corrections to the kalman yakubovich popov lemma for pritchard salamon systems abstract in this note we correct the result in the paper the kalman yakubovich popov lemma for pritchard salamon systems 3 there was a gap in the proof which can be bridged but only by assuming that the system is exactly controllable

testing quasi independence of failure and truncation times via conditional kendall s tau truncated survival data arise when the failure time is observed only if it falls within a subject specific truncating set most analysis methods rely on the key assumption of quasi independence that is factorization of the joint density of failure and truncation times into a product proportional to the individual densities in the observable region unlike independence of failure time and censoring time quasi independence can be tested tests of quasi independence are available for one sided truncation and for truncation that depends on a measured covariate but not for more complex truncation schemes here tests of quasi independence based on a multivariate conditional kendall s tau are proposed for doubly truncated data bivariate left truncated data and other forms of truncated survival data that arise when initiating or terminating event times are interval censored asymptotic properties under the null are derived the tests are illustrated using several real datasets and evaluated via simulation

asymptotic properties of the product limit estimate under random truncation on donne une description precise du comportement asymptotique de l estimateur limite produit incluant une forme explicite simple de la structure de covariance asymptotique

repeated randomization and matching in multi arm trials cluster randomized trials with relatively few clusters have been widely used in recent years for evaluation of health care strategies the balance match weighted bmw design introduced in xu and kalbfleisch 2010 biometrics 66 813 823 applies the optimal full matching with constraints technique to a prospective randomized design with the aim of minimizing the mean squared error mse of the treatment effect estimator this is accomplished through consideration of m independent randomizations of the experimental units and then selecting the one which provides the most balance evaluated by matching on the estimated propensity scores often in practice clinical trials may involve more than two treatment arms and multiple treatment options need to be evaluated therefore we consider extensions of the bmw propensity score matching method to allow for studies with three or more arms in this article we propose three approaches to extend the bmw design to clinical trials with more than two arms and evaluate the property of the extended design in simulation studies

semiparametric regression analysis of length biased interval censored data in prevalent cohort design subjects who have experienced an initial event but not the failure event are preferentially enrolled and the observed failure times are often length biased moreover the prospective follow up may not be continuously monitored and failure times are subject to interval censoring we study the nonparametric maximum likelihood estimation for the proportional hazards model with length biased interval censored data direct maximization of likelihood function is intractable thus we develop a computationally simple and stable expectation maximization algorithm through introducing two layers of data augmentation we establish the strong consistency asymptotic normality and efficiency of the proposed estimator and provide an inferential procedure through profile likelihood we assess the performance of the proposed methods through extensive simulations and apply the proposed methods to the massachusetts health care panel study

semiparametric likelihood ratio based inferences for truncated data abstract in astronomic demographic epidemiologic and other studies the variable of interest say the survival time is often truncated by an associated variable in many situations the distribution of the truncation variable can be described by a parametric form unlike in the standard right censorship model in which the censoring distribution is noninformative knowledge of the truncation distribution can be used to improve estimation of the survival distribution this article derives likelihood ratio based confidence intervals for survival probabilities and for the truncation proportion under the two models in which the truncation distribution is assumed either to be known or to belong to a parametric family our proposed methods enable one to incorporate both the information contained in the data and the available information on the truncation distribution and thus are expected to have better performance than fully nonparametric methods our approach also has applications to some biased sampling p

substantial gains in bias reduction from matching with a variable number of controls summary in observational studies that match several controls to each treated subject substantially greater bias reduction is possible if the number of controls is not fixed but rather is allowed to vary from one matched set to another in certain cases matching with a fixed number of controls may remove only 50 of the bias in a covariate whereas matching with a variable number of controls may remove 90 of the bias even though both control groups have the same number of controls in total an example of matching in a study of surgical mortality is discussed in detail

estimating exposure effects by modelling the expectation of exposure conditional on confounders in order to estimate the causal effects of one or more exposures or treatments on an outcome of interest one has to account for the effect of confounding factors which both covary with the exposures or treatments and are independent predictors of the outcome in this paper we present regression methods which in contrast to standard methods adjust for the confounding effect of multiple continuous or discrete covariates by modelling the conditional expectation of the exposures or treatments given the confounders in the special case of a univariate dichotomous exposure or treatment this conditional expectation is identical to what rosenbaum and rubin have called the propensity score they have also proposed methods to estimate causal effects by modelling the propensity score our methods generalize those of rosenbaum and rubin in several ways first our approach straightforwardly allows for multivariate exposures or treatments each of which may be continuous ordinal or discrete second even in the case of a single dichotomous exposure our approach does not require subclassification or matching on the propensity score so that the potential for residual confounding i e bias due to incomplete matching is avoided third our approach allows a rather general formalization of the idea that it is better to use the estimated propensity score than the true propensity score even when the true score is known the additional power of our approach derives from the fact that we assume the causal effects of the exposures or treatments can be described by the parametric component of a semiparametric regression model to illustrate our methods we reanalyze the effect of current cigarette smoking on the level of forced expiratory volume in one second in a cohort of 2 713 adult white males we compare the results with those obtained using standard methods

a semiparametric model for randomly truncated data abstract for randomly censored data it is known that the maximum likelihood estimate mle of the survival curve is not affected by parametric assumption on the censoring variable the kaplan meier 1958 estimate is the mle for both nonparametric and semiparametric models for randomly truncated data the truncation product limit estimate is the mle for nonparametric models this is not the case if the truncation mechanism is parameterized however specifically let x be a generic random variable and t be the truncation variable if the distribution of t is parameterized and the distribution of x is left unspecified it can be shown that the truncation product limit estimate is not the mle for this semiparametric model even though it is for the fully nonparametric model in this article the mle is characterized for the semiparametric model and the large sample properties of the estimate are established the results show that unlike censoring the parametric information from the truncation mechanism

combining propensity score matching with additional adjustments for prognostic covariates abstract propensity score matching refers to a class of multivariate methods used in comparative studies to construct treated and matched control samples that have similar distributions on many covariates this matching is the observational study analog of randomization in ideal experiments but is far less complete as it can only balance the distribution of observed covariates whereas randomization balances the distribution of all covariates both observed and unobserved an important feature of propensity score matching is that it can be easily combined with model based regression adjustments or with matching on a subset of special prognostic covariates or combinations of prognostic covariates that have been identified as being especially predictive of the outcome variables we extend earlier results by developing approximations for the distributions of covariates in matched samples created with linear propensity score methods for the practically important situation where matching uses both the estimat

a general necessary condition for exact observability suppose a generates an exponentially stable strongly continuous semigroup on the hilbert space x y is another hilbert space and c d a rightarrow y is an admissible observation operator for this semigroup this means that to any initial state in x we can associate an output function in l 2 0 infty y this paper gives a necessary condition for the exact observability of the system defined by a and c this condition called bf e is related to the hautus lemma from finite dimensional systems theory it is an estimate in terms of the operators a and c alone in particular it makes no reference to the semigroup this paper shows that bf e implies approximate observability and if a is bounded it implies exact observability this paper conjectures that bf e is in fact equivalent to exact observability the paper also shows that for diagonal semigroups bf e takes on a very simple form and applies the results to sequences of complex exponential functions

testing the assumption of independence of truncation time and failure time summary for data subject to random censorship it is well known that the assumption of independence between censoring time and failure time cannot be tested nonparametrically for data subject to random truncation however it is possible to test independence of truncation time and failure time a statistic generalizing kendall s tau is proposed for testing the independence assumption and asymptotic properties under the null hypothesis are derived a conditional permutation test is also derived for small data sets generalization to allow right censoring and an application to truncated linear regression are also briefly discussed

a pairwise likelihood augmented cox estimator for left truncated data survival data collected from a prevalent cohort are subject to left truncation and the analysis is challenging conditional approaches for left truncated data could be inefficient as they ignore the information in the marginal likelihood of the truncation times length biased sampling methods may improve the estimation efficiency but only when the underlying truncation time is uniform otherwise they may generate biased estimates we propose a semiparametric method for left truncated data under the cox model with no parametric distributional assumption about the truncation times our approach is to make inference based on the conditional likelihood augmented with a pairwise likelihood which eliminates the truncation distribution yet retains the information about the regression coefficients and the baseline hazard function in the marginal likelihood an iterative algorithm is provided to solve for the regression coefficients and the baseline hazard function simultaneously by empirical process and u process theories it has been shown that the proposed estimator is consistent and asymptotically normal with a closed form consistent variance estimator simulation studies show substantial efficiency gain of our estimator in both the regression coefficients and the cumulative baseline hazard function over the conditional approach estimator when the uniform truncation assumption holds our estimator enjoys smaller biases and efficiency comparable to that of the full maximum likelihood estimator an application to the analysis of a chronic kidney disease cohort study illustrates the utility of the method

the survival curve under monotone density constraints with applications to two dimensional line segment processes summary several situations involving survival data are examined in which the nonparametric maximum likelihood estimator is not the kaplan meier estimator cases covered are inclusion of initial observations in field studies estimation of the length distribution from convex window sampling of line segment processes in two dimensions and estimation of a survival curve with monotone density the first two cases are nonstandard because survival and censoring are not independent and thus form simple tractable variable sum models williams lagakos 1977

nonparametric estimation from cross sectional survival data abstract in many follow up studies survival data are often observed according to a cross sectional sampling scheme data of this type are subject to left truncation in addition to the usual right censoring a number of characteristics and properties of the product limit estimate for left truncated and right censored data have been explored and found to be similar to those of the kaplan meier estimate under the stationarity assumption however it is believed that an alternative estimate has much better efficiency in this article the conditional maximum likelihood estimate mle property of the product limit estimate is visited the non parametric mle of the truncation distribution is derived use of this estimate includes testing the stationarity assumption estimating the proportion of truncated data and other applications in prevalent cohort studies the analysis of the estimation is based on a working data approach the asymptotic properties of the proposed estimates are developed through nonpar

estimating the occurrence rate for prevalent survival data in competing risks models abstract the problem of interest is the estimation of occurrence probabilities based on prevalent data in competing risks models in the literature the development of nonparametric methods has relied heavily on the independent competing risks assumption the primary purpose of this article is to establish a statistical framework without excluding the possibility of dependence among competing risks this is done through the use of crude hazard functions the crude hazard functions not only are estimable regardless of whether the competing risks are independent but also are mathematically more tractable in this article we show that there is a one to one correspondence between the crude hazard functions and the occurrence probabilities the general inversion formulas for the occurrence probabilities are presented from which various representations can be derived under different sampling techniques maximum likelihood estimators are derived using these representations for nonparametric and length bias dat

multiplicative censoring renewal processes deconvolution and decreasing density nonparametric estimation on donne un estimateur du maximum de vraisemblance non parametrique pour une distribution de durees de vie il est base sur un modele d observations censurees de facon multiplicative et il generalise des problemes statistiques courants tels que l estimation d une fonction de repartition sous une contrainte de densite decroissante la deconvolution non parametrique d une variable aleatoire exponentielle ou un probleme d estimation dans les processus de renouvellement

nonparametric estimation for right censored length biased data a pseudo partial likelihood approach to estimate the lifetime distribution of right censored length biased data we propose a pseudo partial likelihood approach that allows us to derive two nonparametric estimators with its closed form estimators and explicit limiting variances this approach retains the simplicity of conditional analysis and has only a small efficiency loss compared with the unconditional analysis under some regularity conditions we show that the two estimators are uniformly consistent and converge weakly to gaussian processes a simulation study demonstrates that the proposed estimators have satisfactory finite sample performance application to an alzheimer s disease study is reported

asymptotic theory of rerandomization in treatment control experiments although complete randomization ensures covariate balance on average the chance of observing significant differences between treatment and control covariate distributions increases with many covariates rerandomization discards randomizations that do not satisfy a predetermined covariate balance criterion generally resulting in better covariate balance and more precise estimates of causal effects previous theory has derived finite sample theory for rerandomization under the assumptions of equal treatment group sizes gaussian covariate and outcome distributions or additive causal effects but not for the general sampling distribution of the difference in means estimator for the average causal effect we develop asymptotic theory for rerandomization without these assumptions which reveals a non gaussian asymptotic distribution for this estimator specifically a linear combination of a gaussian random variable and truncated gaussian random variables this distribution follows because rerandomization affects only the projection of potential outcomes onto the covariate space but does not affect the corresponding orthogonal residuals we demonstrate that compared with complete randomization rerandomization reduces the asymptotic quantile ranges of the difference in means estimator moreover our work constructs accurate large sample confidence intervals for the average causal effect

rerandomization to improve covariate balance in experiments randomized experiments are the gold standard for estimating causal effects yet often in practice chance imbalances exist in covariate distributions between treatment groups if covariate data are available before units are exposed to treatments these chance imbalances can be mitigated by first checking covariate balance before the physical experiment takes place provided a precise definition of imbalance has been specified in advance unbalanced randomizations can be discarded followed by a rerandomization and this process can continue until a randomization yielding balance according to the definition is achieved by improving covariate balance rerandomization provides more precise and trustworthy estimates of treatment effects

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

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

nonparametric estimation of the probability of illness in the illness death model under cross sectional sampling cross sectional sampling is an attractive design that saves resources but results in biased data for proper inference one should first discover the bias function and then weigh observations appropriately we consider cross sectioning of the illness death model with the aim of estimating the probability of visiting the illness state before death we develop simple consistent and asymptotically normal estimators under various assumptions on the model and data collection and in particular compare designs with and without a follow up these designs are common in surveillance of hospital acquired infections but estimators currently in use do not properly correct the bias

equivalent conditions for the solvability of the nonstandard lq problem for pritchard salamon systems equivalent conditions are presented for the solvability of the infinite horizon lq problem with stability for a class of infinite dimensional systems with unbounded input and output operators in particular these equivalent conditions are given in terms of a riccati equation and a frequency domain inequality just as in the finite dimensional case

length biased sampling with right censoring when survival data arise from prevalent cases ascertained through a cross sectional study it is well known that the survivor function corresponding to these data is length biased and different from the survivor function derived from incident cases length biased data have been treated both unconditionally and conditionally in the literature in the latter case where length bias is viewed as being induced by random left truncation of the survival times the truncating distribution is assumed to be unknown conditioning on the observed truncation times hence causes very little loss of information in many instances however it can be supposed that the truncating distribution is uniform and it has been pointed out that under these circumstances an unconditional analysis will be more informative there are no results in the current literature that give the asymptotic properties of the unconditional nonparametric maximum likelihood estimator npmle of the unbiased survivor function in the presence of cen

the kalman yakubovich popov lemma for pritchard salamon systems in this paper we generalize the kalman yakubovich popov lemma to the pritchard salamon class of infinite dimensional systems i e systems determined by semigroups of operators on a hilbert space with unbounded input and output operators at the same time we prove a comparison theorem for riccati equations of the same class

using weighted kaplan meier statistics in nonparametric comparisons of paired censored survival outcomes this research introduces methods for nonparametric testing of weighted integrated survival differences in the context of paired censored survival designs the current work extends work done by pepe and fleming 1989 biometrics 45 497 507 which considered similar test statistics directed toward independent treatment group comparisons an asymptotic closed form distribution of the proposed family of tests is presented along with variance estimates constructed under null and alternative hypotheses using nonparametric maximum likelihood estimates of the closed form quantities the described method allows for additional information from individuals with no corresponding matched pair member to be incorporated into the test statistic in sampling scenarios where singletons are not prone to selection bias simulations presented over a range of potential dependence in the paired censored survival data demonstrate substantial power gains associated with taking into account the dependence structure consequences of ignoring the paired nature of the data include overly conservative tests in terms of power and size in fact simulation results using tests for independent samples in the presence of positive correlation consistently undershot both size and power targets that would have been attained in the absence of correlation this additional worrisome effect on operating characteristics highlights the need for accounting for dependence in this popular family of tests

testing goodness of fit of a uniform truncation model several goodness of fit tests of a lifetime distribution have been suggested in the literature many take into account censoring and or truncation of event times in some contexts a goodness of fit test for the truncation distribution is of interest in particular better estimates of the lifetime distribution can be obtained when knowledge of the truncation law is exploited in cross sectional sampling for example there are theoretical justifications for the assumption of a uniform truncation distribution and several studies have used it to improve the efficiency of their survival estimates the duality of lifetime and truncation in the absence of censoring enables methods for testing goodness of fit of the lifetime distribution to be used for testing goodness of fit of the truncation distribution however under random censoring this duality does not hold and different tests are required in this article we introduce several goodness of fit tests for the truncation distribution and investigate their performance in the presence of censored event times using simulation we demonstrate the use of our tests on two data sets

in sample forecasting with local linear survival densities in this paper in sample forecasting is defined as forecasting a structured density to sets where it is unobserved the structured density consists of one dimensional in sample components that identify the density on such sets we focus on the multiplicative density structure which has recently been seen as the underlying structure of non life insurance forecasts in non life insurance the in sample area is defined as one triangle and the forecasting area as the triangle that 20 added to the first triangle produces a square recent approaches estimate two one dimensional components by projecting an unstructured two dimensional density estimator onto the space of multiplicatively separable functions we show that time reversal reduces the problem to two one dimensional problems where the one dimensional data are left truncated and a one dimensional survival density estimator is needed this paper then uses the local linear density smoother with 25 weighted cross validated and do validated bandwidth selectors full asymptotic theory is provided with and without time reversal finite sample studies and an application to non life insurance are included

interval estimation for treatment effects using propensity score matching in causal studies without random assignment of treatment causal effects can be estimated using matched treated and control samples where matches are obtained using estimated propensity scores propensity score matching can reduce bias in treatment effect estimators in cases where the matched samples have overlapping covariate distributions despite its application in many applied problems there is no universally employed approach to interval estimation when using propensity score matching in this article we present and evaluate approaches to interval estimation when using propensity score matching

design of consensus and adaptive consensus filters for distributed parameter systems this work establishes an abstract framework that considers the distributed filtering of spatially varying processes using a sensor network it is assumed that the sensor network consists of groups of sensors each of which provides a number of state measurements from sensing devices that are not necessarily identical and which only transmit their information to their own sensor group a modification to the local spatially distributed filters provides the non adaptive case of spatially distributed consensus filters which penalize the disagreement amongst themselves in a dynamic manner a subsequent modification to this scheme incorporates the adaptation of the consensus gains in the disagreement terms of all local filters both the well posedness of these two consensus spatially distributed filters and the convergence of the associated observation errors to zero in appropriate norms are presented their performance is demonstrated on three different examples of a diffusion partial differential equation with point measurements

estimating a distribution function with truncated data let mathscr p be a finite population with n geq 1 elements for each e in mathscr p let x e and y e be independent positive random variables with unknown distribution functions f and g and suppose that the pairs x e y e are i i d we consider the problem of estimating f g and n when the data consist of those pairs x e y e for which e in mathscr p and y e leq x e the nonparametric maximum likelihood estimators mles of f and g are described and their asymptotic properties as n rightarrow infty are derived it is shown that the mles are consistent against pairs f g for which f and g are continuous g 1 0 leq f 1 0 and g 1 1 leq f 1 1 sqrt n times estimation error for f converges in distribution to a gaussian process if int infty 0 1 g df infty but may fail to converge if this integral is infinite

comparing estimation approaches for the illness death model under left truncation and right censoring left truncated data arise when lifetimes are observed only if they are larger than independent truncation times for example in a cross sectional sampling only individuals who live long enough to be present on the sampling day are observed there are several ways to perform statistical inference under this setting one can do the following i use an unconditional approach ii condition on the value of the truncation variable or iii condition on all the history up to the time of truncation the latter two approaches are equivalent when analyzing univariate survival outcomes but differ under the multi state framework in this paper we consider the illness death model and compare between the three estimation approaches in a parametric regression framework we show that approach ii is more efficient than the standard approach iii although it requires more computational effort approach i is the most efficient approach but it requires knowledge on the distribution of the truncation variable and hence is less robust the methods are compared using a theoretical example and simulations and are applied to intensive care units data collected in a cross sectional design where the illness state corresponds to a bloodstream infection

optimal a priori balance in the design of controlled experiments summary we develop a unified theory of designs for controlled experiments that balance baseline covariates a priori before treatment and before randomization using the framework of minimax variance and a new method called kernel allocation we show that any notion of a priori balance must go hand in hand with a notion of structure since with no structure on the dependence of outcomes on baseline covariates complete randomization no special covariate balance is always minimax optimal restricting the structure of dependence either parametrically or non parametrically gives rise to certain covariate imbalance metrics and optimal designs this recovers many popular imbalance metrics and designs previously developed ad hoc including randomized block designs pairwise matched allocation and rerandomization we develop a new design method called kernel allocation based on the optimal design when structure is expressed by using kernels which can be parametric or non parametric relying on modern optimization methods kernel allocation which ensures nearly perfect covariate balance without biasing estimates under model misspecification offers sizable advantages in precision and power as demonstrated in a range of real and synthetic examples we provide strong theoretical guarantees on variance consistency and rates of convergence and develop special algorithms for design and hypothesis testing

a comparison of several tests for censored paired data this paper reviews several tests for censored paired data and uses monte carlo methods to evaluate their sizes and powers each of the tests maintains its size the akritas test and the paired prentice wilcoxon test are somewhat more powerful than the gehan statistic or the generalized signed rank test for most of the distributions studied if the survival times follow an exponential distribution then the gehan and the generalized signed rank tests are more powerful against a location shift alternative

improving massive experiments with threshold blocking inferences from randomized experiments can be improved by blocking assigning treatment in fixed proportions within groups of similar units however the use of the method is limited by the difficulty in deriving these groups current blocking methods are restricted to special cases or run in exponential time are not sensitive to clustering of data points and are often heuristic providing an unsatisfactory solution in many common instances we present an algorithm that implements a widely applicable class of blocking threshold blocking that solves these problems given a minimum required group size and a distance metric we study the blocking problem of minimizing the maximum distance between any two units within the same group we prove this is a nondeterministic polynomial time hard problem and derive an approximation algorithm that yields a blocking where the maximum distance is guaranteed to be at most four times the optimal value this algorithm runs in o n log n time with o n space complexity this makes it to our knowledge the first blocking method with an ensured level of performance that works in massive experiments whereas many commonly used algorithms form pairs of units our algorithm constructs the groups flexibly for any chosen minimum size this facilitates complex experiments with several treatment arms and clustered data a simulation study demonstrates the efficiency and efficacy of the algorithm tens of millions of units can be blocked using a desktop computer in a few minutes

full matching in an observational study of coaching for the sat among matching techniques for observational studies full matching is in principle the best in the sense that its alignment of comparable treated and control subjects is as good as that of any alternate method and potentially much better this article evaluates the practical performance of full matching for the first time modifying it in order to minimize variance as well as bias and then using it to compare coached and uncoached takers of the sat in this new version with restrictions on the ratio of treated subjects to controls within matched sets full matching makes use of many more observations than does pair matching but achieves far closer matches than does matching with k 2 controls prior to matching the coached and uncoached groups are separated on the propensity score by 1 1 sds full matching reduces this separation to 1 or 2 of an sd in older literature comparing matching and regression cochran expressed doubts that any method of adjustment could substantially reduce observed bias