a proportional hazards model for interval censored failure time data this paper develops a method for fitting the proportional hazards regression model when the data contain left right or interval censored observations results given for testing the hypothesis of a zero regression coefficient lead to a generalization of the log rank test for comparison of several survival curves the method is used to analyze data from an animal tumorigenicity study and also a clinical trial

combinatorial entropy power inequalities a preliminary study of the stam region we initiate the study of the stam region defined as the subset of the positive orthant in r 2 n 1 that arises from considering the entropy powers of subset sums of n independent random vectors in a euclidean space of finite dimension we show that the class of fractionally superadditive set functions provides an outer bound to the stam region resolving a conjecture of barron and madiman on the other hand the entropy power of a sum of independent random vectors is not supermodular in any dimension we also develop some qualitative properties of the stam region showing for instance that its closure is a logarithmically convex cone

the quadratic shortest path problem complexity approximability and solution methods we consider the problem of finding a shortest path in a directed graph with a quadratic objective function the qspp we show that the qspp cannot be approximated unless p np for the case of a convex objective function an n approximation algorithm is presented where n is the number of nodes in the graph and apx hardness is shown furthermore we prove that even if only adjacent arcs play a part in the quadratic objective function the problem still cannot be approximated unless p np in order to solve the problem we first propose a mixed integer programming formulation and then devise an efficient exact branch and bound algorithm for the general qspp where lower bounds are computed by considering a reformulation scheme that is solvable through a number of minimum cost flow problems in our computational experiments we solve to optimality different classes of instances with up to 1000 nodes

choquet weak convergence of capacity functionals of random sets the results in this paper are about the convergence of capacity functionals of random sets the motivation stems from asymptotic aspects in inference and decision making with coarse data in biostatistics set valued observations as well as connections between random sets with several emerging uncertainty calculi in intelligent systems such as fuzziness belief functions and possibility theory specifically we study the counter part of billingsley s portmanteau theorem for weak convergence of probability measures namely convergence of capacity functionals of random sets in terms of choquet integrals

on metric generators of graphs we study generators of metric spaces sets of points with the property that every point of the space is uniquely determined by the distances from their elements such generators put a light on seemingly different kinds of problems in combinatorics that are not directly related to metric spaces the two applications we present concern combinatorial search problems on false coins known from the borderline of extremal combinatorics and information theory and a problem known from combinatorial optimization connected joins in graphs we use results on the detection of false coins to approximate the metric dimension minimum size of a generator for the metric space defined by the distances of some particular graphs for which the problem was known and open in the opposite direction using metric generators we show that the existence of connected joins in graphs can be solved in polynomial time a problem asked in a survey paper of frank on the negative side we prove that the minimization of the number of components of a join is np hard we further explore the metric dimension with some problems the main problem we are led to is how to extend an isometry given on a metric generator of a metric space

ignorability in general incomplete data models summary rubin 1976 defined ignorability conditions for frequentist and bayes likelihood analyses of data subject to missing observations more recently heitjan rubin 1991 and heitjan 1993 generalised the rubin model to encompass other forms of incompleteness establishing ignorability conditions for bayes likelihood inferences only this paper extends the heitjan rubin model by explicitly defining the observed degree of coarseness as a data element this permits the development of a frequentist theory including a generalisation of missing completely at random the frequentist ignorability condition for missing data the model is applied in a number of incomplete data problems of general interest

linear rank tests for interval censored data with application to pcb levels in adipose tissue of transformer repair workers linear rank statistics are described for testing for differences between groups when the data are interval censored the statistics are closely related to those described by prentice for right censored data problems in calculating the statistics are discussed and several approaches to computation including estimation of the efficient rank scores are described results from a small simulation study are presented the methods are applied to data from a study relating tissue levels of pcbs to occupational exposure

survival curve estimation for informatively coarsened discrete event time data interval censored or more generally coarsened event time data arise when study participants are observed at irregular time periods and experience the event of interest in between study observations such data are often analysed assuming non informative censoring which can produce biased results if the assumption is wrong this paper extends the standard approach for estimating survivor functions to allow informatively interval censored data by incorporating various assumptions about the censoring mechanism into the model we include a bayesian extension in which final estimates are produced by mixing over a distribution of assumed censoring mechanisms we illustrate these methods with a natural history study of hiv infected individuals using assumptions elicited from an aids expert

dual time frequency domain system identification in this paper we obtain the maximum likelihood estimate of the parameters of discrete time linear models by using a dual time frequency domain approach we propose a formulation that considers a reduced rank linear transformation of the available data such a transformation may correspond to different options selection of time domain data transformation to the frequency domain or selection of frequency domain data obtained from time domain samples we use the proposed approach to identify multivariate systems represented in state space form by using the expectation maximisation algorithm we illustrate the benefits of the approach via numerical examples

a new lower bound for the quadratic assignment problem we introduce a new lower bound for the quadratic assignment problem based on a sequence of equivalent formulations of the problem we present a procedure for obtaining tight bounds by sequentially applying our approach in conjunction with the a assad and w xu bound and the n christofides and m gerrard bound

on the metric dimension of corona product graphs given a set of vertices s v 1 v 2 v k of a connected graph g the metric representation of a vertex v of g with respect to s is the vector r v s d v v 1 d v v 2 d v v k where d v v i i 1 k denotes the distance between v and v i s is a resolving set for g if for every pair of distinct vertices u v of g r u s r v s the metric dimension of g dim g is the minimum cardinality of any resolving set for g let g and h be two graphs of order n 1 and n 2 respectively the corona product g h is defined as the graph obtained from g and h by taking one copy of g and n 1 copies of h and joining by an edge each vertex from the ith copy of h with the ith vertex of g for any integer k 2 we define the graph g kh recursively from g h as g kh g k 1h h we give several results on the metric dimension of g kh for instance we show that given two connected graphs g and h of order n 1 2 and n 2 2 respectively if the diameter of h is at most two then dim g kh n 1 n 2 1 k 1dim h moreover if n 2 7 and the diameter of h is greater than five or h is a cycle graph then dim g kh n 1 n 2 1 k 1dim k 1 h

power and sample size calculations for discrete bounded outcome scores we consider power and sample size calculations for randomized trials with a bounded outcome score bos as primary response adjusted for a priori chosen covariates we define bos to be a random variable restricted to a finite interval typically a bos has a j or u shaped distribution hindering traditional parametric methods of analysis when no adjustment for covariates is needed a non parametric test could be chosen however there is still a problem with calculating the power since the common location shift alternative does not hold in general for a bos in this paper we consider a parametric approach and assume that the observed bos is a coarsened version of a true bos which has a logit normal distribution in each treatment group allowing correction for covariates a two step procedure is used to calculate the power firstly the power function is defined conditionally on the covariate values secondly the marginal power is obtained by averaging the conditional power with respect to an assumed distribution for the covariates using monte carlo integration a simulation study evaluates the performance of our method which is also applied to the ecass 1 stroke study

the steiner travelling salesman problem with correlated costs the steiner travelling salesman problem stsp is a variant of the tsp that is suitable for instances defined on road networks we consider an extension of the stsp in which the road traversal costs are both stochastic and correlated this happens for example when vehicles are prone to delays due to rush hours road works or accidents following the work of markowitz on portfolio selection we model this problem as a bi objective mean variance problem then we show how to approximate the efficient frontier via integer programming we also show how to exploit certain special structures in the correlation matrices computational results indicate that our approach is viable for instances with up to 100 nodes it turns out that minimum variance tours can look rather different from minimum expected cost tours

semiparametric estimation of proportional mean residual life model in presence of censoring summary a mean residual life function is the average remaining life of a surviving subject as it varies with time the proportional mean residual life model was proposed by oakes and dasu 1990 biometrika77 409 410 in regression analysis to study its association with related covariates in absence of censoring in this article we develop some semiparametric estimation procedures to take censoring into account the proposed methodology is evaluated via simulation studies and further applied to a clinical trial of chemotherapy in postoperative radiotherapy of lung cancer patients

resolvability and fault tolerant resolvability structures of convex polytopes abstract in this paper we study resolvability and fault tolerant resolvability of convex polytopes and related geometric graphs imran et al 2010 18 raised an open problem asserting that whether or not every family of convex polytope has a constant metric dimension raza et al 2018 28 studied the fault tolerant metric dimension of certain families of convex polytopes they also concluded their study with an open problem asking whether or not every family of convex polytope has a constant fault tolerant metric dimension in this paper we provide negative answers to both of the aforementioned open problems we answer the first question by constructing a family of convex polytopes with an unbounded metric dimension by proving a result between resolvability and fault tolerant resolvability structures of a graph we show that the family of convex polytope with an unbounded metric dimension also possesses an unbounded fault tolerant resolvability structure moreover we construct three more infinite families of graphs which are closely related to convex polytopes having an unbounded metric dimension

an algorithmic and a geometric characterization of coarsening at random we show that the class of conditional distributions satisfying the coarsening at random car property for discrete data has a simple and robust algorithmic description based on randomized uniform multicovers combinatorial objects generalizing the notion of partition of a set however the complexity of a given car mechanism can be large the maximal height of the needed multicovers can be exponential in the number of points in the sample space the results stem from a geometric interpretation of the set of car distributions as a convex polytope and a characterization of its extreme points the hierarchy of car models defined in this way could be useful in parsimonious statistical modeling of car mechanisms though the results also raise doubts in applied work as to the meaningfulness of the car assumption in its full generality

sampling bias and logistic models summary in a regression model the joint distribution for each finite sample of units is determined by a function px y depending only on the list of covariate values x x u1 x un on the sampled units no random sampling of units is involved in biological work random sampling is frequently unavoidable in which case the joint distribution p y x depends on the sampling scheme regression models can be used for the study of dependence provided that the conditional distribution p y x for random samples agrees with px y as determined by the regression model for a fixed sample having a non random configuration x the paper develops a model that avoids the concept of a fixed population of units thereby forcing the sampling plan to be incorporated into the sampling distribution for a quota sample having a predetermined covariate configuration x the sampling distribution agrees with the standard logistic regression model with correlated components for most natural sampling plans such as sequential or simple random sampling the conditional distribution p y x is not the same as the regression distribution unless px y has independent components in this sense most natural sampling schemes involving binary random effects models are biased the implications of this formulation for subject specific and population averaged procedures are explored

on the testability of the car assumption in recent years a popular nonparametric model for coarsened data is an assumption on the coarsening mechanism called coarsening at random car it has been conjectured in several papers that this assumption cannot be tested by the data that is the assumption does not restrict the possible distributions of the data in this paper we will show that this conjecture is not always true an example will be current status data we will also give conditions when the conjecture is true and in doing so we will introduce a generalized version of the car assumption as an illustration we retrieve the well known result that the car assumption cannot be tested in the case of right censored data

rounding error in regression the appropriateness of sheppard s corrections abstract we consider three simple approaches to rounding error in least squares regression the first treats the rounded data as if they were unrounded the second adds an adjustment to the diagonal of the covariance matrix of the variables and the third subtracts an adjustment from the diagonal the third sheppard s corrections can be motivated as maximum likelihood with small rounding error and either 1 joint normal data or 2 normal residuals regular independent variables and large samples although an example and theory suggest that the third approach is usually preferable to the first two a generally satisfactory attack on rounding error in regression requires the specification of the full distribution of variables and convenient computational methods for this problem are not currently available author

ignorability for categorical data we study the problem of ignorability in likelihood based inference from incomplete categorical data two versions of the coarsened at random assumption car are distinguished their compatibility with the parameter distinctness assumption is investigated and several conditions for ignorability that do not require an extra parameter distinctness assumption are established it is shown that car assumptions have quite different implications depending on whether the underlying complete data model is saturated or parametric in the latter case car assumptions can become inconsistent with observed data

ignorability and coarse data we present a general statistical model for data coarsening which includes as special cases rounded heaped censored partially categorized and missing data formally with coarse data observations are made not in the sample space of the random variable of interest but rather in its power set grouping is a special case in which the degree of coarsening is known and nonstochastic we establish simple conditions under which the possible stochastic nature of the coarsening mechanism can be ignored when drawing bayesian and likelihood inferences and thus the data can be validly treated as grouped data the conditions are that the data be coarsened at random a generalization of the condition missing at random and that the parameters of the data and the coarsening process be distinct applications of the general model and the ignorability condition are illustrated in a numerical example and described briefly in a variety of special cases

on the fault tolerant metric dimension of convex polytopes abstract a convex polytopes is a polytope that is also a convex set of points in the n dimensional euclidean space r n by preserving the same adjacency relation between vertices of a convex polytope its graph is constructed the metric dimension problem has been extensively studied for convex polytopes and other families of graphs in this paper we study the fault tolerant metric dimension problem for convex polytopes by using a relation between resolving sets and fault tolerant resolving sets of graphs we prove that certain infinite families of convex polytopes are the families of graphs with constant fault tolerant metric dimension we conclude the paper with some open problems

interval censoring identifiability and the constant sum property the constant sum property given in oller et al 2004 for censoring models justifies the use of a simplified likelihood to obtain the nonparametric maximum likelihood estimator of the lifetime distribution in this paper we study the relevance of the constant sum property in the identifiability of the lifetime distribution we show that the lifetime distribution is not identifiable outside the class of constant sum models we also show that the lifetime probabilities assigned to the observable intervals are identifiable inside the class of constant sum models we illustrate all these notions with several examples

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

estimating incubation period distributions with coarse data the incubation period the time between infection and disease onset is important in the surveillance and control of infectious diseases but is often coarsely observed coarse data arises because the time of infection the time of disease onset or both are not known precisely accurate estimates of an incubation period distribution are useful in real time outbreak investigations and in modeling public health interventions we compare two methods of estimating such distributions the first method represents the data as doubly interval censored the second introduces a data reduction technique that makes the computation more tractable in a simulation study the methods perform similarly when estimating the median but the first method yields more reliable estimates of the distributional tails we conduct a sensitivity analysis of the two methods to violations of model assumption and we apply these methods to historical incubation period data on influenza a and respiratory syncytial virus the analysis of reduced data is less computationally intensive and performs well for estimating the median under a wide range of conditions however for estimation of the tails of the distribution the doubly interval censored analysis is the recommended procedure

constrained 0 1 quadratic programming basic approaches and extensions abstract we describe the simplest technique to tackle 0 1 quadratic programs with linear constraints among those that turn out to be successful in practice this method is due to and familiar to the quadratic assignment experts even if it took some time to realize that most approaches to the problem could be interpreted in these terms whereas it does not appear to be widely known outside this community since the technique is completely general and is by far the most successful one in several other cases such as quadratic knapsack we illustrate it in its full generality pointing out its relationship to lagrangian and linear programming relaxations and discussing further extensions we believe that this method should be in the background of every practitioner in combinatorial optimization

inverse probability weighted estimation for general missing data problems abstract i study inverse probability weighted m estimation under a general missing data scheme examples include m estimation with missing data due to a censored survival time propensity score estimation of the average treatment effect in the linear exponential family and variable probability sampling with observed retention frequencies i extend an important result known to hold in special cases estimating the selection probabilities is generally more efficient than if the known selection probabilities could be used in estimation for the treatment effect case the setup allows a general characterization of a double robustness result due to scharfstein et al 1999 rejoinder journal of the american statistical association 94 1135 1146

sensitivity of the discrete time kaplan meier estimate to nonignorable censoring application in a clinical trial untestable assumptions about association between survival and censoring times can affect the validity of estimates of the survival distribution including the kaplan meier km nonparametric mle this article explores the sensitivity of the km curve to nonignorable censoring by extending the index of local sensitivity to nonignorability isni troxel et al 2004 zhang and heitjan 2006 to the case of a nonparametric survival model the method involves first specifying a coarse data selection model to describe the association between the failure and censoring processes then evaluating the slope of the nonparametric survival mle ordinate with respect to a nonignorability parameter in the neighborhood of the ignorable model we define the nonparametric mle of the survival curve for a fixed value of the nonignorability parameter and show in a simulation that isni analysis effectively captures local sensitivity to nonignorability the method measures sensitivity in the sense of identifying functionals of the nonparametric mle that nonignorability if present can affect substantially we demonstrate the method with an application to a trial comparing mechanical assistance to optimal medical management in the treatment of end stage heart failure

learning reliable classifiers from small or incomplete data sets the naive credal classifier 2 in this paper the naive credal classifier which is a set valued counterpart of naive bayes is extended to a general and flexible treatment of incomplete data yielding a new classifier called naive credal classifier 2 ncc2 the new classifier delivers classifications that are reliable even in the presence of small sample sizes and missing values extensive empirical evaluations show that by issuing set valued classifications ncc2 is able to isolate and properly deal with instances that are hard to classify on which naive bayes accuracy drops considerably and to perform as well as naive bayes on the other instances the experiments point to a general problem they show that with missing values empirical evaluations may not reliably estimate the accuracy of a traditional classifier such as naive bayes this phenomenon adds even more value to the robust approach to classification implemented by ncc2

logistic quantile regression for bounded outcomes when research interest lies in continuous outcome variables that take on values within a known range e g a visual analog scale for pain within 0 and 100 mm the traditional statistical methods such as least squares regression mixed effects models and even classic nonparametric methods such as the wilcoxon s test may prove inadequate frequency distributions of bounded outcomes are often unimodal u shaped and j shaped to the best of our knowledge in the biomedical and epidemiological literature bounded outcomes have seldom been analyzed by appropriate methods that for one correctly constrain inference to lie within the feasible range of values in many respects continuous bounded outcomes can be likened to probabilities or propensities yet what has long been heeded when modeling the probability of binary outcomes with the widespread use of logistic and probit regression so far appears to have been overlooked with continuous bounded outcomes with consequences at times disastrous logistic quantile regression constitutes an effective method to fill this gap

computing the metric dimension of wheel related graphs abstract an ordered set w w 1 w k v g of vertices of g is called a resolving set or locating set for g if every vertex is uniquely determined by its vector of distances to the vertices in w a resolving set of minimum cardinality is called a basis for g and this cardinality is the metric dimension or location number of g denoted by g in this paper we study the metric dimension of certain wheel related graphs namely m level wheels an infinite class of convex polytopes and antiweb gear graphs denoted by w n m q n and awj 2 n respectively we prove that these infinite classes of wheel related graphs have unbounded metric dimension the study of an infinite class of convex polytopes generated by wheel denoted by q n also gives a negative answer to an open problem proposed by imran et al 2012 in 8 open problem is it the case that the graph of every convex polytope has constant metric dimension it is natural to ask for characterization of graphs with unbounded metric dimension

double robust semiparametric estimator for differences in restricted mean lifetimes in observational studies restricted mean lifetime is often of direct interest in epidemiologic studies involving censored survival times differences in this quantity can be used as a basis for comparing several groups for example transplant surgeons nephrologists and of course patients are interested in comparing posttransplant lifetimes among various types of kidney transplants to assist in clinical decision making as the factor of interest is not randomized covariate adjustment is needed to account for imbalances in confounding factors in this report we use semiparametric theory to develop an estimator for differences in restricted mean lifetimes although accounting for confounding factors the proposed method involves building working models for the time to event and coarsening mechanism i e group assignment and censoring we show that the proposed estimator possesses the double robust property i e when either the time to event or coarsening process is modeled correctly the estimator is consistent and asymptotically normal simulation studies are conducted to assess its finite sample performance and the method is applied to national kidney transplant data

remission duration an example of interval censored observations remission duration data from two observational studies the german all aul study on acute lymphoblastic and acute undifferentiated leukaemia and the kiel lymphoma study are used to demonstrate the adequacy of an interval censoring approach the turnbull estimator is contrasted with the conventionally used kaplan meier estimator in addition a parametric model is used for estimation or simulation of the delay times of complete remission diagnosis and relapse diagnosis two possible consequences of the conventional approach are discussed biased estimation for example overestimation of remission duration and underestimation of the true error variance which may lead to false positive results on the other hand the applicability of the interval censoring approach is doubtful when the censoring mechanism examination pattern patient s behaviour is confounded with the endpoints

inference for events with dependent risks in multiple endpoint studies abstract kaplan meier and cumulative incidence functions are not sufficient descriptive devices for studies that have multiple time to event endpoints for example in cancer treatment research the probability of tumor recurrence conditional on not having died from treatment related toxicities and the prevalence of graft versus host disease among leukemia free patients surviving a bone marrow transplant are of interest these quantities can be estimated nonparametrically using simple functions of several kaplan meier and cumulative incidence estimates for events with possibly dependent risks we derive asymptotic distribution theory for such functions by representing kaplan meier cumulative incidence and cumulative hazard estimators as sums of iid random variables variance estimation also follows directly from this representation two sample test statistics with asymptotic null distribution theory are presented several examples illustrate the utility of these results

on families of convex polytopes with constant metric dimension let g be a connected graph and d x y be the distance between the vertices x and y a subset of vertices w w 1 w 2 w k is called a resolving set for g if for every two distinct vertices x y v g there is a vertex w i w such that d x w i d y w i a resolving set containing a minimum number of vertices is called a metric basis for g and the number of vertices in a metric basis is its metric dimension dim g a family g of connected graphs is a family with constant metric dimension if dim g is finite and does not depend upon the choice of g in g in this paper we study the metric dimension of some classes of convex polytopes which are obtained by the combinations of two different graph of convex polytopes it is shown that these classes of convex polytopes have the constant metric dimension and only three vertices chosen appropriately suffice to resolve all the vertices of these classes of convex polytopes

minimal doubly resolving sets and the strong metric dimension of some convex polytopes abstract in this paper we consider two similar optimization problems on graphs the strong metric dimension problem and the problem of determining minimal doubly resolving sets we prove some properties of strong resolving sets and give an integer linear programming formulation of the strong metric dimension problem these results are used to derive explicit expressions in terms of the dimension n for the strong metric dimension of two classes of convex polytopes d n and t n on the other hand we prove that minimal doubly resolving sets of d n and t n have constant cardinality for n 7

efficient estimation in the bivariate censoring model and repairing npmle the npmle in the bivariate censoring model is not consistent the problem is caused by the singly censored observations in this paper we prove that the npmle based on interval censoring the singly censored observations is ecient for this reduced data and moreover if we let the width of the interval converge to zero slowly enough then the npmle is also ecient for the original data we are able to determine a lower bound for the rate at which the bandwidth should converge to zero the eciency proof uses the general identity which holds for npmle of a linear parameter in convex models as proved in van der laan 1993a

ignorability sufficiency and ancillarity this paper explores the relationship between ignorability sufficiency and ancillarity in the coarse data model of heitjan and rubin bayes or likelihood ignorability has a natural relationship to sufficiency and frequentist ignorability an analogous relationship to ancillarity weaker conditions termed observed likelihood sufficiency observed specific sufficiency and observed ancillarity expand the concepts to models where the coarsening mechanism is sometimes but not always ignorable

a note on the partition dimension of cartesian product graphs abstract let g v e be a connected graph the distance between two vertices u v v denoted by d u v is the length of a shortest u v path in g the distance between a vertex v v and a subset p v is defined as min d v x x p and it is denoted by d v p an ordered partition p 1 p 2 p t of vertices of a graph g is a resolving partition of g if all the distance vectors d v p 1 d v p 2 d v p t are different the partition dimension of g denoted by pd g is the minimum number of sets in any resolving partition of g in this article we study the partition dimension of cartesian product graphs more precisely we show that for all pairs of connected graphs g h pd g h pd g pd h and pd g h pd g dim h where dim h denotes the metric dimension of h consequently we show that pd g h dim g dim h 1

inference in randomized studies with informative censoring and discrete time to event endpoints summary in this article we present a method for estimating and comparing the treatment specific distributions of a discrete time to event variable from right censored data our method allows for 1 adjustment for informative censoring due to measured prognostic factors for time to event and censoring and 2 quantification of the sensitivity of the inference to residual dependence between time to event and censoring due to unmeasured factors we develop our approach in the context of a randomized trial for the treatment of chronic schizophrenia we perform a simulation study to assess the practical performance of our methodology