exact controllability of stochastic differential equations with memory abstract in this work we mainly study the exact controllability of stochastic differential equations with memory for time invariant systems by applying forward backward stochastic differential equations some rank criteria ensuring systems exact controllability are provided for time variant systems equivalent conditions guaranteeing systems exact controllability are given for deterministic systems as a special case of stochastic ones more easily checkable rank criteria for time invariant systems and alternative conditions for time variant systems are proposed

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

permutation tests using estimated distribution functions abstract in this article we develop permutation tests for estimated distribution functions the tests are formed by averaging a functional of estimated distribution functions that are calculated from independent sampling units where the units may be a single response a set of repeated responses or a censored response we study primarily two functionals the difference in means functional and the mann whitney functional and two types of responses repeated conditionally independent responses and censored responses for repeated responses the permutation test using the difference in means functional produces a permutation form of the corresponding mixed effects test a new permutation test is developed when we apply the mann whitney functional to the repeated responses this is a case in which the rank transform method does not work on the other hand for right censored or interval censored data we obtain permutation forms of standard rank tests using the mann whitney functional or weighted forms of t

testing violations of the exponential assumption in cancer clinical trials with survival endpoints personalized cancer therapy requires clinical trials with smaller sample sizes compared to trials involving unselected populations that have not been divided into biomarker subgroups the use of exponential survival modeling for survival endpoints has the potential of gaining 35 efficiency or saving 28 required sample size miller 1983 making personalized therapy trials more feasible however the use of exponential survival has not been fully accepted in cancer research practice due to uncertainty about whether or not the exponential assumption holds we propose a test for identifying violations of the exponential assumption using a reduced piecewise exponential approach compared with an alternative goodness of fit test which suffers from inflation of type i error rate under various censoring mechanisms the proposed test maintains the correct type i error rate we conduct power analysis using simulated data based on different types of cancer survival distribution in the seer registry database and demonstrate the implementation of this approach in existing cancer clinical trials

non uniform convergence of finite volume schemes for riemann problems of ideal magnetohydrodynamics this paper presents riemann test problems for ideal magnetohydrodynamics mhd finite volume schemes the test problems place emphasis on the hyperbolic irregularities of the ideal mhd system namely the occurrence of intermediate shocks and non unique solutions we investigate numerical solutions for the test problems obtained by several commonly used methods roe hlle central scheme all methods turned out to show a non uniform convergence behavior which may be paraphrased as pseudo convergence initially the methods show convergence towards a wrong solution with irregular wave patterns only after heavy grid refinement the methods switch to converge to the true solution this behavior is most pronounced whenever the solution should be unique but its phase space trajectory lies in the vicinity of that of a non unique solution we show detailed grid convergence studies and empirical error analysis the results may be related to similar results for a 2 2 model system and to time dependent investigations of other authors the non uniform convergence is expected to be present for any diffusive finite volume method and question the reliability of coarse grid ideal mhd solutions also in higher space dimensions

a class of k sample tests for comparing the cumulative incidence of a competing risk in this paper for right censored competing risks data a class of tests developed for comparing the cumulative incidence of a particular type of failure among different groups the tests are based on comparing weighted averages of the hazards of the subdistribution for the failure type of interest asymptotic results are derived by expressing the statistics in terms of counting processes and using martingale central limit theory it is proposed that weight functions very similar to those for the g p tests from ordinary survival analysis be used simulation results indicate that the asymptotic distributions provide adequate approximations in moderate sized samples

sizing clinical trials when comparing bivariate time to event outcomes clinical trials with multiple primary time to event outcomes are common use of multiple endpoints creates challenges in the evaluation of power and the calculation of sample size during trial design particularly for time to event outcomes we present methods for calculating the power and sample size for randomized superiority clinical trials with two correlated time to event outcomes we do this for independent and dependent censoring for three censoring scenarios i the two events are non fatal ii one event is fatal semi competing risk and iii both are fatal competing risk we derive the bivariate log rank test in all three censoring scenarios and investigate the behavior of power and the required sample sizes separate evaluations are conducted for two inferential goals evaluation of whether the test intervention is superior to the control on 1 all of the endpoints multiple co primary or 2 at least one endpoint multiple primary copyright 2017 john wiley sons ltd

successive approximations of linear control models we present a technique for approximating sequences of linear programs with varying right hand sides and study the geometric properties of this approximation our approximation has an efficiency advantage over optimal solutions when applied to deterministic control problems the suggested technique outperforms the linear feedback model and provides accurate results error of 5 8 in our numerical example numerical experience with stochastic models indicates that this approach may outperform the limited lookahead policies while maintaining low computational requirements

an adaptive finite element procedure for compressible high speed flows abstract a two step explicit finite element procedure for obtaining time accurate solutions to the compressible euler equations is described the method is coupled with an adaptive mesh refinement process which enables steady state solutions of improved quality to be obtained

removal of pseudo convergence in coplanar and near coplanar riemann problems of ideal magnetohydrodynamics solved using finite volume schemes numerical schemes for ideal magnetohydrodynamics mhd that are based on the standard finite volume method fvm exhibit pseudo convergence in which irregular structures no longer exist only after heavy grid refinement we describe a method for obtaining solutions for coplanar and near coplanar cases that consist of only regular structures independent of grid refinement the method referred to as compound wave modification cwm involves removing the flux associated with non regular structures and can be used for simulations in two and three dimensions because it does not require explicitly tracking an alfven wave for a near coplanar case and for grids with 213 points or less we find root square mean errors rmses that are as much as 6 times smaller for the coplanar case in which non regular structures will exist at all levels of grid refinement for standard fvms the rmse is as much as 25 times smaller

small sample properties of censored data rank tests small sample properties of censored data rank tests such as mantel s logrank test the breslow test or the general dass of tests proposed by peto and peto 1972 journal oj the royal statistical society series a 135 185 206 are examined it is found that the latter dass of tests in particular can be substantially nonconservative when applied to small sam pies the most serious inaccuracies occur in unbalanced trials when higher event rates are inferred in the smaller sampie

use of logrank tests and group sequential methods at fixed calendar times this paper presents simulations to determine the operating characteristics of several group sequential boundaries when applied to the repeated analysis of survival data at equal intervals of calendar time because the group sequential boundaries of pocock 1977 biometrika 64 191 199 and o brien and fleming 1979 biometrics 35 549 556 were constructed on the assumption that each interim analysis provides an equal increment of statistical information these boundaries are not theoretically appropriate for interim analysis at prescheduled calendar times nonetheless our simulations show that these boundaries yield size and power near nominal levels for repeated logrank analyses at equal intervals of calendar time

conditional rank tests for the two sample problem under random censorship for the two sample problem with randomly censored data there exists a general asymptotic theory of rank statistics which are functionals of stochastic integrals with respect to certain empirical martingales in the present paper a conditional counterpart of this theory is developed the conditional martingales are versions of the original ones reduced to the unit interval having their jumps at fixed lattice points the resulting conditional tests are strictly distribution free under the null hypothesis of randomness if the censoring distributions in both samples are equal and are asymptotically equivalent to their unconditional counterparts even if the censoring distributions are different simulations for linear rank statistics and kolmogorov smirnov type statistics show superiority of the conditional versions over their unconditional counterparts with respect to size and robustness under unequal censoring in both samples at the same time the power of the conditional and unconditional tests is very similar in most cases

properties of proportional hazards score tests under misspecified regression models the effects are investigated of misspecifying a proportional hazards regression model on the associated partial likelihood score test for comparing two randomized treatments in the presence of covariates the asymptotic efficiency of the proportional hazards score test relative to the optimal partial likelihood test declines slowly as the hazard functions for the two treatments deviate from proportionality the efficiency can be very low when the hazard functions cross or differ only at large survival times misspecification of the functional form of the regression portion of a proportional hazards model introduces a quantitative treatment covariate interaction in the situations that we examine based on a binary covariate this misspecification usually results in only a minor drop in efficiency the omission of a covariate that is balanced across treatments has a negligible effect on the size of the score test but can substantially reduce power when the covariate effect is strong the loss of power from mismodeling a balanced covariate is usually small

null controllability of linear systems with constrained controls the paper considers the problem of steering the state of a linear time varying system to the origin when the control is subject to magnitude constraints necessary and sufficient conditions are given for global constrained controllability as well as a necessary and sufficient condition for the existence of a control satisfying the constraints which steers the system to the origin from a specified initial epoch x 0 t 0 the global result does not require zero to be an interior point of the control set omega and the theorem for constrained controllability at x 0 t 0 only requires that omega be compact not that it contain zero the results are compared to those available in the literature furthermore numerical aspects of the problem are discussed as is a technique for determining a steering control

estimation of descriptive statistics for multiply censored water quality data this paper extends the work of gilliom and helsel 1986 on procedures for estimating descriptive statistics of water quality data that contain less than observations previously procedures were evaluated when only one detection limit was present here we investigate the performance of estimators for data that have multiple detection limits probability plotting and maximum likelihood methods perform substantially better than simple substitution procedures now commonly in use therefore simple substitution procedures e g substitution of the detection limit should be avoided probability plotting methods are more robust than maximum likelihood methods to misspecification of the parent distribution and their use should be encouraged in the typical situation where the parent distribution is unknown when utilized correctly less than values frequently contain nearly as much information for estimating population moments and quantiles as would the same observations had the detection limit been below them

exact log rank tests for unequal follow up les tests asymptotiques du log rank et le test de wilcoxon generalise sont des procedures standards pour comparer des distributions de survie en presence de censures pour la comparaison d echantillons de tailles tres differentes un test exact base sur l ensemble des permutations du log rank ou des scores de wilcoxon est disponible alors que les tests asymptotiques ne conservent pas leur risque nominal lorsque les echantillons sont de tailles tres differentes le test exact base sur les permutations exige cependant un suivi identique dans les echantillons c est pourquoi nous avons developpe deux nouveaux tests exacts adaptes a des suivis inegaux le premier est exactement equivalent au log rank test asymptotique conditionnellement a l ensemble des risques observes alors que la deuxieme approche permute les temps de survie conditionnellement au suivi observe dans chaque groupe dans une etude empirique nous comparons ces nouvelles procedures au log rank test asymptotique au test exact de permutation complete ainsi qu a une approche proposee anterieurement qui egalise les distributions de suivi en les censurant artificiellement les resultats confirment les performances tres satisfaisantes du test exact conditionnellement au suivi observe particulierement dans le cas de suivis inegaux l avantage du nouveau test sur les autres possibilites d analyse est finalement illustre par l analyse d une etude portant sur le cancer du sein

a relationship between two forms of linear rank procedures for censored data summary this paper gives a useful relationship between two popular classes of linear rank statistics for arbitrarily right censored data the relationship allows a linear rank procedure with certain optimal properties to be transformed into the form of a procedure having established asymptotic properties under proportional hazards alternatives

constrained max min controllability the max min controllability concept of heymann pachter and stern 1 is examined for a more general class of problems both strong and weak max min controllability are characterized it is shown that when magnitude constraints on the control are present the two max min controllability concepts are not the same this differs from the result for problems without control magnitude constraints where it has been shown that the two controllability concepts are identical

on the distribution of the maximum of the longrank statistic and the modified wilcoxon statistic the asymptotic distribution of the maximum of the logrank statistic and the modified wilcoxon statistic is examined in order to test the equality of two survival distributions a table is provided to facilitate use of the maximum statistics and monte carlo simulation experiments are used to investigate the small sample properties of the maximum statistic an example is given to illustrate the use of the methods developed in this paper summary in fre excerpt

withdrawal censoring and the sequential logrank procedure the effects of withdrawal censoring on the power of the group sequential logrank procedure are examined in the context of survival studies special attention is given to an assumption that the withdrawal censoring mechanism is only conditionally independent of survival time simulation studies of two sample fixed duration trials under random right censoring staggered entry and exponential life times reveal a general decrease in statistical power that is most pronounced when the withdrawals are unbalanced the majority occurring in the group with the higher hazard rate generally this decrease in power is not of practical concern under typical withdrawal rates except when conditional independence is present in which case large fluctuations in power and type i error rates can occur

effect of unequal censoring on the size and power of the logrank and wilcoxon types of tests for survival data this paper examines the effect of random unequal censoring on the size and power of two sample logrank and wilcoxon types of tests for comparing two survival distributions by simulation with small samples from censored exponential distributions we compared equal sized samples of n 8 16 and 32 with 1000 size and 500 power simulation trials for 16 combinations of the censoring proportions of 0 20 40 and 60 per cent in each of the two samples for n 8 the asymptotic normality an peto peto and the two wilcoxon type tests performed at nominal 5 per cent size expectations but the mantel test exceeded the 5 per cent size acceptance region in 6 of 16 censoring combinations for n 16 and 32 all tests showed proper size with the peto peto test being most conservative in the presence of unequal censoring we compared powers of all tests for exponential hazard ratios of 1 4 and 2 0 the mantal test showed 90 to 95 per cent power efficiency relative to the parametric an test both wilcoxon tests performed identically and had the lowest relative power of all tests examined but appeared most robust to the differential censoring patterns studied a modified version of the peto peto test showed power comparable to the mantel test

nonparametric rank based methods for group sequential monitoring of paired censored survival data summary this research gives methods for nonparametric sequential monitoring of paired censored survival data in the two sample problem using paired weighted log rank statistics with adjustments for dependence in survival and censoring outcomes the joint asymptotic closed form distribution of these sequentially monitored statistics has a dependent increments structure simulations validating operating characteristics of the proposed methods highlight power and size consequences of ignoring even mildly correlated data a motivating example is presented via the early treatment diabetic retinopathy study

non parametric analysis of treatment covariate interaction in the presence of censoring the demonstration of varying treatment efficacy among different subsets of patients is an important part of the analysis of clinical trials the paper commences by clarifying the meaning of interaction and by reviewing valid procedures of analysis in the presence of interaction suitable descriptive measures of treatment covariate interactions are ratios of hazard ratios to which generalized patel hoel tests for qualitative or ordinal categorical covariates are related both the hazard ratios and the tests are given in a formulation for use with different scoring systems such as u or e furthermore the procedures are related to common k sample tests and thus are suitable for proportional and for converging hazards a worked example is included

a two sample censored data rank test for acceleration a score test for the null hypothesis of proportional hazards against rank regression alternatives is proposed as a complement to the logrank test for comparing censored survival curves the test statistic has an asymptotic normal distribution that is independent of the logrank distribution under the null hypothesis and its power is good against acceleration alternatives i e with crossing hazards where the logrank test fails monte carlo studies indicate that its small sample properties are comparable to those of the logrank and ranksum procedures

the analysis of multiple endpoints in clinical trials treatment comparisons in randomized clinical trials usually involve several endpoints such that conventional significance testing can seriously inflate the overall type i error rate one option is to select a single primary endpoint for formal statistical inference but this is not always feasible another approach is to apply bonferroni correction i e multiply each p value by the total number of endpoints its conservatism for correlated endpoints is examined for multivariate normal data a third approach is to derive an appropriate global test statistic and this paper explores one such test applicable to any set of asymptotically normal test statistics quantitative binary and survival endpoints are all considered within this general framework two examples are presented and the relative merits of the proposed strategies are discussed

a class of rank test procedures for censored survival data summary a class of linear rank statistics is proposed for the k sample problem with rightcensored survival data the class contains as special cases the log rank test mantel 1966 cox 1972 and a test essentially equivalent to peto peto s 1972 generalization of the wilcoxon test martingale theory is used to establish asymptotic normality of test statistics under the null hypotheses considered and to derive expressions for asymptotic relative efficiencies under contiguous sequences of alternative hypotheses a class of distributions is presented which corresponds to the class of rank statistics in the sense that for each distribution there is a statistic with some optimal properties for detecting location alternatives from that distribution some monte carlo results are displayed which present small sample behaviour

repeated significance testing for a general class of statistics used in censored survival analysis abstract the asymptotic joint distribution of a class of sequentially computed statistics used in survival analysis is derived when the individuals under study enter serially and are subject to random loss to follow up these results are used for constructing repeated significance tests over real time

on godunov type methods near low densities abstract when the energy of a flow is largely kinetic many conservative differencing schemes may fail by predicting non physical states with negative density or internal energy we describe as positively conservative the subclass of schemes that by contrast always generate physical solutions from physical data and show that the godunov method is positively conservative it is also shown that no scheme whose interface flux derives from a linearised riemann solution can be positively conservative classes of data that will bring about the failure of such schemes are described however the harten lax van leer hlle scheme is positively conservative under certain conditions on the numerical wavespeeds and this observation allows the linearised schemes to be rescued by modifying the wavespeeds employed

implementation of group sequential logrank tests in a maximum duration trial summary to control the type i error probability in a group sequential procedure using the logrank test it is important to know the information times fractions at the times of interim analyses conducted for purposes of data monitoring for the logrank test the information time at an interim analysis is the fraction of the total number of events to be accrued in the entire trial in a maximum information trial design the trial is concluded when a prespecified total number of events has been accrued for such a design therefore the information time at each interim analysis is known however many trials are designed to accrue data over a fixed duration of follow up on a specified number of patients this is termed a maximum duration trial design under such a design the total number of events to be accrued is unknown at the time of an interim analysis for a maximum duration trial design therefore these information times need to be estimated a common practice is to assume that a fixed fraction of information will be accrued between any two consecutive interim analyses and then employ a pocock or o brien fleming boundary in this article we describe an estimate of the information time based on the fraction of total patient exposure which tends to be slightly negatively biased i e conservative if survival is exponentially distributed we then present a numerical exploration of the robustness of this estimate when nonexponential survival applies we also show that the lan demets 1983 biometrika 70 659 663 procedure for constructing group sequential boundaries with the desired level of type i error control can be computed using the estimated information fraction even though it may be biased finally we discuss the implications of employing a biased estimate of study information for a group sequential procedure

cure rate models power of the logrank and generalized wilcoxon tests this paper reports the results of simulations that compare the power of the logrank and generalized wilcoxon tests in situations where the cure rate model is appropriate

a monte carlo study of some two sample rank tests with censored data abstract the powers of several nonparametric tests for the two sample problem with censored data are compared by simulation the tests studied include gehan s efron s and peto s and prentice s generalized wilcoxon tests along with the logrank test the test with the greatest power changes with the sample sizes censoring mechanism and distribution of the random variables the test that performed the best overall was the peto prentice generalized wilcoxon statistic with an asymptotic variance estimate

the asymptotic joint distribution of the efficient scores test for the proportional hazards model calculated over time the log rank test derived by mantel 1966 and peto 1972 is a special case of the efficient scores test for the proportional hazards model it is used frequently in the analysis of survival duration in clinical trials where patients entering the study are assigned at random to different treatments and are followed until they either fail or the study is terminated most survival studies are designed so that the log rank test is calculated at the termination of the study however it is not unusual for the investigator to monitor the experiment periodically it would be very useful to know the joint distribution of the test statistic at different points in time in order to adjust for the effect of repeated significance testing although the joint distribution has not been derived previously sequential procedures for the analysis of survival data in clinical trials have been given by several authors including armitage 1975 pp 140 6 jones whitehead 1979 and nagelkerke hart 1980 in this paper we establish the asymptotic joint distribution of the more general efficient scores test for the proportional hazards model calculated at different points in time and indicate how this can be used for repeated significance testing

a review of methods for futility stopping based on conditional power conditional power cp is the probability that the final study result will be statistically significant given the data observed thus far and a specific assumption about the pattern of the data to be observed in the remainder of the study such as assuming the original design effect or the effect estimated from the current data or under the null hypothesis in many clinical trials a cp computation at a pre specified point in the study such as mid way is used as the basis for early termination for futility when there is little evidence of a beneficial effect brownian motion can be used to describe the distribution of the interim z test value the corresponding b value and the cp values under a specific assumption about the future data a stopping boundary on the cp value specifies an equivalent boundary on the b value from which the probability of stopping for futility can then be computed based on the planned study design sample size and duration and the assumed true effect size this yields expressions for the total type i and ii error probabilities as the probability of stopping increases the probability of a type i error alpha decreases from the nominal desired level e g 0 05 while the probability of a type ii error beta increases from the level specified in the study design thus a stopping boundary on the b value can be determined such that the inflation in type ii error probability is controlled at a desired level an iterative procedure is also described that determines a stopping boundary on the b value and a final test critical z value with specified type i and ii error probabilities the implementation in conjunction with a group sequential analysis for effectiveness is also described

resampling procedures to compare two survival distributions in the presence of right censored data summary in this simulation study the accuracy of the size of four classes of test procedures asymptotic normal test permutation test bootstrap hypothesis test and bootstrap interval test were compared using the logrank and prentice wilcoxon two sample test statistics sample sizes of 20 and 50 per group were used twenty observations per group yielded differences in the test procedures when the prentice wilcoxon test statistic was employed the asymptotic test procedure was the most accurate resampling procedures did not improve upon its accuracy using the logrank test statistic the permutation or bootstrap hypothesis testing procedures were closest to the nominal significance level the more popular asymptotic normal logrank test was consistently anticonservative when the number of observations in each group was increased to 50 the test procedures were comparable power comparisons were also examined the test with the greatest power was dependent upon the two survival patterns and the choice of test statistic

nonparametric statistical methods for comparing two sites based on data with multiple nondetect limits as concern over the effects of trace amounts of pollutants has increased so has the need for statistical methods that deal appropriately with data that include values reported as less than the detection limit it has become increasingly common for water quality data to include censored values that reflect more than one detection limit for a single analyte for such multiply censored data sets standard statistical methods for example to compare analyte concentration in two areas are not valid in such cases methods from the biostatistical field of survival analysis are applicable several common two sample censored data rank tests are explained and their behaviors are studied via a monte carlo simulation in which sample sizes and censoring mechanisms are varied under an assumed lognormal distribution these tests are applied to shallow groundwater chemistry data from two sites in the san joaquin valley california the best overall test in terms of maintained level is the normal scores test based on a permutation variance in cases where the level is maintained however the peto prentice statistic based on an asymptotic variance performs as well or better

robust controllability for a class of uncertain linear time invariant mimo systems this note studies the problem of robust controllability of linear time invariant multiple input multiple output systems with a being or a and b both being sign invariant interval matrices for controllability sufficient conditions as well as necessary and sufficient conditions based on interval division method are presented the note also provides a way to handle interval systems that are not sign invariant in the a matrix some examples illustrate the results

shock capturing approach and nonevolutionary solutions in magnetohydrodynamics shock capturing methods have become an effective tool for the solution of hyperbolic partial differential equations both upwind and symmetric tvd schemes in the framework of the shock capturing approach are thoroughly investigated and applied with great success to a number of complicated multidimensional gasdynamic problems the extension of these schemes to magnetohydrodynamic mhd equations is not a simple task first the exact solution of the mhd riemann problem is too multivariant to be used in regular calculations on the other hand the extensions of roe s approximate riemann problem solvers for mhd equations in general case are nonunique and need further investigation that is why some simplified approaches should be constructed in this work the second order of accuracy in time and space high resolution lax friedrichs type scheme is suggested that gives a drastic simplification of the numerical algorithm comparing to the precise characteristic splitting of jacobian matrices the necessity is shown to solve the full set of mhd equations for modeling of multishocked flows even when the problem is axisymmetric to obtain evolutionary solutions for the numerical example the mhd riemann problem is used with the initial data consisting of two constant states lying to the right and to the left from the centerline of the computational domain if the problem is solved as purely coplanar a slow compound wave appears in the self similar solution obtained by any shock capturing scheme if the full set of mhd equations is used and a small uniform tangential disturbance is added to the magnetic field vector a rotational jump splits from the compound wave and it degrades into a slow shock the reconstruction process of the nonevolutionary compound wave into evolutionary shocks is investigated presented results should be taken into account in the development of shock capturing methods for mhd flows

global and point controllability of uncertain dynamical systems this paper analyzes the problem of controllability in the presence of additive uncertainty unlike the stochastic controllability problem the uncertain parameters here are described in a set theoretic manner i e no a priori statistics are assumed for the uncertainty q cdot only a bounding set q is taken as given loosely speaking the state x cdot of a dynamical system s is said to be omega q controllable to a given target x if one can guarantee by choice of a measurable control u t in omega the transfer of x cdot to x in finite time this guarantee above must hold for all measurable q t in q known results on constrained controllability of deterministic systems are derived as a special case by setting q 0 the finite dimensional nature of the omega q controllability criteria is perhaps the most salient feature of the results given here instead of searching over the function space of controls one can decide on the question of controllability by solving an equivalent problem in r where n is the state dimension the generation of this equivalent problem involves artificially inducing a saddle point via a certain enveloping operation a number of examples are given to illustrate the method of computing numerical solutions

controllability results for systems with a nonconvex target this paper considers the problem of steering the state x t of the system dot x t a t x t f t u t to a prescribed target x the input u t is restricted to lie in a prespecified set which is assumed compact unlike the results of previous authors we allow x to be any set and do not require x to be convex or closed necessary conditions and sufficient conditions for the existence of a control which steers the system to the target from a specified initial condition are given conditions for global controllability to the target are also derived an additional concept of controllability that we investigate is that of complete controllability complete controllability is concerned with the ability to steer the system from any initial point to any final point one of the most important results of this paper is that we develop a technique for constructing a steering control previous work on the constrained controllability problem has dealt with methods for determining a steering control in only a limited way finally numerical techniques for checking controllability and for constructing a steering control are described and the results obtained from the application of our algorithm to several examples are presented

a versatile test for equality of two survival functions based on weighted differences of kaplan meier curves with censored event time observations the logrank test is the most popular tool for testing the equality of two underlying survival distributions although this test is asymptotically distribution free it may not be powerful when the proportional hazards assumption is violated various other novel testing procedures have been proposed which generally are derived by assuming a class of specific alternative hypotheses with respect to the hazard functions the test considered by pepe and fleming 1989 is based on a linear combination of weighted differences of the two kaplan meier curves over time and is a natural tool to assess the difference of two survival functions directly in this article we take a similar approach but choose weights that are proportional to the observed standardized difference of the estimated survival curves at each time point the new proposal automatically makes weighting adjustments empirically the new test statistic is aimed at a one sided general alternative hypothesis and is distributed with a short right tail under the null hypothesis but with a heavy tail under the alternative the results from extensive numerical studies demonstrate that the new procedure performs well under various general alternatives with a caution of a minor inflation of the type i error rate when the sample size is small or the number of observed events is small the survival data from a recent cancer comparative study are utilized for illustrating the implementation of the process copyright 2015 john wiley sons ltd

two sample repeated significance tests based on the modified wilcoxon statistic abstract the asymptotic distribution theory of sequentially computed modified wilcoxon scores is developed for two sample survival data with random staggered entry and random loss to follow up the asymptotic covariance indicates generally dependent modified wilcoxon increments contradicting the authors reading of jones and whitehead 1979 a repeated significance testing procedure is presented for testing the equality of two survival distributions based on the asymptotic theory the early stopping properties of this procedure are illustrated by a prostate cancer example

constrained controllability of discrete time systems the constrained controllability of the discrete time system xk 1 a k xk b k u k is considered where the control uk is termed admissible if it satisfies specified magnitude constraints constrained controllability is concerned with the existence of an admissible control which steers the state x to a given target set from a specified initial state conditions for checking constrained controllability to a given target set from a specified initial state are presented these conditions involve solving finite dimensional optimization problems and can be checked via numerical computation in addition conditions for checking global constrained controllability to a given target set are presented a system is globally constrained controllable if for every initial state there exists an admissible control that steers the system to the target if a given discrete time system is constrained controllable it may be desirable to obtain an admissible control that steers the system to the target from a specified initial s

sequential monitoring of clinical trials the role of information and brownian motion sequential monitoring has been a topic of major interest in clinical trials methodology over the past two decades this paper presents a unified conceptual framework for sequential monitoring that covers a wide variety of monitoring procedures in a wide variety of clinical trial settings the central elements of this framework consist of a suitable concept of statistical information and a scheme for using this concept as a basis for summarizing the accumulating results of a trial in a standardized form through a stochastic process that can be shown to approximate classical brownian motion the ideas are developed in a simple step by step fashion and illustrated by several practical examples

permutational distribution of the log rank statistic under random censorship with applications to carcinogenicity assays in the random censorship model the log rank test is often used for comparing a control group with different dose groups if the number of tumors is small so called exact methods are often applied for computing critical values from a permutational distribution two of these exact methods are discussed and shown to be incorrect the correct permutational distribution is derived and studied with respect to its behavior under unequal censoring in the light of recent results proving that the permutational version and the unconditional version of the log rank test are asymptotically equivalent even under unequal censoring the log rank test is studied by simulations of a realistic scenario from a bioassay with small numbers of tumors

functional laws of the iterated logarithm for the product limit estimator of a distribution function under random censorship or truncation functional laws of the iterated logarithm are established for a modified version of the classical product limit estimator of a distribution function when the data are subject to random censorship or truncation making use of stochastic integral representations and empirical process theory strong approximations involving i i d continuous parameter martingales are developed for the product limit estimator and these strong approximations are then applied to derive the functional laws

controllability and observability of linear time invariant uncertain systems irrespective of bounds of uncertain parameters in this paper the controllability and observability of linear time invariant uncertain systems are investigated the systems under consideration contain time invariant uncertain parameters that may take arbitrarily large values in such a situation the locations of uncertain parameters in system matrices play an important role we examine the permissible locations of uncertain parameters in system matrices for a linear uncertain system to be controllable and observable independently of the bounds of the uncertain parameters the objective of this paper is to show that a linear uncertain system is controllable and observable irrespective of the bounds of uncertain parameters if and only if the system has a particular configuration called a complete generalized antisymmetric stepwise configuration cgasc furthermore the dual configuration of a cgasc is introduced and studied here

estimating durbin s approximation summary some statistical procedures involve boundary crossing probabilities for processes that converge weakly to continuous gaussian limits when carrying out these procedures boundary crossing probabilities associated with the limit processes may sometimes be substituted for the probabilities of interest an approach to estimating durbin s approximation to boundary crossing probabilities for continuous gaussian processes is described here when the covariance of the limit process satisfies a certain condition the approach may be used to estimate the boundary crossing probabilities associated with the limit processes two examples illustrate the applicability of the approach and the results of some simulation experiments are described