a large sample study of cox s regression model strong consistency and asymptotic normality are established for the maximum partial likelihood estimate of the regression parameter in cox s regression model estimates are also derived for the underlying cumulative hazard function and survival distribution we establish the asymptotic normality of these estimates and calculate the limiting variances

misspecified proportional hazard models summary the properties of an estimator based on a proportional hazards model are investigated when the model is incorrect the estimator from the partial likelihood is shown to be consistent for a parameter that is defined implicitly the results are used to investigate the effects on estimation if the true model is accelerated failure time or if covariates are omitted from the proportional hazards model

robust covariate adjusted log rank statistics and corresponding sample size formula for recurrent events data recurrent events data are frequently encountered in clinical trials this article develops robust covariate adjusted log rank statistics applied to recurrent events data with arbitrary numbers of events under independent censoring and the corresponding sample size formula the proposed log rank tests are robust with respect to different data generating processes and are adjusted for predictive covariates it reduces to the kong and slud 1997 biometrika 84 847 862 setting in the case of a single event the sample size formula is derived based on the asymptotic normality of the covariate adjusted log rank statistics under certain local alternatives and a working model for baseline covariates in the recurrent event data context when the effect size is small and the baseline covariates do not contain significant information about event times it reduces to the same form as that of schoenfeld 1983 biometrics 39 499 503 for cases of a single event or independent event times within a subject we carry out simulations to study the control of type i error and the comparison of powers between several methods in finite samples the proposed sample size formula is illustrated using data from an rhdnase study

asymptotic properties of moment estimators for overdispersed counts and proportions summary consistency and asymptotic normality of moment estimates of regression parameters and an overdispersion parameter are shown for data with extra binomial and extrapoisson variation the asymptotic covariance of the regression parameters is found to be unaffected by estimation of the overdispersion parameter the moment estimates may be obtained using iterated weighted least squares

sample size calculations in the presence of competing risks recently with the growth of statistical developments for competing risks analysis some methods have been proposed to compute sample size in this context these methods differ from a modelling approach one is based on the cox regression model for the cause specific hazard while another relies on the fine and gray regression model for the subdistribution hazard of a competing risk in this work we compare these approaches derive a new sample size for comparing cumulative incidence functions when the hazards are not proportional either cause specific or subdistribution and give practical advices to choose the approach best suited for the study question

the asymptotic properties of nonparametric tests for comparing survival distributions the asymptotic distribution under alternative hypotheses is derived for a class of statistics used to test the equality of two survival distributions in the presence of arbitrary and possibly unequal right censoring the test statistics include equivalents to the log rank statistic the modified wilcoxon statistic and the class of rank invariant test procedures introduced by peto peto when there are equal censoring distributions and the hazard functions are proportional the sample size formula for the f test used to compare exponential samples is shown to be valid for the log rank test in certain situations the power of the log rank test falls as the amount of censoring decreases

bundle methods for sum functions with easy components applications to multicommodity network design we propose a version of the bundle scheme for convex nondifferentiable optimization suitable for the case of a sum function where some of the components are easy that is they are lagrangian functions of explicitly known compact convex programs this corresponds to a stabilized partial dantzig wolfe decomposition where suitably modified representations of the easy convex subproblems are inserted in the master problem as an alternative to iteratively inner approximating them by extreme points thus providing the algorithm with exact information about a part of the dual objective function the resulting master problems are potentially larger and less well structured than the standard ones ruling out the available specialized techniques and requiring the use of general purpose solvers for their solution this strongly favors piecewise linear stabilizing terms as opposed to the more usual quadratic ones which in turn may have an adverse effect on the convergence speed of the algorithm so that the overall performance may depend on appropriate tuning of all these aspects yet very good computational results are obtained in at least one relevant application the computation of tight lower bounds for fixed charge multicommodity min cost flow problems

robust estimation of the variance in moment methods for extra binomial and extra poisson variation when faced with data in the form of overdispersed counts or proportions moment methods allow consistent parameter estimation when only the form of the mean and variance is specified if the variance form is misspecified these methods still yield consistent parameter estimates though with lower efficiency and the variances of the estimates will be inconsistent a variance correction is available that yields consistent variance estimates in these circumstances the asymptotic and small sample efficiencies of this correction are calculated and its performance under variance misspecification is studied a group randomized breast self examination prevention study that is now underway serves as a focal point for the study of these properties the use of the variance correction in modelling is illustrated on a teratology data set

methods for combining rates from several studies when several independent groups have conducted studies to estimate a procedure s success rate it is often of interest to combine the results of these studies in the hopes of obtaining a better estimate for the true unknown success rate of the procedure in this paper we present two hierarchical methods for estimating the overall rate of success both methods take into account the within study and between study variation and assume in the first stage that the number of successes within each study follows a binomial distribution given each study s own success rate they differ however in their second stage assumptions the first method assumes in the second stage that the rates of success from individual studies form a random sample having a constant expected value and variance generalized estimating equations gee are then used to estimate the overall rate of success and its variance the second method assumes in the second stage that the success rates from different studies follow a beta distribution both methods use the maximum likelihood approach to derive an estimate for the overall success rate and to construct the corresponding confidence intervals we also present a two stage bootstrap approach to estimating a confidence interval for the success rate when the number of studies is small we then perform a simulation study to compare the two methods finally we illustrate these two methods and obtain bootstrap confidence intervals in a medical example analysing the effectiveness of hyperdynamic therapy for cerebral vasospasm

properties of a nonparametric test for early comparison of treatments in clinical trials in the presence of surrogate endpoints summary a nonparametric test is derived for comparing treatments with respect to the final endpoint in clinical trials in which the final endpoint has been observed for a random subset of patients but results are available for a surrogate endpoint for a larger sample of patients the test is an adaptation of the wilcoxon mann whitney two sample test with an adjustment that involves a comparison of the ranks of the surrogate endpoints between patients with and without final endpoints the validity of the test depends on the assumption that the patients with final endpoints represent a random sample of the patients registered in the study this assumption is viable in trials in which the final endpoint is evaluated at a landmark timepoint in the patients natural history a small sample simulation study demonstrates that the test has a size that is close to the nominal value for all configurations evaluated when compared with the conventional test based only on the final endpoints the new test delivers substantial increases in power only when the surrogate endpoint is highly correlated with the true endpoint our research indicates that in the absence of modeling assumptions auxiliary information derived from surrogate endpoints can provide significant additional information only under special circumstances

upward planar drawing of single source acyclicdigraphs an upward plane drawing of a directed acyclic graph is a plane drawing of the digraph in which each directed edge is represented as a curve monotone increasing in the vertical direction thomassen has given a nonalgorithmic graph theoretic characterization of those directed graphs with a single source that admit an upward plane drawing this paper presents an efficient algorithm to test whether a given single source acyclic digraph has an upward plane drawing and if so to find a representation of one such drawing this result is made more significant in light of the recent proof by garg and tamassia that the problem is np complete for general digraphs the algorithm decomposes the digraph into biconnected and triconnected components and defines conditions for merging the components into an upward plane drawing of the original digraph to handle the triconnected components we provide a linear algorithm to test whether a given plane drawing of a single source digraph admits an upward plane drawing with the same faces and outer face which also gives a simpler algorithmic proof of thomassen s result the entire testing algorithm for general single source directed acyclic graphs operates in o n 2 time and o n space n being the number of vertices in the input digraph and represents the first polynomial time solution to the problem

on the structure of all minimum cuts in a network and applications this paper presents a characterization of all minimum cuts separating a source from a sink in a network a binary relation is associated with any maximum flow in this network and minimum cuts are identified with closures for this relation as a consequence finding all minimum cuts reduces to a straightforward enumeration applications of this results arise in sensitivity and parametric analyses of networks the vertex packing and maximum closure problems in unconstrained pseudo boolean optimization and project selection as well as in other areas of application of minimum cuts

scaling algorithms for the shortest paths problem we describe a new method for designing scaling algorithms for the single source shortest paths problem and use this method to obtain an o sqrt n m log n algorithm for the problem here n and m is the number of nodes and arcs in the input network and n is essentially the absolute value of the most negative arc length and arc lengths are assumed to be integral this improves previous bounds for the problem the method extends to related problems

beyond the flow decomposition barrier we introduce a new approach to the maximum flow problem this approach is based on assigning arc lengths based on the residual flow value and the residual arc capacities our approach leads to an o min n 2 3 m 1 2 m log n 2 m log u time bound for a network with n vertices m arcs and integral arc capacities in the range 1 u this is a fundamental improvement over the previous time bounds we also improve bounds for the gomory hu tree problem the parametric flow problem and the approximate s t cut problem

tests of hypotheses in overdispersed poisson regression and other quasi likelihood models abstract test statistics for evaluating the significance of added variables in a regression equation are developed for mixed poisson models where the structural parameter that determines the mean variance relationship var 2 is estimated by the method of moments and the regression coefficients are estimated by quasi likelihood the formulas presented for test statistics and related estimating equations are applicable generally to quasi likelihood models specified by an arbitrary mean value function x together with a variance function v that contains one or more unknown parameters two versions of the wald and score tests are investigated one calculated from the usual model based covariance matrix whose validity depends on correct specification of the variance function and another using an empirical covariance matrix that has a more general asymptotic justification monte carlo simulations demonstrate that the quasi likelihood method of moments ql m procedures yield ap

correlated binomial variates properties of estimator of intraclass correlation and its effect on sample size calculation in group randomized studies the sample size calculations are complicated by within group worksite community etc correlation we compare by simulation the moment method and the more standard anova method of estimating the intraclass correlation we find the former is less biased for a small to moderate number of clusters but the difference disappears when the appropriate degree of freedom is used for the anova estimator we propose a simulation approach for sample size determination and illustrate it with an example

a polyhedral study of production ramping we give strong formulations of ramping constraints used to model the maximum change in production level for a generator or machine from one time period to the next and production limits for the two period case we give a complete description of the convex hull of the feasible solutions the two period inequalities can be readily used to strengthen ramping formulations without the need for separation for the general case we define exponential classes of multi period variable upper bound and multi period ramping inequalities and give conditions under which these inequalities define facets of ramping polyhedra finally we present exact polynomial separation algorithms for the inequalities and report computational experiments on using them in a branch and cut algorithm to solve unit commitment problems in power generation

analysis of two way layout of count data involving multiple counts in each cell abstract multiple counts may occur in each cell of an a b two way layout balanced or unbalanced of two fixed factors a and b standard log linear model analysis based on a poisson distribution assumption of the cell counts is not applicable here because of the unbalanced nature of the table or because the poisson distribution assumption is not valid we develop c tests for interaction and main effects assuming data to be poisson distributed and also assuming that data within the cells have extra over under dispersion beyond that explained by a poisson distribution for this we consider an extended negative binominal distribution and a semiparametric model using the quasi likelihood we show that in all situations the c tests for interaction are of very simple forms for c tests for the main effect in presence of no interaction such simplification is possible only under certain conditions a score test for detecting extra dispersion in presence of interaction is also obtained and is of sim

regression analysis of multivariate incomplete failure time data by modeling marginal distributions abstract many survival studies record the times to two or more distinct failures on each subject the failures may be events of different natures or may be repetitions of the same kind of event in this article we consider the regression analysis of such multivariate failure time observations each marginal distribution of the failure times is formulated by a cox proportional hazards model no specific structure of dependence among the distinct failure times on each subject is imposed the regression parameters in the cox models are estimated by maximizing the failure specific partial likelihoods the resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated simultaneous inferential procedures are then proposed extensive monte carlo studies indicate that the normal approximation is adequate for practical use the new methods allow time dependent covariates missing observations and arbitrary patterns of censorship they are illustrat

on linear and quadratic estimating functions summary in some cases maximum quasi likelihood estimation which is at the core of glim can fail to give reasonable results a more general class of estimating functions is investigated which avoids such failure and also is not restricted to the particular forms of mean and variance function of glim

a simple method for analysing overdispersion in clustered poisson data a simple method is proposed for analysing grouped count data exhibiting overdispersion relative to a poisson model the method is similar to the approach suggested for the analysis of clustered binary data in rao and scott 1992 it requires no specific model for the overdispersion and it can be implemented easily using standard programs designed to handle independent poisson counts after a small amount of preprocessing

using surrogate failure time data to increase cost effectiveness in clinical trials summary in clinical trials with failure time outcomes the cost of follow up for the endpoint of primary interest is sometimes expensive in many of these settings one or more secondary or surrogate failure time outcomes are also available which either occur much earlier or are much less expensive to follow than the primary outcome this paper presents a method for using these secondary outcomes to increase the power of detecting a treatment effect on the primary outcome only without introducing bias the proposed method requires that patients be randomized to either extended or limited follow up a test statistic is constructed by forming a minimum variance linear combination of a linear rank statistic based on the primary outcome and a mean zero weighted sum of linear rank statistics based on secondary outcomes from both follow up arms large sample distribution theory for this statistic is developed while moderate sample behaviour is explored through a simulation study

solving nonlinear single unit commitment problems with ramping constraints we present a dynamic programming algorithm for solving the single unit commitment 1uc problem with ramping constraints and arbitrary convex cost functions the algorithm is based on a new approach for efficiently solving the single unit economic dispatch ed problem with ramping constraints and arbitrary convex cost functions improving on previously known ones that were limited to piecewise linear functions for simple convex functions such as the quadratic ones typically used in applications the solution cost of all the involved ed problems consisting of finding an optimal

sample size calculation for cluster randomization trials with a time to event endpoint cluster randomization trials randomize groups called clusters of subjects called subunits between intervention arms and observations are collected from each subject in this case subunits within each cluster share common frailties so that the observations from subunits of each cluster tend to be correlated oftentimes the outcome of a cluster randomization trial is a time to event endpoint with censoring in this article we propose a closed form sample size formula for weighted rank tests to compare the marginal survival distributions between intervention arms under cluster randomization with possibly variable cluster sizes extensive simulation studies are conducted to evaluate the performance of our sample size formula under various design settings real study examples are taken to demonstrate our method

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

transform both sides approach for overdispersed binomial data when n is unobserved abstract a common complication in analyzing binomial data is overdispersion where the observed variation exceeds that predicted from the binomial distribution with parameters n and p we consider the situation where n is not observed and variable to estimate the regression parameters associated with covariates we apply the transform both sides method based on the first order asymptotic variance stabilizing transformation we develop the arcsine transformation family indexed by a single parameter this family includes the square root and the arcsine transformations as special cases asymptotic properties of the transformation methods are obtained simulation study indicates that the arcsine transformation family is more efficient than the square root and arcsine transformations when there is moderate overdispersion these approaches are applied to a data set from radiobiology

covariate adjustment for non parametric tests for censored survival data we develop a method for covariate adjustment for a general class of non parametric tests for censored survival data which includes the widely used logrank and wilcoxon tests the covariate adjusted tests improve the power of the unadjusted counterparts and have advantages over the covariate adjusted cox score test when there are outliers in the covariable space we investigate the small sample properties of such test statistics through monte carlo simulations examples are given to illustrate the proposed procedures

sample size calculations for the two sample problem using the multiplicative intensity model in this paper we propose formulae for calculating the expected number of events or alternatively the required trial duration for clinical trials involving two treatment groups in which patients may potentially experience multiple events and the data will be analysed using a multiplicative intensity mi model we use a partial likelihood based approach and examine in detail two mi models one that includes a binary treatment variable as the only covariate and a three state markov process model in which a binary time varying covariate is added to the previous model for the simpler model our formula coincides with those derived by cook using full likelihood methods we present applications of the derived formulae to chronic granulomatous disease and breast cancer data sets

sample size calculations for comparative clinical trials with over dispersed poisson process data this paper develops a new formula for sample size calculations for comparative clinical trials with poisson or over dispersed poisson process data the criteria for sample size calculations is developed on the basis of asymptotic approximations for a two sample non parametric test to compare the empirical event rate function between treatment groups this formula can accommodate time heterogeneity inter patient heterogeneity in event rate and also time varying treatment effects an application of the formula to a trial for chronic granulomatous disease is provided

on minimal valid inequalities for mixed integer conic programs we study disjunctive conic sets involving a general regular closed convex full dimensional and pointed cone x1d4a6 such as the nonnegative orthant the lorentz cone or the positive semidefinite cone in a unified framework we introduce x1d4a6 minimal inequalities and show that under mild assumptions these inequalities together with the trivial cone implied inequalities are sufficient to describe the convex hull we focus on the properties of x1d4a6 minimal inequalities by establishing algebraic necessary conditions for an inequality to be x1d4a6 minimal this characterization leads to a broader algebraically defined class of x1d4a6 sublinear inequalities we demonstrate a close connection between x1d4a6 sublinear inequalities and the support functions of convex sets with a particular structure this connection results in practical ways of verifying x1d4a6 sublinearity and or x1d4a6 minimality of inequalities our study generalizes some of the results from the mixed integer linear case it is well known that the minimal inequalities for

two sample asymptotically distribution free tests for incomplete multivariate observations abstract asymptotically distribution free tests for equality of two multivariate distributions based on censored observations are proposed by choosing appropriate test scores we obtain the multivariate versions of the gehan and log rank tests an important application of the proposed tests is in the area in which multiple observations are collected on study subjects some of whom may have missing observations the patterns of missing observations are allowed to differ for the two groups to be compared these tests are particularly useful for longitudinal studies for example the analysis of repeated measurements and growth curves real examples are also provided for illustration

group sequential tests with censored survival data adjusting for covariates summary group sequential tests for the analysis of survival data that compare two treatments and allow for the adjustment of other concomitant variables are discussed these methods allow early termination of a study if large treatment differences occur based on simulation results we compare the operating characteristics of these adjusted tests with the unadjusted sequentially computed log rank test

computing maximal polymatroidal network flows in the classical network flow model flows are constrained by the capacities of individual arcs in the polymatroidal network flow model introduced in this paper flows are constrained by the capacities of sets of arcs yet the essential features of the classical model are retained the augmenting path theorem the integral flow theorem and the max flow min cut theorem arc all shown to yield to straightforward generalization we describe a maximal flow algorithm which finds augmenting paths by labeling arcs instead of nodes as in the case of the classical model as a counterpart of a known result for the classical model we prove that the number of augmentations required to achieve a maximal value flow is bounded by the cube of the number of arcs in the network provided each successive augmentation is made along a shortest augmenting path with ties between shortest paths broken by lexicography

analysis of proportions in the presence of over under dispersion procedures for testing homogeneity of proportions in the presence of over dispersion or underdispersion occurring in several groups in toxicology teratology or mutagenicity or other similar fields are developed we consider c a neyman 1959 in probability and statistics the harold cramer volume pp 213 234 new york wiley or score type tests rao 1947 proceedings of the cambridge philosophical society 44 50 57 based on a parametric model namely the extended beta binomial model prentice 1986 journal of the american statistical association 81 321 327 and two semi parametric models using quasi likelihood wedderburn 1974 biornetrika 61 439447 and extended quasi likelihood nelder and pregibon 1987 biometrika 74 221 232 these procedures and a recent procedure by rao and scott 1992 biometrics 48 577 585 based on the concept of design effect and effective sample size are compared through simulation in terms of size power and robustness for departures from data distribution and dispersion homogeneity to study robustness in terms of departure from data distribution we simulate data from the betabinomial distribution the probit normal binomial distribution and the logit normal binomial distribution simulation shows evidence that for litter sizes and number of litters that may arise in practice a score test based on the quasi likelihood performs best in that it holds nominal level well in all data distribution situations considered here it shows some edge in power over some other statistics in some situations and also shows robustness in presence of moderate dispersion heterogeneity this statistic has a very simple form and it requires estimates of the parameters only under the null hypotheses

a faster strongly polynomial minimum cost flow algorithm in this paper we present a new strongly polynomial time algorithm for the minimum cost flow problem based on a refinement of the edmonds karp scaling technique our algorithm solves the uncapacitated minimum cost flow problem as a sequence of on log n shortest path problems on networks with n nodes and m arcs and runs in on log nm n log n time using a standard transformation this approach yields an om log nm n log n algorithm for the capacitated minimum cost flow problem this algorithm improves the best previous strongly polynomial time algorithm due to z galil and e tardos by a factor of n2 m our algorithm for the capacitated minimum cost flow problem is even more efficient if the number of arcs with finite upper bounds say m is much less than m in this case the running time of the algorithm is om n log nm n log n

case studies in binary dispersion it is common in biomedical studies with binary responses that variability in the observed number of events exceeds binomial variability a phenomenon known as overdispersion failure to make an adjustment to the nominal standard errors can lead to seriously misleading inference for regression analysis in this note we examine a series of examples drawn from the literature to see which of two commonly used variance formulas is more adequate for describing overdispersion in applications two methods residual analysis and formal comparison are introduced we recommend that both methods be employed in seeking an appropriate variance expression for binary responses each of the five data sets exhibits substantial overdispersion one favoring the beta binomial form another favoring a constant overdispersion factor the remaining three examples exhibit no preference

causal inference on the difference of the restricted mean lifetime between two groups summary when comparing survival times between two treatment groups it may be more appropriate to compare the restricted mean lifetime i e the expectation of lifetime restricted to a time l rather than mean lifetime in order to accommodate censoring when the treatments are not assigned to patients randomly as in observational studies we also need to account for treatment imbalances in confounding factors in this article we propose estimators for the difference of the restricted mean lifetime between two groups that account for treatment imbalances in prognostic factors assuming a proportional hazards relationship large sample properties of our estimators based on martingale theory for counting processes are also derived simulation studies were conducted to compare these estimators and to assess the adequacy of the large sample approximations our methods are also applied to an observational database of acute coronary syndrome patients from duke university medical center to estimate the treatment effect on the restricted mean lifetime over 5 years

sample size formula for clustered survival data using weighted log rank statistics summary we present a simple sample size formula for weighted log rank statistics applied to clustered survival data with variable cluster sizes and arbitrary treatment assignments within clusters this formula is based on the asymptotic normality of weighted log rank statistics under certain local alternatives in the clustered data context we also provide consistent variance estimators the derived sample size formula reduces to schoenfeld s 1983 formula for cases of no clustering or independence within clusters simulation results verify control of the type i error and accuracy of the sample size formula use of the sample size formula in an event driven clinical trial design is illustrated using data from the early treatment diabetic retinopathy study

sample size calculations for ordered categorical data many clinical trials yield data on an ordered categorical scale such as very good good moderate poor under the assumption of proportional odds such data can be analysed using techniques of logistic regression in simple comparisons of two treatments this approach becomes equivalent to the mann whitney test in this paper sample size formulae consistent with an eventual logistic regression analysis are derived the influence on efficiency of the number and breadth of categories will be examined effects of misclassification and of stratification are discussed and examples of the calculations are given

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

semiparametric regression for the mean and rate functions of recurrent events the counting process with the cox type intensity function has been commonly used to analyse recurrent event data this model essentially assumes that the underlying counting process is a time transformed poisson process and that the covariates have multiplicative effects on the mean and rate function of the counting process recently pepe and cai and lawless and co workers have proposed semiparametric procedures for making inferences about the mean and rate function of the counting process without the poisson type assumption in this paper we provide a rigorous justification of such robust procedures through modern empirical process theory furthermore we present an approach to constructing simultaneous confidence bands for the mean function and describe a class of graphical and numerical techniques for checking the adequacy of the fitted mean rate model the advantages of the robust procedures are demonstrated through simulation studies an illustration with multiple infection data taken from a clinical study on chronic granulomatous disease is also provided

the effect of estimating weights in weighted least squares abstract in weighted least squares it is typical that the weights are unknown and must be estimated most packages provide standard errors assuming that the weights are known this is fine for sufficiently large sample sizes but what about for small to moderate sample sizes the investigation of this article into the effect of estimating weights proceeds under the assumption typical in practice that one has a parametric model for the variance function in this context generalized least squares consists of a an initial estimate of the regression parameter b a method for estimating the variance function and c the number of iterations in reweighted least squares by means of expansions for the covariance it is shown that each of a c can matter in problems of small to moderate size a few conclusions may be of practical interest first estimated standard errors assuming that the weights are known can be too small in practice the investigation indicates that a simple bootstrap operation resul

towards a general asymptotic theory for cox model with staggered entry a general asymptotic theory is established for the two parameter cox score process with staggered entry data it extends in several directions the existing theory developed by sellke and siegmund slud and gu and lai an essential tool employed here is a modern empirical process theory as elucidated in a recent monograph by pollard

separation dimension and facet algorithms for node flow polyhedra production planning problems such as an available to promise atp model of chen et al 2002 can involve material compatibility constraints that specify when components from various suppliers can be feasibly assembled into a final product in a companion paper to chen et al 2002 ball et al 2003 showed that in many cases such constraints can be modeled as the set of feasible source sink flows through an acyclic network the flow through a node is the sum of the flows on all paths containing it the number of paths is often exponential in the number of nodes and so it is more computationally tractable to consider the set of node flows in place of that of path flows here nodes represent components and paths represent product configurations in the context of np hard mixed integer programming models such as the atp model when the description of the set of node flows is too complicated to be explicitly written out the material compatibility constraints can be handled in a cutting plane framework by using a separation algorithm ball et al characterized the polyhedron of node flows for some special cases we extend this work in various practical and theoretical directions we allow arbitrary directed networks we allow both upper and lower bounds on flows we characterize which valid inequalities are facets we give fast algorithms for separation violation and dimension and we put all the pieces together into an algorithm for facet separation all algorithms are very efficient as they are based on max flow and min cost flow subroutines

variance function estimation abstract heteroscedastic regression models are used in fields including economics engineering and the biological and physical sciences often the heteroscedasticity is modeled as a function of the covariates or the regression and other structural parameters standard asymptotic theory implies that how one estimates the variance function in particular the structural parameters has no effect on the first order properties of the regression parameter estimates there is evidence however both in practice and higher order theory to suggest that how one estimates the variance function does matter further in some settings estimation of the variance function is of independent interest or plays an important role in estimation of other quantities in this article we study variance function estimation in a unified way focusing on common methods proposed in the statistical and other literature to make both general observations and compare different estimation schemes we show that there are significant di

sample size formula for the proportional hazards regression model a formula is derived for determining the number of observations necessary to test the equality of two survival distributions when concomitant information is incorporated this formula should be useful in designing clinical trials with a heterogeneous patient population schoenfeld 1981 biometrika 68 316 319 derived the asymptotic power of a class of statistics used to test the equality of two survival distributions that result is extended to the case where concomitant information is available for each individual and where the proportional hazards model holds the loss of efficiency caused by ignoring concomitant variables is also computed

on the computational behavior of a polynomial time network flow algorithm a variation on the edmonds karp scaling approach to the minimum cost network flow problem is examined this algorithm which scales costs rather than right hand sides also runs in polynomial time large scale computational experiments indicate that the computational behavior of such scaling algorithms may be much better than had been presumed within several distributions of square dense capacitated transportation problems a cost scaling code scale exhibits linear growth in average execution time with the number of edges while two network simplex codes rnet and gnet exhibit greater than linear growth our experiments reveal that median and mean execution times are predictable with surprising accuracy for all of the three codes and all three distributions from which test problems were generated moreover for fixed problem size individual execution times appear to behave as though they are approximately lognormally distributed with constant variance the experiments also reveal sensitivity of the parameters in the models and in the models themselves to variations in the distribution of problems this argues for caution in the interpretation of such computational studies beyond the realm in which the computations were performed

some simple robust methods for the analysis of recurrent events nelson discussed a method of estimating the cumulative mean function for identically distributed processes of recurrent events we show that a similar approach can be used with more general models including regression the key idea is to use point estimates based on poisson models and to develop robust variance estimates that are valid more generally the methods are illustrated on reliability and warranty data

on the number of upward planar orientations of maximal planar graphs we consider the problem of determining the maximum and the minimum number of upward planar orientations a maximal planar graph can have we show that every n vertex maximal planar graph has at least w 1 189 n and at most o 4 n upward planar orientations moreover we show that there exist n vertex maximal planar graphs having o 2 n upward planar orientations and n vertex maximal planar graphs having w 2 599 n upward planar orientations further we present bounds for the maximum and the minimum number of acyclic orientations a maximal planar graph can have

power and sample size calculation for paired recurrent events data based on robust nonparametric tests the purpose of this paper is to develop a formula for calculating the required sample size for paired recurrent events data the developed formula is based on robust non parametric tests for comparing the marginal mean function of events between paired samples this calculation can accommodate the associations among a sequence of paired recurrent event times with a specification of correlated gamma frailty variables for a proportional intensity model we evaluate the performance of the proposed method with comprehensive simulations including the impacts of paired correlations homogeneous or nonhomogeneous processes marginal hazard rates censoring rate accrual and follow up times as well as the sensitivity analysis for the assumption of the frailty distribution the use of the formula is also demonstrated using a premature infant study from the neonatal intensive care unit of a tertiary center in southern taiwan copyright 2017 john wiley sons ltd

upward planar graphs and their duals we consider upward planar drawings of directed graphs in the plane up and on standing sup and rolling cylinders rup in the plane and on the standing cylinder the edge curves are monotonically increasing in y direction on the rolling cylinder they wind unidirectionally around the cylinder there is a strict hierarchy of classes of upward planar graphs up sup rup in this paper we show that rolling and standing cylinders switch roles when considering an upward planar graph and its dual in particular we prove that a strongly connected graph is rup if and only if its dual is a sup dipole a dipole is an acyclic graph with a single source and a single sink all rup graphs are characterized in terms of their duals using generalized dipoles moreover we obtain a characterization of the primals and duals of wsup graphs which are upward planar graphs on the standing cylinder and allow for horizontal edge curves

a model informed rank test for right censored data with intermediate states the generalized wilcoxon and log rank tests are commonly used for testing differences between two survival distributions we modify the wilcoxon test to account for auxiliary information on intermediate disease states that subjects may pass through before failure for a disease with multiple states where patients are monitored periodically but exact transition times are unknown e g staging in cancer we first fit a multi state markov model to the full data set when censoring precludes the comparison of survival times between two subjects we use the model to estimate the probability that one subject will have survived longer than the other given their censoring times and last observed status and use these probabilities to compute an expected rank for each subject these expected ranks form the basis of our test statistic simulations demonstrate that the proposed test can improve power over the log rank and generalized wilcoxon tests in some settings while maintaining the nominal type 1 error rate the method is illustrated on an als data set

divide to conquer decomposition methods for energy optimization modern electricity systems provide a plethora of challenging issues in optimization the increasing penetration of low carbon renewable sources of energy introduces uncertainty in problems traditionally modeled in a deterministic setting the liberalization of the electricity sector brought the need of designing sound markets ensuring capacity investments while properly reflecting strategic interactions in all these problems hedging risk possibly in a dynamic manner is also a concern the fact of representing uncertainty and or competition of different companies in a multi settlement power market considerably increases the number of variables and constraints for this reason usually a trade off needs to be found between modeling and numerical tractability the more details are brought into the model the harder becomes the optimization problem for structured optimization and generalized equilibrium problems we explore some variants of solution methods based on lagrangian relaxation and on benders decomposition throughout we keep as a leading thread the actual practical value of such techniques in terms of their efficiency to solve energy related problems

finding minimum cost circulations by successive approximation we develop a new approach to solving minimum cost circulation problems our approach combines methods for solving the maximum flow problem with successive approximation techniques based on cost scaling we measure the accuracy of a solution by the amount that the complementary slackness conditions are violated we propose a simple minimum cost circulation algorithm one version of which runs in on3lognc time on an n vertex network with integer arc costs of absolute value at most c by incorporating sophisticated data structures into the algorithm we obtain a time bound of onm logn2 mlognc on a network with m arcs a slightly different use of our approach shows that a minimum cost circulation can be computed by solving a sequence of on lognc blocking flow problems a corollary of this result is an on2log nlognc time m processor parallel minimum cost circulation algorithm our approach also yields strongly polynomial minimum cost circulation algorithms our results provide evidence that the minimum cost circulation problem is not much harder than the maximum flow problem we believe that a suitable implementation of our method will perform extremely well in practice

a cutting plane approach to capacitated lot sizing with start up costs we consider a mixed integer model for multi item single machine production planning incorporating both start up costs and machine capacity the single item version of this model is studied from the polyhedral point of view and several families of valid inequalities are derived for some of these inequalities we give necessary and sufficient facet inducing conditions and efficient separation algorithms we use these inequalities in a cutting plane branch and bound procedure a set of real life based problems with 5 items and up to 36 periods is solved to optimality

an entropy based nonparametric test for the validation of surrogate endpoints we present a nonparametric test to validate surrogate endpoints based on measure of divergence and random permutation this test is a proposal to directly verify the prentice statistical definition of surrogacy the test does not impose distributional assumptions on the endpoints and it is robust to model misspecification our simulation study shows that the proposed nonparametric test outperforms the practical test of the prentice criterion in terms of both robustness of size and power we also evaluate the performance of three leading methods that attempt to quantify the effect of surrogate endpoints the proposed method is applied to validate magnetic resonance imaging lesions as the surrogate endpoint for clinical relapses in a multiple sclerosis trial copyright 2012 john wiley sons ltd

inference using surrogate outcome data and a validation sample summary in the context of estimating 3 from the regression model p yi x relating response y to covariates x suppose that only a surrogate response s is available for most study subjects suppose that for a random subsample of the study cohort termed the validation sample the true outcome y is available in addition to s we consider maximum likelihood estimation of 3 from such data and show that it is nonrobust to misspecification of the distribution relating the surrogate to the true outcome p s i y x an alternative semiparametric method is also considered which is nonparametric with respect to p s i y x large sample distribution theory for maximum estimated likelihood estimates is developed an illustrative example is presented

lower bounds in lot sizing models a polyhedral study variable lower bounds in mixed integer programs are constraints with the general form x ly where xis a continuous variable and y is a binary or an integer variable this type of constraints is present in some lot sizing models where x represents the amount of some article produced by a machine and y 0 1 indicates whether the machine is set up for that articley 1 or not y 0 in these models production below some level is not allowed in order to make full use of resources in this paper we study from the polyhedral viewpoint the mixed integer models whose feasible set includes an additive constraint xj d and constraints lyj xj kyj where xj are continuous variables yj are integer or binary variables and k is a large constant we derive families of strong valid inequalities and show they are sufficient to describe completely the convex hulls of the sets of feasible solutions moreover we develop polynomial algorithms to solve the separation problem associated to each of the families obtained finally we incorporate the inequalities obtained in a cutting plane algorithm and test their ability to solve some multi item lot sizing problems

on the computational complexity of upward and rectilinear planarity testing a directed graph is upward planar if it can be drawn in the plane such that every edge is a monotonically increasing curve in the vertical direction and no two edges cross an undirected graph is rectilinear planar if it can be drawn in the plane such that every edge is a horizontal or vertical segment and no two edges cross testing upward planarity and rectilinear planarity are fundamental problems in the effective visualization of various graph and network structures for example upward planarity is useful for the display of order diagrams and subroutine call graphs while rectilinear planarity is useful for the display of circuit schematics and entity relationship diagrams we show that upward planarity testing and rectilinear planarity testing are np complete problems we also show that it is np hard to approximate the minimum number of bends in a planar orthogonal drawing of an n vertex graph with an o n 1 epsilon error for any epsilon 0

combining incomplete information from independent assessment surveys for estimating masonry deterioration construction materials used in building structures such as masonry wood and reinforced concrete deteriorate over time because of many factors including poor design defective materials or manufacture and poor workmanship this article is concerned with estimates of masonry deterioration and the effects of covariates on the damage to bricks on the walls of five multiple story buildings of a residential complex located in the bronx new york in this case study the damage of primary interest was a spall a physical separation of a portion of the brick face from the body of the brick eventually the face becomes so damaged that portions fall off the result is an unattractive appearance and a hazard to passersby in this study spall damage was assessed by means of three different and independent condition assessment surveys an expensive precise and hence very limited scaffold drop survey and two additional inexpensive but more detailed photographic and visual surveys the photographic survey wa

tight mip formulations for bounded up down times and interval dependent start ups switching machines on and off is an important aspect of unit commitment problems and production planning problems among others here we study tight mixed integer programming formulations for two aspects of such problems bounded length on and off intervals and interval dependent start ups the problem with both these aspects admits a general dynamic programming shortest path formulation which leads to a tight extended formulation with a number of binary variables that is quadratic in the number n of time periods we are thus interested in tight formulations with a linear number of binary variables for the bounded interval problem we present a tight network dual formulation based on new integer cumulative variables that allows us to simultaneously treat lower and upper bounds on the interval lengths and also to handle time varying bounds this in turn leads to more general results including simpler proofs of known tight formulations for problems with just lower bounds for the interval dependent start up problem we develop a path formulation that allows us to describe the convex hull of solutions in the space of machine state variables and interval dependent start up variables

variable selection and model averaging in semiparametric overdispersed generalized linear models we express the mean and variance terms in a double exponential regression model as additive functions of the predictors and use bayesian variable selection to determine which predictors enter the model and whether they enter linearly or flexibly when the variance term is null we obtain a generalized additive model which becomes a generalized linear model if the predictors enter the mean linearly the model is estimated using markov chain monte carlo simulation and the methodology is illustrated using real and simulated data sets

relative efficiency of the log rank test within a multiplicative intensity model summary for large sample clinical trials with independent individuals randomly allocated to two treatment groups in which survival times follow a log linear multiplicative intensity model with treatment group as one covariate this paper calculates the asymptotic relative efficiency of the log rank test for treatment effect as compared with the optimal score test the method is to exhibit the failure hazard intensity not of proportional hazards form obtained by ignoring all covariates other than treatment group the efficiency formulae are illustrated in two examples and estimation from data of the loss of efficiency is illustrated for two clinical trial datasets

bayesian tests of extra binomial variability a simple model for extra binomial variability is the beta binomial a complication in testing the binomial against the beta binomial alternative is that the binomial lies on the boundary of the beta binomial which forces modifications to the usual asymptotic arguments in this paper we propose a bayesian test using a pair of approximate bayes factors one for the case in which the maximum likelihood estimator mle of the extra binomial variability is zero and one for the case in which it is positive these approximate bayes factors are easy to compute we evaluate the operating characteristics of the bayes factors and find them to be more powerful than the likelihood ratio test we then apply the method to three data sets including one in which the issue is whether a logistic regression intercept should be considered a random effect in each case our approximate bayes factors are close to the exact bayes factors which may also be computed with additional effort copyright 2004 john wiley sons ltd

how to compute least infeasible flows it is well known how to use maximum flow to decide when a flow problem with demands lower bounds and upper bounds is infeasible less well known is how to compute a flow that is least infeasible this paper considers many possible ways to define least infeasible and shows how to compute optimal flows for each definition for each definition it also gives a dual characterization in terms of cuts a polynomial routine for recognizing that type of least infeasible flow and relates that definition to dual cut canceling min cost flow network algorithms

a new approach to the maximum flow problem all previously known efficient maximum flow algorithms work by finding augmenting paths either one path at a time as in the original ford and fulkerson algorithm or all shortest length augmenting paths at once using the layered network approach of dinic an alternative method based on the preflow concept of karzanov is introduced a preflow is like a flow except that the total amount flowing into a vertex is allowed to exceed the total amount flowing out the method maintains a preflow in the original network and pushes local flow excess toward the sink along what are estimated to be shortest paths the algorithm and its analysis are simple and intuitive yet the algorithm runs as fast as any other known method on dense graphs achieving an o n 3 time bound on an n vertex graph by incorporating the dynamic tree data structure of sleator and tarjan we obtain a version of the algorithm running in o nm log n 2 m time on an n vertex m edge graph this is as fast as any known method for any graph density and faster on graphs of moderate density the algorithm also admits efficient distributed and parallel implementations a parallel implementation running in o n 2 log n time using n processors and o m space is obtained this time bound matches that of the shiloach vishkin algorithm which also uses n processors but requires o n 2 space

robust covariate adjusted logrank tests summary in testing for significance of treatment effect within two sample censored survival data with measured covariates it is known tsiatis rosner tritchler 1985 that adjusting the logrank test statistic using a proportional hazards model for covariate effect can substantially increase efficiency extending the robust score statistics described by lin wei 1989 we show how to estimate and optimise the relative efficiencies of such score statistics based on various possible working models providing a flexible and statistically valid two sample testing methodology which improves upon the purely nonparametric logrank without sacrificing model robustness numerical calculations indicate some nonproportional hazard settings within which the power of the logrank is erratic while the tests described here have reliably good power

local polynomial estimation in multiparameter likelihood models abstract the nonparametric regression technique of local polynomial fitting is extended to multiparameter likelihood models some well known appealing features of local polynomial smoothers such as the behavior at the boundary are shown to carry over to the multiparameter case asymptotic consistency and normality of the resulting estimators are derived under suitable regularity conditions this work is motivated by the need for a nonparametric alternative to parametric dose response models for clustered binary data probability models for clustered binary response data include a success probability parameter and one or more correlation parameters the proposed local polynomial estimators can play an important role as a diagnostic tool or to suggest the form of the functional relationships in parametric likelihood models as an illustration it is shown how the local likelihood estimation procedure can be implemented for fitting a dose response curve based on the beta binomial model a data example and

on the use of the quasi likelihood method in teratological experiments this paper concerns the impact of litter effects on the inference of dose response relationships in teratological experiments with binary response kupper et al 1986 biometrics 42 85 98 concluded that when intra litter correlations are dose dependent the use of a common intra litter correlation likelihood based on the beta binomial distribution could lead to severe bias in estimation of the parameter beta which characterizes the dose response relationship we show here that the problems of bias and coverage probability for beta could still be substantial when one uses the likelihood with heterogeneous intra litter correlations we then examine through a simulation study the performance of the quasi likelihood method wedderburn 1974 biometrika 61 439 447 and recommend that this method with a common intra litter correlation parameter be used when the number of litters is small or modest

a randomized maximum flow algorithm a randomized algorithm for computing a maximum flow is presented for an n vertex m edge network the running time is o nm n 2 log n 2 with probability at least 1 2 sqrt nm the algorithm is always correct and in the worst case runs in o nm log n time the only use of randomization is to randomly permute the adjacency lists of the network vertices at the start of the execution the analysis introduces the notion of premature target relabeling ptr events and shows that each ptr event contributes o log n amortized time to the overall running time the number of ptr events is always o nm however it is shown that when the adjacency lists are randomly permuted then this quantity is o n 3 2 m 1 2 n 2 log n with high probability

polynomial time approximation schemes for euclidean traveling salesman and other geometric problems we present a polynomial time approximation scheme for euclidean tsp in fixed dimensions for every fixed c 1 and given any n nodes in r 2 a randomized version of the scheme finds a 1 1 c approximation to the optimum traveling salesman tour in o n log n o c time when the nodes are in r d the running time increases to o n log n o d c d 1 for every fixed c d the running time is n poly log n that is nearly linear in n the algorithmm can be derandomized but this increases the running time by a factor o n d the previous best approximation algorithm for the problem due to christofides achieves a 3 2 aproximation in polynomial time we also give similar approximation schemes for some other np hard euclidean problems minimum steiner tree k tsp and k mst the running times of the algorithm for k tsp and k mst involve an additional multiplicative factor k the previous best approximation algorithms for all these problems achieved a constant factor approximation we also give efficient approximation schemes for euclidean min cost matching a problem that can be solved exactly in polynomial time all our algorithms also work with almost no modification when distance is measured using any geometric norm such as e p for p 1 or other minkowski norms they also have simple parallel i e nc implementations

cutting planes for the multistage stochastic unit commitment problem as renewable energy penetration rates continue to increase in power systems worldwide new challenges arise for system operators in both regulated and deregulated electricity markets to solve the security constrained coal fired unit commitment problem with intermittent generation due to renewables and uncertain load in order to ensure system reliability and maintain cost effectiveness in this paper we study a security constrained coal fired stochastic unit commitment model which we use to enhance the reliability unit commitment process for day ahead power system operations in our approach we first develop a deterministic equivalent formulation for the problem which leads to a large scale mixed integer linear program then we verify that the turn on off inequalities provide a convex hull representation of the minimum up down time polytope under the stochastic setting next we develop several families of strong valid inequalities mainly through lifting schemes in particular by exploring sequence independent lifting and subadditive approximation lifting properties for the lifting schemes we obtain strong valid inequalities for the ramping and general load balance polytopes finally branch and cut algorithms are developed to employ these valid inequalities as cutting planes to solve the problem our computational results verify the effectiveness of the proposed approach

a comparison of methods for testing homogeneity of proportions in teratologic studies summary we consider teratologic studies in which the aim is to compare the survival rate of animals in a treatment group to the corresponding rate in a control group the design of such studies often involves the allocation of intact litters of animals to treatment invalidating the application of standard statistical methods we review the strengths and weaknesses of several approaches for dealing with this problem including methodology recently developed for the analysis of clustered binary data a simulation study is conducted in which litter sizes are generated from a distribution having specified mean and degree of imbalance it is recommended on the basis of this study and on theoretical considerations that the choice of method should depend on whether the comparison of interest is experimental or observational for experimental comparisons involving the random assignment of litters to different treatment groups methods based on the adjustment of standard chi square statistics are recommended unless the number of litters in each group is very large

upward and quasi upward planarity testing of embedded mixed graphs mixed graphs have both directed and undirected edges and have received considerable attention in the literature we study two upward planarity testing problems for embedded mixed graphs give some np hardness results and describe integer linear programming techniques to solve them experiments show the efficiency of our approach