analysis of proportional mean residual life model with latent variables end stage renal disease esrd is one of the most serious diabetes complications numerous studies have been devoted to revealing the risk factors of the onset time of esrd in this article we propose a proportional mean residual life mrl model with latent variables to assess the effects of observed and latent risk factors on the mrl function of esrd in a cohort of chinese type 2 diabetic patients the proposed model generalizes the conventional proportional mrl model to accommodate the latent risk factor that cannot be measured by a single observed variable we employ a factor analysis model to characterize the latent risk factors via multiple observed variables we develop a borrow strength estimation procedure which incorporates the expectation maximization algorithm and an extended estimating equation approach the asymptotic properties of the proposed estimators are established simulation shows that the performance of the proposed methodology is satisfactory the application to the study of type 2 diabetes reveals insights into the prevention of esrd copyright 2016 john wiley sons ltd

estimating medical costs with censored data incompleteness of follow up data is a common problem in estimating medical costs naive analysis using summary statistics on the collected data can result in severely misleading statistical inference this paper focuses on the problem of estimating the mean medical cost from a sample of individuals whose medical costs may be right censored a class of weighted estimators which account appropriately for censoring are introduced our estimators are shown to be consistent and asymptotically normal with easily estimated variances the efficiency of these estimators is studied with the goal of finding as efficient an estimator for the mean medical cost as is feasible extensive simulation studies are used to show that our estimators perform well in finite samples even with heavily censored data for a variety of circumstances the methods are applied to a set of cost data from a cardiology trial conducted by the duke university medical center extensions to other censored data problems are also discussed

omnibus tests for comparison of competing risks with adjustment for covariate effects summary this article develops omnibus tests for comparing cause specific hazard rates and cumulative incidence functions at specified covariate levels confidence bands for the difference and the ratio of two conditional cumulative incidence functions are also constructed the omnibus test is formulated in terms of a test process given by a weighted difference of estimates of cumulative cause specific hazard rates under cox proportional hazards models a simulation procedure is devised for sampling from the null distribution of the test process leading to graphical and numerical techniques for detecting significant differences in the risks the approach is applied to a cohort study of type specific hiv infection rates

a note on residual life summary two further characterizations are given of a family of survival distributions introduced by hall wellner 1984 the second result involves a new family of semiparametric models requiring proportional mean residual life theorem 1 let s x be an absolutely continuous survivor function with s o 1 and suppose that the residual life distribution s y x of s x satisfies 4 for some nonnegative function 0 x then 0 x is linear and s x satisfies 3 proof equation 4 gives 0 x s x 0 x y s x s y we may deduce successively i that s x 0 implies 0 x 0 ii s 0 0 implies s x 0 implies x q s x supposing that s x y0 x 0 we may apply q to 4 to obtain

linear life expectancy regression with censored data summary in the statistical literature life expectancy is usually characterised by the mean residual life function regression models are thus needed to study the association between the mean residual life functions and their covariates in this paper we consider a linear mean residual life model and develop inference procedures in the presence of potential censoring the new model and inference procedures are applied to the stanford heart transplant data semiparametric efficiency calculations and information bounds are also considered

efficient estimation of the distribution of quality adjusted survival time quality of life is an important aspect in evaluation of clinical trials of chronic diseases such as cancer and aids quality adjusted survival analysis is a method that combines both the quantity and quality of a patient s life into one single measure in this paper we discuss the efficiency of weighted estimators for the distribution of quality adjusted survival time using the general representation theorem for missing data processes we are able to derive an estimator that is more efficient than the one proposed in zhao and tsiatis 1997 biometrika 84 339 348 simulation experiments are conducted to assess the small sample properties of this estimator and to compare it with the semiparametric efficiency bound the value of this estimator is demonstrated from an application of the method to a data set obtained from a breast cancer clinical trial

a goodness of fit approach to testing mean residual times the random residual lifetime is a random variable representing the remaining life of a system of age x 0 the mean residual life at age x is the expected value of the remaining life beyond that age which is well known and extensively studied for both testing and estimation in this article a new approach is presented for testing constant versus decreasing residual life the new test is much simpler to compute asymptotically normal and performs better than previous tests in terms of power and pitman asymptotic efficiencies for several alternatives

nonparametric survival analysis with time dependent covariate effects a penalized partial likelihood approach techniques are developed for nonparametric analysis of data under a cox regression like model permitting time dependent covariate effects determined by a regression function beta 0 t estimators resulting from maximization of an appropriate penalized partial likelihood are shown to exist and a computational approach is outlined weak uniform consistency with a rate of convergence and pointwise asymptotic normality of the estimators are established under regularity conditions a consistent estimator of a common baseline hazard function is presented and used to construct a consistent estimator of the asymptotic variance of the estimator of the regression function extensions to multiple covariates general relative risk functions and time dependent covariates are discussed

regression models for the restricted residual mean life for right censored and left truncated data the hazard ratios resulting from a cox s regression hazards model are hard to interpret and to be converted into prolonged survival time as the main goal is often to study survival functions there is increasing interest in summary measures based on the survival function that are easier to interpret than the hazard ratio the residual mean time is an important example of those measures however because of the presence of right censoring the tail of the survival distribution is often difficult to estimate correctly therefore we consider the restricted residual mean time which represents a partial area under the survival function given any time horizon and is interpreted as the residual life expectancy up to of a subject surviving up to time t we present a class of regression models for this measure based on weighted estimating equations and inverse probability of censoring weighted estimators to model potential right censoring furthermore we show how to extend the models and the estimators to deal with delayed entries we demonstrate that the restricted residual mean life estimator is equivalent to integrals of kaplan meier estimates in the case of simple factor variables estimation performance is investigated by simulation studies using real data from danish monitoring cardiovascular risk factor surveys we illustrate an application to additive regression models and discuss the general assumption of right censoring and left truncation being dependent on covariates copyright 2017 john wiley sons ltd

on estimation of partially linear transformation models we study a general class of partially linear transformation models which extend linear transformation models by incorporating nonlinear covariate effects in survival data analysis a new martingale based estimating equation approach consisting of both global and kernel weighted local estimation equations is developed for estimating the parametric and nonparametric covariate effects in a unified manner we show that with a proper choice of the kernel bandwidth parameter one can obtain the consistent and asymptotically normal parameter estimates for the linear effects asymptotic properties of the estimated nonlinear effects are established as well we further suggest a simple resampling method to estimate the asymptotic variance of the linear estimates and show its effectiveness to facilitate the implementation of the new procedure an iterative algorithm is developed numerical examples are given to illustrate the finite sample performance of the procedure supplementary materials are available online

a mathematical theory of super resolution by using a system of sub wavelength helmholtz resonators a rigorous mathematical theory is developed to explain the super resolution phenomenon observed in the experiment lemoult et al phys rev lett 107 064301 2011 a key ingredient is the calculation of the resonances and the green function in the half space with the presence of a system of helmholtz resonators in the quasi stationary regime by using boundary integral equations and generalized rouche s theorem the existence and the leading asymptotic of the resonances are rigorously derived the integral equation formulation also yields the leading order terms in the asymptotics of the green function the methodology developed in the paper provides an elegant and systematic way for calculating resonant frequencies for helmholtz resonators in assorted space settings as well as in various frequency regimes by using the asymptotics of the green function the analysis of the imaging functional of the time reversal wave fields becomes possible which clearly demonstrates the super resolution property the result provides the first mathematical theory of super resolution in the context of a deterministic medium and sheds light on the mechanism of super resolution and super focusing for waves in deterministic complex media

focusing and imaging using eigenfunctions of the scattering operator an inverse scattering method that uses eigenfunctions of the scattering operator is presented this approach provides a unified framework that encompasses eigenfunction methods of focusing and quantitative image reconstruction in arbitrary media scattered acoustic fields are described using a compact normal operator the eigenfunctions of this operator are shown to correspond to the far field patterns of source distributions that are directly proportional to the position dependent contrast of a scattering object conversely the eigenfunctions of the scattering operator specify incident wave patterns that focus on these effective source distributions these focusing properties are employed in a new inverse scattering method that represents unknown scattering media using products of numerically calculated fields of eigenfunctions a regularized solution to the nonlinear inverse scattering problem is shown to result from combinations of these products so that the products comprise a natural basis for efficient and accurate reconstructions of unknown inhomogeneities the corresponding linearized problem is solved analytically resulting in a simple formula for the low pass filtered scattering potential the linear formula is analytically equivalent to known filtered backpropagation formulas for born inversion and at least in the case of small scattering objects has advantages of computational simplicity and efficiency a similarly efficient and simple formula is derived for the nonlinear problem in which the total acoustic pressure can be determined based on an estimate of the medium computational results illustrate focusing of eigenfunctions on discrete and distributed scattering media quantitative imaging of inhomogeneous media using products of retransmitted eigenfunctions inverse scattering in an inhomogeneous background medium and reconstructions for data corrupted by noise

prediction of cumulative incidence function under the proportional hazards model in the presence of dependent competing risks in survival analysis the cox model can be utilized to examine the covariate effects on the cause specific hazard function for the failure type of interest for this situation the cumulative incidence function provides an intuitively appealing summary curve for marginal probabilities of this particular event in this paper we show how to construct confidence intervals and bands for such a function under the cox model for future patients with certain covariates our proposals are illustrated with data from a prostate cancer trial

adjusting for nonignorable drop out using semiparametric nonresponse models abstract consider a study whose design calls for the study subjects to be followed from enrollment time t 0 to time t t at which point a primary endpoint of interest y is to be measured the design of the study also calls for measurements on a vector v t of covariates to be made at one or more times t during the interval 0 t we are interested in making inferences about the marginal mean 0 of y when some subjects drop out of the study at random times q prior to the common fixed end of follow up time t the purpose of this article is to show how to make inferences about 0 when the continuous drop out time q is modeled semiparametrically and no restrictions are placed on the joint distribution of the outcome and other measured variables in particular we consider two models for the conditional hazard of drop out given v t y where v t denotes the history of the process v t through time t t 0 t in the first model we assume that q t v t y exp 0 y where 0 is a scalar paramet

toward a curse of dimensionality appropriate coda asymptotic theory for semi parametric models we argue that due to the curse of dimensionality there are major difficulties with any pure or smoothed likelihood based method of inference in designed studies with randomly missing data when missingness depends on a high dimensional vector of variables we study in detail a semi parametric superpopulation version of continuously stratified random sampling we show that all estimators of the population mean that are uniformly consistent or that achieve an algebraic rate of convergence no matter how slow require the use of the selection randomization probabilities we argue that in contrast to likelihood methods which ignore these probabilities inverse selection probability weighted estimators continue to perform well achieving uniform n 1 2 rates of convergence we propose a curse of dimensionality appropriate coda asymptotic theory for inference in non and semi parametric models in an attempt to formalize our arguments we discuss whether our results constitute a fatal blow to the likelihood principle and study the attitude toward these that a committed subjective bayesian would adopt finally we apply our coda theory to analyse the effect of the curse of dimensionality in several interesting semi parametric models including a model for a two armed randomized trial with randomization probabilities depending on a vector of continuous pretreatment covariates x we provide substantive settings under which a subjective bayesian would ignore the randomization probabilities in analysing the trial data we then show that any statistician who ignores the randomization probabilities is unable to construct nominal 95 per cent confidence intervals for the true treatment effect that have both i an expected length which goes to zero with increasing sample size and ii a guaranteed expected actual coverage rate of at least 95 per cent over the ensemble of trials analysed by the statistician during his or her lifetime however we derive a new interval estimator depending on the randomization probabilities that satisfies i and ii

some diagnostic methods for cox regression models through hazard smoothing in this paper some graphical methods are proposed for evaluating the fit of cox regression models in survival analysis the simplest procedure proposed is to estimate the baseline hazard separately within subgroups by applying kernel based smoothing to standard cumulative hazard estimates the different estimates should be the same to within sampling variability when the model is correct a modification of this procedure gives a direct way of calculating smooth estimates of hazard ratios over time a further modification gives estimates of ratios as a function of a continuous covariate and time the methods are applied to data taken from a clinical trial of adjuvant therapy for breast cancer

assortativity and act degree distribution of some collaboration networks empirical investigation results on weighted and un weighted assortativity act degree distribution degree distribution and node strength distribution of nine real world collaboration networks have been presented the investigations propose that act degree distribution degree distribution and node strength distribution usually show so called shifted power law spl function forms which can continuously vary from an ideal power law to an ideal exponential decay two parameters a and z can be used for description of the distribution functions another conclusion is that assortativity coefficient and the parameter a or z is monotonously dependent on each other by the collaboration network evolution model introduced in a reference p zhang et al physica a 360 2006 599 we analytically derived the spl distributions which typically appeared in general situations where nodes are selected partially randomly with a probability p and partially by linear preferential principle with the probability 1 p the analytic discussion gives an explicit expression on the relationship between the random selection proportion p and the parameters a and z the numerical simulation results by the model show a monotonic dependence of assortativity on the random selection proportion p the empirically obtained assortativity versus a or z curve for the four collaboration networks with small maximal act size t max shows a good agreement with the model prediction according to the curves one can qualitatively judge the random selection proportion of the real world network in its evolution process r 2007 elsevier b v all rights reserved

a note on linear rank tests and gill and schumacher s tests of proportionality summary gill schumacher 1987 assess proportionality of hazards in the two sample case by comparing two generalized linear rank tests with different weights they consider the difference of the two linear rank statistics under proportionality the expected value of this difference is zero and its variance may be estimated the purpose of this note is to show that one can perform a similar procedure within the traditional regression setting the procedure has the advantage of generalizability to multi sample or continuous data and is computable using existing regression programs

a nonparametric test to compare survival distributions with covariate adjustment summary the analysis of covariance is a technique that is used to improve the power of a k sample test by adjusting for concomitant variables if the end point is the time of survival and some observations are right censored the score statistic from the cox proportional hazards model is the method that is most commonly used to test the equality of conditional hazard functions in many situations however the proportional hazards model assumptions are not satisfied specifically the relative risk function is not time invariant or represented as a log linear function of the covariates we propose an asymptotically valid k sample test statistic to compare conditional hazard functions which does not require the assumption of proportional hazards a parametric specification of the relative risk function or randomization of group assignment simulation results indicate that the performance of this statistic is satisfactory the methodology is demonstrated on a data set in prostate cancer

exploring the evolutionary mechanism of complex supply chain systems using evolving hypergraphs abstract a new evolutionary model is proposed to describe the characteristics and evolution pattern of supply chain systems using evolving hypergraphs in which nodes represent enterprise entities while hyperedges represent the relationships among diverse trades the nodes arrive at the system in accordance with a poisson process with the evolving process incorporating the addition of new nodes linking of old nodes and rewiring of links grounded in the poisson process theory and continuum theory the stationary average hyperdegree distribution is shown to follow a shifted power law spl and the theoretical predictions are consistent with the results of numerical simulations testing the impact of parameters on the model yields a positive correlation between hyperdegree and degree the model also uncovers macro characteristics of the relationships among enterprises due to the microscopic interactions among individuals

semiparametric estimation of proportional mean residual life model in presence of censoring summary a mean residual life function is the average remaining life of a surviving subject as it varies with time the proportional mean residual life model was proposed by oakes and dasu 1990 biometrika77 409 410 in regression analysis to study its association with related covariates in absence of censoring in this article we develop some semiparametric estimation procedures to take censoring into account the proposed methodology is evaluated via simulation studies and further applied to a clinical trial of chemotherapy in postoperative radiotherapy of lung cancer patients

near field imaging of infinite rough surfaces this paper is concerned with an inverse rough surface scattering problem in near field optical imaging which is to reconstruct the scattering surface with a resolution beyond the diffraction limit the surface is assumed to be a small and smooth deformation of a plane surface based on a transformed field expansion the boundary value problem with complex scattering surface is converted into a successive sequence of two point boundary value problems in the frequency domain where an analytic solution for the direct scattering problem is derived from the method of integrated solution by neglecting the high order terms in the power series expansion the nonlinear inverse problem is linearized and an explicit inversion formula is obtained a spectral cut off regularization is adopted to suppress the exponential growth of the noise in the evanescent wave components which carry high spatial frequency of the scattering surface and contribute to the superresolution in the near field regime the method works f

score tests for homogeneity of regression effect in the proportional hazards model a simple model containing the proportional hazards regression model as a special case is presented the purpose of the model is to provide a framework in which specific alternatives to the proportional hazards assumption may be tested rank invariant score tests for linear quadratic or exponential trends can for instance all be undertaken within this framework in the case of the two sample problem the required calculations are shown to take a particularly simple form special consideration is given to the two sample case in which there is an inversion of the regression effect i e where the hazard functions cross at some given point both of the motivating examples are concerned with this problem computational aspects are relatively straightforward and some discussion on this is provided

semiparametric regression analysis of mean residual life with censored survival data summary as function of time t a mean residual life is the remaining life expectancy of a subject given survival up to t the proportional mean residual life model proposed by oakes dasu 1990 provides an alternative to the cox proportional hazards model for studying the association between survival times and covariates in the presence of censoring we use counting process theory to develop semiparametric inference procedures for the regression coefficients of the oakes dasu model simulation studies and an application to the well known veterans administration lung cancer survival data are presented

semiparametric transformation models for point processes in this article we propose a family of semiparametric transformation models for point processes with positive jumps of arbitrary sizes these models offer great flexibilities in formulating the effects of covariates on the mean function of the point process while leaving the stochastic structure completely unspecified we develop a class of estimating equations for the baseline mean function and the vector valued regression parameter based on censored point processes and covariate data these equations can be solved easily by the standard newton raphson algorithm the resultant estimator of the regression parameter is consistent and asymptotically normal with a covariance matrix that can be estimated consistently furthermore the estimator of the baseline mean function is uniformly consistent and upon proper normalization converges weakly to a zero mean gaussian process with an easily estimated covariance function we demonstrate through extensive simulation studies that the proposed inference procedu

asymptotic properties of a general class of nonparametric tests for survival analysis many of the popular nonparametric test statistics for censored survival data used in two sample s sample trend and single continuous covariate situations are special cases of a general statistic differing only in the choice of covariate based label and weight function formulated in terms of counting processes and martingales this general statistic standardized by the square root of its consistent variance estimator is shown to be asymptotically normal under the null hypothesis and under a sequence of contiguous hazard alternatives that includes both relative and excess risk models

testing causal effects in observational survival data using propensity score matching design time to event data are very common in observational studies unlike randomized experiments observational studies suffer from both observed and unobserved confounding biases to adjust for observed confounding in survival analysis the commonly used methods are the cox proportional hazards ph model the weighted logrank test and the inverse probability of treatment weighted cox ph model these methods do not rely on fully parametric models but their practical performances are highly influenced by the validity of the ph assumption also there are few methods addressing the hidden bias in causal survival analysis we propose a strategy to test for survival function differences based on the matching design and explore sensitivity of the p values to assumptions about unmeasured confounding specifically we apply the paired prentice wilcoxon ppw test or the modified ppw test to the propensity score matched data simulation studies show that the ppw type test has higher power in situations when the ph assumption fails for potential hidden bias we develop a sensitivity analysis based on the matched pairs to assess the robustness of our finding following rosenbaum s idea for nonsurvival data for a real data illustration we apply our method to an observational cohort of chronic liver disease patients from a mayo clinic study the ppw test based on observed data initially shows evidence of a significant treatment effect but this finding is not robust as the sensitivity analysis reveals that the p value becomes nonsignificant if there exists an unmeasured confounder with a small impact

regression by local fitting methods properties and computational algorithms abstract local regression is a procedure for estimating regression surfaces by the local fitting of linear or quadratic functions of the independent variables in a moving fashion that is analogous to how a moving average is computed for a time series the advantage of the methodology over the global fitting of parametric functions of the independent variables by least squares the current paradigm in regression studies is that a much wider class of regression functions can be estimated without distortion in this paper we discuss the methods their statistical properties and computational algorithms

a class of transformed mean residual life models with censored survival data this article features online supplementary material the mean residual life function is an attractive alternative to the survival function or the hazard function of a survival time in practice it provides the remaining life expectancy of a subject surviving up to time t in this study we propose a class of transformed mean residual life models for fitting survival data under right censoring to estimate the model parameters we make use of the inverse probability of censoring weighting approach and develop a system of estimating equations efficiency and robustness of the estimators are also studied both asymptotic and finite sample properties of the proposed estimators are established and the approach is applied to two real life datasets collected from clinical trials

goodness of fit analysis for the cox regression model based on a class of parameter estimators abstract in this article we propose a class of estimation functions for the vector of regression parameters in the cox proportional hazards model with possibly time dependent covariates by incorporating the weight functions commonly used in weighted log rank tests into the partial likelihood score function the resulting estimators behave much like the conventional maximum partial likelihood estimator in that they are consistent and asymptotically normal when the cox model is inappropriate however the estimators with different weight functions generally converge to nonidentical constant vectors for example the magnitude of the parameter estimator using the kaplan meier survival estimator as the weight function will be stochastically larger than that of the maximum partial likelihood estimator if covariate effects diminish over time such facts motivate us to develop goodness of fit methods for the cox regression model by comparing parameter estimators with different weight functions under the assume

mathematical analysis of plasmonic resonances for nanoparticles the full maxwell equations abstract in this paper we use the full maxwell equations for light propagation in order to analyze plasmonic resonances for nanoparticles we mathematically define the notion of plasmonic resonance and analyze its shift and broadening with respect to changes in size shape and arrangement of the nanoparticles using the layer potential techniques associated with the full maxwell equations we present an effective medium theory for resonant plasmonic systems and derive a condition on the volume fraction under which the maxwell garnett theory is valid at plasmonic resonances

proportional hazards tests and diagnostics based on weighted residuals summary nonproportional hazards can often be expressed by extending the cox model to include time varying coefficients e g for a single covariate the hazard function for subject i is modelled as exp fl t zi t a common example is a treatment effect that decreases with time we show that the function 3 t can be directly visualized by smoothing an appropriate residual plot also many tests of proportional hazards including those of cox 1972 gill schumacher 1987 harrell 1986 lin 1991 moreau o quigley mesbah 1985 nagelkerke oosting hart 1984 o quigley pessione 1989 schoenfeld 1980 and wei 1984 are related to time weighted score tests of the proportional hazards hypothesis and can be visualized as a weighted least squares line fitted to the residual plot

a simple test for goodness of fit of cox s proportional hazards model cox s proportional hazards model for survival analysis 1972 has gained widespread attention from both applied and theoretical statisticians and is central to most work on survival analysis to verify the assumption of proportional hazards underlying the model several methods have recently been put forward cox 1979 schoenfeld 1980 andersen 1982 kalbfleisch and prentice 1980 these methods consist either of graphical techniques designed so as to visualize departures from the proportional hazards ph assumption or of formal tests based on parameterizing the interaction between covariates and time in this paper a simple test statistic is proposed for detecting departures from the ph assumption the proposed test is computationally and conceptually straightforward expressions for the first two moments of the test statistic are presented

martingale based residuals for survival models summary graphical methods based on the analysis of residuals are considered for the setting of the highly used cox 1972 regression model and for the andersen gill 1982 generalization of that model we start with a class of martingale based residuals as proposed by barlow prentice 1988 these residuals and or their transforms are useful for investigating the functional form of a covariate the proportional hazards assumption the leverage of each subject upon the estimates of 13 and the lack of model fit to a given subject 1 1 model consider a set of n independent subjects such that the counting process ni ni t t o for the ith subject in the set indicates the number of observed events experienced over time t the sample paths of the ni are step functions with jumps of size 1 and with ni 0 0 we assume that the intensity function for ni t is given by yi t da t zi t yi t ep z t dao t 1 where yi t is a 0 1 process indicating whether the ith subject is a risk at time t 13 is a vector of regression coefficients zi t is a p dimensional vector of covariate processes and ao is the baseline cumulative hazard function several familar survival models fit into this framework the andersen gill 1982 generalization of the cox 1972 model arises when ao t is completely unspecified the further restriction that yi t 1 until the first event or censoring and is 0 thereafter yields the cox model the parametric form ao t t yields a poisson model or an exponential if restricted to a single event per subject and ao t tp a weibull model our attention will focus primarily on the andersen gill and cox models however the

subgraph centrality and clustering in complex hyper networks abstract the representation of complex systems as networks is inappropriate for the study of certain problems we show several examples of social biological ecological and technological systems where the use of complex networks gives very limited information about the structure of the system consequently we extend the concepts of subgraph centrality and clustering for complex networks represented by hypergraphs complex hyper networks the first parameter characterizes the node participation in different sub hypergraphs and the second one characterizes the transitivity in the hyper network through the proportion of hyper triangles to paths of length two another measure characterizing the formation of triples of mutually adjacent groups in the hyper network is also introduced all of these characteristics are studied in three different hyper networks a scientific collaboration hyper network an ecological competition hyper network and the hyper network formed by the american corporate elite in 1999

additive expectancy regression regression is a useful tool for studying association between an outcome variable and its covariates in a classical linear regression model the outcome s expectation is usually a function of the covariates and some regression parameters and the underlying distribution is often normal in this article we propose a new class of additive expectancy regression models in which the outcomes tend to be positively skewed in the new regression models regression parameters are practically meaningful and also useful with inferences on the means of skewed outcomes parametric and semiparametric methods are developed for model estimation and inferences model based prediction and model adequacy assessment are discussed the proposed methodologies are demonstrated by two real data analyses

median regression with censored cost data because of the skewness of the distribution of medical costs we consider modeling the median as well as other quantiles when establishing regression relationships to covariates in many applications the medical cost data are also right censored in this article we propose semiparametric procedures for estimating the parameters in median regression models based on weighted estimating equations when censoring is present numerical studies are conducted to show that our estimators perform well with small samples and the resulting inference is reliable in circumstances of practical importance the methods are applied to a dataset for medical costs of patients with colorectal cancer

towards a mathematical theory of super resolution this paper develops a mathematical theory of super resolution broadly speaking super resolution is the problem of recovering the fine details of an object the high end of its spectrum from coarse scale information only from samples at the low end of the spectrum suppose we have many point sources at unknown locations in 0 1 and with unknown complex valued amplitudes we only observe fourier samples of this object up to a frequency cutoff fc we show that one can super resolve these point sources with infinite precision i e recover the exact locations and amplitudes by solving a simple convex optimization problem which can essentially be reformulated as a semidefinite program this holds provided that the distance between sources is at least 2 fc this result extends to higher dimensions and other models in one dimension for instance it is possible to recover a piecewise smooth function by resolving the discontinuity points with infinite precision as well we also show that the theory and methods are robust to noise in particular in the discrete setting we develop some theoretical results explaining how the accuracy of the super resolved signal is expected to degrade when both the noise level and the super resolution factor vary 2014 wiley periodicals inc

testing goodness of fit for proportional hazards model with censored observations abstract a numerical omnibus test of fit for the two sample proportional hazards model is proposed for randomly censored observations the test is derived from cox s partial likelihood and does not need a dummy time dependent covariate or any partition of the time axis consistency of the test is established examples are provided for illustration

mean residual life models with time dependent coefficients under right censoring the mean residual life provides the remaining life expectancy of a subject who has survived to a certain time point when covariates are present regression models are needed to study the association between the mean residual life function and potential regression covariates in this paper we propose a flexible class of semiparametric mean residual life models where some effects may be time varying and some may be constant over time in the presence of right censoring we use the inverse probability of censoring weighting approach and develop inference procedures for estimating the model parameters in addition we provide graphical and numerical methods for model checking and tests for examining whether or not the covariate effects vary with time asymptotic and finite sample properties of the proposed estimators are established and the approach is applied to real life datasets collected from clinical trials copyright 2012 oxford university press

martingale difference residuals as a diagnostic tool for the cox model the proportional hazards model makes two major assumptions the hazard ratio is constant over time and the relationship between the hazard and continuous covariates is log linear methods exist for checking and relaxing each of these assumptions but in both cases the methods rely on the other assumption being true problems can occur if neither of the assumptions is appropriate or even if only one of the assumptions is appropriate but it is not known which we propose a new kind of residual for checking the two assumptions simultaneously the smoothed residuals provide a flexible estimate of the hazard ratio which may deviate from the standard proportional hazards model by having a time dependent hazard ratio transformed covariates or both the methods are illustrated using data from the medical research council s myeloma trials

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

semiparametric regression for the mean and rate functions of recurrent events the counting process with the cox type intensity function has been commonly used to analyse recurrent event data this model essentially assumes that the underlying counting process is a time transformed poisson process and that the covariates have multiplicative effects on the mean and rate function of the counting process recently pepe and cai and lawless and co workers have proposed semiparametric procedures for making inferences about the mean and rate function of the counting process without the poisson type assumption in this paper we provide a rigorous justification of such robust procedures through modern empirical process theory furthermore we present an approach to constructing simultaneous confidence bands for the mean function and describe a class of graphical and numerical techniques for checking the adequacy of the fitted mean rate model the advantages of the robust procedures are demonstrated through simulation studies an illustration with multiple infection data taken from a clinical study on chronic granulomatous disease is also provided