admissibility analysis of discrete linear time varying descriptor systems abstract this paper deals with the problem of admissibility analysis i e regularity causality and exponential stability of discrete time linear descriptor systems with uncertain time varying parameters in the system state space model matrices the parameters enter affinely into all the matrices and both their admissible values and variations are assumed to belong to given intervals first necessary and sufficient admissibility conditions for uncertainty free discrete linear time varying descriptor systems are presented next strict linear matrix inequality conditions based on parameter dependent lyapunov functions are proposed to ensure robust admissibility of uncertain linear descriptor systems both the cases of lyapunov functions with affine and quadratic dependence on the system uncertain parameters are considered the robust admissibility analysis methods incorporate information on available bounds on both the admissible values and variation of the uncertain parameters numerical examples are presented to demonstrate the potentials of the proposed methods

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

galerkin s method for ordinary differential equations subject to generalized nonlinear boundary conditions where xk belongs to tc a finite dimensional subspace of cc l 11 r il ii and i qj is a projection mapping cc l 11 r i i x r onto a subspace of c 1 11 r 11 ii having the same dimension as rck there is a vast collection of literature concerning the application of galerkin s method to differential equations 1 3 12 16231 we make a special reference to the papers of cesari 4 5 and urabe 22 23 our results provide an extension and a unification of previous results of urabe that were conderned with the determination of periodic solutions to systems of ordinary differential equations 22 and with the solvability of 112 0022 0396192 3 00

projection methods for nonlinear boundary value problems where l d l c x y is a linear map n x y is nonlinear and x and y are banach spaces recently cesari and mckenna s proved that if the underlying spaces possess a schauder basis or more generally they have what the authors call property l it is theoretically possible to establish a finite dimensional alternative problem for 1 3 their paper unities previous results 12 131 that established conditions under which 1 3 could be reduced to finite 282 0022 0396 85 3 00

hazard function estimation using b splines summary a flexible parametric procedure is given to model the hazard function as a linear combination of cubic b splines and to obtain maximum likelihood estimates from censored survival data the approach yields smooth estimates of the hazard and suivivorship functions that are intermediate in structure between strongly parametric and non parametric models a simple method is described for selecting the number and location of knots simulation results show favorable root mean square error compared to non parametric estimates for both the hazard and survivorship functions three methods are given to calculate confidence intervals based on the delta method profile likelihood and bootstrap respectively the procedure is applied to estimate hazard rates for acquired immunodeficiency syndrome aids following infection with human immunodeficiency virus hiv spline methods can accommodate complex censoring mechanisms such as those that arise in the aids setting to illustrate hiv infection incidence is estimated for a cohort of hemophiliacs in which the dates of hiv infection are interval censored and some subjects were born after the onset of the hiv epidemic this report develops flexible parametric methods based on splines to estimate the hazard function hi t that describes the rate of disease onset among persons still susceptible at time t the observed data derive from a random sample yi i 1 n n of disease onset times with survivorship function s t py t the yi are right censored by independent random variables ci drawn from h c p c c one observes xi min yi ci and 3i i y ci the indicator for the event that yi is censored the hazard function

a partially parametric estimator of survival in the presence of randomly censored data many biological or medical experiments have as their goal to estimate the survival function of a specified population of subjects when the time to the specified event may be censored due to loss to follow up the occurrence of another event that precludes the occurrence of the event of interest or the study being terminated before the event of interest occurs this paper suggests an improvement of the kaplan meier product limit estimator when the censoring mechanism is random the proposed estimator treats the uncensored observations nonparametrically and uses a parametric model only for the censored observations one version of this proposed estimator always has a smaller bias and mean squared error than the product limit estimator an example estimating the survival function of patients enrolled in the ohio state university bone marrow transplant program is presented

what price kaplan meier summary the asymptotic efficiency of the kaplan meier product limit estimator relative to the maximum likelihood estimator of a parametric survival function is examined under a random censoring model

nonlinear discrete systems with global boundary conditions abstract this paper is devoted to the study of boundary value problems on infinite time intervals for nonlinear discrete time systems for problems of the form x k 1 f k x k h k k 0 1 2 subject to constraints or nonlocal boundary conditions of the form k 0 g k x k y we analyze how perturbations in h and y affect the existence of l solutions of this problem in this setting h is an element of l and y belongs to r p we also study the existence and behavior of bounded solutions to problems of the form x k 1 f k x k k 0 1 2 subject to k 0 g k x k 0 we place particular importance on the behavior of the solutions as a function of the parameter

the price of kaplan meier miller has studied the asymptotic efficiency of the nonparametric kaplan meier survival estimator relative to parametric estimates based on the exponential and weibull distributions he concluded that in certain cases the asymptotic efficiency is low and recommended that analysts give more consideration to parametric estimators particularly for estimation of small tail probabilities in this article we revisit this issue and examine the performance of the nonparametric procedure for estimation not only of a point on the survival curve but also of the mean or restricted mean lifetime in addition to the exponential and weibull families we consider the performance of the kaplan meier procedure relative to a more flexible parametric model proposed by efron we find that the reduction in efficiency of the kaplan meier survival estimate becomes negligible fairly quickly as the number of parameters in the parametric model increases moreover for estimation of the mean or restricted mean the loss in eff

parametric versus non parametric methods for estimating cure rates based on censored survival data if a patient s failure time is incorrectly recorded as being too early the correction will lower the plateau of the kaplan meier curve and hence the associated estimated cure rate implications of this counter intuitive observation are discussed in addition a parametric approach based on the gompertz distribution to the problem of cure rate estimation is presented

a generalization of the weibull distribution with application to the analysis of survival data abstract the weibull distribution which is frequently used for modeling survival data is embedded in a larger family obtained by introducing an additional shape parameter this generalized family not only contains distributions with unimodal and bathtub hazard shapes but also allows for a broader class of monotone hazard rates furthermore the distributions in this family are analytically tractable and computationally manageable the modeling and analysis of survival data using this family is discussed and illustrated in terms of a lifetime dataset and the results of a two arm clinical trial

bayesian nonparametric estimation for incomplete data via successive substitution sampling in the problem of estimating an unknown distribution function f in the presence of censoring one can use a nonparametric estimator such as the kaplan meier estimator or one can consider parametric modeling there are many situations where physical reasons indicate that a certain parametric model holds approximately in these cases a nonparametric estimator may be very inefficient relative to a parametric estimator on the other hand if the parametric model is only a crude approximation to the actual model then the parametric estimator may perform poorly relative to the nonparametric estimator and may even be inconsistent the bayesian paradigm provides a reasonable framework for this problem in a bayesian approach one would try to put a prior distribution on f that gives most of its mass to small neighborhoods of the entire parametric family we show that certain priors based on the dirichlet process prior can be used to accomplish this for these priors the posterior distribution of f given the censored data appears to be analytically intractable we provide a method for approximating this posterior distribution through the use of a successive substitution sampling algorithm we also show convergence of the algorithm

a semiparametric approach to hazard estimation with randomly censored observations abstract one method for estimating the hazard function is to use a parametric estimator provided that the underlying distribution of the data can be assumed to belong to some well known family of distributions depending on an unknown possibly vector valued parameter another approach is to use nonparametric estimators such as cox s proportional hazard models kernel hazard estimators and so on however nonparametric estimators are less efficient than suitably chosen parametric models but regardless of how suitable a parametric model may be because of errors associated with data collection it is impossible to determine with certainty whether the observed data are actually generated by the postulated model consequently instead of using exclusively a parametric or a nonparametric estimator we propose to fit a weighted average of both the weight is estimated by minimizing the mean square error of the combination the main point is that we expect the proposed model to assign more weight to the est

robust analysis and control of parameter dependent uncertain descriptor systems in this paper we address the robust admissibility analysis and control of descriptor systems with parameter dependent possibly time varying uncertainties first we propose a new necessary and sufficient condition for the admissibility of linear time invariant lti descriptor systems this condition uses a strict linear matrix inequality lmi formulation and involves two additional matrix variables usually called slack variables then we present an extension of this condition to robust admissibility of time varying parameter dependent descriptor systems using parameter dependent lyapunov functions and employing two slack variables this extension states robust admissibility lmi conditions that are less restrictive as supported by our numerical examples than the existing ones our robust admissibility analysis result which can be directly used for state estimation cannot be so for state feedback control design this is due to the absence of duality between state estimation and state feedback control in the case of parameter dependent systems with uncertain parameters as recently reported in the literature in order to overcome this problem we also present in this paper a new robust admissibility analysis result involving only one slack variable which we apply to state feedback control design

logistic regression survival analysis and the kaplan meier curve abstract we discuss the use of standard logistic regression techniques to estimate hazard rates and survival curves from censored data these techniques allow the statistician to use parametric regression modeling on censored data in a flexible way that provides both estimates and standard errors an example is given that demonstrates the increased structure that can be seen in a parametric analysis as compared with the nonparametric kaplan meier survival curves in fact the logistic regression estimates are closely related to kaplan meier curves and approach the kaplan meier estimate as the number of parameters grows large

dilated lmi conditions for time varying polytopic descriptor systems the discrete time case this article addresses the admissibility analysis and state feedback control synthesis problems of discrete time polytopic descriptor systems with possibly time varying parameters first we present a new necessary and sufficient strict linear matrix inequality lmi condition for the admissibility analysis of linear time invariant lti descriptor systems then based on the concept of poly quadratic admissibility introduced in this article we extend this result to the admissibility analysis of possibly time varying parameter dependent descriptor systems this extension which applies to both uncertain and measurable parameters uses parameter dependent lyapunov functions and employs two slack variables the extended conditions are also expressed as strict lmi conditions which are easily tractable numerically compared to the non strict ones often encountered when dealing with descriptor systems note that we have proposed two separate admissibility analysis conditions one directly exploitable for stat

estimates of absolute cause specific risk in cohort studies in this paper we study methods for estimating the absolute risk of an event c1 in a time interval t1 t2 given that the individual is at risk at t1 and given the presence of competing risks we discuss some advantages of absolute risk for measuring the prognosis of an individual patient and some difficulties of interpretation for comparing two treatment groups we also discuss the importance of the concept of absolute risk in evaluating public health measures to prevent disease variance calculations permit one to gauge the relative importance of random and systematic errors in estimating absolute risk efficiency calculations were also performed to determine how much precision is lost in estimating absolute risk with a nonparametric approach or with a flexible piecewise exponential model rather than a simple exponential model and other calculations indicate the extent of bias that arises with the simple exponential model when that model is invalid such calculations suggest that the more flexible models will be useful in practice simulations confirm that asymptotic methods yield reliable variance estimates and confidence interval coverages in samples of practical size

survival estimation using splines a nonparametric maximum likelihood procedure is given for estimating the survivor function from right censored data it approximates the hazard rate by a simple function such as a spline with different approximations yielding different estimators a special case is that proposed by nelson 1969 journal of quality technology 1 27 52 and altshuler 1970 mathematical biosciences 6 1 11 the estimators are uniformly consistent and have the same asymptotic weak convergence properties as the kaplan meier 1958 journal of the american statistical association 53 457 481 estimator however in small and in heavily censored samples the simplest spline estimators have uniformly smaller mean squared error than do the kaplan meier and nelson altshuler estimators the procedure is extended to estimate the baseline hazard rate and regression coefficients in the cox 1972 journal of the royal statistical society series b 34 187 220 proportional hazards model and is illustrated using experimental carcinogenesis data

bootstrap type confidence intervals for quantiles of the survival distribution in this paper we outline and illustrate an easy to program method for analytically calculating both parametric and non parametric bootstrap type confidence intervals for quantiles of the survival distribution based on right censored data this new approach allows for the incorporation of covariates within the framework of parametric models the procedure is based upon the notion of fractional order statistics and is carried forth using a simple beta transformation of the estimated survival function parametric or non parametric it is the only direct method currently available in the sense that all other methods are based on inverting test statistics or employing confidence intervals for other survival quantities we illustrate that the new method has favourable coverage probabilities for median confidence intervals as compared to six other competing methods

semiparametric two sample tests in clinical trials with a post randomisation response indicator in many clinical trials involving survival endpoints one has additional data on some binary indicator of response such as initial tumour shrinkage in cancer trials this paper studies the case of randomised clinical trials where the response indicator is available shortly after randomisation and where one can assume that within each stratum defined by the response indicator a two treatment group proportional hazards model holds the same model may also describe some incompletely randomised or observational studies asymptotic relative efficiencies for kaplan meier based estimators versus maximum partial likelihood estimators are examined under this model for estimating either the difference in survival probabilities at a specified time or the parameter estimated by the logrank numerator it is shown that the efficiency gains using the model are more promising when estimating the difference in survival probabilities an example is given comparing the long term survival experience of two groups of patients with advanced hodgkin s disease

an alternative method for boundary value problems with large nonlinearities where g r r is continuously differentiable and b and d are nonsingular 12 x n matrices historically lyapunov schmidt and the alternative method are able to reduce the problem to a finite dimensional one provided the norm of the nonlinear term is sufficiently small in the region of interest that is the weakly nonlinear case recently the finite dimensional reduction for ordinary differential equations with periodic boundary conditions was accomplished 161 in this paper a constructive technique is developed that allows us to reduce 1 1 to a finite dimensional problem

technical communique new dilated lmi characterizations for continuous time multiobjective controller synthesis this paper provides new dilated linear matrix inequality lmi characterizations for continuous time controller synthesis the dilated lmis enable us to parametrize controllers without involving the lyapunov variables in the parametrizations taking advantage of this feature we can readily design multiobjective controllers with non common lyapunov variables whereas we are forced to employ a common one in the well known lyapunov shaping paradigm in particular it is shown that the proposed dilated lmi based approach to h 2 d stability synthesis encompasses the corresponding lyapunov shaping paradigm as a special case in this sense the results of this paper can be viewed as partial counterparts of those obtained in the discrete time setting

on nonlinear discrete boundary value problems mo x 1 x n 0 1 4 where n is a fixed positive integer 8 represent n by n constant matrices a t is an n by n matrix for each te 0 l h t belongs to ir for each nonnegative integer t u is in r 1 is a real parameter f and g are continuously differentiable f r i ir and g r i r for systems 1 1 1 2 we prove that if the linear system x t l a l x t h t 1 5 subject to

detectability and stabilizability of time varying discrete time linear systems the concepts of detectability and stabilizability are explored for time varying systems we study duality invariance under feedback an extended version of the lemma of lyapunov existence of stabilizing feedback laws linear quadratic filtering and control and the existence of approximate canonical forms