ordinal and cardinal utility an integration of the two dimensions of the welfare concept abstract in this paper we distinguish two dimensions of the utility concept the first is the behavioral dimension described by indifference curves in a commodity space it may be estimated by observing consumer purchase behavior the second dimension is the welfare dimension i e the cardinal utility levels corresponding to indifference curves the second dimension may be estimated by means of the income evaluation approach we deal with methodological issues and show by means of empirical evidence the validity of the income evaluation approach in the same time we propose some major modifications of the method secondly we show how the two dimensions may be combined this is illustrated with respect to the aids and the translog model in this way we find how price and income variations influence measured individual welfare

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

constructing a quasi concave quadratic objective function from interviewing a decision maker abstract a model for constructing quadratic objective functions utility functions from interviewing a decision maker is considered the interview is designed to guarantee a unique non trivial output of the model and to enable estimating both cardinal and ordinal utility depending on interview scenarios the model is provided with operational restrictions for the monotonicity of the objective function either only growth or only decrease in every variable and its quasi concavity convexity of the associated preference thereby constructing a monotonic quasi concave quadratic objective function is reduced to a problem of non linear programming to support interactive editing of a quadratic objective function the stability of the model the continuous dependence of the output ordinal preference on the input data is proved in illustration we construct a quadratic objective function of ski station customers then it is used to adjust prices of 10 ski stations in the south of stuttgart

estimation in change point hazard rate models summary this paper discusses the estimation of parameters in hazard rate models with a changepoint due to the irregularity of the models the classical maximum likelihood method and the method of moments cannot be used a consistent estimator of the change point is obtained by examining the properties of the density represented as a mixture the performance of the estimator is checked via simulation

a sequential testing approach to detecting multiple change points in the proportional hazards model the semi parametric proportional hazards model has been widely adopted in clinical trials with time to event outcomes a key assumption in the model is that the hazard ratio function is a constant over time which is frequently violated as there is often a lag period before an experimental treatment reaches its full effect one existing approach uses maximal score tests and monte carlo sampling to identify multiple change points in the hazard ratio function which requires the number of change points that exist in the model to be known we propose a sequential testing approach to detecting multiple change points in the hazard ratio function using likelihood ratio tests and the distributions of the likelihood ratio statistics under the null hypothesis are evaluated via resampling an important feature of the proposed approach is that the number of change points in the model is inferred from the data and does not need to be specified numerical results based on simulated clinical trials and a real time to event study show that the proposed approach can accurately detect the change points in the hazard ratio function

failure time regression with continuous covariates measured with error summary we consider failure time regression analysis with an auxiliary variable in the presence of a validation sample we extend the nonparametric inference procedure of zhou and pepe to handle a continuous auxiliary or proxy covariate we estimate the induced relative risk function with a kernel smoother and allow the selection probability of the validation set to depend on the observed covariates we present some asymptotic properties for the kernel estimator and provide some simulation results the method proposed is illustrated with a data set from an on going epidemiologic study

estimation in a cox regression model with a change point according to a threshold in a covariate we consider a nonregular cox model for independent and identically distributed right censored survival times with a change point according to the unknown threshold of a covariate the maximum partial likelihood estimators of the parameters and the estimator of the baseline cumulative hazard are studied we prove that the estimator of the change point is n consistent and the estimator of the regression parameters are n 1 2 consistent and we establish the asymptotic distributions of the estimators the estimators of the regression parameters and of the baseline cumulative hazard are adaptive in the sense that they do not depend on the knowledge of the change point

a monte carlo approach for change point detection in the cox proportional hazards model detecting a time lag of treatment effect or identifying change points in a hazard function is of great interest and importance in survival analysis the testing procedures hereto are primarily based on analytical approximations for the asymptotic null distribution of either the likelihood ratio test or the score test in the presence of random censoring and or covariates however the justification for the limiting distribution often requires some technical assumptions and conditions that are difficult to verify in practice moreover a satisfactory asymptotic theory for testing the existence of multiple change points in hazard function has not emerged in this paper we consider maximal score tests for detecting change point s in the cox proportional hazards model with censored data we propose to use a simple monte carlo approach for assessing the statistical significance of tests the proposed approach is applicable for testing a single change point in the cox model with covariates and sample stratifications over various types of candidate regions including discrete time point sets or disjoint intervals we also show that the proposed test statistics and the monte carlo procedure are well applicable under situations with multiple change points simulation studies and an analysis of a real data from a randomized cancer trial are conducted to demonstrate the finite sample performance of the proposed approach

new thoughts on old results of r t seeley in this paper we show that the lp realization of a vector valued elliptic boundary value problem j admits a bounded calculus on lp g e 1 p provided the top order coefficients of are holder continuous here g denotes a domain in n with compact c2m boundary and e a banach space of class our proof is based on an abstract perturbation result for operators admitting bounded calculus and kernel estimates for the solution of j

a resampling method based on pivotal estimating functions summary suppose that under a semiparametric model setting one is interested in drawing inferences about a finite dimensi onal parameter vector based on an estimating function generally a consistent point estimator j for 0 the true value for j can be easily obtained by finding a root of the corresponding estimating equation to estimate the variance of ft however may involve complicated and subjective nonparametric functional estimates in this paper a general and simple resampling method for inferences about js0 based on pivotal estimating functions is proposed the new procedure is illustrated with the quantile and rank regression models for both cases our proposal can be easily and efficiently implemented with existing statistical software

on a time dependent bio reactor model with chemotaxis long time dynamics of solutions to a strongly coupled system of parabolic equations modeling the competition in bio reactors with chemotaxis will be studied if the parameters of the system are periodic sufficient conditions for positive periodic solutions will be derived in terms of parabolic eigenvalue problems

cox s periodic regression model le modele de cox peut etre adapte pour modeliser un processus ponctuel ayant une intensite periodique

a case cohort design for epidemiologic cohort studies and disease prevention trials summary suppose that a cohort of individuals is to be followed in order to relate failure rates to preceding covariate histories a design is proposed which involves covariate data only for cases experiencing failure and for members of a randomly selected subcohort odds ratio and relative risk estimation procedures are presented for such a case cohort design a small simulation study compares case cohort relative risk estimation procedures to full cohort and synthetic case control analyses relevance to epidemiologic cohort studies and disease prevention trials is discussed

finite time blowup and global in time unbounded solutions to a parabolic parabolic quasilinear keller segel system in higher dimensions abstract in this paper we consider quasilinear keller segel type systems of two kinds in higher dimensions in the case of a nonlinear diffusion system we prove an optimal with respect to possible nonlinear diffusions generating explosion in finite time of solutions finite time blowup result in the case of a cross diffusion system we give results which are optimal provided one assumes some proper non decay of a nonlinear chemical sensitivity moreover we show that once we do not assume the above mentioned non decay our result cannot be as strong as in the case of nonlinear diffusion without nonlinear cross diffusion terms to this end we provide an example interesting by itself of global in time unbounded solutions to the nonlinear cross diffusion keller segel system with chemical sensitivity decaying fast enough in a range of parameters in which there is a finite time blowup result in a corresponding case without nonlinear cross diffusion

information criteria for firth s penalized partial likelihood approach in cox regression models in the estimation of cox regression models maximum partial likelihood estimates might be infinite in a monotone likelihood setting where partial likelihood converges to a finite value and parameter estimates converge to infinite values to address monotone likelihood previous studies have applied firth s bias correction method to cox regression models however while the model selection criteria for firth s penalized partial likelihood approach have not yet been studied a heuristic aic type information criterion can be used in a statistical package application of the heuristic information criterion to data obtained from a prospective observational study of patients with multiple brain metastases indicated that the heuristic information criterion selects models with many parameters and ignores the adequacy of the model moreover we showed that the heuristic information criterion tends to select models with many regression parameters as the sample size increases thereby in the present study we propose an alternative aic type information criterion based on the risk function a bayesian information criterion type was also evaluated further the presented simulation results confirm that the proposed criteria performed well in a monotone likelihood setting the proposed aic type criterion was applied to prospective observational study data copyright 2017 john wiley sons ltd

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

a positive stable frailty model for clustered failure time data with covariate dependent frailty summary in this article we propose a positive stable shared frailty cox model for clustered failure time data where the frailty distribution varies with cluster level covariates the proposed model accounts for covariate dependent intracluster correlation and permits both conditional and marginal inferences we obtain marginal inference directly from a marginal model then use a stratified cox type pseudo partial likelihood approach to estimate the regression coefficient for the frailty parameter the proposed estimators are consistent and asymptotically normal and a consistent estimator of the covariance matrix is provided simulation studies show that the proposed estimation procedure is appropriate for practical use with a realistic number of clusters finally we present an application of the proposed method to kidney transplantation data from the scientific registry of transplant recipients

global strong solution to the semi linear keller segel system of parabolic parabolic type with small data in scale invariant spaces abstract we shall show existence of global strong solution to the semi linear keller segel system in r n n 3 of parabolic parabolic type with small initial data u 0 h n r 2 r r n and v 0 h n r r r n for max 1 n 4 r n 2 our method is based on the perturbation of linealization together with the l p l q estimates of the heat semigroup and the fractional powers of the laplace operator as a by product of our method we shall prove the decay property of solutions as the time goes to infinity

nonlinear hypotheses inequality restrictions and non nested hypotheses exact simultaneous tests in linear regressions in the context of the classical linear model the problem of comparing two arbitrary hypotheses on the regression coefficients is considered problems involving nonlinear hypotheses inequality restrictions or non nested hypotheses are included as special cases exact bounds on the null distribution of likelihood ratio statistics are derived the bounds are based on the central fisher distribution and are very easy to use in an important special case a bounds test similar to the durbin watson test is proposed multiple testing problems are also studied the bounds obtained for a single pair of hypotheses are shown to enjoy a simultaneity property that allows one to combine any number of tests this result extends to nonlinear hypotheses a well known result given by scheffe for linear hypotheses a method of building bounds induced tests is also suggested

on the application of linear relative risk regression models motivations for considering linear relative risk models are described these include covariate data reduction and the testing of additivity of covariate effects on the relative risk a simulation study was conducted in order to study properties of asymptotic distributional approximations and iterative convergence properties parameter transformations and likelihood ratio approximations are considered for confidence interval calculation

testing for change point in the covariate effects based on the cox regression model models with change point in covariates have wide applications in cancer research with the response being the time to a certain event a cox model with change point in covariate is considered at which the pattern of the change point effects can be flexibly specified to test for the existence of the change point effects three statistical tests namely the maximal score maximal normalized score and maximal wald tests are proposed the asymptotic properties of the test statistics are established monte carlo approaches to simulate the critical values are suggested a large scale simulation study is carried out to study the finite sample performance of the proposed test statistics under the null hypothesis of no change points and various alternative hypothesis settings each of the proposed methods provides a natural estimate for the location of the change point but it is found that the performance of the maximal score test can be sensitive to the true location of the change point in some cases while the performance of the maximal wald test is very satisfactory in general even in cases with moderate sample size for illustration the proposed methods are applied to two medical datasets concerning patients with primary biliary cirrhosis and breast cancer respectively

goodness of fit tests in models for life history data based on cumulative hazard rates to check the validity of an assumed parametric model for survival data one may compare t the nonparametric nelson aalen plot of the cumulative hazard rate with a t the estimated parametric cumulative hazard rate being for example the maximum likelihood estimator convergence in distribution of n t a t and more general processes is studied employing the general framework of counting processes which allows for quite general models for life history data and for quite general censoring schemes the results are applied to the construction of 2 type statistics for goodness of fit cramer von mises and kolmogorov smirnov type tests are presented in the case where the unknown parameter is one dimensional

relative risk regression models with inverse polynomials the proportional hazards model assumes that the log hazard ratio is a linear function of parameters in the current paper we model the log relative risk as an inverse polynomial which is particularly suitable for modeling bounded and asymmetric functions the parameters estimated by maximizing the partial likelihood are consistent and asymptotically normal the advantages of the inverse polynomial model over the ordinary polynomial model and the fractional polynomial model for fitting various asymmetric log relative risk functions are shown by simulation the utility of the method is further supported by analyzing two real data sets addressing the specific question of the location of the minimum risk threshold

asymptotic distribution theory for cox type regression models with general relative risk form the theory and application of the cox 1972 failure time regression model has almost without exception assumed an exponential form for the dependence of the hazard function on regression variables other regression forms may be more natural or descriptive in some applications for example a linear relative risk regression model provides a convenient framework for studying epidemiologic risk factor interactions this note uses the counting process formulation of andersen and gill 1982 to develop asymptotic distribution theory for a class of intensity function regression models in which the usual exponential regression form is relaxed to an arbitrary non negative twice differentiable form some stability and regularity conditions beyond those of andersen and gill are required to show the consistency of the observed information matrix which in general need not be positive semidefinite

asymptotic score statistic processes and tests for constant hazard against a change point alternative the problem of testing for a constant failure rate against alternatives with failure rates involving a single change point is considered the asymptotic significance level for tests based on maximal score statistics are shown to involve the solution to a first passage time problem for an ornstein uhlenbeck process an example illustrates the methodology

a model for ordinally constructing additive objective functions abstract we investigate a method for constructing piecewise linear approximations of an additive called also separable objective function in n target variables from a few indifference points in two dimensional planes it is shown that a the data used by the method are ordinal simplest and minimal b the limit ordinal preference is independent of the cardinal utility scale used in intermediate computations since the accuracy of the approximations is estimated in the hausdorff metric on the space of binary relations the method is illustrated with an example of constructing an additive objective function of german economic policy in four target variables inflation unemployment gnp growth and increase in public debt we provide some modifications of the model aimed at user s convenience

methods for the analysis of sampled cohort data in the cox proportional hazards model methods are provided for regression parameter and cumulative baseline hazard estimation in the cox proportional hazards model when the cohort is sampled according to a predictable sampling probability law the key to the methodology is to define counting processes which count joint failure and sampled risk sets occurrences and to derive the appropriate intensities for these counting processes leading to estimation methods parallel to those for full cohort data these techniques are illustrated for a number of sampling designs including three novel designs counter matching with additional randomly sampled controls quota sampling of controls and nested case control sampling with number of controls dependent on the failure s exposure status general asymptotic theory is developed for the maximum partial likelihood estimator and cumulative baseline hazard estimator and is used to derive the asymptotic distributions for estimators from a large class of designs

robust variance estimation for rate ratio parameter estimates from individually matched case control data the asymptotic variance and robust variance estimators of rate ratios estimated using conditional logistic regression from individually matched case control data are derived when the presumed proportional hazards model ismisspecified the robust variance estimators are easily computed using schoenfeld residuals generated from standard partial likelihood estimation software for failure time data simulation studies indicate that the robust variance estimators perform well for typical sizes and that the rare disease version should be adequate for all practical purposes it was also found that model misspecification must be quite extreme before the model based i e inverse information variance is significantly biased and that the robust variance estimators are somewhat more variable than the model based we conclude that the model based variance estimator can be used when model misspecification is not severe the robust estimator should be used when the presumed model clearly fits the data poorly

a note on identifiability of the regression parameter and validity of the partial likehood approach in general relativerisk regression summary in this note we deal with the question of identifiability of the regression parameter in general relative risk regression we show that apart from the well understood kind of nonidentifiability as usually occurs with regression there is a second kind of nonidentifiability of the regression parameter which may still be present even if the information matrix is positive definite however when this happens the partial likelihood approach is still valid even though some caution is advised we show that the partial likelihood estimates still converge to the true parameter in some weak sense we give some criteria for the identifiability and a list of link functions which do not allow such nonidentifiability the list contains most of the link functions so far proposed in the literature

asymptotic theory for nested case control sampling in the cox regression model by providing a probabilistic model for nested case control sampling in epidemiologic cohort studies consistency and asymptotic normality of the maximum partial likelihood estimator of regression parameters in a cox proportional hazards model can be derived using process and martingale theory as in andersen and gill a general expression for the asymptotic variance is given and used to calculate asymptotic relative efficiencies relative to the full cohort variance in some important special cases

tests of loglinear and linear relative risks for cox s model summary a score test statistic is derived to test for the loglinear relative risk function in the cox proportional hazards model for failure time data the loglinear and linear relative risk functions are embedded within a power family transformation of the linear predictor in two simple cases some empirical results are obtained for the score test statistic using expected information and for the likelihood ratio statistic both statistics have distributions well approximated by the chi squared distribution problems of identifiability and problems associated with the linear relative risk model are also discussed a real example is given

boundedness in a quasilinear parabolic parabolic keller segel system with subcritical sensitivity abstract we consider the quasilinear parabolic parabolic keller segel system u t d u u s u v x t 0 v t v v u x t 0 under homogeneous neumann boundary conditions in a convex smooth bounded domain r n with n 1 it is proved that if s u d u c u with 2 n and some constant c 0 for all u 1 then the classical solutions to the above system are uniformly in time bounded provided that d u satisfies some technical conditions such as algebraic upper and lower growth resp decay estimates as u this boundedness result is optimal according to a recent result by the second author winkler 2010 27 which says that if s u d u c u for u 1 with c 0 and some 2 n n 2 then for each mass m 0 there exist blow up solutions with mass u 0 m in addition this paper also proves a general boundedness result for quasilinear non uniformly parabolic equations by modifying the iterative technique of moser alikakos alikakos 1979 1

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

weighted log rank type statistics for comparing survival curves when there is a time lag in the effectiveness of treatment summary in certain long term treatment trials one expects some lag period before the treatment is fully effective this paper presents two weighted log rank type statistics designed to have good efficiency over a wide range of lags a maximin efficiency robust statistic and a simplified version of this statistic both statistics can be computed as easily as the log rank statistic asymptotic efficiency calculations supported by small sample simulations show that the two proposed statistics are substantially more efficient than the conventional log rank statistic in certain lag situations with comparatively little efficiency loss relative to the log rank statistic when no lag exists we recommend the maximin statistic for situations where a lag is expected but cannot be specified precisely in advance

redistribution of university budgets with respect to the status quo abstract university budgets are redistributed proportionally to five target criteria the approach has been implemented in several models and applied to 15 north rhine westfalia state universities in the given paper the problem is considered from the viewpoint of the general techniques for constructing objective functions for evaluating alternatives it enables us to formulate three additional models aimed at best respecting the status quo with minimizing absolute changes of actual budgets with minimizing relative changes of actual budgets and with minimizing changes of individual rules for budget accounting the models are based on either linear or quadratic objective functions the latter being considered under several optional assumptions local monotonicity global monotonicity concavity and convexity the paper is illustrated with computer results

residuals for relative risk regression summary several possible definitions of residuals are given for relative risk regression with time varying covariates each such residual has a representation as an estimator of a stochastic integral with respect to the martingale arising from a subject s failure time counting process previously proposed residuals for individual study subjects and for specific time points are shown to be special cases of this definition as are previously derived regression diagnostics an illustration and various generalizations are also given able methods are required to detect various departures from modelling assumptions suitably defined residuals may play an important role in such identification however the nonparametric aspect of the model the possibility that modelled regression variables may be varying with follow up time and most importantly the usual presence of right censorship implies that specialized residual definitions are required the class of residuals considered here is most easily formulated using counting process notation for the failure time data let ni t yi t and zi t represent respectively for the ith subject the values of counting censoring and covariate processes at follow up time t i 1 n while ni u yi u zi u 0c u t specifies the corresponding histories for the ith subject prior to time t thus in a typical univariate failure time application ni with right continuous sample paths will take value zero prior to the time of failure on the ith subject and value one thereafter while yi with left continuous sample paths will take value one at times at which the ith subject is at risk for an observed failure and value zero otherwise the counting process ni can be uniquely decomposed so that for all t i

corrected score estimation in the proportional hazards model with misclassified discrete covariates we consider cox proportional hazards regression when the covariate vector includes error prone discrete covariates along with error free covariates which may be discrete or continuous the misclassification in the discrete error prone covariates is allowed to be of any specified form building on the work of nakamura and his colleagues we present a corrected score method for this setting the method can handle all three major study designs internal validation design external validation design and replicate measures design both functional and structural error models and time dependent covariates satisfying a certain localized error condition we derive the asymptotic properties of the method and indicate how to adjust the covariance matrix of the regression coefficient estimates to account for estimation of the misclassification matrix we present the results of a finite sample simulation study under weibull survival with a single binary covariate having known misclassification rates the performance of the method described here was similar to that of related methods we have examined in previous works specifically our new estimator performed as well as or in a few cases better than the full weibull maximum likelihood estimator we also present simulation results for our method for the case where the misclassification probabilities are estimated from an external replicate measures study our method generally performed well in these simulations the new estimator has a broader range of applicability than many other estimators proposed in the literature including those described in our own earlier work in that it can handle time dependent covariates with an arbitrary misclassification structure we illustrate the method on data from a study of the relationship between dietary calcium intake and distal colon cancer

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

mixture symmetry and quadratic utility the independence axiom of expected utility theory has recently been weakened to the betweenness axiom in this paper an even weaker axiom called mixture symmetry is presented the corresponding functional structure is such that utility is a betweenness functional on part of its domain and quadratic in probabilities elsewhere the experimental evidence against betweenness provides one motivation for the more general theory presented here another advantage of the mixture symmetric class of utility functions is that it is sufficiently flexible to permit the disentangling of attitudes towards risk and towards randomization

the operator valued marcinkiewicz multiplier theorem and maximal regularity given a closed linear operator on a umd space we characterize maximal regularity of the non homogeneous problem

modelling marginal hazards in multivariate failure time data we consider the problem of estimating relative risk parameters in the marginal distribution of failure times from a sample in which individuals are grouped into clusters and failure times for individuals within clusters may be dependent we assume that the marginal hazard of failure for individuals within a cluster is specified by a relative risk regression model and the structure of dependence between individuals within a cluster is left unspecified estimating equations for the regression parameters and an estimator for the cumulative base line marginal hazard are described

identifying optimal risk windows for self controlled case series studies of vaccine safety in vaccine safety studies subjects are considered at increased risk for adverse events for a period of time after vaccination known as risk window to our knowledge risk windows for vaccine safety studies have tended to be pre defined and not to use information from the current study inaccurate specification of the risk window can result in either including the true control period in the risk window or including some of the risk window in the control period which can introduce bias we propose a data based approach for identifying the optimal risk windows for self controlled case series studies of vaccine safety the approach involves fitting conditional poisson regression models to obtain incidence rate ratio estimates for different risk window lengths for a specified risk window length l the average time at risk t l is calculated when the specified risk window is shorter than the true the incidence rate ratio decreases with 1 t l increasing but there is no explicit relationship when the specified risk window is longer than the true the incidence rate ratio increases linearly with 1 t l increasing theoretically the risk window with the maximum incidence ratio is the optimal risk window because of sparse data problem we recommend using both the maximum incidence rate ratio and the linear relationship when the specified risk window is longer than the true to identify the optimal risk windows both simulation studies and vaccine safety data applications show that our proposed approach is effective in identifying medium and long risk windows

strong time periodic solutions to keller segel systems an approach by the quasilinear arendt bu theorem abstract it is shown that the classical as well as quasilinear keller segel systems with non degenerate diffusion possess for given t periodic and sufficiently small forcing functions a unique strong t time periodic solution the proof given relies on the existence of strong t periodic solutions for the linearized system its characterization in terms of maximal l p regularity of the underlying operator and a quasilinear version of the arendt bu theorem the latter is of independent interest and yields the existence of strong t periodic solutions to general quasilinear evolution equations under suitable conditions on the operators and the forcing terms

information bounds for the conditional hazard ratio in a nested family of regression models information bounds are obtained for a parametric treatment effect in a nested family of models for the conditional distribution of survival given confounding variables the family extends from the fully parametric weibull model to a completely nonparametric model for right censored data and includes the cox model and the stratified version of it it is shown that in certain special cases there is no loss of information about the treatment effect when going from a fully parametric to a nonparametric specification of the conditional hazard function

new critical exponents in a fully parabolic quasilinear keller segel system and applications to volume filling models abstract we carry on our studies related to the fully parabolic quasilinear keller segel system started in 6 and continued in 7 in the above mentioned papers we proved finite time blowup of some radially symmetric solutions to the quasilinear keller segel system if the nonlinear chemosensitivity is strong enough and an adequate relation between nonlinear diffusion and chemosensitivity holds on the other hand we proved that once chemosensitivity is weak enough solutions exist globally in time the present paper is devoted to looking for critical exponents distinguishing between those two behaviors moreover we apply our results to the so called volume filling models with a power type jump probability function the most important consequence of our investigations of the latter is a critical mass phenomenon found in dimension 2 namely we find a value m such that when the solution to the two dimensional volume filling keller segel system starts with mass smaller than m then it is bounded while for some initial data with mass exceeding m solutions are unbounded though being defined for any time t 0

tests of the null hypothesis in case control studies the relative merits of the likelihood ratio statistic the wald statistic and the score statistic are examined by an empirical evaluation based on matched case control data a mixture model for the relative odds function is used the likelihood ratio statistic is relatively constant for reasonable values of the mixture parameter but the wald statistic is unstable the score statistic is shown to be independent of the mixture parameter an exact expression is derived for the change in the score statistic upon deletion of risk sets and an approximation is numerically evaluated

auxiliary covariate data in failure time regression summary we consider the problem of missing covariate data in the context of censored failure time relative risk regression auxiliary covariate data which are considered informative about the missing data but which are not explicitly part of the relative risk regression model may be available full covariate information is available for a validation set an estimated partial likelihood method is proposed for estimating relative risk parameters this method is an extension of the estimated likelihood regression analysis method for uncensored data pepe 1992 pepe fleming 1991 a key feature of the method is that it is nonparametric with respect to the association between the missing and observed including auxiliary covariate components asymptotic distribution theory is derived for the proposed estimated partial likelihood estimator in the case where the auxiliary or mismeasured covariates are categorical asymptotic efficiencies are calculated for exponential failure times using an exponential relative risk model the estimated partial likelihood estimator compares favourably with a fully parametric maximum likelihood analysis comparisons are also made with a standard partial likelihood analysis which ignores the incomplete observations important efficiency gains can be made with the estimated partial likelihood method small sample properties are investigated through simulation studies

polynomial spline estimation and inference of proportional hazards regression models with flexible relative risk form the cox proportional hazards model usually assumes an exponential form for the dependence of the hazard function on covariate variables however in practice this assumption may be violated and other relative risk forms may be more appropriate in this article we consider the proportional hazards model with an unknown relative risk form issues in model interpretation are addressed we propose a method to estimate the relative risk form and the regression parameters simultaneously by first approximating the logarithm of the relative risk form by a spline and then employing the maximum partial likelihood estimation an iterative alternating optimization procedure is developed for efficient implementation statistical inference of the regression coefficients and of the relative risk form based on parametric asymptotic theory is discussed the proposed methods are illustrated using simulation and an application to the veteran s administration lung cancer data

stochastic calculus as a tool in survival analysis a review this paper gives a brief survey of the uses of stochastic calculus in survival analysis the role played by martingale central limit theory in deriving asymptotic distributions of estimators and test statistics is described the nelson aalen estimator the kaplan meier estimator cox s proportional hazards model aalen s additive risk model and a goodness of fit test for cox s model are discussed sketches of the proofs of the main results are included

constructing a monotonic quadratic objective function in n variables from a few two dimensional indifferences abstract we develop a model for constructing quadratic objective functions in n target variables at the input a decision maker is asked a few simple questions about his ordinal preferences comparing two dimensional alternatives in terms better worse indifferent at the output the model mathematically derives a quadratic objective function used to evaluate n dimensional alternatives thus the model deals with some imaginary decisions criteria aggregates at the input and disaggregates the decision maker s preference into partial criteria and their cross correlations a quadratic objective function therefore the model provides an approximation step which is next to the disaggregation of a preference into additively separable linear criteria with weight coefficients the model is based on least squares fitting a quadratic indifference hypersurface if n 2 indifference curve to several alternatives which are supposed to be equivalent in preference the resulting ordinal preference is independent of the cardinal utility scale used in intermediate computations which implies that the model is ordinal the monotonicity of the quadratic objective function is implemented by means of a finite number of linear constraints so that the computational model is reduced to restricted least squares in illustration we construct a quadratic objective function of german economic policy in four target variables inflation unemployment gnp growth and increase in public debt this objective function is used to evaluate the german economic development in 1980 1994 in another application we construct a quadratic objective function of ski station customers then it is used to adjust prices of 10 ski stations to the south of stuttgart in appendix a we provide an original fast algorithm for restricted least squares and quadratic programming used in the main model

periodic traveling waves in a reaction diffusion model with chemotaxis and nonlocal delay effect abstract in this paper we study the existence of periodic traveling wave solutions with large wave speed for a reaction diffusion model with chemotaxis and nonlocal delay effect by applying the perturbation method the proof relies on an abstract formulation of the wave profile as a solution of an operator equation in a certain banach space coupled with the lyapunov schmidt reduction and the implicit function theorem