some aspects of the spline smoothing approach to non parametric regression curve fitting non parametric regression using cubic splines is an attractive flexible and widely applicable approach to curve estimation although the basic idea was formulated many years ago the method is not as widely known or adopted as perhaps it should be the topics and examples discussed in this paper are intended to promote the understanding and extend the practicability of the spline smoothing methodology particular subjects covered include the basic principles of the method the relation with moving average and other smoothing methods the automatic choice of the amount of smoothing and the use of residuals for diagnostic checking and model adaptation the question of providing inference regions for curves and for relevant properties of curves is approached via a finite dimensional bayesian formulation

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

splines in statistics abstract this is a survey article that attempts to synthesize a broad variety of work on splines in statistics splines are presented as a nonparametric function estimating technique after a general introduction to the theory of interpolating and smoothing splines splines are treated in the nonparametric regression setting the method of cross validation for choosing the smoothing parameter is discussed and the general multivariate regression surface estimation problem is addressed an extensive discussion of splines as nonparametric density estimators is followed by a discussion of their role in time series analysis a comparison of the spline and isotonic regression methodologies leads to a formulation of a hybrid estimator the closing section provides a brief overall summary and formulates a number of open unsolved problems relating to splines in statistics

robustness of stochastic discrete time switched linear systems with application to control with shared resources motivated by control applications relying on shared resources such as computation time or bandwidth we analyze the stability and robustness of discrete time switched linear systems with stochastic commutations we show that a wide class of shared resources control strategies can be modeled by a stochastic jump linear system involving two stochastic processes the class of systems we study encompasses markov chains and independent and identically distributed switching processes for these systems we recall existing definitions of stability and robustness by relying on the input to state stability iss property we show that for the class of systems under concern delta moment stability is equivalent to delta moment iss and that they both imply almost sure iss several sufficient conditions are provided to guarantee these properties anytime control design for a translational oscillator rotational actuator tora system is used to illustrate all these concepts

asymptotic behavior of interior point methods a view from semi infinite programming we study the asymptotic behavior of interior point methods for linear programming problems attempts to solve larger problems using interior point methods lead to the question of how these algorithms behave as n the number of variables goes to infinity here we take a different point of view and investigate what happens when n is infinite motivated by this approach we study the limits of search directions potential functions and central paths we also suggest that the complexity of some linear programming problems may depend on the smoothness of the given problem rather than the number of variables we prove that when n is infinite for some subclasses of problems one can still obtain a bound on the number of iterations required in terms of the smoothness of the problem and the desired accuracy

a proportional hazards model for arbitrarily censored and truncated data turnbull 1976 journal of royal statistical society series b 38 290 295 proposed a method for nonparametric estimation of the distribution function when the data are incomplete because of censoring and truncation however as noted by frydman 1994 journal of royal statistical society series b 56 71 74 turnbull s method has to be modified to accommodate both truncation and censoring this paper presents a detailed correction of turnbull s method and an extension to the regression analysis a method of fitting the proportional hazards model for arbitrarily censored and truncated data is developed the method allows partial testing for zero regression coefficients the test can be performed using the likelihood ratio test or the wald test the methodology is applied to estimate the distribution of the induction time of patients diagnosed with transfusion associated aids and to estimate the distribution of time from diabetes onset to development of diabetic nephropathy for insulin dependent diabetics

self controlled case series method with smooth age effect the self controlled case series method commonly used to investigate potential associations between vaccines and adverse events requires information on cases only and automatically controls all age independent multiplicative confounders while allowing for an age dependent baseline incidence in the parametric version of the method we modelled the age specific relative incidence by using a piecewise constant function whereas in the semiparametric version we left it unspecified however mis specification of age groups in the parametric version can lead to biassed estimates of exposure effect and the semiparametric approach runs into computational problems when the number of cases in the study is moderately large we thus propose to use a penalized likelihood approach where the age effect is modelled using splines we use a linear combination of cubic m splines to approximate the age specific relative incidence and integrated splines for the cumulative relative incidence we conducted a simulation study to evaluate the performance of the new approach and its efficiency relative to the parametric and semiparametric approaches results show that the new approach performs equivalently to the existing methods when the sample size is small and works well for large data sets we applied the new spline based approach to data on febrile convulsions and paediatric vaccines copyright 2013 john wiley sons ltd

implementation of an inexact approach to solving linear semi infinite programming problems abstract in this paper we implement an extended version of the inexact approach proposed by fang and wu 1994 for solving linear semi infinite programming problems some interesting numerical results are reported the results confirm that the inexact approach is indeed more efficient and more robust than the exact approach

an implementation of karmarkar s algorithm for linear programming this paper describes the implementation of power series dual affine scaling variants of karmarkar s algorithm for linear programming based on a continuous version of karmarkar s algorithm two variants resulting from first and second order approximations of the continuous trajectory are implemented and tested linear programs are expressed in an inequality form which allows for the inexact computation of the algorithm s direction of improvement resulting in a significant computational advantage implementation issues particular to this family of algorithms such as treatment of dense columns are discussed the code is tested on several standard linear programming problems and compares favorably with the simplex codeminos 4 0

semi parametric latent process model for longitudinal ordinal data application to cognitive decline ordinal and quantitative discrete data are frequent in biomedical and neuropsychological studies we propose a semi parametric model for the analysis of the change over time of such data in longitudinal studies a threshold model is defined where the outcome value depends on the current value of an underlying gaussian latent process the latent process model is a gaussian linear mixed model with a non parametric function of time f t to model the expected change over time this model includes random effects and a stochastic error process to flexibly handle correlation between repeated measures the function f t and all the model parameters are estimated by penalized likelihood using a cubic spline approximation for f t the smoothing parameter is estimated by an approximate cross validation criterion confidence bands may be computed for the estimated curves for the latent process and using a monte carlo approach for the outcome in its natural scale the method is applied to the paquid cohort data to compare the time course over 14 years of two cognitive scores in a sample of 350 future alzheimer patients and in a matched sample of healthy subjects

penalized likelihood approach to estimate a smooth mean curve on longitudinal data this paper aims to propose a penalized likelihood approach to estimate a smooth mean curve for the evolution with time of a gaussian variable taking into account the correlation structure of longitudinal data the model is an extension of the mixed effects linear model including an unspecified function of time f t the estimator f t is defined as the solution of the maximization of the penalized likelihood and is approximated on a basis of cubic m spline with a reduced number of knots we present modifications of four criteria cross validation generalized cross validation t of rice akaike s criterion to estimate the smoothing parameter when data are correlated these four criteria gave very similar results in the simulation study the simulation study showed also the superiority of the bayesian confidence bands of the mean curve over the frequentist ones we develop empirical bayes estimates of subject specific deviations this approach was applied to study the progression of cd4 lymphocyte counts in a cohort of hiv patients treated with protease inhibitors copyright 2002 john wiley sons ltd

penalized likelihood estimation of hazard and intensity functions summary a non parametric estimate is proposed for the hazard function using penalized likelihood methods the estimate turns out to be a hyperbolic spline function which is continuous with its first derivative discontinuous only at a finite number of points it always assumes positive values unlike anderson and senthilselvan s 1980 quadratic spline estimate this method is modified for the estimation of the intensity function of a nonstationary poisson process an example is given for comparison of the new estimator with the estimator of anderson and senthilselvan 1980

affine scaling for linear programs with free variables the affine scaling modification of karmarkar s algorithm is extended to solve problems with free variables this extended primal algorithm is used to prove two important results first the geometrically elegant feasibility algorithm proposed by chandru and kochar is the same algorithm as the one obtained by appending a single column of residuals to the constraint matrix second the dual algorithm as first described by adler et al is the same as the extended primal algorithm applied to the dual

a penalized likelihood approach for arbitrarily censored and truncated data application to age specific incidence of dementia the cos model is the model of choice when analyzing survival data presenting only right censoring and left truncation there is a need for methods that can accommodate more complex observation schemes involving general censoring and truncation in addition it is important in many epidemiological applications to have a smooth estimate of the hazard function we show that the penalized likelihood approach gives a solution to these problems the solution of the maximum of the penalized likelihood is approximated on a basis of splines the smoothing parameter is estimated using approximate cross validation confidence bands can be given a simulation study shows that this approach gives better results than the smoothed nelson aalen estimator we apply this method to the analysis of data from a large cohort study on cerebral aging the age specific incidence of dementia is estimated and risk factors of dementia studied

investigating trial and treatment heterogeneity in an individual patient data meta analysis of survival data by means of the penalized maximum likelihood approach in a meta analysis combining survival data from different clinical trials an important issue is the possible heterogeneity between trials such intertrial variation can not only be explained by heterogeneity of treatment effects across trials but also by heterogeneity of their baseline risk in addition one might examine the relationship between magnitude of the treatment effect and the underlying risk of the patients in the different trials such a scenario can be accounted for by using additive random effects in the cox model with a random trial effect and a random treatment by trial interaction we propose to use this kind of model with a general correlation structure for the random effects and to estimate parameters and hazard function using a semi parametric penalized marginal likelihood method maximum penalized likelihood estimators this approach gives smoothed estimates of the hazard function which represents incidence in epidemiology the idea for the approach in this paper comes from the study of heterogeneity in a large meta analysis of randomized trials in patients with head and neck cancers meta analysis of chemotherapy in head and neck cancers and the effect of adding chemotherapy to locoregional treatment the simulation study and the application demonstrate that the proposed approach yields satisfactory results and they illustrate the need to use a flexible variance covariance structure for the random effects

bayesian confidence intervals for the cross validated smoothing spline summary we consider the model y t g ti ei i 17 2 n where g t t 0 1 is a smooth function and the ei are independent n 0 a2 errors with g2 unknown the cross validated smoothing spline can be used to estimate g non parametrically from

affine scaling trajectories associated with a semi infinite linear program semi infinite linear programs often arise as the limit of a sequence of approximating linear programs hence studying the behavior of extensions of linear programming algorithms to semi infinite problems can yield valuable insight into the behavior of the underlying linear programming algorithm when the number of constraints or the number of variables is very large in this paper we study the behavior of the affine scaling algorithm on a particular semi infinite linear programming problem we show that the continuous trajectories converge to the optimal solution but that for any strictly positive step there are starting points for which the discrete algorithm converges to nonoptimal boundary points

a penalized likelihood approach for a progressive three state model with censored and truncated data application to aids summary we consider the estimation of the intensity and survival functions for a continuous time progressive three state semi markov model with intermittently observed data the estimator of the intensity function is defined nonparametrically as the maximum of a penalized likelihood we thus obtain smooth estimates of the intensity and survival functions this approach can accommodate complex observation schemes such as truncation and interval censoring the method is illustrated with a study of hemophiliacs infected by hiv the intensity functions and the cumulative distribution functions for the time to infection and for the time to aids are estimated covariates can easily be incorporated into the model

nonparametric analysis of truncated survival data with application to aids summary one source of data for the induction distribution of aids arises from persons infected by the aids virus from contaminated blood transfusions analyses of these data are complicated because the number of individuals infected by transfusion is unknown information is available only for those who are infected and develop aids within a certain chronologic time interval the statistical problem is one of making inferences about a stochastic process of infection and disease for which realizations are right truncated in chronologic time by considering the process in reverse time we transform the problem to one of analysing survival data that are left truncated in internal time we develop nonparametric methods for estimating and comparing the identifiable aspects of the induction distributions of several groups an important feature of the natural history and population dynamics of aids is the induction period between infection with the aids virus and the onset of clinical aids this time is sometimes referred to as the latency period or incubation period follow up studies of individuals at risk of being infected will provide direct observations from the induction distribution but most of these studies will not be completed for several years one alternative source of information arises from persons infected with the aids virus from a contaminated blood transfusion of persons infected in this way only those who develop aids by a certain date can be identified the total number who are infected is not known a similar sampling distribution arises in the study of pediatric aids children who contract aids as a result of being infected in utero or at birth can be identified but the total number infected in this way is unknown the statistical problem is one of making inferences about a stochastic process of infection and subsequent disease in which realizations are right truncated in chronologic time by considering the process in reverse time the problem can be transformed to one of survival data that are left truncated in internal time we use this relationship to develop nonparametric methods for estimating and comparing the identifiable aspects of the induction distributions for

on affine scaling and semi infinite programming we consider an extension of the affine scaling algorithm for linear programming problems with free variables to problems having infinitely many constraints and explore the relationship between this algorithm and the finite affine scaling method applied to a discretization of the problem

semiparametric regression splines in matched case control studies nous developpons des methodes semi parametriques pour des etudes cas temoin apparies en utilisant les splines de regression trois methodes sont developpees un schema approximatif de validation croisee pour estimer le parametre de lissage inherent aux splines de regression et egalement des methodes monte carlo de type em mcem et bayesienne pour ajuster le modele de spline de regression nous comparons l approche approximative de validation croisee les approches mcem et bayesienne par simulation et nous montrons qu elles apparaissent approximativement de meme efficacite la methode approximative par validation croisee semblant la plus interessante sur le plan des calculs un exemple d epidemiologie equine ayant motive ce travail est utilise pour expliciter nos approches

nested frailty models using maximum penalized likelihood estimation the frailty model is a random effect survival model which allows for unobserved heterogeneity or for statistical dependence between observed survival data the nested frailty model accounts for the hierarchical clustering of the data by including two nested random effects nested frailty models are particularly appropriate when data are clustered at several hierarchical levels naturally or by design in such cases it is important to estimate the parameters of interest as accurately as possible by taking into account the hierarchical structure of the data we present a maximum penalized likelihood estimation mpnle to estimate non parametrically a continuous hazard function in a nested gamma frailty model with right censored and left truncated data the estimators for the regression coefficients and the variance components of the random effects are obtained simultaneously the simulation study demonstrates that this semi parametric approach yields satisfactory results in this complex setting in order to illustrate the mpnle method and the nested frailty model we present two applications one is for modelling the effect of particulate air pollution on mortality in different areas with two levels of geographical regrouping the other application is based on recurrent infection times of patients from different hospitals we illustrate that using a shared frailty model instead of a nested frailty model with two levels of regrouping leads to inaccurate estimates with an overestimation of the variance of the random effects we show that even when the frailty effects are fairly small in magnitude they are important since they alter the results in a systematic pattern

smooth semiparametric regression analysis for arbitrarily censored time to event data a general framework for regression analysis of time to event data subject to arbitrary patterns of censoring is proposed the approach is relevant when the analyst is willing to assume that distributions governing model components that are ordinarily left unspecified in popular semiparametric regression models such as the baseline hazard function in the proportional hazards model have densities satisfying mild smoothness conditions densities are approximated by a truncated series expansion that for fixed degree of truncation results in a parametric representation which makes likelihood based inference coupled with adaptive choice of the degree of truncation and hence flexibility of the model computationally and conceptually straightforward with data subject to any pattern of censoring the formulation allows popular models such as the proportional hazards proportional odds and accelerated failure time models to be placed in a common framework provides a principled basis for choosing among them and renders useful extensions of the models straightforward the utility and performance of the methods are demonstrated via simulations and by application to data from time to event studies

generalized additive models with interval censored data and time varying covariates application to human immunodeficiency virus infection in hemophiliacs summary we describe a method for extending smooth nonparametric modeling methods to time to event data where the event may be known only to lie within a window of time maximum penalized likelihood is used to fit a discrete proportional hazards model that also models the baseline hazard and left truncation and time varying covariates are accommodated the implementation follows generalized additive modeling conventions allowing both parametric and smooth terms and specifying the amount of smoothness in terms of the effective degrees of freedom we illustrate the method on a well known interval censored data set on time of human immunodeficiency virus infection in a multicenter study of hemophiliacs the ability to examine time varying covariates not available with previous methods allows detection and modeling of nonproportional hazards and use of a time varying covariate that fits the data better and is more plausible than a fixed alternative

nonparametric analysis of dependently interval censored failure time data failure time studies based on observational cohorts often have to deal with irregular intermittent observation of individuals which produces interval censored failure times when the observation times depend on factors related to a person s failure time the failure times may be dependently interval censored inverse intensity of visit weighting methods have been developed for irregularly observed longitudinal or repeated measures data and recently extended to parametric failure time analysis this article develops nonparametric estimation of failure time distributions using weighted generalized estimating equations and monotone smoothing techniques simulations are conducted for examination of the finite sample performance of proposed estimators this research is motivated in part by the toronto psoriatic arthritis cohort study and the proposed methodology is applied to this study