confidence intervals for the generalized roc criterion receiver operating characteristic roc curves are frequently used to assess the usefulness of diagnostic markers when several diagnostic markers are available they can be combined by a best linear combination that is when the area under the roc curve of this combination is maximized among all possible linear combinations this maximal area is the generalized roc criterion which provides a measure of how effective the combination of the markers is this criterion needs to be estimated from the data and is usually evaluated against single markers in the present paper we provide confidence intervals for the generalized roc criterion under the assumption of homogeneous covariance matrices derive an approximation for the heterogeneous covariance matrices case and evaluate the approximation via a simulation study finally we present an illustrative example

estimation of roc curves based on stably distributed biomarkers subject to measurement error and pooling mixtures additive measurement errors and pooling design are objectively two different issues which have been separately and extensively dealt with in the biostatistics literature however these topics usually correspond to problems of reconstructing a summand s distribution of the biomarker by the distribution of the convoluted observations thus we associate the two issues into one stated problem the integrated approach creates an opportunity to investigate new fields e g a subject of pooling errors issues regarding pooled data affected by measurement errors to be specific we consider the stated problem in the context of the receiver operating characteristic roc curves analysis which is the well accepted tool for evaluating the ability of a biomarker to discriminate between two populations the present paper considers a wide family of biospecimen distributions in addition applied assumptions which are related to distribution functions of biomarkers are mainly conditioned by the reconstructing problem we propose and examine maximum likelihood techniques based on the following data a biomarker with measurement error pooled samples and pooled samples with measurement error the obtained methods are illustrated by applications to real data studies

explained variation in survival analysis several measures of explained variation have been suggested for the cox proportional hazards regression model we have categorized these measures into three classes which correspond to three different definitions of multiple r2 of the general linear model in an empirical study we compared the performance of these measures and classified them by their adherence to a set of criteria which we think should be met by a measure of explained variation for survival data we suggest that currently there is no uniformly superior measure particularly as the concepts of either uncensored or censored populations may lead to different choices for uncensored populations a measure by kent and o quigley and the squared rank correlation between survival time and the predictor from a cox regression model appear recommendable choices for the latter censored survival times are terminated using a very recent data augmentation algorithm for multiple imputation under proportional hazards with censored populations schemper s measure v2 could be considered we give an introductory example discuss aspects of application and stress the desirability of routinely evaluating explained variation in studies of survival

a unified approach to nonparametric comparison of receiver operating characteristic curves for longitudinal and clustered data we present a unified approach to nonparametric comparisons of receiver operating characteristic roc curves for a paired design with clustered data treating empirical roc curves as stochastic processes their asymptotic joint distribution is derived in the presence of both between marker and within subject correlations a monte carlo method is developed to approximate their joint distribution without involving nonparametric density estimation the developed theory is applied to derive new inferential procedures for comparing weighted areas under the roc curves confidence bands for the difference function of roc curves confidence intervals for the set of specificities at which one diagnostic test is more sensitive than the other and multiple comparison procedures for comparing more than two diagnostic markers our methods demonstrate satisfactory small sample performance in simulations we illustrate our methods using clustered data from a glaucoma study and repeated measurement data from a startle re

estimating a time dependent concordance index for survival prediction models with covariate dependent censoring given a predictive marker and a time to event response variable the proportion of concordant pairs in a data set is called concordance index a specifically useful marker is the risk predicted by a survival regression model this article extends the existing methodology for applications where the length of the follow up period depends on the predictor variables a class of inverse probability of censoring weighted estimators is discussed in which the estimates rely on a working model for the conditional censoring distribution the estimators are consistent for a truncated concordance index if the working model is correctly specified and if the probability of being uncensored at the truncation time is positive in this framework all kinds of prediction models can be assessed and time trends in the discrimination ability of a model can be captured by varying the truncation time point for illustration we re analyze a study on risk prediction for prostate cancer patients the effects of misspecification of the censoring model are studied in simulated data

controllability of quantum systems with switching control this article focuses on wavefunction controllability of a class of quantum systems with switching control first we present a specific quantum system which is not wavefunction controllable under the action of any one of two controllers with different fixed structures however we prove that the system is wavefunction controllable if the control input is allowed to switch between the two controllers then we present a sufficient condition for wavefunction controllability of a class of quantum systems with switching control and briefly discuss the problem of control design for such quantum control systems finally two illustrative examples are presented to demonstrate a possible control design process for the proposed method

approximate controllability for stochastic evolution inclusions of clarke s subdifferential type in this paper we deal with the approximate controllability of stochastic evolution inclusions of clarke s subdifferential type firstly by using stochastic analysis nonsmooth analysis theory of operator semigroups and fixed point theorems of multivalued maps we show the existence of mild solutions for the stochastic evolution inclusions then we provide a sufficient condition to guarantee the approximate controllability of the stochastic evolution inclusions actually our results cover a broader class of inclusion problems involving time depending operators finally an example is included to illustrate the applicability of the main results

visualizing and assessing discrimination in the logistic regression model logistic regression models are widely used in medicine for predicting patient outcome prognosis and constructing diagnostic tests diagnosis multivariable logistic models yield an approximately continuous risk score a transformation of which gives the estimated event probability for an individual a key aspect of model performance is discrimination that is the model s ability to distinguish between patients who have or will have an event of interest and those who do not or will not graphical aids are important in understanding a logistic model the receiver operating characteristic roc curve is familiar but not necessarily easy to interpret we advocate a simple graphic that provides further insight into discrimination namely a histogram or dot plot of the risk score in the outcome groups the most popular performance measure for the logistic model is the c index numerically equivalent to the area under the roc curve we discuss the comparative merits of the c index and the standardized mean difference in risk score between the outcome groups the latter statistic sometimes known generically as the effect size has been computed in slightly different ways by several different authors including glass cohen and hedges an alternative measure is the overlap between the distributions in the outcome groups defined as the area under the minimum of the two density functions the larger the overlap the weaker the discrimination under certain assumptions about the distribution of the risk score the c index effect size and overlap are functionally related we illustrate the ideas with simulated and real data sets

uniform stability of large scale delay discrete impulsive systems this article investigates the problem of uniform stability for the large scale delay dis discrete impulsive systems by establishing the comparison principle for the general delay dis uniform stability criteria are derived for three kinds linear affine and non linear of large scale delay dis the obtained criteria shows that the stability properties of non linear large scale delay dis can be derived by comparing to a linear and lower dimension delay dis with known stability properties some examples are given to illustrate results obtained by us

roc curve analysis for biomarkers based on pooled assessments interleukin 6 is a biomarker of inflammation which has been suggested as having potential discriminatory ability for myocardial infarction because of its high assaying cost it is very expensive to evaluate this marker in order to reduce this cost we propose pooling the specimens in this paper we examine the efficiency of roc curve analysis specifically the estimation of the area under the roc curve when dealing with pooled data we study the effect of pooling when there are only a fixed number of individuals available for testing and pooling is carried out to save on the number of assays alternatively we examine how many pooled assays of size g are necessary to provide essentially the same information as n individual assays we measure loss of information by means of the change in root mean square error of the estimate of the area under the roc curve and study the extent of this loss via a simulation study

comparison of quantitative diagnostic tests type i error power and sample size for a quantitative laboratory test the 0 975 fractile of the distribution of reference values is commonly used as a discrimination limit and the sensitivity of the test is the proportion of diseased subjects with values exceeding this limit a comparison of the estimates of sensitivity between two tests without taking into account the sampling variation of the discrimination limits can increase the type i error to about seven times the nominal value of 0 05 correct statistical procedures are considered and the power and required sample size are studied for gaussian and log gaussian distributions of diagnostic test values the results may be useful for the planning phase of studies to evaluate quantitative diagnostic tests

nonparametric and semiparametric group sequential methods for comparing accuracy of diagnostic tests summary comparison of the accuracy of two diagnostic tests using the receiver operating characteristic roc curves from two diagnostic tests has been typically conducted using fixed sample designs on the other hand the human experimentation inherent in a comparison of diagnostic modalities argues for periodic monitoring of the accruing data to address many issues related to the ethics and efficiency of the medical study to date very little research has been done on the use of sequential sampling plans for comparative roc studies even when these studies may use expensive and unsafe diagnostic procedures in this article we propose a nonparametric group sequential design plan the nonparametric sequential method adapts a nonparametric family of weighted area under the roc curve statistics wieand et al 1989 biometrika 76 585 592 and a group sequential sampling plan we illustrate the implementation of this nonparametric approach for sequentially comparing roc curves in the context of diagnostic screening for nonsmall cell lung cancer we also describe a semiparametric sequential method based on proportional hazard models we compare the statistical properties of the nonparametric approach with alternative semiparametric and parametric analyses in simulation studies the results show the nonparametric approach is robust to model misspecification and has excellent finite sample performance

assessment of diagnostic markers by goodness of fit tests receiver operating characteristic roc curves are useful statistical tools used to assess the precision of diagnostic markers or to compare new diagnostic markers with old ones the most common index employed for these purposes is the area under the roc curve theta and several statistical tests exist that test the null hypotheses h 0 theta 0 5 or h 0 theta1 theta2 in the case of two marker comparisons against alternatives of interest in this paper we show that goodness of fit of uniformity of the distribution of the false positive true positive rates can be used instead of tests based on the area index a semi parametric approach is based on a completely specified distribution of marker measurements for either the healthy f or diseased g subjects and this is extended to the two marker case we then extend to the one and two marker case when neither distribution is specified the non parametric case in general roc based tests are more powerful than goodness of fit tests for location differences between the distributions of healthy and diseased subjects however roc based tests are less powerful when location scale differences exist producing roc curves that cross the diagonal and are incapable of discriminating between healthy and diseased samples when theta 0 5 but f not equal g in these cases goodness of fit tests have a distinct advantage over roc based tests in conclusion roc methodology should be used with recognition of its potential limitations and should be replaced by goodness of fit tests when appropriate the latter are a viable alternative and can be used as a black box or as an exploratory first step in the evaluation of novel diagnostic markers

on controllability of linear stochastic systems we discuss several concepts of controllability for partially observable stochastic systems complete controllability approximate controllability controllability and s controllability and show that complete and approximate controllability notions are equivalent and in turn are equivalent to the controllability for linear stochastic systems controlled by gaussian processes we derive necessary and sufficient conditions for these concepts of controllability these criteria reduce to the well known rank condition

biorthogonal spline type wavelets let f be an orthonormal scaling function with approximation degree p 1 and let b nbe the b spline of order n then spline type scaling functions defined by n b n n 1 2 possess higher approximation order p n 1 and compact support the corresponding biorthogonal wavelet functions are also constructed this technique is extended to the case of biorthogonal scaling function system as an application of the method supplied in this paper one can easily construct a sequence of pairs of biorthogonal spline type scaling functions from one pair of biorthogonal scaling functions or an orthonormal scaling function in particular if both the method and the lifting scheme of sweldens see 1 are applied then all pairs of biorthogonal spline type scaling functions shown in references 2 and 3 can be constructed from the haar scaling function

distributed h state estimation with stochastic parameters and nonlinearities through sensor networks the finite horizon case this paper deals with the distributed h state estimation problem for a class of discrete time varying nonlinear systems with both stochastic parameters and stochastic nonlinearities the system measurements are collected through sensor networks with sensors distributed according to a given topology the purpose of the addressed problem is to design a set of time varying estimators such that the average estimation performance of the networked sensors is guaranteed over a given finite horizon through available output measurements from not only the individual sensor but also its neighboring sensors a necessary and sufficient condition is established to achieve the h performance constraint and then the estimator design scheme is proposed via a certain h 2 type criterion the desired estimator parameters can be obtained by solving coupled backward recursive riccati difference equations rdes a numerical simulation example is provided to demonstrate the effectiveness and applicability of the proposed estimator design approach

bayesian bootstrap estimation of roc curve receiver operating characteristic roc curve is widely applied in measuring discriminatory ability of diagnostic or prognostic tests this makes the roc analysis one of the most active research areas in medical statistics many parametric and semiparametric estimation methods have been proposed for estimating the roc curve and its functionals in this paper we propose the bayesian bootstrap bb a fully nonparametric estimation method for the roc curve and its functionals such as the area under the curve auc the bb method offers a bandwidth free smoothing approach to the empirical estimate and gives credible bounds the accuracy of the estimate of the roc curve in the simulation studies is examined by the integrated absolute error in comparison with other existing curve estimation methods the bb method performs well in terms of accuracy robustness and simplicity we also propose a procedure based on the bb approach to test the binormality assumption

approximate controllability of semilinear deterministic and stochastic evolution equations in abstract spaces various sufficient conditions for approximate controllability of linear evolution systems in abstract spaces have been obtained but approximate controllability of semilinear control systems usually requires some complicated and limited assumptions in this paper we show the approximate controllability of the abstract semilinear deterministic and stochastic control systems under the natural assumption that the associated linear control system is approximately controllable the results are obtained using new properties of symmetric operators which are proved in this paper compact semigroups the schauder fixed point theorem and or the contraction mapping principle

estimating regression parameters using linear rank tests for censored data a class of estimates for regression parameters in a linear model with right censored data is proposed these estimates are derived by using linear rank tests for right censored data as estimating equations they are shown to be consistent and asymptotically normal with covariance matrix for which estimates are proposed efficient estimates within this class are derived together with conditions when they are fully efficient 0 introduction the problem of estimating regression coefficients using ranks has received much attention in the literature for uncensored data and the results are summarized very nicely in hettmansperger 1984 there has also been some work with censored data for the two sample problem specifically louis 1981 considered estimation of a scale change between two distributions with the use of a log rank test whereas wei and gail 1983 generalize to other linear rank tests as well we shall consider the general problem of multiple linear regression and show how linear rank tests can be used as estimating equations the resulting linear rank estimates will be shown to be asymptotically normal with variances that can be estimated consistently we shall also look at the efficiency of these estimates under various situations

approximate controllability of stochastic impulsive functional systems with infinite delay this paper studies the approximate controllability of stochastic impulsive functional system with infinite delay in abstract space by using the contraction mapping principle some sufficient conditions are given with no compactness condition imposed on the semigroup generated by the linear part of the system then with the help of the nussbaum fixed point theorem the restriction of the combination of system parameters is dropped finally an example is shown to illustrate our results

overall c as a measure of discrimination in survival analysis model specific population value and confidence interval estimation the assessment of the discrimination ability of a survival analysis model is a problem of considerable theoretical interest and important practical applications this issue is however more complex than evaluating the performance of a linear or logistic regression several different measures have been proposed in the biostatistical literature in this paper we investigate the properties of the overall c index introduced by harrell as a natural extension of the roc curve area to survival analysis we develop the overall c index as a parameter describing the performance of a given model applied to the population under consideration and discuss the statistic used as its sample estimate we discover a relationship between the overall c and the modified kendall s tau and construct a confidence interval for our measure based on the asymptotic normality of its estimate then we investigate via simulations the length and coverage probability of this interval finally we present a real life example evaluating the performance of a framingham heart study model

approximate controllability of nonlinear stochastic impulsive systems with control acting on the nonlinear terms this paper is concerned with the approximate controllability of the stochastic impulsive system with control acting on the nonlinear terms in the case that the nonlinear terms are dependent on the control the control cannot be expressed explicitly and analysed in this situation we generate the control sequence by the approximate equations and give the properties of the control sequence and the driven solution sets some discussions on the assumptions are given to impose on the system the hausdorff measure is adopted to relax the requirement of the compactness condition it is also shown that under some sufficient conditions the stochastic impulsive system is approximately controllable without the requirement of the controllability of the associated linear system the results of this paper can be degraded into special cases and coincide with some existing ones

advances in statistical methodology for the evaluation of diagnostic and laboratory tests the roc plot is a useful tool in the evaluation of the performance of medical tests for separating two populations for a two state decision rule based on such a test the roc plot is the graph of all observed 1 specificity sensitivity pairs each point on this empirical plot can be represented by a 2 x 2 contingency table the non parametric statistics of mann whitney and kolmogorov smirnov can be immediately identified on this plot local non parametric confidence interval procedures related to the theoretical roc curve are briefly reviewed for continuous data two new simultaneous confidence regions associated with the roc curve are presented one based on kolmogorov smirnov confidence bands for distribution functions and the other based on bootstrapping two different tests on the same patients can be compared on the roc scale for continuous data one important problem concerns the comparison of two roc plots as would arise from two correlated diagnostic tests on each patient using a sup norm this metric can detect differences that the roc area cannot the distribution of a statistic based on this norm is studied using the bootstrap a biomedical example illustrates the methodologies

statistical inference for pr y x the normal case this article examines statistical inference for pr y x where x and y are independent normal variates with unknown means and variances the case of unequal variances is stressed x can be interpreted as the strength of a component subjected to a stress y and pr y x is the component s reliability two approximate methods for obtaining confidence intervals and an approximate bayesian probability interval are obtained the actual coverage probabilities of these intervals are examined by simulation

a unified bayesian semiparametric approach to assess discrimination ability in survival analysis the discriminatory ability of a marker for censored survival data is routinely assessed by the time dependent roc curve and the c index the time dependent roc curve evaluates the ability of a biomarker to predict whether a patient lives past a particular time t the c index measures the global concordance of the marker and the survival time regardless of the time point we propose a bayesian semiparametric approach to estimate these two measures the proposed estimators are based on the conditional distribution of the survival time given the biomarker and the empirical biomarker distribution the conditional distribution is estimated by a linear dependent dirichlet process mixture model the resulting roc curve is smooth as it is estimated by a mixture of parametric functions the proposed c index estimator is shown to be more efficient than the commonly used harrell s c index since it uses all pairs of data rather than only informative pairs the proposed estimators are evaluated through simulations and illustrated using a lung cancer dataset

comparing the areas under two or more correlated receiver operating characteristic curves a nonparametric approach methods of evaluating and comparing the performance of diagnostic tests are of increasing importance as new tests are developed and marketed when a test is based on an observed variable that lies on a continuous or graded scale an assessment of the overall value of the test can be made through the use of a receiver operating characteristic roc curve the curve is constructed by varying the cutpoint used to determine which values of the observed variable will be considered abnormal and then plotting the resulting sensitivities against the corresponding false positive rates when two or more empirical curves are constructed based on tests performed on the same individuals statistical analysis on differences between curves must take into account the correlated nature of the data this paper presents a nonparametric approach to the analysis of areas under correlated roc curves by using the theory on generalized u statistics to generate an estimated covariance matrix

semiparametric estimation of an accelerated failure time model with time dependent covariates summary a class of semiparametric accelerated failure time models is introduced that are useful for modelling the relationship of survival distributions to time dependent covariates a class of semiparametric rank estimators is derived for the parameters in this model when the survival data are right censored these estimates are shown to be consistent and asymptotically normal with variances that can be consistently estimated it is also shown that estimators within this class achieve the semiparametric efficiency bound we consider an accelerated failure time model for time to event data in which the survival distribution is scaled by a factor which may be a function of time dependent covariates these models directly model the effect of covariates on the length of survival this is in contrast to the more commonly used proportional hazards model which models the hazard rate itself in some applications it may be easier to visualize the concept that a treatment intervention or exposure to an environmental contaminant increases or decreases the length of survival by a certain proportion as compared to the concept that the hazard rate is changed for time independent covariates say z z1 zp the class of accelerated failure time models assumes that the survival distribution at time t given a set of covariates z z is given by f t i z f0 h z t the proportionality constant h z can be interpreted as the scale factor by which lifetime is decreased as a function of the covariates z often h z is taken to be log linear or h z exp b z in such cases if z 0 we can interpret fo t as the baseline survival distribution or the survival distribution for individuals with covariates all equal to zero a useful way of envisioning this model is to consider a hypothetical random variable u that corresponds to an individual s survival time if that individual had covariate values all equal to zero this baseline failure time u would be modified for values of the covariate different than zero for example if we denote the actual survival time by t then for an individual with covariate value z we have t e zu the parameters b in this model have a direct interpretation in terms of the increase or decrease in lifespan as a function of the covariates the assumption that u is independent of z in this hypothetical construct induces the probabilistic model

measures of explained variation for survival data the predictive power of a set of prognostic variables in a survival time model is a concept distinct from the statistical significance of the variables or the adequacy of the model fit in this paper we discuss the importance of quantifying the predictive power of a prognostic model and suggest measures of explained variation as a possible quantification the important features of our approach are that 1 the measures are completely model based 2 a specification of the time range of interest is easily incorporated and 3 the null models used for comparison are derived as mixtures of the predicted distributions

optimal linear combinations of multiple diagnostic biomarkers based on youden index in practice usually multiple biomarkers are measured on the same subject for disease diagnosis combining these biomarkers into a single score could improve diagnostic accuracy many researchers have addressed the problem of finding the optimal linear combination based on maximizing the area under roc curve auc actually such combined score might have less than optimal property at the diagnostic threshold in this paper we propose the idea of using youden index as an objective function for searching the optimal linear combination the combined score directly achieves the maximum overall correct classification rate at the diagnostic threshold corresponding to youden index in other words it is the optimal linear combination score for making the disease diagnosis we present both empirical and numerical searching methods for the optimal linear combination we carry out extensive simulation study to investigate the performance of the proposed methods additionally we empirically compare the optimal overall classification rates between the proposed combination based on youden index and the traditional one based on auc and demonstrate a significant gain in diagnostic accuracy for the proposed combination in the end we apply the proposed methods to a real data set

analysis on binary responses with ordered covariates and missing data summary we consider the situation of two ordered categorical variables and a binary outcome variable where one or both of the categorical variables may have missing values the goal is to estimate the probability of response of the outcome variable for each cell of the contingency table of categorical variables while incorporating the fact that the categorical variables are ordered the probability of response is assumed to change monotonically as each of the categorical variables changes level a probability model is used in which the response is binomial with parameters pij for each cell i j and the number of observations in each cell is multinomial estimation approaches that incorporate gibbs sampling with order restrictions on pij induced via a prior distribution two dimensional isotonic regression and multiple imputation to handle missing values are considered the methods are compared in a simulation study using a fully bayesian approach with a strong prior distribution to induce ordering can lead to large gains in efficiency but can also induce bias utilizing isotonic regression can lead to modest gains in efficiency while minimizing bias and guaranteeing that the order constraints are satisfied a hybrid of isotonic regression and gibbs sampling appears to work well across a variety of scenarios the methods are applied to a pancreatic cancer case control study with two biomarkers copyright q 2007 john wiley sons ltd

addressing issues associated with evaluating prediction models for survival endpoints based on the concordance statistic prediction models for disease risk and prognosis play an important role in biomedical research and evaluating their predictive accuracy in the presence of censored data is of substantial interest the standard concordance c statistic has been extended to provide a summary measure of predictive accuracy for survival models motivated by a prostate cancer study we address several issues associated with evaluating survival prediction models based on c statistic with a focus on estimators using the technique of inverse probability of censoring weighting ipcw compared to the existing work we provide complete results on the asymptotic properties of the ipcw estimators under the assumption of coarsening at random car and propose a sensitivity analysis under the mechanism of noncoarsening at random ncar in addition we extend the ipcw approach as well as the sensitivity analysis to high dimensional settings the predictive accuracy of prediction models for cancer recurrence after prostatectomy is assessed by applying the proposed approaches we find that the estimated predictive accuracy for the models in consideration is sensitive to ncar assumption and thus identify the best predictive model finally we further evaluate the performance of the proposed methods in both settings of low dimensional and high dimensional data under car and ncar through simulations

using logistic regression procedures for estimating receiver operating characteristic curves summary estimation of a receiver operating characteristic roc curve is usually based either on a fully parametric model such as a normal model or on a fully nonparametric model in this paper we explore a semiparametric approach by assuming a density ratio model for disease and disease free densities this model has a natural connection with the logistic regression model the proposed semiparametric approach is more robust than a fully parametric approach and is more efficient than a fully nonparametric approach two real examples demonstrate that the roc curve estimated by our semiparametric method is much smoother than that estimated by the nonparametric method

maximum likelihood ratio tests for comparing the discriminatory ability of biomarkers subject to limit of detection in this article we consider comparing the areas under correlated receiver operating characteristic roc curves of diagnostic biomarkers whose measurements are subject to a limit of detection lod a source of measurement error from instruments sensitivity in epidemiological studies we propose and examine the likelihood ratio tests with operating characteristics that are easily obtained by classical maximum likelihood methodology

an application of harrell s c index to ph frailty models frailty models are encountered in many medical applications yet little research has been devoted to develop measures that quantify the predictive ability of these models in this paper we elaborate on the concept of the concordance probability to clustered data resulting in an overall conditional c index or bfc o c and an overall marginal c index or c o m both overall c indices can be split up into a between conditional or c b c and a between marginal c index or c b m and into a within conditional or c w c and a within marginal c index or c w m for ph frailty models of the power variance family c w c and c w m are equivalent resulting in one within c index c w we propose an application of harrell s c index to estimate the proposed indices within a likelihood and a bayesian context and the performances of their point estimates and confidence credible intervals are compared in an extensive simulation study this simulation study shows that the point estimates of c w and c b m perform good within both a likelihood and bayesian context but that the point estimates of c b c show less bias for the bayesian approach than for the likelihood approach the 95 per cent confidence credible intervals also possess good coverage properties given that the point estimates perform good the performance of the c indices is evaluated on a real data set

measuring the effectiveness of diagnostic markers in the presence of measurement error through the use of roc curves the area under the receiver operating characteristic curve is frequently used to assess the effectiveness of diagnostic markers in distinguishing between diseased and healthy individuals these markers are generally subject to measurement error in this paper confidence intervals for the area under the curve are developed which take measurement error into account these intervals depend on the availability of replicated observations for the subject both equal and unequal numbers of replicates per subject are considered the practice of averaging over replicates and then ignoring measurement error is examined and found wanting

concordance probability and discriminatory power in proportional hazards regression summary the concordance probability is used to evaluate the discriminatory power and the predictive accuracy of nonlinear statistical models we derive an analytical expression for the concordance probability in the cox proportional hazards model the proposed estimator is a function of the regression parameters and the covariate distribution only and does not use the observed event and censoring times for this reason it is asymptotically unbiased unlike harrell s c index based on informative pairs the asymptotic distribution of the concordance probability estimate is derived using u statistic theory and the methodology is applied to a predictive model in lung cancer

mra frame wavelets with certain regularities associated with the refinable generators of shift invariant spaces in this paper we will start the discussion with the refinable generators of the shift invariant si spaces in l2 r that possess the largest possible regularities and required vanishing moments for the pseudo scaling generators the corresponding mra frame wavelets with certain regularities are constructed in addition the stability of the refinable si spaces and the corresponding complementary spaces biorthogonality of the si spaces and the approximation property of the spaces are also discussed

on comparing 2 correlated c indices with censored survival data as new biomarkers and risk prediction procedures are in rapid development it is of great interest to develop valid methods for comparing predictive power of 2 biomarkers or risk score systems harrell c statistic has been routinely used as a global adequacy assessment of a risk score system and the difference of 2 harrell c statistics as a test statistic has been suggested in recent literature for comparison of predictive power of 2 biomarkers for censored outcome in this study we showed that such a test can have severely inflated type i errors as the difference between the 2 harrell c statistics does not converge to zero under the null hypothesis of equal predictive power measured by concordance probabilities as illustrated by 2 counterexamples and corresponding numerical simulations we further investigate a necessary and sufficient condition under which the difference of 2 harrell c statistics converges to zero under the null hypothesis

semiparametric receiver operating characteristic analysis to evaluate biomarkers for disease the receiver operating characteristic roc curve is a popular method for characterizing the accuracy of diagnostic tests when test results are not binary various methodologies for estimating and comparing roc curves have been developed one approach due to pepe uses a parametric regression model rocx u g h0 u 0x with the baseline function h0 u specified up to a finite dimensional parameter in this article we extend the regression models by allowing arbitrary nonparametric baseline functions we also provide asymptotic distribution theory and procedures for making statistical inference we illustrate our approach with dataset from a prostate cancer biomarker study simulation studies suggest that the extra flexibility inherent in the semiparametric method is gained with little loss in statistical efficiency

a measure of explained variation for event history data there is no shortage of proposed measures of prognostic value of survival models in the statistical literature they come under different names including explained variation correlation explained randomness and information gain but their goal is common to define something analogous to the coefficient of determination r 2 in linear regression none however have been uniformly accepted none have been extended to general event history data including recurrent events and many cannot incorporate time varying effects or covariates we present here a measure specifically tailored for use with general dynamic event history regression models the measure is applicable and interpretable in discrete or continuous time with tied data or otherwise with time varying time fixed or dynamic covariates with time varying or time constant effects with single or multiple event times with parametric or semiparametric models and under general independent censoring observation for single event survival data with neither censoring nor time dependency it reduces to the concordance index we give expressions for its population value and the variance of the estimator and explore its use in simulations and applications a web link to r software is provided

a comparison of estimators to evaluate the discriminatory power of time to event models discrimination measures for continuous time to event outcomes have become an important tool in medical decision making the idea behind discrimination measures is to evaluate the performance of a prediction model by measuring its ability to distinguish between observations having an event and those having no event researchers proposed a variety of approaches to estimate discrimination measures from a set of right censored data these approaches rely on different regularity assumptions that are needed to ensure consistency of the respective estimators typical examples of regularity assumptions include the proportional hazards assumption in cox regression and the random censoring assumption because regularity assumptions are often violated in practice conducting a sensitivity analysis of the estimators is of considerable interest the aim of the paper is to analyze and to compare the most popular estimators of discrimination measures for event time outcomes on the basis of the results of an extensive simulation study and the analysis of molecular data we investigate the behavior of the estimators in situations where the underlying regularity assumptions do not hold we show that violations of the regularity assumptions may induce a nonignorable bias and may therefore result in biased medical decision making

validation and updating of predictive logistic regression models a study on sample size and shrinkage a logistic regression model may be used to provide predictions of outcome for individual patients at another centre than where the model was developed when empirical data are available from this centre the validity of predictions can be assessed by comparing observed outcomes and predicted probabilities subsequently the model may be updated to improve predictions for future patients as an example we analysed 30 day mortality after acute myocardial infarction in a large data set gusto i n 40 830 we validated and updated a previously published model from another study timi ii n 3339 in validation samples ranging from small 200 patients 14 deaths to large 10 000 patients 700 deaths updated models were tested on independent patients updating methods included re calibration re estimation of the intercept or slope of the linear predictor and more structural model revisions re estimation of some or all regression coefficients model extension with more predictors we applied heuristic shrinkage approaches in the model revision methods such that regression coefficients were shrunken towards their re calibrated values parsimonious updating methods were found preferable to more extensive model revisions which should only be attempted with relatively large validation samples in combination with shrinkage copyright 2004 john wiley sons ltd

a statistical method for the comparison of a discrete diagnostic test with several continuous diagnostic tests summary in this paper we study a statistic that is suitable for comparing a discrete diagnostic marker to one or more continuous diagnostic markers test procedures and confidence intervals are based on asymptotic normality the statistic is applicable for correlated data in which all the markers are obtained for each subject the statistic was studied for use in comparing two markers for rectal bleeding examples for this application and two more general applications are presented

bayesian multivariate hierarchical transformation models for roc analysis a bayesian multivariate hierarchical transformation model bmhtm is developed for receiver operating characteristic roc curve analysis based on clustered continuous diagnostic outcome data with covariates two special features of this model are that it incorporates non linear monotone transformations of the outcomes and that multiple correlated outcomes may be analysed the mean variance and transformation components are all modelled parametrically enabling a wide range of inferences the general framework is illustrated by focusing on two problems 1 analysis of the diagnostic accuracy of a covariate dependent univariate test outcome requiring a box cox transformation within each cluster to map the test outcomes to a common family of distributions 2 development of an optimal composite diagnostic test using multivariate clustered outcome data in the second problem the composite test is estimated using discriminant function analysis and compared to the test derived from logistic regression analysis where the gold standard is a binary outcome the proposed methodology is illustrated on prostate cancer biopsy data from a multi centre clinical trial

exponential stability for second order neutral stochastic differential equations with impulses in this paper we investigate the problem on the exponential stability of mild solution for the second order neutral stochastic partial differential equations with impulses by utilising the cosine function theory a set of novel sufficient conditions is derived by establishing an impulsive integral inequality as a final point an example is given to illustrate the effectiveness of the obtained theory

testing for improvement in prediction model performance authors have proposed new methodology in recent years for evaluating the improvement in prediction performance gained by adding a new predictor y to a risk model containing a set of baseline predictors x for a binary outcome d we prove theoretically that null hypotheses concerning no improvement in performance are equivalent to the simple null hypothesis that y is not a risk factor when controlling for x h0 p d 1 x y p d 1 x therefore testing for improvement in prediction performance is redundant if y has already been shown to be a risk factor we also investigate properties of tests through simulation studies focusing on the change in the area under the roc curve auc an unexpected finding is that standard testing procedures that do not adjust for variability in estimated regression coefficients are extremely conservative this may explain why the auc is widely considered insensitive to improvements in prediction performance and suggests that the problem of insensitivity has to do with use of invalid procedures for inference rather than with the measure itself to avoid redundant testing and use of potentially problematic methods for inference we recommend that hypothesis testing for no improvement be limited to evaluation of y as a risk factor for which methods are well developed and widely available analyses of measures of prediction performance should focus on estimation rather than on testing for no improvement in performance copyright 2013 john wiley sons ltd

controllability of non linear stochastic systems complete controllability of a semi linear stochastic system assuming controllability of the associated linear sytem is studied it is also shown that a non linear stochastic system is locally null controllable provided that the corrsponding linearized system is controllable

existence of optimal controls for a general class of impulsive systems on banach spaces this paper presents some results on the question of existence of optimal controls for a large class of semilinear impulsive systems in infinite dimensional spaces with admissible controls from the space of vector measures this also includes as a special case the class of purely impulsive controls two physical examples are presented for illustration

a note on bias of measures of explained variation for survival data papers evaluating measures of explained variation or similar indices almost invariably use independence from censoring as the most important criterion and they always end up suggesting that some measures meet this criterion and some do not most of the time leading to a conclusion that the first is better than the second as a consequence users are offered measures that cannot be used with time dependent covariates and effects not to mention extensions to repeated events or multi state models we explain in this paper that the aforementioned criterion is of no use in studying such measures because it simply favors those that make an implicit assumption of a model being valid everywhere measures not making such an assumption are disqualified even though they are better in every other respect we show that if these allegedly inferior measures are allowed to make the same assumption they are easily corrected to satisfy the independent from censoring criterion even better it is enough to make such an assumption only for the times greater than the last observed failure time which in contrast with the preferred measures makes it possible to use all the modeling flexibility up to and assume whatever one wants after as a consequence we claim that some of the measures being preferred as better in the existing reviews are in fact inferior

an interpretation for the roc curve and inference using glm procedures the accuracy of a medical diagnostic test is often summarized in a receiver operating characteristic roc curve this paper puts forth an interpretation for each point on the roc curve as being a conditional probability of a test result from a random diseased subject exceeding that from a random nondiseased subject this interpretation gives rise to new methods for making inference about roc curves it is shown that inference can be achieved with binary regression techniques applied to indicator variables constructed from pairs of test results one component of the pair being from a diseased subject and the other from a nondiseased subject within the generalized linear model glm binary regression framework roc curves can be estimated and we highlight a new semiparametric estimator covariate effects can also be evaluated with the glm models the methodology is applied to a pancreatic cancer dataset where we use the regression framework to compare two different serum biomarkers asymptotic distribution theory is developed to facilitate inference and to provide insight into factors influencing variability of estimated model parameters

joint confidence region estimation for area under roc curve and youden index in the field of diagnostic studies the area under the roc curve auc serves as an overall measure of a biomarker diagnostic test s accuracy youden index defined as the overall correct classification rate minus one at the optimal cut off point is another popular index for continuous biomarkers of binary disease status although researchers mainly evaluate the diagnostic accuracy using auc for the purpose of making diagnosis youden index provides an important and direct measure of the diagnostic accuracy at the optimal threshold and hence should be taken into consideration in addition to auc furthermore auc and youden index are generally correlated in this paper we initiate the idea of evaluating diagnostic accuracy based on auc and youden index simultaneously as the first step toward this direction this paper only focuses on the confidence region estimation of auc and youden index for a single marker we present both parametric and non parametric approaches for estimating joint confidence region of auc and youden index we carry out extensive simulation study to evaluate the performance of the proposed methods in the end we apply the proposed methods to a real data set copyright 2013 john wiley sons ltd

partial controllability of stochastic linear systems the controllability concepts for linear stochastic differential equations driven by different kinds of noise processes can be reduced to the partial controllability concepts for the same systems driven by correlated white noises based on this fact in this article we study the conditions of exact and approximate controllability for linear stochastic control systems under various kinds of noise processes including correlated white noises as well as coloured wide band and shifted white noises it is proved that such systems are never exactly controllable while their approximate controllability is equivalent to the approximate controllability of the associated linear deterministic systems at all past time moments

investigating the effects of ties on measures of concordance the concordance between predicted and observed outcomes referred to as the c index or c statistic is frequently used to quantify the discriminatory ability of a prognostic model it also commonly serves as a basis for distinguishing predictive strength between different models two alternative formulations of the c index are widely used one completely excluding ties from the computation c tied out and the other including ties c tied in however there has been little research concerning the effects of ties on these two measures in this paper we characterize changes in the performance of c tied in and c tied out for progressively less coarse or more coarse partitions of the data our theoretical and simulation results show that both measures can be heavily dependent on the number of tied pairs and their results can be substantially divergent we examine potential ambiguities that can occur when the two measures diverge in the presence of a substantial proportion of tied pairs we recommend that both c indices be computed as lower and upper bounds and that when feasible the c indices should be computed with respect to partitions corresponding to the same percentiles for the models being compared when it is desired to estimate the overall concordance the average value of the two c indices might also be considered we use the data from the hemodialysis clinical trial to illustrate our evaluation and methods

regression modelling strategies for improved prognostic prediction regression models such as the cox proportional hazards model have had increasing use in modelling and estimating the prognosis of patients with a variety of diseases many applications involve a large number of variables to be modelled using a relatively small patient sample problems of overfitting and of identifying important covariates are exacerbated in analysing prognosis because the accuracy of a model is more a function of the number of events than of the sample size we used a general index of predictive discrimination to measure the ability of a model developed on training samples of varying sizes to predict survival in an independent test sample of patients suspected of having coronary artery disease we compared three methods of model fitting 1 standard step up variable selection 2 incomplete principal components regression and 3 cox model regression after developing clinical indices from variable clusters we found regression using principal components to offer superior predictions in the test sample whereas regression using indices offers easily interpretable models nearly as good as the principal components models standard variable selection has a number of deficiencies

on linear combinations of biomarkers to improve diagnostic accuracy we consider combining multiple biomarkers to improve diagnostic accuracy su and liu derived the linear combinations that maximize the area under the receiver operating characteristic roc curves these linear combinations however may have unsatisfactory low sensitivity over a certain range of desired specificity in this paper we consider maximizing sensitivity over a range of specificity we first present a simpler proof for su and liu s main theorem and further investigate some other optimal properties of their linear combinations we then derive alternative linear combinations that have higher sensitivity over a range of high or low specificity the methods are illustrated using data from a study evaluating biomarkers for coronary heart disease

estimating treatment effects in a two arm parallel trial of a continuous outcome for a continuous outcome in a two arm trial that satisfies normal distribution assumptions we can transform the standardized mean difference with the use of the cumulative distribution function to be the effect size measure p x

the effect of random measurement error on receiver operating characteristic roc curves in this paper confidence intervals for the area under the roc curve are adjusted for the presence of measurement error a parametric normal model is assumed the ratio of intra individual to inter individual variance provides a relative measure of the amount of measurement error an exact adjusted confidence interval is developed for the equal variance case and an approximation is derived for the unequal variance case we illustrate using an example the effect of ignoring the measurement error on the confidence interval for the area and show that the effect can be substantial on the decision as to the diagnostic effectiveness of the marker we also examine by means of a simulation study the coverage probability of the unadjusted confidence interval and show that it can be far from its nominal value when measurement error is present

approximate controllability of impulsive differential equations with state dependent delay in order to describe various real world problems in physical and engineering sciences subject to abrupt changes at certain instants during the evolution process impulsive differential equations have been used to describe the system model in this article the problem of approximate controllability for nonlinear impulsive differential equations with state dependent delay is investigated we study the approximate controllability for nonlinear impulsive differential system under the assumption that the corresponding linear control system is approximately controllable using methods of functional analysis and semigroup theory sufficient conditions are formulated and proved finally an example is provided to illustrate the proposed theory

comparing two correlated c indices with right censored survival outcome a one shot nonparametric approach the area under the receiver operating characteristic curve is often used as a summary index of the diagnostic ability in evaluating biomarkers when the clinical outcome truth is binary when the clinical outcome is right censored survival time the c index motivated as an extension of area under the receiver operating characteristic curve has been proposed by harrell as a measure of concordance between a predictive biomarker and the right censored survival outcome in this work we investigate methods for statistical comparison of two diagnostic or predictive systems of which they could either be two biomarkers or two fixed algorithms in terms of their c indices we adopt a u statistics based c estimator that is asymptotically normal and develop a nonparametric analytical approach to estimate the variance of the c estimator and the covariance of two c estimators a z score test is then constructed to compare the two c indices we validate our one shot nonparametric method via simulation studies in terms of the type i error rate and power we also compare our one shot method with resampling methods including the jackknife and the bootstrap simulation results show that the proposed one shot method provides almost unbiased variance estimations and has satisfactory type i error control and power finally we illustrate the use of the proposed method with an example from the framingham heart study

brief paper complete controllability of impulsive stochastic integro differential systems this paper is concerned with the controllability of impulsive stochastic integro differential systems sufficient conditions of complete controllability for impulsive stochastic integro differential systems are obtained by using schaefer s fixed point theorem a numerical example is provided to show the effectiveness of the proposed results

predictive accuracy and explained variation in cox regression summary we suggest a new measure of the proportion of the variation of possibly censored survival times explained by a given proportional hazards model the proposed measure termed v shares several favorable properties with an earlier v1 but also improves the handling of censoring the statistic contrasts distance measures between individual 1 0 survival processes and fitted survival curves with and without covariate information these distance measures dx and d respectively are themselves informative as summaries of absolute rather than relative predictive accuracy we recommend graphical comparisons of survival curves for prognostic index groups to improve the understanding of obtained values for v dx and d their use and interpretation is exemplified for a yorkshire lung cancer study on survival from this and an overview for several well known clinical data sets we show that the likely amount of relative or absolute predictive accuracy is often low even if there are highly significant and relatively strong prognostic factors

boundary type quadrature and boundary element method in this paper we apply a boundary type quadrature technique to derive a type of boundary element scheme which is used to solve the boundary value problems of partial differential equations numerical examples for solving the exterior boundary value problem of helmholtz equation by using the spline approximation and the spline wavelet approximation are given

brief paper a notion of possible controllability for uncertain linear systems with structured uncertainty this paper introduces a notion of possible controllability for a class of uncertain linear systems with structured uncertainty described by averaged integral quadratic constraints this notion relates to the question of when a state is controllable for some possible value of the uncertainty the notion of possible controllability is motivated by a desire to extend the theory of minimal realization for linear time invariant systems to the case of uncertain systems with structured uncertainty

a family of nonparametric statistics for comparing diagnostic markers with paired or unpaired data summary in this paper we study a broad class of nonparametric statistics for comparing two diagnostic markers one can compare the sensitivities of these diagnostic markers over restricted ranges of specificity by selecting an appropriate statistic from this class as special cases one can compare the entire area under the receiver operator curve hanley mcneil 1982 or one can compare the sensitivities at a fixed common specificity usually we would recommend a comparison based on an average of sensitivities over a restricted high level of specificities test procedures and confidence intervals are based on asymptotic normality these procedures are applicable for paired data in which both diagnostic markers are performed on each subject and for unpaired data the procedures may be used to compare two real functions of multiple diagnostic markers as well as to compare individual markers

learning transformation models for ranking and survival analysis this paper studies the task of learning transformation models for ranking problems ordinal regression and survival analysis the present contribution describes a machine learning approach termed minlip the key insight is to relate ranking criteria as the area under the curve to monotone transformation functions consequently the notion of a lipschitz smoothness constant is found to be useful for complexity control for learning transformation models much in a similar vein as the margin is for support vector machines for classification the use of this model structure in the context of high dimensional data as well as for estimating non linear and additive models based on primal dual kernel machines and for sparse models is indicated given n observations the present method solves a quadratic program existing of o n constraints and o n unknowns where most existing risk minimization approaches to ranking problems typically result in algorithms with o n2 constraints or unknowns we specify the minlip method for three different cases the first one concerns the preference learning problem secondly it is specified how to adapt the method to ordinal regression with a finite set of ordered outcomes finally it is shown how the method can be used in the context of survival analysis where one models failure times typically subject to censoring the current approach is found to be particularly useful in this context as it can handle in contrast with the standard statistical model for analyzing survival data all types of censoring in a straightforward way and because of the explicit relation with the proportional hazard and accelerated failure time models the advantage of the current method is illustrated on different benchmark data sets as well as for estimating a model for cancer survival based on different micro array and clinical data sets

bootstrap confidence intervals for the sensitivity of a quantitative diagnostic test we examine bootstrap approaches to the analysis of the sensitivity of quantitative diagnostic test data methods exist for inference concerning the sensitivity of one or more tests for fixed levels of specificity taking into account the variability in the sensitivity due to variability in the test values for normal subjects however parametric methods do not adequately account for error particularly when the data are non normally distributed and non parametric methods have low power we implement bootstrap methods for confidence limits for the sensitivity of a test for a fixed specificity and demonstrate that under certain circumstances the bootstrap method gives more accurate confidence intervals than do other methods while it performs at least as well as other methods in many standard situations

a non inferiority test for diagnostic accuracy based on the paired partial areas under roc curves non inferiority is a reasonable approach to assessing the diagnostic accuracy of a new diagnostic test if it provides an easier administration or reduces the cost the area under the receiver operating characteristic roc curve is one of the common measures for the overall diagnostic accuracy however it may not differentiate the various shapes of the roc curves with different diagnostic significances the partial area under the roc curve pauroc may present an alternative that can provide additional and complimentary information for some diagnostic tests which require false positive rate that does not exceed a certain level non parametric and maximum likelihood methods can be used for the non inferiority tests based on the difference in paired paurocs however their performance has not been investigated in finite samples we propose to use the concept of generalized p value to construct a non inferiority test for diagnostic accuracy based on the difference in paired paurocs simulation results show that the proposed non inferiority test not only adequately controls the size at the nominal level but also is uniformly more powerful than the non parametric methods the proposed method is illustrated with a numerical example using published data

semi parametric maximum likelihood estimates for roc curves of continuous scale tests in this paper we propose a new semi parametric maximum likelihood ml estimate of a receiver operating characteristic roc curve that satisfies the property of invariance of the roc curve and is easy to compute we show that our new estimator is sqrt n consistent and has an asymptotically normal distribution our extensive simulation studies show that the proposed method is efficient and robust finally we illustrate the application of the proposed estimator in a real data set

comparison of two correlated roc curves at a given specificity or sensitivity level the receiver operating characteristic roc curve is the most popular statistical tool for evaluating the discriminatory capability of a given continuous biomarker the need to compare two correlated roc curves arises when individuals are measured with two biomarkers which induces paired and thus correlated measurements many researchers have focused on comparing two correlated roc curves in terms of the area under the curve auc which summarizes the overall performance of the marker however particular values of specificity may be of interest we focus on comparing two correlated roc curves at a given specificity level we propose parametric approaches transformations to normality and nonparametric kernel based approaches our methods can be straightforwardly extended for inference in terms of roc 1 t this is of particular interest for comparing the accuracy of two correlated biomarkers at a given sensitivity level extensions also involve inference for the auc and accommodating covariates we evaluate the robustness of our techniques through simulations compare them with other known approaches and present a real data application involving prostate cancer screening copyright 2016 john wiley sons ltd

construction of confidence regions in the roc space after the estimation of the optimal youden index based cut off point after establishing the utility of a continuous diagnostic marker investigators will typically address the question of determining a cut off point which will be used for diagnostic purposes in clinical decision making the most commonly used optimality criterion for cut off point selection in the context of roc curve analysis is the maximum of the youden index the pair of sensitivity and specificity proportions that correspond to the youden index based cut off point characterize the performance of the diagnostic marker confidence intervals for sensitivity and specificity are routinely estimated based on the assumption that sensitivity and specificity are independent binomial proportions as they arise from the independent populations of diseased and healthy subjects respectively the youden index based cut off point is estimated from the data and as such the resulting sensitivity and specificity proportions are in fact correlated this correlation needs to be taken into account in order to calculate confidence intervals that result in the anticipated coverage in this article we study parametric and non parametric approaches for the construction of confidence intervals for the pair of sensitivity and specificity proportions that correspond to the youden index based optimal cut off point these approaches result in the anticipated coverage under different scenarios for the distributions of the healthy and diseased subjects we find that a parametric approach based on a box cox transformation to normality often works well for biomarkers following more complex distributions a non parametric procedure using logspline density estimation can be used

asymptotic distribution of auc nris and idi based on theory of u statistics the change in area under the curve auc the integrated discrimination improvement idi and net reclassification index nri are commonly used measures of risk prediction model performance some authors have reported good validity of associated methods of estimating their standard errors se and construction of confidence intervals whereas others have questioned their performance to address these issues we unite the auc idi and three versions of the nri under the umbrella of the u statistics family we rigorously show that the asymptotic behavior of auc nris and idi fits the asymptotic distribution theory developed for u statistics we prove that the auc nris and idi are asymptotically normal unless they compare nested models under the null hypothesis in the latter case asymptotic normality and existing se estimates cannot be applied to auc nris or idi in the former case se formulas proposed in the literature are equivalent to se formulas obtained from u statistics theory if we ignore adjustment for estimated parameters we use sukhatme randles dewet condition to determine when adjustment for estimated parameters is necessary we show that adjustment is not necessary for ses of the auc and two versions of the nri when added predictor variables are significant and normally distributed the ses of the idi and three category nri should always be adjusted for estimated parameters these results allow us to define when existing formulas for se estimates can be used and when resampling methods such as the bootstrap should be used instead when comparing nested models we also use the u statistic theory to develop a new se estimate of auc copyright 2017 john wiley sons ltd

finite time stability of linear time varying singular systems with impulsive effects in this paper we introduce a new concept of finite time stability of linear time varying singular systems with impulses at fixed times and present new results for the above mentioned class of system in the form of sufficient conditions a sufficient condition is given in terms of matrix inequalities which gives the opportunity of fitting the finite time control problem in the general framework via impulsive control a numerical example is presented to illustrate the efficiency of the proposed result

prognostic modelling with logistic regression analysis a comparison of selection and estimation methods in small data sets logistic regression analysis may well be used to develop a prognostic model for a dichotomous outcome especially when limited data are available it is difficult to determine an appropriate selection of covariables for inclusion in such models also predictions may be improved by applying some sort of shrinkage in the estimation of regression coefficients in this study we compare the performance of several selection and shrinkage methods in small data sets of patients with acute myocardial infarction where we aim to predict 30 day mortality selection methods included backward stepwise selection with significance levels alpha of 0 01 0 05 0 157 the aic criterion or 0 50 and the use of qualitative external information on the sign of regression coefficients in the model estimation methods included standard maximum likelihood the use of a linear shrinkage factor penalized maximum likelihood the lasso or quantitative external information on univariable regression coefficients we found that stepwise selection with a low alpha for example 0 05 led to a relatively poor model performance when evaluated on independent data substantially better performance was obtained with full models with a limited number of important predictors where regression coefficients were reduced with any of the shrinkage methods incorporation of external information for selection and estimation improved the stability and quality of the prognostic models we therefore recommend shrinkage methods in full models including prespecified predictors and incorporation of external information when prognostic models are constructed in small data sets

smooth semiparametric receiver operating characteristic curves for continuous diagnostic tests we propose a semiparametric kernel distribution function estimator based on which a new smooth semiparametric estimator of the receiver operating characteristic roc curve is constructed we derive the asymptotic bias and variance of the newly proposed distribution function estimator and show that it is more efficient than the traditional non parametric kernel distribution estimator we also derive the asymptotic bias and variance of our new roc curve estimator and show that it is more efficient than the smooth non parametric roc curve estimator proposed by zou et al stat med 1997 16 2143 2156 and lloyd j am stat assoc 1998 93 1356 1364 for our proposed estimators we derive data based methods for bandwidth selection in addition we present some results on the analysis of two real data sets finally a simulation study is presented to show that our estimators are better than the non parametric counterparts in terms of bias standard error and mean square error

short time fourier transform integral wavelet transform and wavelet functions associated with splines abstract in this article we discuss short time fourier transforms integral wavelet transforms and wavelet series expansions associated with spline functions in shift invariant spaces of b splines a recurrence relation formula and the corresponding algorithm about the b wavelets are also given

a new concordance measure for risk prediction models in external validation settings concordance measures are frequently used for assessing the discriminative ability of risk prediction models the interpretation of estimated concordance at external validation is difficult if the case mix differs from the model development setting we aimed to develop a concordance measure that provides insight into the influence of case mix heterogeneity and is robust to censoring of time to event data we first derived a model based concordance mbc measure that allows for quantification of the influence of case mix heterogeneity on discriminative ability of proportional hazards and logistic regression models this mbc can also be calculated including a regression slope that calibrates the predictions at external validation c mbc hence assessing the influence of overall regression coefficient validity on discriminative ability we derived variance formulas for both mbc and c mbc we compared the mbc and the c mbc with commonly used concordance measures in a simulation study and in two external validation settings the mbc was asymptotically equivalent to a previously proposed resampling based case mix corrected c index the c mbc remained stable at the true value with increasing proportions of censoring while harrell s c index and to a lesser extent uno s concordance measure increased unfavorably variance estimates of mbc and c mbc were well in agreement with the simulated empirical variances we conclude that the mbc is an attractive closed form measure that allows for a straightforward quantification of the expected change in a model s discriminative ability due to case mix heterogeneity the c mbc also reflects regression coefficient validity and is a censoring robust alternative for the c index when the proportional hazards assumption holds copyright 2016 john wiley sons ltd

c1 quadratic macroelements and c1 orthogonal multiresolution analyses in 2d each triangle of an arbitrary regular triangulation of a polygonal region in r2 is subdivided into twelve subtriangles by using three connecting lines joining three arbitrarily chosen points on its edges three connecting lines from an arbitrarily chosen interior point in the triangle to its three vertices and three connecting lines joining the points on the edges and the interior point in this refinement gd of c1 quadratic finite elements can be constructed in this paper we will give explicit bezier coefficients of elements in terms of the parameters that describe function and first partial derivative values at vertices and values of the normal derivatives at vertices of subtriangles that lie on the edges of consequently the basis and approximation properties of c1 quadratic spline space under refined grid partition gd can be found finally we discuss the construction of c1 orthogonal scaling functions by using c1 quadratic macroelements

the bootstrap and identification of prognostic factors via cox s proportional hazards regression model this paper describes the use of the bootstrap 1 2 a new computer based statistical methodology to help validate a regression model resulting from the fitting of cox s proportional hazards model3 to a set of censored survival data as an example we define a prognostic model for outcome in childhood acute lymphocytic leukemia with the cox model and use of a training set of 224 patients to validate the accuracy of the model we use a bootstrap resampling technique to mimic the population under study in two stages first we select the important prognostic factors via a stepwise regression procedure with 100 bootstrap samples secondly we estimate the corresponding regression parameters for these important factors with 400 bootstrap samples the bootstrap result suggests that the model constructed from the training set is reasonable

a permutation test to compare receiver operating characteristic curves summary we developed a permutation test in our earlier paper venkatraman and begg 1996 biometrika83 835 848 to test the equality of receiver operating characteristic curves based on continuous paired data here we extend the underlying concepts to develop a permutation test for continuous unpaired data and we study its properties through simulations