semiparametric transformation models for semicompeting survival data semicompeting risk outcome data e g time to disease progression and time to death are commonly collected in clinical trials however analysis of these data is often hampered by a scarcity of available statistical tools as such we propose a novel semiparametric transformation model that improves the existing models in the following two ways first it estimates regression coefficients and association parameters simultaneously second the measure of surrogacy for example the proportion of the treatment effect that is mediated by the surrogate and the ratio of the overall treatment effect on the true endpoint over that on the surrogate endpoint can be directly obtained we propose an estimation procedure for inference and show that the proposed estimator is consistent and asymptotically normal extensive simulations demonstrate the valid usage of our method we apply the method to a multiple myeloma trial to study the impact of several biomarkers on patients semicompeting outcomes namely time to progression and time to death

reader reaction instrumental variable additive hazards models with exposure dependent censoring li fine and brookhart 2015 presented an extension of the two stage least squares 2sls method for additive hazards models which requires an assumption that the censoring distribution is unrelated to the endogenous exposure variable we present another extension of 2sls that can address this limitation

bias testing bias correction and confounder selection using an instrumental variable model instrumental variable iv analysis can be used to address bias due to unobserved confounding when estimating the causal effect of a treatment on an outcome of interest however if a proposed iv is correlated with unmeasured confounders and or weakly correlated with the treatment the standard iv estimator may be more biased than an ordinary least squares ols estimator several methods have been proposed that compare the bias of the iv and ols estimators relying on the belief that measured covariates can be used as proxies for the unmeasured confounder despite these developments there is lack of discussion about approaches that can be used to formally test whether the iv estimator may be less biased than the ols estimator thus we have developed a testing framework to compare the bias and a criterion to select informative measured covariates for bias comparison and regression adjustment we also have developed a bias correction method which allows one to use an invalid iv to correct the bias of the ols or iv estimator numerical studies demonstrate that the proposed methods perform well with realistic sample sizes

a stable richardson iteration method for complex linear systems the richardson iteration method is conceptually simple as well as easy to program and parallelize this makes the method attractive for the solution of large linear systems of algebraic equations with matrices with complex eigenvalues we change the ordering of the relaxation parameters of a richardson iteration method proposed by eiermann niethammer and varga for the solution of such problems the new method obtained is shown to be stable and to have better convergence properties

one sided cross validation abstract a new method of selecting the smoothing parameters of nonparametric regression estimators is introduced the method termed one sided cross validation oscv has the objectivity of cross validation and statistical properties comparable to those of a plug in rule the new method may be viewed as an application of the prequential model selection method of dawid as such our results identify a situation in which the prequential method is a more efficient model selector than cross validation an example simulations and theoretical results demonstrate the utility of oscv when used with local linear and kernel estimators

a smoothed maximum score estimator for the binary response model this paper describes a semiparametric estimator for binary response models in which there may be arbitrary heteroskedasticity of unknown form the estimator is obtained by maximizing a smoothed version of the objective function of c manski s maximum score estimator the smoothing procedure is similar to that used in kernel nonparametric density estimation the resulting estimator s rate of convergence in probability is the fastest possible under the assumptions that are made the centered normalized estimator is asymptotically normally distributed methods are given for consistently estimating the parameters of the limiting distribution and for selecting the bandwidth required by the smoothing procedure copyright 1992 by the econometric society

how far are automatically chosen regression smoothing parameters from their optimum abstract we address the problem of smoothing parameter selection for nonparametric curve estimators in the specific context of kernel regression estimation call the optimal bandwidth the minimizer of the average squared error we consider several automatically selected bandwidths that approximate the optimum how far are the automatically selected bandwidths from the optimum the answer is studied theoretically and through simulations the theoretical results include a central limit theorem that quantifies the convergence rate and gives the differences asymptotic distribution the convergence rate turns out to be excruciatingly slow this is not too disappointing because this rate is of the same order as the convergence rate of the difference between the minimizers of the average squared error and the mean average squared error in some simulations by john rice the selectors considered here performed quite differently from each other we anticipated that these differences would be reflected in differ

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

numerical stability of the cyclic richardson iteration the success of the cyclic richardson iteration depends on the proper ordering of the acceleration parameters we give a rigorous error analysis to show that with the proper ordering the relative error in the iterative method when properly terminated is not larger than the error incurred in stable direct methods such as cholesky factorization for both the computed approximation tilde u tou l 1f satisfies left u tilde u right cond l u 2 t and this bound is attainable we also show that the residual norm left f l tilde u right is bounded by l cond l left tilde u right 2 t this bound is attainable for a small cycle lengthn our analysis suggests that for a larger cycle lengthn the residuals are bounded by sqrt cond l left l right left tilde u right 2 t we construct a theoretical example in which this bound is attainable however we observed in all numerical tests that ultimately the residual norms were of order left l right left tilde u right 2 t we explain why in practice even the factor sqrt cond l is never encountered therefore the residual stopping criterion for the richardson iteration appears to be very reliable and the method itself appears to be stable

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

bias in causal estimates from mendelian randomization studies with weak instruments mendelian randomization studies using genetic instrumental variables ivs are now being commonly used to estimate the causal association of a phenotype on an outcome even when the necessary underlying assumptions are valid estimates from analyses using ivs are biased in finite samples the source and nature of this bias appear poorly understood in the epidemiological field we explain why the bias is in the direction of the confounded observational association with magnitude relating to the statistical strength of association between the instrument and phenotype we comment on the size of the bias from simulated data showing that when multiple instruments are used although the variance of the iv estimator decreases the bias increases we discuss ways to analyse mendelian randomization studies to alleviate the problem of weak instrument bias

nonparametric censored and truncated regression we propose new estimators of the latent regression function in nonparametric cen sored and truncated regression models our estimators are computationally convenient consisting only of two nonparametric regressions and a univariate integral we establish consistency and asymptotic normality for an implementation based on local linear ker nel estimators an extension permits estimation in the presence of a general form of heteroscedasticity both the function m and the distribution f of the error e are unknown the errors are not assumed to be symmetric this paper provides a simple consistent estimator of m x k for some constant k under an additional tail condition we provide a consistent estimator of m x when m is the conditional mean function of the uncensored population also we show that f can be estimated given m x the proposed estimator is extended to deal with the truncated regression model where yi is only observed when it is not censored we also describe extensions to deal with a general form of heteroskedasticity in which the distribution of e could depend in unknown ways on a subset of elements of x for any continuously distributed element xk of x let mk x am x axk we also provide direct estimators of the derivatives mk x in both the censored and truncated regression models these derivatives are interpretable as the marginal effect of a change in x on the underlying uncensored population they can also be used to test or estimate parametric or semiparametric specifications of m x for example mk x is constant if m x is linear in xk and mk x depends only on xk if m x is additive in a function of xk

semiparametric analysis of the additive risk model in contrast to the proportional hazards model the additive risk model specifies that the hazard function associated with a set of possibly time varying covariates is the sum of rather than the product of the baseline hazard function and the regression function of covariates this formulation describes a different aspect of the association between covariates and the failure time than the proportional hazards model and is more plausible than the latter for many applications in the present paper simple procedures with high efficiencies are developed for making inference about the regression parameters under the additive risk model with an unspecified baseline hazard function

empirical likelihood based inference in conditional moment restriction models this paper proposes an asymptotically efficient method for estimating models with conditional moment restrictions our estimator generalizes the maximum empirical likelihood estimator mele of qin and lawless 1994 using a kernel smoothing method we efficiently incorporate the information implied by the conditional moment restrictions into our empirical likelihood based procedure this yields a one step estimator which avoids estimating optimal instruments our likelihood ratio type statistic for parametric restrictions does not require the estimation of variance and achieves asymptotic pivotalness implicitly the estimation and testing procedures we propose are normalization invariant simulation results suggest that our new estimator works remarkably well in finite samples

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

optimal smoothing in nonparametric conditional quantile derivative function estimation abstract marginal effect in nonparametric quantile regression is of special interest as it quantitatively measures how one unit change in explanatory variable heterogeneously affects dependent variable ceteris paribus at distinct quantiles in this paper we propose a data driven bandwidth selection procedure based on the gradient of an unknown quantile regression function our method delivers the bandwidth with the oracle property in the sense that it is asymptotically equivalent to the optimal bandwidth if the true gradient were known the results of monte carlo simulations are reported and the finite sample performance of our proposed method confirms our theoretical analysis an empirical application is also provided showing that our proposed method delivers more reasonable and reliable quantile derivative estimates than traditional cross validation method

efficient estimation of semiparametric transformation models for counting processes summary a class of semiparametric transformation models is proposed to characterise the effects of possibly time varying covariates on the intensity functions of counting processes the class includes the proportional intensity model and linear transformation models as special cases nonparametric maximum likelihood estimators are developed for the regression parameters and cumulative intensity functions of these models based on censored data the estimators are shown to be consistent and asymptotically normal the limiting variances for the estimators of the regression parameters achieve the semi parametric efficient bounds and can be consistently estimated the limiting variances for the estimators of smooth functionals of the cumulative intensity function can also be consistently estimated simulation studies reveal that the proposed inference procedures perform well in practical settings two medical studies are provided

nonparametric estimation of regression functions with both categorical and continuous data abstract in this paper we propose a method for nonparametric regression which admits continuous and categorical data in a natural manner using the method of kernels a data driven method of bandwidth selection is proposed and we establish the asymptotic normality of the estimator we also establish the rate of convergence of the cross validated smoothing parameters to their benchmark optimal smoothing parameters simulations suggest that the new estimator performs much better than the conventional nonparametric estimator in the presence of mixed data an empirical application to a widely used and publicly available dynamic panel of patent data demonstrates that the out of sample squared prediction error of our proposed estimator is only 14 20 of that obtained by some popular parametric approaches which have been used to model this data set

bandwidth choice and confidence intervals for derivatives of noisy data summary we propose a method for automatic bandwidth selection for kernel estimators of derivatives of a regression function the finite sample behaviour of this new method is compared with that of other methods in a monte carlo study the automatic estimation of derivatives can be employed for the construction of asymptotic local confidence intervals for the nonparametric estimate of the regression function and its first derivatives

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

a generalized cp criterion for derivative estimation the performance of a nonparametric regression method depends on the values chosen for one or more tuning parameters although much attention has been given to tuning parameter selection for recovering a mean response function comparatively few studies have addressed tuning parameter selection for derivative estimation and most of these studies have focused on a specific nonparametric regression method such as kernel smoothing in this article we propose using a generalized cp gcp criterion to select tuning parameters for derivative estimation this approach can be used with any nonparametric regression method that estimates derivatives linearly in the observed responses including but not limited to kernel smoothing local regression and smoothing splines the gcp criterion is a proxy for the unobservable sum of squared errors in estimating the derivative and thus one can better estimate the derivative by selecting tuning parameters at which gcp is small we provide both empirical support for gcp

nonparametric instrumental variables estimation of a quantile regression model we consider nonparametric estimation of a regression function that is identified by requiring a specified quantile of the regression error conditional on an instrumental variable to be zero the resulting estimating equation is a nonlinear integral equation of the first kind which generates an ill posed inverse problem the integral operator and distribution of the instrumental variable are unknown and must be estimated nonparametrically we show that the estimator is mean square consistent derive its rate of convergence in probability and give conditions under which this rate is optimal in a minimax sense the results of monte carlo experiments show that the estimator behaves well in finite samples

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

instrumental variable with competing risk model in this paper we discuss causal inference on the efficacy of a treatment or medication on a time to event outcome with competing risks although the treatment group can be randomized there can be confoundings between the compliance and the outcome unmeasured confoundings may exist even after adjustment for measured covariates instrumental variable methods are commonly used to yield consistent estimations of causal parameters in the presence of unmeasured confoundings on the basis of a semiparametric additive hazard model for the subdistribution hazard we propose an instrumental variable estimator to yield consistent estimation of efficacy in the presence of unmeasured confoundings for competing risk settings we derived the asymptotic properties for the proposed estimator the estimator is shown to be well performed under finite sample size according to simulation results we applied our method to a real transplant data example and showed that the unmeasured confoundings lead to significant bias in the estimation of the effect about 50 attenuated copyright 2017 john wiley sons ltd

mendelian randomization using semiparametric linear transformation models mendelian randomization mr uses genetic information as an instrumental variable iv to estimate the causal effect of an exposure of interest on an outcome in the presence of unknown confounding we are interested in the causal effect of cigarette smoking on lung cancer survival which is subject to confounding by underlying pulmonary functions despite the well developed iv analyses for the continuous and binary outcomes the scarcity of methodology for the survival outcome limits its utility for the time to event data collected in many observational studies we propose an iv analysis method in the survival context estimating causal effects on a transformed survival time and survival probabilities using semiparametric linear transformation models we study the conditions under which hazard ratio and the effect on survival probability can be approximated for statistical inference we construct estimating equations to circumvent the difficulty in deriving joint likelihood of the exposure and the outcome due to the unknown confounding asymptotic properties of the proposed estimators are established without parametric assumptions about confounders we study the finite sample performance in extensive simulation studies the mr analysis of a lung cancer study suggests a harmful prognostic effect of smoking pack years that would have been missed by the crude association

data driven bandwidth selection in local polynomial fitting variable bandwidth and spatial adaptation when estimating a mean regression function and its derivatives locally weighted least squares regression has proven to be a very attractive technique the present paper focuses on the important issue of how to select the smoothing parameter or bandwidth in the case of estimating curves with a complicated structure a variable bandwidth is desirable furthermore the bandwidth should be indicated by the data themselves recent developments in nonparametric smoothing techniques inspired us to propose such a data driven bandwidth selection procedure which can be used to select both constant and variable bandwidths the idea is based on a residual squares criterion along with a good approximation of the bias and variance of the estimator the procedure can be applied to select bandwidths not only for estimating the regression curve but also for estimating its derivatives the resulting estimation procedure has the necessary flexibility for capturing complicated shapes of curves this is illustrated via a large variety of testing examples including examples with a large spatial variability the results are also compared with wavelet thresholding techniques and it seems that our results are at least comparable i e local polynomial regression using our data driven variable bandwidth has spatial adaptation properties that are similar to wavelets

a general approach to evaluating the bias of 2 stage instrumental variable estimators unmeasured confounding is a common concern when researchers attempt to estimate a treatment effect using observational data or randomized studies with nonperfect compliance to address this concern instrumental variable methods such as 2 stage predictor substitution 2sps and 2 stage residual inclusion 2sri have been widely adopted in many clinical studies of binary and survival outcomes 2sri has been accepted as the method of choice over 2sps but a compelling theoretical rationale has not been postulated we evaluate the bias and consistency in estimating the conditional treatment effect for both 2sps and 2sri when the outcome is binary count or time to event we demonstrate analytically that the bias in 2sps and 2sri estimators can be reframed to mirror the problem of omitted variables in nonlinear models and that there is a direct relationship with the collapsibility of effect measures in contrast to conclusions made by previous studies terza et al 2008 we demonstrate that the consistency of 2sri estimators only holds under the following conditions 1 when the null hypothesis is true 2 when the outcome model is collapsible or 3 when estimating the nonnull causal effect from cox or logistic regression models the strong and unrealistic assumption that the effect of the unmeasured covariates on the treatment is proportional to their effect on the outcome needs to hold we propose a novel dissimilarity metric to provide an intuitive explanation of the bias of 2sri estimators in noncollapsible models and demonstrate that with increasing dissimilarity between the effects of the unmeasured covariates on the treatment versus outcome the bias of 2sri increases in magnitude

semiparametric transformation models for causal inference in time to event studies with all or nothing compliance we consider causal inference in randomized survival studies with right censored outcomes and all or nothing compliance using semiparametric transformation models to estimate the distribution of survival times in treatment and control groups conditional on covariates and latent compliance type estimands depending on these distributions for example the complier average causal effect cace the complier effect on survival beyond time t and the complier quantile effect are then considered maximum likelihood is used to estimate the parameters of the transformation models using a specially designed expectation maximization em algorithm to overcome the computational difficulties created by the mixture structure of the problem and the infinite dimensional parameter in the transformation models the estimators are shown to be consistent asymptotically normal and semiparametrically efficient inferential procedures for the causal parameters are developed a simulation study is conducted to evaluate the finite sample performance of the estimated causal parameters we also apply our methodology to a randomized study conducted by the health insurance plan of greater new york to assess the reduction in breast cancer mortality due to screening

reducing variability of crossvalidation for smoothing parameter choice one of the attractions of crossvalidation as a tool for smoothing parameter choice is its applicability to a wide variety of estimator types and contexts however its detractors comment adversely on the relatively high variance of crossvalidatory smoothing parameters noting that this compromises the performance of the estimators in which those parameters are used we show that the variability can be reduced simply significantly and reliably by employing bootstrap aggregation or bagging we establish that in theory when bagging is implemented using an adaptively chosen resample size the variability of crossvalidation can be reduced by an order of magnitude however it is arguably more attractive to use a simpler approach based for example on half sample bagging which can reduce variability by approximately 50

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

richardson s iteration for nonsymmetric matrices abstract to solve the linear n n system 1 ax a for any nonsingular matrix a richardson s iteration 2 x j 1 x j j ax j a j 1 2 n which is applied in a cyclic manner with cycle length n is investigated where the j are free parameters the objective is to minimize the error x n 1 x where x is the solution of 1 if the spectrum of a is known to lie in a compact set s one is led to the chebyshev type approximation problem 3 min p 1 v n max z s p z where v n is the linear span of z z 2 z n if p solves 3 then the reciprocals of the zeros of p are optimal iteration parameters j it is shown that for a real problem 1 the iteration 2 can be carried out with real arithmetic alone even when there are complex j the stationary case n 1 is solved completely i e for all compact sets s the problem 3 is solved explicitly as a consequence the converging stationary iteration processes can be characterized for arbitrary closed disks s the problem 3 can be solved for all n n and a simple proof is provided the lemniscates associated with s are introduced they appear as an important tool for studying the stability of the iteration 2

empirical bias bandwidths for local polynomial nonparametric regression and density estimation abstract a data based local bandwidth selector is proposed for nonparametric regression by local fitting of polynomials the estimator called the empirical bias bandwidth selector ebbs is rather simple and easily allows multivariate predictor variables and estimation of any order derivative of the regression function ebbs minimizes an estimate of mean squared error consisting of a squared bias term plus a variance term the variance term used is exact not asymptotic though it involves the conditional variance of the response given the predictors that must be estimated the bias term is estimated empirically not from an asymptotic expression thus ebbs is similar to the double smoothing approach of hardle hall and marron and a local bandwidth selector of schucany but is developed here for a far wider class of estimation problems than what those authors considered ebbs is tested on simulated data and its performance seems quite satisfactory local polynomial smoothing of a histogram is a high

semiparametric analysis of transformation models with censored data summary a unified estimation procedure is proposed for the analysis of censored data using linear transformation models which include the proportional hazards model and the proportional odds model as special cases this procedure is easily implemented numerically and its validity does not rely on the assumption of independence between the covariates and the censoring variable the estimator is the same as the cox partial likelihood estimator in the case of the proportional hazards model moreover the asymptotic variance of the proposed estimator has a closed form and its variance estimator is easily obtained by plug in rules the method is illustrated by simulation and is applied to the veterans administration lung cancer data

local polynomial estimation of nonparametric simultaneous equations models abstract we define a new procedure for consistent estimation of nonparametric simultaneous equations models under the conditional mean independence restriction of newey et al 1999 nonparametric estimation of triangular simultaneous equation models econometrica 67 565 603 it is based upon local polynomial regression and marginal integration techniques we establish the asymptotic distribution of our estimator under weak data dependence conditions simulation evidence suggests that our estimator may significantly outperform the estimators of pinkse 2000 nonparametric two step regression estimation when regressors and errors are dependent canadian journal of statistics 28 289 300 and newey and powell 2003 instrumental variable estimation of nonparametric models econometrica 71 1565 1578

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

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

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

instrumental variable estimation in semi parametric additive hazards models instrumental variable methods allow unbiased estimation in the presence of unmeasured confounders when an appropriate instrumental variable is available two stage least squares and residual inclusion methods have recently been adapted to additive hazard models for censored survival data the semi parametric additive hazard model which can include time independent and time dependent covariate effects is particularly suited for the two stage residual inclusion method since it allows direct estimation of time independent covariate effects without restricting the effect of the residual on the hazard in this article we prove asymptotic normality of two stage residual inclusion estimators of regression coefficients in a semi parametric additive hazard model with time independent and time dependent covariate effects we consider the cases of continuous and binary exposure estimation of the conditional survival function given observed covariates is discussed and a resampling scheme is proposed to obtain simultaneous confidence bands the new methods are compared to existing ones in a simulation study and are applied to a real data set the proposed methods perform favourably especially in cases with exposure dependent censoring

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

instrumental variable additive hazards models summary instrumental variable iv methods are popular in non experimental studies to estimate the causal effects of medical interventions these approaches allow for the consistent estimation of treatment effects even if important confounding factors are unobserved despite the increasing use of these methods there have been few extensions of iv methods to censored data problems in this article we discuss challenges in applying iv techniques to the proportional hazards model and demonstrate the utility of the additive hazards formulation for iv analyses with censored data assuming linear structural equation models for the hazard function we develop a closed form two stage estimator for the causal effect in the additive hazard model the methods permit both continuous and discrete exposures and enable the estimation of causal relative survival measures the asymptotic properties of the estimators are derived and the resulting inferences are shown to perform well in simulation studies and in an application to a data set on the effectiveness of a novel chemotherapeutic agent for colon cancer

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

two stage residual inclusion for survival data and competing risks an instrumental variable approach with application to seer medicare linked data instrumental variable is an essential tool for addressing unmeasured confounding in observational studies two stage predictor substitution 2sps estimator and two stage residual inclusion 2sri are two commonly used approaches in applying instrumental variables recently 2sps was studied under the additive hazards model in the presence of competing risks of time to events data where linearity was assumed for the relationship between the treatment and the instrument variable this assumption may not be the most appropriate when we have binary treatments in this paper we consider the 2sri estimator under the additive hazards model for general survival data and in the presence of competing risks which allows generalized linear models for the relation between the treatment and the instrumental variable we derive the asymptotic properties including a closed form asymptotic variance estimate for the 2sri estimator we carry out numerical studies in finite samples and apply our methodology to the linked surveillance epidemiology and end results seer medicare database comparing radical prostatectomy versus conservative treatment in early stage prostate cancer patients

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

a linear regression model for the analysis of life times a linear model is suggested for the influence of covariates on the intensity function this approach is less vulnerable than the cox model to problems of inconsistency when covariates are deleted or the precision of covariate measurements is changed a method of non parametric estimation of regression functions is presented this results in plots that may give information on the change over time in the influence of covariates a test method and two goodness of fit plots are also given the approach is illustrated by simulation as well as by data from a clinical trial of treatment of carcinoma of the oropharynx

further results on the non parametric linear regression model in survival analysis this paper gives further developments of a non parametric linear regression model in survival analysis three subjects are studied first martingale residuals originally developed for the cox model are introduced for our linear model their theory is developed and they are shown to be useful for judging goodness of fit the second focus of the paper is on the use of bootstrap replications to judge which features of the cumulative regression plots are likely to reflect real phenomena and not merely random variation in particular this is applied to judging whether the effect of a covariate disappears over time a problem for which no formal test exists the third subject is density type or kernel estimation of the regression functions themselves this might give more direct information than the cumulative plots the approaches are illustrated by data from a clinical trial of carcinoma of the oropharynx and by survival times of grafts in renal patients

semi nonparametric iv estimation of shape invariant engel curves this paper studies a shape invariant engel curve system with endogenous total expenditure in which the shape invariant specification involves a common shift parameter for each demographic group in a pooled system of nonparametric engel curves we focus on the identification and estimation of both the nonparametric shapes of the engel curves and the parametric specification of the demographic scaling parameters the identification condition relates to the bounded completeness and the estimation procedure applies the sieve minimum distance estimation of conditional moment restrictions allowing for endogeneity we establish a new root mean squared convergence rate for the nonparametric instrumental variable regression when the endogenous regressor could have unbounded support root n asymptotic normality and semiparametric efficiency of the parametric components are also given under a set of low level sufficient conditions our empirical application using the u k family expenditure survey shows the importance of adjusting for endogeneity in terms of both the nonparametric curvatures and the demographic parameters of systems of engel curves

choosing the number of instruments properties of instrumental variable estimators are sensitive to the choice of valid instruments even in large cross section applications in this paper we address this problem by deriving simple mean square error criteria that can be minimized to choose the instrument set we develop these criteria for two stage least squares 2sls limited information maximum likelihood liml and a bias adjusted version of 2sls b2sls we give a theoretical derivation of the mean square error and show optimality in monte carlo experiments we find that the instrument choice generally yields an improvement in performance also in the angrist and krueger 1991 returns to education application when the instrument set is chosen in the way we consider it turns out that both 2sls and liml give similar large returns to education

testing and imposing slutsky symmetry in nonparametric demand systems maximization of utility implies that consumer demand systems have a slutsky matrix which is everywhere symmetric however previous non and semi parametric approaches to the estimation of consumer demand systems do not give estimators that are restricted to satisfy this condition nor do they offer powerful tests of this restriction we use nonparametric modeling to test and impose slutsky symmetry in a system of expenditure share equations over prices and expenditure in this context slutsky symmetry is a set of nonlinear cross equation restrictions on levels and derivatives of consumer demand equations the key insight is that due to the differing convergence rates of levels and derivatives and due to the fact that the symmetry restrictions are linear in derivatives both the test and the symmetry restricted estimator behave asymptotically as if these restrictions were locally linear we establish large and finite sample properties of our methods and show that our test has advantages over the only other comparable test all methods we propose are implemented with canadian micro data we find that our nonparametric analysis yields statistically significantly and qualitatively different results from traditional parametric estimators and tests

finite precision behavior of stationary iteration for solving singular systems a stationary iterative method for solving a singular system ax b converges for any starting vector if limi gi exists where g is the iteration matrix and the solution to which it converges depends on the starting vector we examine the behavior of stationary iteration in finite precision arithmetic a pertubation bound for singular systems is derived and used to define forward stability of a numerical method a rounding error analysis enables us to deduce conditions under which a stationary iterative method is forward stable or backward stable the component of the forward error in the null space of a can grow linearly with the number of iterations but it is innocuous as long as the iteration converges reasonably quickly as special cases we show that when a is symmetric positive semidefinite the richardson iteration with optimal parameter is forward stable and if a also has unit diagonal and property a then the gauss seidel method is both forward and backward stable two numerical examples are given to illustrate the analysis

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

analysis of transformation models with censored data summary in this paper we consider a class of semi parametric transformation models under which an unknown transformation of the survival time is linearly related to the covariates with various completely specified error distributions this class of regression models includes the proportional hazards and proportional odds models inference procedures derived from a class of generalised estimating equations are proposed to examine the covariate effects with censored observations numerical studies are conducted to investigate the properties of our proposals for practical sample sizes these transformation models coupled with the new simple inference procedures provide many useful alternatives to the cox regression model in survival analysis

functional coefficient regression models for nonlinear time series abstract the local linear regression technique is applied to estimation of functional coefficient regression models for time series data the models include threshold autoregressive models and functional coefficient autoregressive models as special cases but with the added advantages such as depicting finer structure of the underlying dynamics and better postsample forecasting performance also proposed are a new bootstrap test for the goodness of fit of models and a bandwidth selector based on newly defined cross validatory estimation for the expected forecasting errors the proposed methodology is data analytic and of sufficient flexibility to analyze complex and multivariate nonlinear structures without suffering from the curse of dimensionality the asymptotic properties of the proposed estimators are investigated under the mixing condition both simulated and real data examples are used for illustration

analysis of survival data by the proportional odds model a model is presented for the analysis of lifetime data in which the rates of mortality for separate groups of patients converge with time a non parametric estimate is given for the survivor function the theoretical basis for the model assumes that prognostic factors have a multiplicative effect on the odds against survival beyond any given time the model is fitted to data using maximum likelihood estimation and an example of its use in the analysis of a lung cancer trial is given

gradient based smoothing parameter selection for nonparametric regression estimation abstract estimating gradients is of crucial importance across a broad range of applied economic domains here we consider data driven bandwidth selection based on the gradient of an unknown regression function this is a difficult problem given that direct observation of the value of the gradient is typically not observed the procedure developed here delivers bandwidths which behave asymptotically as though they were selected knowing the true gradient simulated examples showcase the finite sample attraction of this new mechanism and confirm the theoretical predictions

nonparametric estimation of a generalized additive model with an unknown link function mean of a random scalar y conditional on a random vector x e rd let h x e yix x denote the conditional mean function this paper is concerned with estimating h under weak assumptions about its functional form when x is a multidimensional continuous random variable the paper describes a model that nests single index additive and multiplicative models and that can be estimated with a faster rate of convergence in probability than can a fully nonparametric model nonparametric estimation of h is usually unattractive when x is multidimensional the rate of convergence of nonparametric estimators decreases rapidly as the dimension of x increases and nonparametric estimates can be very imprecise with samples of practical size when x is multidimensional the curse of dimensionality this problem can be overcome through the use of dimension reduction methods they reduce the effective dimension of the estimation problem by making assumptions about the functional form of h that are stronger than those of a fully nonparametric estimator but weaker than those of a finite dimensional parametric model one method of dimension reduction is semiparametric single index modeling the best known and most easily estimated semiparametric single index model assumes that 1 1 h x g 3 x where 3 is an unknown d x 1 vector and g is an unknown function the vector 3 can be estimated with an n 1 2 rate of convergence in probability which is the rate that would be obtained if g were known han 1987 hardle and stoker 1989 horowitz and hardle 1996 ichimura 1993 klein and spady 1993 newey and stoker 1993 powell stock and stoker 1989 sherman 1993 stoker 1991 g can be estimated with the rate of convergence n r 2r 1 where r is an integer that depends on the smoothness of g but not on d dimension reduction can also be achieved by using a nonparametric generalized additive model in such a model