an input normal form homotopy for the l sup 2 optimal model order reduction problem in control system analysis and design finding a reduced order model optimal in the l sup 2 sense to a given system model is a fundamental problem the problem is very difficult without the global convergence of homotopy methods and a homotopy based approach has been proposed the issues are the number of degrees of freedom the well posedness of the finite dimensional optimization problem and the numerical robustness of the resulting homotopy algorithm a homotopy algorithm based on the input normal form characterization of the reduced order model is developed here and is compared with the homotopy algorithms based on hyland and bernstein s optimal projection equations the main conclusions are that the input normal form algorithm can be very efficient but can also be very ill conditioned or even fail

linear systems with locally integrable trajectories abstract the locally integrable function space l 1 loc is made a module over the ring of proper rational functions using this module structure the notion of relative dimension is defined naturally for every linear subspace in l 1 loc q it is shown that the property of having finite relative dimension together with the property of having sufficiently many smooth trajectories and the evident property of differentiation invariance characterize the weak solutions sets of linear constant coefficient differential systems among all linear subspaces

a power series method for computing singular solutions to nonlinear analytic systems given a system of analytic equations having a singular solution we show how to develop a power series representation for the solution this series is computable and when the multiplicity of the solution is small highly accurate estimates of the solution can be generated for a moderate computational cost in this paper a theorem is proven using results from several complex variables which establishes the basis for the approach then a specific numerical method is developed and data from numerical experiments are given

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

supremum weighted log rank test and sample size for comparing two stage adaptive treatment strategies summary in two stage adaptive treatment strategies patients receive an induction treatment followed by a maintenance therapy given that the patient responded to the induction treatment they received to test for a difference in the effects of different induction and maintenance treatment combinations a modified supremum weighted log rank test is proposed the test is applied to a dataset from a two stage randomized trial and the results are compared to those obtained using a standard weighted log rank test a sample size formula is proposed based on the limiting distribution of the supremum weighted log rank statistic the sample size formula reduces to eng and kosorok s sample size formula for a two sample supremum log rank test when there is no second randomization monte carlo studies show that the proposed test provides sample sizes that are close to those obtained by standard weighted log rank test under a proportional hazards alternative however the proposed test is more powerful than the standard weighted log rank test under non proportional hazards alternatives

homotopy methods for solving the optimal projection equations for the h2 reduced order model problem the optimal projection approach to solving the h2 reduced order model problem produces two coupled highly nonlinear matrix equations with rank conditions as constraints due to the resemblance of these equations to standard matrix lyapunov equations they are called modified lyapunov equations the algorithms proposed herein utilize probability one homotopy theory as the main tool it is shown that there is a family of systems the homotopy that make a continuous transformation from some initial system to the final system with a carefully chosen initial problem a theorem guarantees that all the systems along the homotopy path will be asymptotically stable controllable and observable one method which solves the equations in their original form requires a decomposition of the projection matrix using the drazin inverse of a matrix it is shown that the appropriate inverse is a differentiable function an effective algorithm for computing the derivative of the projection matrix that involves solving a set of sylvester equations is given another class of methods considers the equations in a modified form using a decomposition of the pseudogramians based on a contragredient transformation some freedom is left in making an exact match between the number of equations and the number of unknowns thus effectively generating a family of methods

restricted mean survival time for interval censored data restricted mean survival time rmst evaluates the mean event free survival time up to a prespecified time point it has been used as an alternative measure of treatment effect owing to its model free structure and clinically meaningful interpretation of treatment benefit for right censored data in clinical trials another type of censoring called interval censoring may occur if subjects are examined at several discrete time points and the survival time falls into an interval rather than being exactly observed the missingness of exact observations under interval censored cases makes the nonparametric measure of treatment effect more challenging employing the linear smoothing technique to overcome the ambiguity we propose a new model free measure for the interval censored rmst as an alternative to the commonly used log rank test we further construct a hypothesis testing procedure to assess the survival difference between two groups simulation studies show that the bias of our proposed interval censored rmst estimator is negligible and the testing procedure delivers promising performance in detecting between group difference with regard to size and power under various configurations of survival curves the proposed method is illustrated by reanalyzing two real datasets containing interval censored observations

sample size formulae for two stage randomized trials with survival outcomes two stage randomized trials are growing in importance in developing adaptive treatment strategies i e treatment policies or dynamic treatment regimes usually the first stage involves randomization to one of the several initial treatments the second stage of treatment begins when an early nonresponse criterion or response criterion is met in the second stage nonresponding subjects are re randomized among second stage treatments sample size calculations for planning these two stage randomized trials with failure time outcomes are challenging because the variances of common test statistics depend in a complex manner on the joint distribution of time to the early nonresponse criterion or response criterion and the primary failure time outcome we produce simple albeit conservative sample size formulae by using upper bounds on the variances the resulting formulae only require the working assumptions needed to size a standard single stage randomized trial and in common settings are only mildly conservative these sample size formulae are based on either a weighted kaplan meier estimator of survival probabilities at a fixed time point or a weighted version of the log rank test

efficiency of age adjusted tests in animal carcinogenicity experiments based on asymptotic relative efficiency calculations ryan 1985 biometrics 41 525 531 concludes that in the analysis of animal carcinogenicity experiments age adjusted tests of tumor rates should be routinely preferred to simple proportions tests for both lethal and nonlethal tumors we recalculate the asymptotic efficiencies of the simple proportions test relative to the log rank test for the lethal tumor case for a simplified model it is shown that the relative efficiency may be easily computed as a function of the crude tumor rate and the survival rate at the time of terminal sacrifice more generally we calculate by numerical quadrature the asymptotic relative efficiency for all models considered by ryan and using simulations examine the relevance of asymptotic efficiencies to typical sample sizes contrary to the numerical results of ryan we find for experiments with good survival and typical tumor rates that the relative efficiencies are greater than 95 usually about 99 in the nonlethal tumor case similar results follow from ryan for tumor rates and survival rates typically encountered in practice as it is often difficult to determine whether or not a tumor is lethal we conclude for equal interim mortality rates that the simple proportions test is usually adequate in evaluating animal carcinogenicity experiments

balanced forms canonicity and parameterization we show that balanced forms are canonical and continuously parameterize the set of systems of a given order which are asymptotically stable minimal and have distinct singular values the advantage of the balanced canonical form over other classical canonical forms lies precisely in the guaranteed stability and minimality of the parameterization we also derive formulas allowing the synthesis of systems using gradient methods in balanced form

on permutation tests for comparing restricted mean survival time with small sample from randomized trials between group comparison based on the restricted mean survival time rmst is getting attention as an alternative to the conventional logrank hazard ratio approach for time to event outcomes in randomized controlled trials rcts the validity of the commonly used nonparametric inference procedure for rmst has been well supported by large sample theories however we sometimes encounter cases with a small sample size in practice where we cannot rely on the large sample properties generally the permutation approach can be useful to handle these situations in rcts however a numerical issue arises when implementing permutation tests for difference or ratio of rmst from two groups in this article we discuss the numerical issue and consider six permutation methods for comparing survival time distributions between two groups using rmst in rcts setting we conducted extensive numerical studies and assessed type i error rates of these methods our numerical studies demonstrated that the inflation of the type i error rate of the asymptotic methods is not negligible when sample size is small and that all of the six permutation methods are workable solutions although some permutation methods became a little conservative no remarkable inflation of the type i error rates were observed we recommend using permutation tests instead of the asymptotic tests especially when the sample size is less than 50 per arm

sequential linear rank tests for two sample censored survival data under extremely general patterns of patient arrival allocation to treatment and loss to follow up in randomized clinical trial settings the sequentially computed logrank statistic mantel 1966 is shown under the null hypothesis of identically distributed lifetimes to have exactly uncorrelated increments and is shown via rebolledo s 1980 martingale invariance principle to satisfy a functional central limit theorem justifying sequential logrank tests of jones and whitehead 1979 generalizations are made to other twosample rank tests for censored survival data and practical applicability to real randomized clinical trials is discussed

linear subspaces of smooth vector fields as a kernel of some linear first order partial differential equation abstract there are given sufficient conditions for linear subspaces s v c g r n r n of smooth vector fields to be written as a kernel of some linear first order partial differential equation pde in particular it implies that an overdetermined system of linear first order pde has a nontrivial solution and in addition the control system associated with s v is not controllable

a comparison of homotopies for alternative formulations of the l 2 optimal model order reduction problem abstract a fundamental problem in control systems theory is finding a reduced order model that is optimal in the l 2 sense to a given full order system model the numerical solution of this problem is challenging and the global convergence properties of homotopy methods are advantageous a number of homotopy based approaches have been developed the primary numerical issues are the number of degrees of freedom in the homotopy parameter vector the well posedness of the finite dimensional optimization problem and the numerical robustness of the resulting homotopy algorithm this paper develops two new homotopy algorithms for optimal model reduction and uses several examples to compare their performance with the performance of two previous algorithms the results show that the numerical well conditioning is inversely related to the algorithmic efficiency and that the relative performance of a given algorithm is problem dependent

weighted kaplan meier statistics a class of distance tests for censored survival data a class of statistics based on the integrated weighted difference in kaplan meier estimators is introduced for the two sample censored data problem with positive weight functions these statistics are intuitive for and sensitive against the alternative of stochastic ordering the standard weighted log rank statistics are not always sensitive against this alternative particularly if the hazard functions cross qualitative comparisons are made between the weighted log rank statistics and these weighted kaplan meier wkm statistics a statement of null asymptotic distribution theory is given and the choice of weight function is discussed in some detail results from small sample simulation studies indicate that these statistics compare favorably with the log rank procedure even under the proportional hazards alternative and may perform better than it under the crossing hazards alternative

component cost analysis of large scale systems abstract a brief summary of component cost analysis cca is given cca provides a means to determine the contribution of each dynamical element of the system in the overall performance metric using cca a theory of cost equivalent realizations is developed cost equivalent realizations are realizations that have the same value of the performance metric as the original system and they can be of lower order than kalman s minimal realization

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

probability one homotopy algorithms for solving the coupled lyapunov equations arising in reduced order h2 h modeling estimation and control optimal reduced order modeling estimation and control with respect to combined h 2 h criteria give rise to coupled lyapunov and riccati equations to develop reliable numerical algorithms for these problems this paper focuses on the coupled lyapunov equations which appear as a subset of the synthesis equations in particular this paper systematically examines the requirements of probability one homotopy algorithms to guarantee global convergence homotopy algorithms for nonlinear systems of equations construct a continuous family of systems and solve the given system by tracking the continuous curve of solutions to the family the main emphasis is on guaranteeing transversality for several homotopy maps based upon the pseudogramian formulation of the coupled lyapunov equations and variations based upon canonical forms these results are essential to the probability one homotopy approach by guaranteeing good numerical properties in the computational implementation of the homotopy algorithms

restricted mean life with adjustment for covariates abstract although the mean is the most widely used measure of location in comparing two distributions its use is essentially precluded in the presence of substantial censoring typical in survival analysis of medical therapies to accommodate censoring irwin 1949 proposed estimation of the expectation of life restricted to a time t using the actuarial estimator of the survival function in this article we examine the restricted mean as an index for comparing survival in two groups and then extend the method to incorporate covariates into the analysis for this purpose it is convenient to depart slightly from the actuarial approach and to consider piecewise exponential models asymptotic properties are explored and the assumption of piecewise exponentiality is shown to be rather mild as departures from the model have a relatively small effect on estimation of the restricted mean the methodology is illustrated using published data from a study conducted by the radiation therapy oncology group rtog

computing singular solutions to nonlinear analytic systems a method to generate an accurate approximation to a singular solution of a system of complex analytic equations is presented since manyreal systems extend naturally tocomplex analytic systems this porvides a method for generating approximations to singular solutions to real systems examples include systems of polynomials and systems made up of trigonometric exponential and polynomial terms the theorem on which the method is based is proven using results from several complex variables no special conditions on the derivatives of the system such as restrictions on the rank of the jacobian matrix at the solution are required the numerical method itself is developed from techniques of homotopy continuation and 1 dimensional quadrature a specific implementation is given and the results of numerical experiments in solving five test problems are presented

the optimal projection equations for model reduction and the relationships among the methods of wilson skelton and moore first order necessary conditions for quadratically optimal reduced order modeling of linear time invariant systems are derived in the form of a pair of modified lyapunov equations coupled by an oblique projection which determines the optimal reduced order model this form of the necessary conditions considerably simplifies previous results of wilson 1 and clearly demonstrates the quadratic extremality and nonoptimality of the balancing method of moore 2 the possible existence of multiple solutions of the optimal projection equations is demonstrated and a relaxation type algorithm is proposed for computing these local extrema a component cost analysis of the model error criterion similar to the approach of skelton 3 is utilized at each iteration to direct the algorithm to the global minimum

a parameterization of minimal plants we present the input normal riccati parameterization a generalization of kabamba s input normal form which allows the continuous parameterization of the set of minimal linear systems of a given order that have distinct singular values the input normal riccati form has no requirement that the underlying system be stable we also present formulas for the use of the input normal riccati parameterization for the synthesis of systems via gradient methods

estimation of the average hazard ratio summary simple estimators of the average hazard ratio are obtained for the two sample problem with censored failure time data these estimators are compared with estimators arising out of the partial likelihood within the proportional hazards class efficiency results are found to be generally quite favourable provided the hazard ratio is not too large some comments are made on extensions to the k sample problem

on the empirical choice of the time window for restricted mean survival time the t year mean survival or restricted mean survival time rmst has been used as an appealing summary of the survival distribution within a time window 0 t rmst is the patient s life expectancy until time t and can be estimated nonparametrically by the area under the kaplan meier curve up to t in a comparative study the difference or ratio of two rmsts has been utilized to quantify the between group difference as a clinically interpretable alternative summary to the hazard ratio the choice of the time window 0 t may be prespecified at the design stage of the study based on clinical considerations on the other hand after the survival data have been collected the choice of time point t could be data dependent the standard inferential procedures for the corresponding rmst which is also data dependent ignore this subtle yet important issue in this paper we clarify how to make inference about a random parameter moreover we demonstrate that under a rather mild condition on the censoring distribution one can make inference about the rmst up to t where t is less than or even equal to the largest follow up time either observed or censored in the study this finding reduces the subjectivity of the choice of t empirically the proposal is illustrated with the survival data from a primary biliary cirrhosis study and its finite sample properties are investigated via an extensive simulation study

a simple estimator for a shared frailty regression model summary we propose a simple estimation procedure for a proportional hazards frailty regression model for clustered survival data in which the dependence is generated by a positive stable distribution inferences for the frailty parameter can be obtained by using output from cox regression analyses the computational burden is substantially less than that of the other approaches to estimation the large sample behaviour of the estimator is studied and simulations show that the approximations are appropriate for use with realistic sample sizes the methods are motivated by studies of familial associations in the natural history of diseases their practical utility is illustrated with sib pair data from beaver dam wisconsin

the versatility of function indexed weighted log rank statistics abstract two sample weighted log rank statistics are used in the presence of right censoring to test whether failure times from two populations have different survival distributions kosorok has showed that large families of these statistics form stochastic processes indexed by weight functions and that these function indexed statistics can be used to construct versatile test procedures simultaneously sensitive to a wide array of both ordered hazards and stochastic ordering alternatives the complexity of the asymptotic distribution of these statistics precludes obtaining p values through analytical means in this article we develop a monte carlo method for accurately obtaining these p values and we evaluate the moderate sample size properties of this method and compare the power of function indexed statistics with previously developed weighted log rank tests these statistics are also examined in a data analysis of the beta blocker heart attack trial bhat the results of this article demonstrate that

sample size considerations for the evaluation of prognostic factors in survival analysis when the role of a new prognostic factor is investigated careful planning of an appropriate study is required this includes an assessment of the power of the study in terms of sample sizes an adequate analysis of the independent prognostic effect of a new factor has to be adjusted for the existing standard factors with survival time as endpoint this will usually be done with the cox proportional hazards model sample size and power formulae in survival analysis have been developed by schoenfeld for randomized treatment comparisons in the analysis of prognostic factors the covariates included are expected to be correlated with the factor of primary interest in this situation the existing sample size and power formulae are not valid and may not be applied in this paper schoenfeld s formula is first extended to the situation where a correlated factor is included in the analysis the validity of the resulting approximate asymptotic formula is investigated for its asymptotic behaviour by numerical integration and for its finite behaviour by simulation second an approximate formula for sample size and power is provided to detect an interaction between the interesting and a second correlated factor this extends the formula for independent effects finally the approach is illustrated by an example on the prognostic impact of dna ploidy and other factors in advanced ovarian cancer

effects of mismodelling and mismeasuring explanatory variables on tests of their association with a response variable we consider three commonly used statistical tests for assessing the association between an explanatory variable and a measured binary or survival time response variable and investigate the loss in efficiency from mismodelling or mismeasuring the explanatory variable with respect to mismodelling we examine the consequences of using an incorrect dose metameter in a test for trend of mismodelling a continuous explanatory variable and of discretizing a continuous explanatory variable we also examine the consequences of classification errors for a discrete explanatory variable and of measurement errors for a continuous explanatory variable for all three statistical tests the asymptotic relative efficiency are corresponding to each type of mis specification equals the square of the correlation between the correct and fitted form of the explanatory variable this result is evaluated numerically for the different types of mis specification to provide insight into the selection of tests the interpretation of results and the design of studies where the correct explanatory variable cannot be measured exactly

the robust inference for the cox proportional hazards model abstract we derive the asymptotic distribution of the maximum partial likelihood estimator for the vector of regression coefficients under a possibly misspecified cox proportional hazards model as in the parametric setting this estimator converges to a well defined constant vector in addition the random vector n 1 2 is asymptotically normal with mean 0 and with a covariance matrix that can be consistently estimated the newly proposed robust covariance matrix estimator is similar to the so called sandwich variance estimators that have been extensively studied for parametric cases for many misspecified cox models the asymptotic limit or part of it can be interpreted meaningfully in those circumstances valid statistical inferences about the corresponding covariate effects can be drawn based on the aforementioned asymptotic theory of and the related results for the score statistics extensive studies demonstrate that the proposed robust tests and interval estimation procedures

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

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

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

supremum versions of the log rank and generalized wilcoxon statistics abstract considerable progress has been made in generalizing to censored data hypothesis tests based on rank statistics the most commonly used generalizations are the log rank test statistic which extends the savage exponential scores statistic cox 1972 mantel 1966 and the generalized wilcoxon statistics gehan 1965 peto and peto 1972 gill 1980 showed that in the two sample problem the asymptotic efficiency properties of the savage and wilcoxon statistics are maintained in censored data by the log rank and peto and peto wilcoxon statistics respectively when censoring is the same in both samples heuristics and simulations have implied that some recently proposed supremum statistics closely related to these two popular linear rank statistics can be used to construct tests that provide good power against a much wider range of nonlocal alternatives see e g fleming and harrington 1981 fleming o brien o fallon and harrington 1980 gill 1980 schumacher 1984 in this article we consider n

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

investigating maximum power losses in survival studies with nonstratified randomization in studies with nonstratified randomization imbalances may occur which lead to power loss we investigate how much power may be lost at worst that is with small but nonnegligible probability the situation considered is a two treatment trial with censored survival data and three to five strata we also derive asymptotic results as the sample size and or number of strata increase in addition we consider how much a projected sample size needs to be increased to be confident at a certain probability level that the intended power will be retained conditionally on the unbalanced configuration

weighted kaplan meier statistics large sample and optimality considerations summary we propose a cumulative weighted difference in the kaplan meier estimates as a test statistic for equality of distributions in the two sample censored data survival analysis problem for stability of such a statistic the absolute value of the possibly random weight function must be bounded above by a multiple of c 1 2 6 where 1 c is the left continuous censoring distribution function and 6 0 for these weighted kaplan meier wkm statistics asymptotic distribution theory is presented along with expressions for the efficacy under a sequence of local alternatives a simple censored data generalization of the two sample difference in means test z test is a member of this class and in large samples is seen to be quite efficient relative to the popular log rank test under a range of alternatives including the proportional hazards alternative optimal weight functions are also calculated the optimal wkm statistic is as efficient as the optimal weighted log rank statistic for any particular sequence of local alternatives stratified statistics and trend statistics are also presented

efficiency of two sample tests via the restricted mean survival time for analyzing event time observations in comparing two treatments with the event time observations the hazard ratio hr estimate is routinely used to quantify the treatment difference however this model dependent estimate may be difficult to interpret clinically especially when the proportional hazards ph assumption is violated an alternative estimation procedure for treatment efficacy based on the restricted means survival time or t year mean survival time t mst has been discussed extensively in the statistical and clinical literature on the other hand a statistical test via the hr or its asymptotically equivalent counterpart the logrank test is asymptotically distribution free in this article we assess the relative efficiency of the hazard ratio and t mst tests with respect to the statistical power under various ph and non ph models theoretically and empirically when the ph assumption is valid the t mst test performs almost as well as the hr test for non ph models the t mst test can substantially outperform its hr counterpart on the other hand the hr test can be powerful when the true difference of two survival functions is quite large at end but not the beginning of the study unfortunately for this case the hr estimate may not have a simple clinical interpretation for the treatment effect due to the violation of the ph assumption

a log rank type test to compare net survival distributions in population based cancer studies it is often interesting to compare cancer survival between different populations however in such studies the exact causes of death are often unavailable or unreliable net survival methods were developed to overcome this difficulty net survival is the survival that would be observed if the disease under study was the only possible cause of death the pohar perme estimator ppe is a nonparametric consistent estimator of net survival in this article we present a log rank type test for comparing net survival functions as estimated by ppe between several groups we put the test within the counting process framework to introduce the inverse probability weighting procedure as required by the ppe we built a stratified version to control for categorical covariates that affect the outcome we performed simulation studies to evaluate the performance of this test and worked an application on real data

the loss in efficiency from misspecifying covariates in proportional hazards regression models summary this note considers partial likelihood score tests for association between a covariate process and survival time based on a proportional hazards regression model we derive the asymptotic efficiency of the test based on a misspecified form of the covariate process relative to the test based on the correct form the results can be used to assess the consequences of various types of misspecification

local uncontrollability for affine control systems with jumps abstractthis paper investigates affine control systems with jumps for which the ideal if g1 gm generated by the drift vector field f in the lie algebra l f g1 gm can be imbedded as a kernel of a linear first order partial differential equation it will lead us to uncontrollable affine control systems with jumps for which the corresponding reachable sets are included in explicitly described differentiable manifolds

restricted mean life with covariates modification and extension of a useful survival analysis method abstract karrison has presented a method for covariate adjusted comparison of two groups with respect to survival when the group effect is expected to not be of proportional hazards form this article describes a simplified procedure for implementing karrison s basic approach along with an extended version designed to achieve robustness against misspecification in the underlying analytical model a simulation study of these techniques is presented and the techniques are illustrated with an example taken from karrison

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

a class of tests for the equality of k cause specific hazard rates in a competing risks model a class of asymptotically distribution free tests for the equality of the k risks in a competing risks model is considered the tests can be derived by martingale theory or by a marginal likelihood approach when the risks are dependent the quantities to be compared would be the cause specific hazard rates or equivalently the pseudosurvivor functions related to the cause specific hazard rates this class of tests allows one to compare k risks simultaneously for k 2 is able to handle possibly right censored data and is extremely simple to apply choices of the optimal weight functions leading to the locally most powerful rank tests for a general class of semiparametric alternative hypotheses are discussed the performances of the tests are studied by simulation under various alternative hypotheses

when are linear differentiation invariant spaces differential it is shown that a linear differentiation invariant subspace of a c trajectory space is differential i e can be represented as the kernel of a linear constant coefficient differential operator if and only if its mcmillan degree is finite

the optimal projection equations for fixed order dynamic compensation first order necessary conditions for quadratically optimal steady state fixed order dynamic compensation of a linear time invariant plant in the presence of disturbance and observation noise are derived in a new and highly simplified form in contrast to the pair of matrix riccati equations for the full order lqg case the optimal steady state fixed order dynamic compensator is characterized by four matrix equations two modified riccati equations and two modified lyapunov equations coupled by a projection whose rank is precisely equal to the order of the compensator and which determines the optimal compensator gains the coupling represents a graphic portrayal of the demise of the classical separation principle for the reduced order controller case

balanced gains and their significance for l 2 model reduction the singular values do not give enough information for model reduction in the l2sense other invariants are introduced which help describe the contribution of each state to the l2magnitude of the impulse response this leads to another suboptimal balanced truncation criterion

issues of efficiency in combining proportions of deaths from several clinical trials the mantel haenszel test provides a straightforward method to combine results from several clinical trials when only summary information such as the proportion of deaths is available for each trial more efficient tests such as the stratified logrank test should be used if the survival and censoring times are known for all individuals but in practice the cost and effort of obtaining this information may be prohibitive the purpose of this paper is to derive a general expression for the asymptotic relative efficiency are of the mantel haenszel test with respect to the stratified logrank test and to compute the are in situations which are likely to be of practical interest the results show that under realistic assumptions about the survival distribution losses to follow up and duration of accrual the are frequently exceeds 80 per cent an example is given to show the usefulness of the approach when combining proportions of deaths from several cancer clinical trials

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