misspecified proportional hazard models summary the properties of an estimator based on a proportional hazards model are investigated when the model is incorrect the estimator from the partial likelihood is shown to be consistent for a parameter that is defined implicitly the results are used to investigate the effects on estimation if the true model is accelerated failure time or if covariates are omitted from the proportional hazards model

goodness of fit test for monotone proportional subdistribution hazards assumptions based on weighted residuals recently goodness of fit tests have been proposed for checking the proportional subdistribution hazards assumptions in the fine and gray regression model zhou fine and laird proposed weighted schoenfeld type residuals tests derived under an assumed model with specific form of time varying regression coefficients li sheike and zhang proposed an omnibus test based on cumulative sums of schoenfeld type residuals in this article we extend the class of weighted residuals tests by allowing random weights of schoenfeld type residuals at ordered event times in particular it is demonstrated that weighted residuals tests using monotone weight functions of time are consistent against monotone proportional subdistribution hazards assumptions extensive monte carlo studies were conducted to evaluate the finite sample performance of recent goodness of fit tests results from simulation studies show that weighted residuals tests using monotone random weight functions commonly used in non proportional hazards regression settings tend to be more powerful for detecting monotone departures than other goodness of fit tests assuming no specific time varying effect or misspecified time varying effects two examples using real data are provided for illustrations copyright 2016 john wiley sons ltd

cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

the grothendieck duality theorem via bousfield s techniques and brown representability grothendieck proved that if f x y is a proper morphism of nice schemes then rf has a right adjoint which is given as tensor product with the relative canonical bundle the original proof was by patching local data deligne proved the existence of the adjoint by a global argument and verdier showed that this global adjoint may be computed locally in this article we show that the existence of the adjoint is an immediate consequence of brown s representability theorem lit follows almost as imme diately by smashing arguments that the adjoint is given by tensor product with a dualising complex verdier s base change theorem is an easy conse quence department of mathematics university of virginia charlottesville virginia 22903 e mail address an3rqvirginia edu this content downloaded from 157 55 39 27 on wed 07 sep 2016 06 26 19 utc all use subject to http about jstor org terms

properties of proportional hazards score tests under misspecified regression models the effects are investigated of misspecifying a proportional hazards regression model on the associated partial likelihood score test for comparing two randomized treatments in the presence of covariates the asymptotic efficiency of the proportional hazards score test relative to the optimal partial likelihood test declines slowly as the hazard functions for the two treatments deviate from proportionality the efficiency can be very low when the hazard functions cross or differ only at large survival times misspecification of the functional form of the regression portion of a proportional hazards model introduces a quantitative treatment covariate interaction in the situations that we examine based on a binary covariate this misspecification usually results in only a minor drop in efficiency the omission of a covariate that is balanced across treatments has a negligible effect on the size of the score test but can substantially reduce power when the covariate effect is strong the loss of power from mismodeling a balanced covariate is usually small

delta matrix factorization for fast propagation through solid layers in a fluid solid medium propagator techniques for computation of wave propagation in layered fluid solid media are well established in underwater acoustics and seismology delta matrices for solid layers provide a convenient way of computing the boundary values at a fluid solid interface with loss of precision control a certain vector is propagated through a sequence of multiplications with delta matrices we show that computations of this kind can be performed more efficiently if each delta matrix is decomposed as a product of sparse matrices which are applied in sequence we propose two kinds of delta matrix factorizations in connection with dispersion computations our first factorization turns out to give a method that is very much related to the powerful fast form of knopoff s method our algorithm is slightly more efficient however furthermore the derivation gives insight into the structure of the delta matrix propagator and other applications such as propagation in connection with wavenumber integration for point source studies become immediate our second delta matrix factorization gives a dispersion function method that is significantly faster than the fast form of knopoff s method the most conspicuous gains in comparison to previous methods however appear for applications to wavenumber integration techniques such as the reflectivity method very few arithmetic operations are needed this factorization also provides a good basis for analyzing the numerical performance of delta matrix propagation it becomes quite obvious how to perform scaling so as to avoid overflow for arbitrarily thick homogeneous layers without layer splitting in connection with multi frequency computations distinct advantages are obtained

quantifying the totality of treatment effect with multiple event time observations in the presence of a terminal event from a comparative clinical study to evaluate the totality of one treatment s benefit risk profile relative to an alternative treatment via a longitudinal comparative clinical study the timing and occurrence of multiple clinical events are typically collected during the patient s follow up these multiple observations reflect the patient s disease progression burden over time the standard practice is to create a composite endpoint from the multiple outcomes the timing of the occurrence of the first clinical event to evaluate the treatment via the standard survival analysis techniques by ignoring all events after the composite outcome this type of assessment may not be ideal various parametric or semiparametric procedures have been extensively discussed in the literature for the purposes of analyzing multiple event time data many existing methods were developed based on extensive model assumptions when the model assumptions are not plausible the resulting inferences for the treatment effect may be misleading in this article we propose a simple nonparametric inference procedure to quantify the treatment effect which has an intuitive clinically meaningful interpretation we use the data from a cardiovascular clinical trial for heart failure to illustrate the procedure a simulation study is also conducted to evaluate the performance of the new proposal

estimation of the survival function for gray s piecewise constant time varying coefficients model gray s extension of cox s proportional hazards ph model for right censored survival data allows for a departure from the ph assumption via introduction of time varying regression coefficients tvc using penalized splines gray s work focused on estimation inference and residual analyses but no estimator for the survival function has been proposed we derive a survival function estimator for one important member of the class of tvc models a piecewise constant time varying coefficients pc tvc model we also derive an estimate for the confidence limits of the survival function accuracy in estimating underlying survival times and survival quantiles is assessed for both cox s and gray s pc tvc model using a simulation study featuring scenarios violating the ph assumption finally an example of the estimated survival functions and the corresponding confidence limits derived from cox s ph and gray s pc tvc model respectively is presented for a liver transplant data set in the second part of the thesis we examine the effect of model misspecification for two classes of regression models for right censored survival data additive and multiplicative models for the conditional hazard rate a particular attention is given to data exhibiting time varying regression coefficients the class of multiplicative models is represented by cox ph model and gray s tvc model respectively and for additive models we use aalen s linear model both gray s tvc model and aalen s linear model incorporate time varying coefficients a simulation study is performed to cross analyze survival data which follows either a multiplicative or an additive model for the conditional hazard rate the effect of misspecifying the true model for the conditional hazard rate is assessed by looking at the power of the individual models to detect an existing effect bias and mean square error observed for each conditional model based estimator of survival we also show that aalen s model formulae is a first order taylor series approximation of that of gray s model which explains the comparably higher flexibility on part of the aalen s model as compared to the cox ph when the gray s tvc model for the data is misspecified

estimation of the proportional hazard in two treatment group clinical trials two easily computed approximate methods of obtaining an estimate of the ratio of the hazard rates for two treatments in survival analysis are compared by simulation with the partial maximum likelihood cml estimator which assumes the cox model with no covariates the two methods studied are the mantel haenszel estimator and the o e method which employs the ratio of the relative death rates for the two treatments uncensored and censored cases are examined for both continuous and tied data with the assumption of either an underlying exponential distribution or a weibull distribution with shape parameter 2 the o e method is biased but within the range of values of the ratio of the hazard rates of interest in clinical trials it is more efficient in terms of mean square error than either cml or the mantel haenszel method for all but the largest trials the mantel haenszel method is minimally biased gives answers very close to those obtained using cml and may be used to provide satisfactory approximate confidence intervals

survival analysis 1982 1991 the second decade of the proportional hazards regression model a short review of the cox regression model and its development from publication to 1982 is given i discuss how the model is used and presented in medical journals and how improvement may be achieved finally some extensions of the model are outlined

checking the cox model with cumulative sums of martingale based residuals summary this paper presents a new class of graphical and numerical methods for checking the adequacy of the cox regression model the procedures are derived from cumulative sums of martingale based residuals over follow up time and or covariate values the distributions of these stochastic processes under the assumed model can be approximated by zero mean gaussian processes each observed process can then be compared both visually and analytically with a number of simulated realizations from the approximate null distribution these comparisons enable the data analyst to assess objectively how unusual the observed residual patterns are special attention is given to checking the functional form of a covariate the form of the link function and the validity of the proportional hazards assumption an omnibus test consistent against any model misspecification is also studied the proposed techniques are illustrated with two real data sets

smashing subcategories and the telescope conjecture an algebraic approach we prove a modified version of ravenel s telescope conjecture it is shown that every smashing subcategory of the stable homotopy category is generated by a set of maps between finite spectra this result is based on a new characterization of smashing subcategories which leads in addition to a classification of these subcategories in terms of the category of finite spectra the approach presented here is purely algebraic it is based on an analysis of pure injective objects in a compactly generated triangulated category and covers therefore also situations arising in algebraic geometry and representation theory

functional form diagnostics for cox s proportional hazards model summary we propose a new type of residual and an easily computed functional form test for the cox proportional hazards model the proposed test is a modification of the omnibus test for testing the overall fit of a parametric regression model developed by stute gonzalez manteiga and presedo quindimil 1998 journal of the american statistical association93 141 149 and is based on what we call censoring consistent residuals in addition we develop residual plots that can be used to identify the correct functional forms of covariates we compare our test with the functional form test of lin wei and ying 1993 biometrika80 557 572 in a simulation study the practical application of the proposed residuals and functional form test is illustrated using both a simulated data set and a real data set

doubly robust estimator for net survival rate in analyses of cancer registry data cancer population studies based on cancer registry databases are widely conducted to address various research questions in general cancer registry databases do not collect information on cause of death the net survival rate is defined as the survival rate if a subject would not die for any causes other than cancer this counterfactual concept is widely used for the analyses of cancer registry data perme stare and esteve 2012 proposed a nonparametric estimator of the net survival rate under the assumption that the censoring time is independent of the survival time and covariates kodre and perme 2013 proposed an inverse weighting estimator for the net survival rate under the covariate dependent censoring an alternative approach to estimating the net survival rate under covariate dependent censoring is to apply a regression model for the conditional net survival rate given covariates in this article we propose a new estimator for the net survival rate the proposed estimator is shown to be doubly robust in the sense that it is consistent at least one of the regression models for survival time and for censoring time we examine the theoretical and empirical properties of our proposed estimator by asymptotic theory and simulation studies we also apply the proposed method to cancer registry data for gastric cancer patients in osaka japan

a simple estimator for a shared frailty regression model summary we propose a simple estimation procedure for a proportional hazards frailty regression model for clustered survival data in which the dependence is generated by a positive stable distribution inferences for the frailty parameter can be obtained by using output from cox regression analyses the computational burden is substantially less than that of the other approaches to estimation the large sample behaviour of the estimator is studied and simulations show that the approximations are appropriate for use with realistic sample sizes the methods are motivated by studies of familial associations in the natural history of diseases their practical utility is illustrated with sib pair data from beaver dam wisconsin

the impact of time dependent bias in proportional hazards modelling in the clinical literature time dependent exposure status has regularly been analysed as if known at time origin although statisticians agree that such an analysis yields biased results when analysing the effect on the time until some endpoint of interest this paper is the first to study in detail the bias arising in a proportional hazards analysis we show that the biased hazard ratio estimate will always be less than the unbiased one this leads to either an inflated or a damped effect of exposure depending on the sign of the correct log hazard ratio estimate we find an explicit formula of the asymptotic bias based on generalized rank estimators and we investigate the role of censoring which may prevent an individual from being considered as being baseline exposed in the biased analysis we illustrate our results with data on hospital infection status and different censoring patterns

graphical representation of survival curves associated with a binary non reversible time dependent covariate the use of time dependent covariates has allowed for incorporation into analysis of survival data intervening events that are binary and non reversible for example heart transplant initial response to chemotherapy we can represent this type of intervening event as a three state stochastic process with a starting state s an intervening state i and an absorbing state d which usually represents death in this paper we present three procedures for calculating survivorship functions which attempt to display the prognostic significance of the time dependent covariate the first method compares survival from baseline for the two possible paths through the stochastic process the second method compares overall survival to survival with state i removed from the process and the third method compares survival for those already in state i at a landmark time x to those in state s at time x who will never enter state i we develop discrete hazard estimates for the survival curves associated with the three methods two examples illustrate how these methods can yield different results and in which situations one might employ each of the three methods extensions to applications with reversible binary time dependent covariates and models with both baseline and time dependent covariates are suggested

the robust inference for the cox proportional hazards model abstract we derive the asymptotic distribution of the maximum partial likelihood estimator for the vector of regression coefficients under a possibly misspecified cox proportional hazards model as in the parametric setting this estimator converges to a well defined constant vector in addition the random vector n 1 2 is asymptotically normal with mean 0 and with a covariance matrix that can be consistently estimated the newly proposed robust covariance matrix estimator is similar to the so called sandwich variance estimators that have been extensively studied for parametric cases for many misspecified cox models the asymptotic limit or part of it can be interpreted meaningfully in those circumstances valid statistical inferences about the corresponding covariate effects can be drawn based on the aforementioned asymptotic theory of and the related results for the score statistics extensive studies demonstrate that the proposed robust tests and interval estimation procedures

the mizon richard encompassing test for the cox and aalen additive hazards models summary the cox hazards model cox 1972 journal of the royal statistical society series b 34 187 220 for survival data is routinely used in many applied fields sometimes however with too little emphasis on the fit of the model a useful alternative to the cox model is the aalen additive hazards model aalen 1980 in lecture notes in statistics 2 1 25 that can easily accommodate time changing covariate effects it is of interest to decide which of the two models that are most appropriate to apply in a given application this is a nontrivial problem as these two classes of models are nonnested except only for special cases in this article we explore the mizon richard encompassing test for this particular problem it turns out that it corresponds to fitting of the aalen model to the martingale residuals obtained from the cox regression analysis we also consider a variant of this method which relates to the proportional excess model martinussen and scheike 2002 biometrika 89 283 298 large sample properties of the suggested methods under the two rival models are derived the finite sample properties of the proposed procedures are assessed through a simulation study the methods are further applied to the well known primary biliary cirrhosis data set

orlov spectra bounds and gaps the orlov spectrum is a new invariant of a triangulated category it was introduced by d orlov building on work of a bondal m van den bergh and r rouquier the supremum of the orlov spectrum of a triangulated category is called the ultimate dimension in this work we study orlov spectra of triangulated categories arising in mirror symmetry we introduce the notion of gaps and outline their geometric significance we provide the first large class of examples where the ultimate dimension is finite categories of singularities associated to isolated hypersurface singularities similarly given any nonzero object in the bounded derived category of coherent sheaves on a smooth calabi yau hypersurface we produce a generator by closing the object under a certain monodromy action and uniformly bound this generator s generation time in addition we provide new upper bounds on the generation times of exceptional collections and connect generation time to braid group actions to provide a lower bound on the ultimate dimension of the derived fukaya category of a symplectic surface of genus greater than one

estimation of treatment effect under non proportional hazards and conditionally independent censoring in clinical trials with time to event outcomes it is common to estimate the marginal hazard ratio from the proportional hazards model even when the proportional hazards assumption is not valid this is unavoidable from the perspective that the estimator must be specified a priori if probability statements about treatment effect estimates are desired marginal hazard ratio estimates under non proportional hazards are still useful as they can be considered to be average treatment effect estimates over the support of the data however as many have shown under non proportional hazard the usual unweighted marginal hazard ratio estimate is a function of the censoring distribution which is not normally considered to be scientifically relevant when describing the treatment effect in addition in many practical settings the censoring distribution is only conditionally independent e g differing across treatment arms which further complicates the interpretation in this paper we investigate an estimator of the hazard ratio that removes the influence of censoring and propose a consistent robust variance estimator we compare the coverage probability of the estimator to both the usual cox model estimator and an estimator proposed by xu and o quigley 2000 when censoring is independent of the covariate the new estimator should be used for inference that does not depend on the censoring distribution it is particularly relevant to adaptive clinical trials where by design censoring distributions differ across treatment arms copyright 2012 john wiley sons ltd

generalized martingale residual processes for goodness of fit inference in cox s type regression models in the paper a general class of stochastic processes based on the sums of weighted martingale transform residuals for goodness of fit inference in general cox s type regression models is studied their form makes the inference robust to covariate outliers a weak convergence result for such processes is obtained giving the possibility of establishing the randomness of their graphs together with the construction of the formal x 2 type goodness of fit tests by using the khmaladze innovation approach a modified version of the initial class of processes is also defined weak convergence results for the processes are derived this leads to the main application which concerns the formal construction of the kolmogorov smirnov and cramer von mises type goodness of fit tests this is done within the general situation considered

generating survival times to simulate cox proportional hazards models with time varying covariates simulations and monte carlo methods serve an important role in modern statistical research they allow for an examination of the performance of statistical procedures in settings in which analytic and mathematical derivations may not be feasible a key element in any statistical simulation is the existence of an appropriate data generating process one must be able to simulate data from a specified statistical model we describe data generating processes for the cox proportional hazards model with time varying covariates when event times follow an exponential weibull or gompertz distribution we consider three types of time varying covariates first a dichotomous time varying covariate that can change at most once from untreated to treated e g organ transplant second a continuous time varying covariate such as cumulative exposure at a constant dose to radiation or to a pharmaceutical agent used for a chronic condition third a dichotomous time varying covariate with a subject being able to move repeatedly between treatment states e g current compliance or use of a medication in each setting we derive closed form expressions that allow one to simulate survival times so that survival times are related to a vector of fixed or time invariant covariates and to a single time varying covariate we illustrate the utility of our closed form expressions for simulating event times by using monte carlo simulations to estimate the statistical power to detect as statistically significant the effect of different types of binary time varying covariates this is compared with the statistical power to detect as statistically significant a binary time invariant covariate copyright 2012 john wiley sons ltd

comparing nonnested cox models summary we derive the limiting distribution of the partial likelihood ratio under general conditions the multiplicative hazards models being fitted may be nonnested and misspecified the true model is not assumed to contain either model under consideration the null hypothesis is that the models are equidistant in kullback leibler metric applied to the rank likelihood the statistic is consistent for the model which is closer to the truth its distribution depends on the unknown data generating mechanism a sequential testing procedure is proposed for nonnested comparisons which is valid regardless of the true model this involves a novel statistic for the equality of the fitted models which is separate from the partial likelihood the methodology has important applications in model assessment simulations and a real example demonstrate its utility in selecting the functional forms of covariates and relative risks

a risk set calibration method for failure time regression by using a covariate reliability sample regression parameter estimation in the cox failure time model is considered when regression variables are subject to measurement error assuming that repeat regression vector measurements adhere to a classical measurement model we can consider an ordinary regression calibration approach in which the unobserved covariates are replaced by an estimate of their conditional expectation given available covariate measurements however since the rate of withdrawal from the risk set across the time axis due to failure or censoring will typically depend on covariates we may improve the regression parameter estimator by recalibrating within each risk set the asymptotic and small sample properties of such a risk set regression calibration estimator are studied a simple estimator based on a least squares calibration in each risk set appears able to eliminate much of the bias that attends the ordinary regression calibration estimator under extreme measurement error circumstances corresponding asymptotic distribution theory is developed small sample properties are studied using computer simulations and an illustration is provided

effect of misspecification of regression models in the analysis of survival data the accelerated life and proportional hazards families of models are widely used in the analysis of survival data we examine the question if interest lies in the qualitative effect on failure of various explanatory variables how critical is the choice of model family in assessing the relative importance of the explanatory variables we consider small effects when censoring is independent of the explanatory variables to first order the regression parameters are proportional under the alternative models this is not true when the censoring varies appreciably with the explanatory variables some higherorder theory is examined for the special case of the two sample problem

derived categories of sheaves on singular schemes with an application to reconstruction abstract we prove that the bounded derived category of coherent sheaves with proper support is equivalent to the category of locally finite cohomological functors on the perfect derived category of a quasi projective scheme over a field we introduce the notions of pseudo adjoints and rouquier functors and study them as an application of these ideas and results we extend the reconstruction result of bondal and orlov to gorenstein projective varieties

dunnett type inference in the frailty cox model with covariates a frequent objective in medical research is the investigation of differences in patient survival between several experimental treatments and one standard treatment in order to assess these differences statistically we have to apply adjustments for multiple comparisons to prevent an increased number of false positive findings the most prominent procedure of this type is the bonferroni correction which maintains the error level but leads to conservative results on the basis of a general statistical framework for simultaneous inference we propose a new statistical procedure for many to one comparisons of treatments with adjustment for covariates for clustered survival data modeled by a frailty cox model in contrast to the bonferroni method dependencies between estimated effects are taken into account the resulting simultaneous confidence intervals for the hazard ratios of the experimental treatments compared with a control can be interpreted in terms of both statistical significance and clinical importance the quality of the new procedure is judged by the coverage probability for the simultaneous confidence intervals simulation results show an acceptable performance in balanced and various unbalanced designs the practical merits are demonstrated by a reanalysis of a chronic myelogeneous leukemia clinical trial the procedure presented here works well for multiple comparisons with a control with adjustment for covariates for survival data from multicenter clinical trials

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

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

uniqueness of enhancement for triangulated categories the paper contains general results on the uniqueness of a dg enhancement for trian gulated categories as a consequence we obtain such uniqueness for the unbounded categories of quasi coherent sheaves for the triangulated categories of perfect complexes and for the bounded de rived categories of coherent sheaves on quasi projective schemes if a scheme is projective then we also prove a strong uniqueness for the triangulated category of perfect complexes and for the bounded de rived categories of coherent sheaves these results directly imply that fully faithful functors from the bounded derived categories of coherent sheaves and the triangulated categories of perfect complexes on projective schemes can be represented by objects on the product

double robust semiparametric estimator for differences in restricted mean lifetimes in observational studies restricted mean lifetime is often of direct interest in epidemiologic studies involving censored survival times differences in this quantity can be used as a basis for comparing several groups for example transplant surgeons nephrologists and of course patients are interested in comparing posttransplant lifetimes among various types of kidney transplants to assist in clinical decision making as the factor of interest is not randomized covariate adjustment is needed to account for imbalances in confounding factors in this report we use semiparametric theory to develop an estimator for differences in restricted mean lifetimes although accounting for confounding factors the proposed method involves building working models for the time to event and coarsening mechanism i e group assignment and censoring we show that the proposed estimator possesses the double robust property i e when either the time to event or coarsening process is modeled correctly the estimator is consistent and asymptotically normal simulation studies are conducted to assess its finite sample performance and the method is applied to national kidney transplant data

a versatile test for equality of two survival functions based on weighted differences of kaplan meier curves with censored event time observations the logrank test is the most popular tool for testing the equality of two underlying survival distributions although this test is asymptotically distribution free it may not be powerful when the proportional hazards assumption is violated various other novel testing procedures have been proposed which generally are derived by assuming a class of specific alternative hypotheses with respect to the hazard functions the test considered by pepe and fleming 1989 is based on a linear combination of weighted differences of the two kaplan meier curves over time and is a natural tool to assess the difference of two survival functions directly in this article we take a similar approach but choose weights that are proportional to the observed standardized difference of the estimated survival curves at each time point the new proposal automatically makes weighting adjustments empirically the new test statistic is aimed at a one sided general alternative hypothesis and is distributed with a short right tail under the null hypothesis but with a heavy tail under the alternative the results from extensive numerical studies demonstrate that the new procedure performs well under various general alternatives with a caution of a minor inflation of the type i error rate when the sample size is small or the number of observed events is small the survival data from a recent cancer comparative study are utilized for illustrating the implementation of the process copyright 2015 john wiley sons ltd

mode structure for fluid solid media as derived by low frequency asymptotics abstract the modes in a laterally homogeneous fluid solid medium can be classified according to their low frequency behaviour for each mode the horizontal wavenumber k will tend to a complex limit q possibly infinite but that appears to be exceptional as the angular frequency tends to zero the modes with vanishing wavenumber limits q can be listed explicitly they are finite in number for each particular medium the non zero finite limits q appear as the zeros of certain entire analytic functions one particular function for each fluid or solid region in the medium and also for each riemann sheet in the presence of homogeneous half spaces the resulting low frequency mode structure can be uncovered for each fluid solid medium by computing the wavenumber limits q as provided by the different regions efficient and reliable numerical techniques for this purpose are proposed for homogeneously layered media based on compound matrix factorization the mode structure can be carried to higher frequencies by tracking dispersion curves the behaviour at double roots and branch points needs special consideration two examples are studied in detail one from plate acoustics and one from underwater acoustics

robust alternatives to ancova for estimating the treatment effect via a randomized comparative study in comparing two treatments via a randomized clinical trial the analysis of covariance ancova technique is often utilized to estimate an overall treatment effect the ancova is generally perceiv

low frequency slow wave dispersion computations by compound matrix propagation slow p sv modes whose horizontal slowness tends to infinity while the horizontal wave number tends to zero as the frequency tends to zero exist in certain laterally homogeneous fluid solid media these modes can be characterized by an asymptotic analysis of the dispersion function only certain powers of frequency are possible for the asymptotic increase of the horizontal slowness as the frequency tends to zero 1 3 1 2 3 5 and 2 3 in order to investigate the accuracy of the asymptotic predictions dispersion curve computations by propagator techniques are attempted for media composed of homogeneous fluid and solid layers however numerical precision is lost by cancellation effects for the elements of the solid layer compound matrix propagators that are involved guided by the asymptotic growth of these compound matrix elements cancellation free expressions are derived for applications to the slow modes at very low frequencies the harmful contributions causing loss of numerical precision are eliminated analytically to demonstrate the success a numerical case study is performed leading to conjectures about the next to leading terms in low frequency asymptotic expansions of the slow mode modal slownesses

asymptotically efficient two step estimators of the hazards ratio for follow up studies and survival data summary asymptotically efficient estimators of a common hazard rate ratio for follow up studies and the proportional hazards ratio for survival studies are obtained by a single iteration of the mantelhaenszel estimator appropriate for each setting estimators of their variance are also developed the two step estimator for survival data and its variance estimator are shown by simulation to be minimally biased and the estimator is shown to be efficient relative to the cox partial likelihood estimator in small samples

biased estimates of treatment effect in randomized experiments with nonlinear regressions and omitted covariates summary certain important nonlinear regression models lead to biased estimates of treatment effect even in randomized experiments if needed covariates are omitted the asymptotic bias is determined both for estimates based on the method of moments and for maximum likelihood estimates the asymptotic bias from omitting covariates is shown to be zero if the regression of the response variable on treatment and covariates is linear or exponential and in regular cases this is a necessary condition for zero bias many commonly used models do have such exponential regressions thus randomization ensures unbiased treatment estimates in a large number of important nonlinear models for moderately censored exponential survival data analysis with the exponential survival model yields less biased estimates of treatment effect than analysis with the proportional hazards model of cox if needed covariates are omitted simulations confirm that calculations of asymptotic bias are in excellent agreement with the bias observed in experiments of modest size

cox regression with incomplete covariate measurements abstract this article provides a general solution to the problem of missing covariate data under the cox regression model the estimating function for the vector of regression parameters is an approximation to the partial likelihood score function with full covariate measurements and reduces to the pseudolikelihood score function of self and prentice in the special setting of case cohort designs the resulting parameter estimator is consistent and asymptotically normal with a covariance matrix for which a simple and consistent estimator is provided extensive simulation studies show that the large sample approximations are adequate for practical use the proposed approach tends to be more efficient than the complete case analysis especially for large cohorts with infrequent failures for case cohort designs the new methodology offers a variance covariance estimator that is much easier to calculate than the existing ones and allows multiple subcohort augmentations to improve efficiency real data taken f