this task because they partition the data space we briefly review existing regression tree algorithms then we introduce three new ones that are practically free of selection bias and are applicable to data from randomized trials with two or more treatments censored response variables and missing values in the predictor variables the algorithms extend the guide approach by using three key ideas i treatment as a linear predictor ii chi squared tests to detect residual patterns and lack of fit and iii proportional hazards modeling via poisson regression importance scores with thresholds for identifying influential variables are obtained as by products a bootstrap technique is used to construct confidence intervals for the treatment effects in each node the methods are compared using real and simulated data