calculating the hilbert transform on spaces with energy concentration convergence and divergence regions in many different applications it is important to determine the hilbert transform of a given function however it is generally impossible to calculate it in closed form therefore hilbert transform approximations are used this paper studies the convergence and divergence behavior of general classes of such approximation methods these classes are characterized by two very natural axioms and they include basically all known traditional numerical algorithms the convergence of these methods is investigated on a family of signal spaces of continuous functions with finite energy these spaces are parametrized by a number which measures the energy concentration in the low frequency components of the signal it is shown that stable methods only exist on signal spaces with a sufficient energy concentration and this paper gives some explicit examples of convergent methods on all other spaces in the family of signal spaces every sampling based hilbert transform approximation shows a blowup behavior of its peak value i e on these spaces every sampling based hilbert transform approximation diverges

efficiencies of experimental designs for an illness death model disease development is described by the progressive markov illness death model with one disease the efficiencies of four experimental designs are discussed the simple survival experiment serial sacrifice periodic diagnosis and complete observation the discussion is based on the semiparametric assumption of piecewise constant intensities simple survival experiments are shown to have very low efficiency serial sacrifice experiments to be moderately efficient and periodic diagnosis to be almost as efficient as complete observation an application to the analysis of the development of leukaemia in laboratory mice is given

an index of tumorigenic potency a new index of tumorigenic potency is derived using a survival adjusted quantal response estimator given by bailer and portier 1988 biometrics 44 417 431 the small sample bias and mean squared error properties of this estimator are explored using computer simulations of animal carcinogenicity experiments and are compared to the characteristics of the td50 an estimator proposed by sawyer et al 1984 biometrics 40 27 40 it is observed that this new index tends to have smaller bias and mean squared error relative to the td50 over varying shapes of the tumor onset distribution levels of tumor lethality and levels of treatment lethality

estimating the tumour onset distribution in animal carcinogenesis experiments summary in most survival sacrifice experiments for the detection and quantification of risks from chronic exposure to chemical agents the onset of the condition of interest is not clinically observable cancer is typically such an event in this paper an approximate maximum likelihood method is proposed for parametric estimation of the distribution of unobservable tumour onset times in the presence of competing risks when cause ofdeath information is unavailable

nonparametric estimation of lifetime and disease onset distributions from incomplete observations in this paper we derive and investigate nonparametric estimators of the distributions of lifetime and time until onset associated with an irreversible disease that is detectable only at death the nonparametric maximum likelihood solution requires an iterative algorithm an alternative though closely related pair of estimators for the lifetime and onset distributions exists in closed form these estimators are the familiar kaplan meier estimator and an isotonic regression estimator respectively first order approximations provide variance estimators the proposed methods generalize and shed additional light on the constrained estimators presented by kodell shaw and johnson 1982 biometrics 38 43 58 data from an animal experiment illustrate the techniques

nonparametric estimation of a markov illness death process from interval censored observations with application to diabetes survival data summary the nonparametric estimation of the cumulative transition intensity functions in a threestate time nonhomogeneous markov process with irreversible transitions an illness death model is considered when times of the intermediate transition e g onset of a disease are interval censored the times of death are assumed to be known exactly or to be rightcensored in addition the observed process may be left truncated data of this type arise when the process is sampled periodically for example when the patients are monitored through periodic examinations the observations on times of change in their disease status will be interval censored under the sampling scheme considered here the nelson aalen estimator aalen 1978 for a cumulative transition intensity is not applicable in the proposed method the maximum likelihood estimators of some of the transition intensities are derived from the estimators of the corresponding subdistribution functions the maximum likelihood estimators are shown to have a self consistency property the self consistency algorithm is developed for the computation of the estimators this approach generalises the results from turnbull 1976 and frydman 1992 the methods are illustrated with diabetes survival data

on the convergence of spline product quadratures for cauchy principal value integrals abstract in a recent paper this journal 1990 the authors proposed product integration formulas for the numerical evaluation of the cauchy principal value integral f1 1u x f x x dx based on cubic spline interpolation of f and obtained convergence results for functions f ck 1 1 k 1 2 or 3 in this report the same rules are considered and their convergence is investigated for a larger class of functions f an error bound and some uniform convergence results are established in the case of equally spaced quadrature nodes for functions f satisfying a holder condition of order on 1 1 0

a modified log rank test for competing risks with missing failure type summary we propose a modified log rank test for the analysis of competing risks survival data when failure type is missing for some individuals the proposed test reduces to a standard log rank test when all failure types are known the test arises from a partial likelihood constructed under semiparametric assumptions on the relationship between cause specific hazards

existence uniqueness and invariant measures for stochastic semilinear equations on hilbert spaces a class of stochastic evolution equations with additive noise and weakly continuous drift is considered first regularity properties of the corresponding ornstein uhlenbeck transition semigrouprt are obtained we show thatrt is a compactc0 semigroup in all sobolev spaceswn p which are built on its invariant measure then we show the existence uniqueness compactness and smoothing properties of the transition semigroup for semilinear equations inlp spaces and spacesw1 p as a consequence we prove the uniquencess of martingale solutions to the stochastic equation and the existence of a unique invariant measure equivalent to it is shown also that the density of this measure with respect to is inlp for allp 1

efficiency of age adjusted tests in animal carcinogenicity experiments based on asymptotic relative efficiency calculations ryan 1985 biometrics 41 525 531 concludes that in the analysis of animal carcinogenicity experiments age adjusted tests of tumor rates should be routinely preferred to simple proportions tests for both lethal and nonlethal tumors we recalculate the asymptotic efficiencies of the simple proportions test relative to the log rank test for the lethal tumor case for a simplified model it is shown that the relative efficiency may be easily computed as a function of the crude tumor rate and the survival rate at the time of terminal sacrifice more generally we calculate by numerical quadrature the asymptotic relative efficiency for all models considered by ryan and using simulations examine the relevance of asymptotic efficiencies to typical sample sizes contrary to the numerical results of ryan we find for experiments with good survival and typical tumor rates that the relative efficiencies are greater than 95 usually about 99 in the nonlethal tumor case similar results follow from ryan for tumor rates and survival rates typically encountered in practice as it is often difficult to determine whether or not a tumor is lethal we conclude for equal interim mortality rates that the simple proportions test is usually adequate in evaluating animal carcinogenicity experiments

nonparametric methods for survival sacrifice experiments in many carcinogenicity studies the time to disease occurrence is not clinically observable a survival sacrifice experiment is considered for nonparametric inference about the rate of disease occurrence a multistate model for disease development and death is considered and an algorithm of the em type for maximum likelihood estimation is obtained questions of identifiability and estimability are addressed under the model interval hazards for disease occurrence are identifiable for intervals defined by the sacrifice times a score test is developed appropriate for the comparison of two groups with respect to disease development without need of any assumption concerning lethality of the disease concerned

efficiency robust score tests for rodent tumourigenicity experiments summary the standard statistical test for assessing adverse effects in rodent tumourigenicity experiments is based on a time adjusted analysis of lethal and incidental tumours this test is shown to arise as the sum of two score statistics for fatal and incidental lesions respectively the former optimal against extreme value hazard alternatives and the latter optimal against logistic prevalence alternatives in terms of asymptotic relative efficiency in the pitman sense an efficiency robust test is developed which retains near full efficiency in the extreme value logistic situation as well as in other situations where the standard test may be only 70 efficient rodent tumourigenicity experiments are used to determine whether or not a particular agent results in an increase in tumour occurrence in animals exposed to this substance throughout their lifetimes as compared to unexposed controls the tumour status of an individual animal is normally determined at the time of death since many animals will die either from natural mortality or as a result of tumour development prior to the end of the study period information on tumourigenicity will accrue throughout the course of the experiment typically lasting about two years animals surviving to the end of the experiment are sacrificed and subjected to the same pathological evaluation as those dying prior to the termination time peto et al 1980 have proposed life table analysis of the lethal or fatal tumours and a prevalence analysis of the nonlethal or incidental tumours in the present paper we show that when the substance under study affects the occurrence of fatal and incidental lesions in a similar fashion their test can be formally derived as the sum of two score statistics for fatal and incidental tumours respectively the former statistic is the score test under extreme value hazard alternatives whereas the latter statistic is optimal against logistic prevalence alternatives because the true form of the underlying hazard and prevalence functions is unknown we develop in 3 an efficiency robust version of this test this is done by maximizing the minimum asymptotic relative efficiency within a finite class of hazard and prevalence functions applications of the maximin efficiency robust test are discussed in 4

optimal control of a stochastic delay heat equation with boundary noise and boundary control in this paper a controlled stochastic delay heat equation with neumann boundary noise and boundary control is considered the existence and uniqueness of the mild solution for the associated hamilton jacobi bellman equations are obtained by means of the backward stochastic differential equations which is applied to the optimal control problem

on the convergence of an interpolatory product rule for evaluating cauchy principal value integrals etablissement des theoremes de convergence des regles de produits interpolatoires pour l evaluation d integrales singulieres de cauchy avec estimation asymptotique du reste amelioration et generalisation de resultats anterieurs

product integration of logarithmic singular integrands based on cubic splines abstract this paper is concerned with the practical evaluation of the product integral 1 1 f x k x d x for the case when k x in x 1 1 and f is bounded in 1 1 the approximation is a quadrature rule where the weights w n n i are chosen to be exact when f is given by a linear combination of a chosen set of functions n j in this paper the functions n j are chosen to be cubic b splines an error bound for product quadrature rules based on cubic splines is provided examples that test the performance of the product quadrature rules for different choices of the function are given a comparison is made with product quadrature rules based on first kind chebyshev polynomials

improving the em algorithm summary a modification of the em algorithm is proposed for situations in which the maximization of the complete data likelihood function does not have a closed form solution self consistency of the modified algorithm is established application to carcinogenicity experiments is illustrated and the results of a simulation study comparing the original and modified versions indicate that use of the proposed modification can lead to significant computational savings

survival analysis with uncertain endpoints summary in some survival analysis applications the endpoint of interest has a degree of uncertainty associated with it these events are typically classified by the investigator or by an endpoint committee as true or false according to some decision rule and the analysis proceeds using only the true endpoints this procedure has two drawbacks the cutpoint for the decision rule is somewhat arbitrary and the information contained in the level of certainty is lost this paper introduces a modification of the cox regression model that allows all potential endpoints to be included in the analysis along with the level of certainty of each simulation results show this procedure to considerably increase the power of the standard procedure in a wide range of situations

spline approximation for cauchy principal value integrals abstract in this paper we prove the uniform convergence of some quadrature formulas based on spline approximation for cauchy principal value integrals of the type f b a w x f k x x y d x k 0 1 and we present some numerical applications in particular we apply our rules to the well known prandtl s integral equation

a dose response test via closed form solutions for constrained mles in survival sacrifice experiments in most survival sacrifice experiments in animal carcinogenicity studies the onset of the tumour of interest is not clinically observable due to the complexity of constraints for a biological justification recently developed methods for estimating the tumour onset function and tumour specific survival function employ computer intensive numerical solutions in this paper closed form solutions for nonparametric maximum likelihood estimators are derived under explicit and implicit inequality constraints obtained from the monotonicity of the survival functions our methods do not require cause of death information the proposed methods can be used to estimate the tumour onset function and the survival function of the tumour of interest we use the proposed estimators for the development of our new dose response trend test a modification of the poly k test is made by replacing the time at risk weight to a function of the tumour onset survival function the weighted least square regression method is applied to the estimated survival functions in order to construct a dose response trend test a simulation study is conducted to evaluate the performance of the proposed test and compare it with existing trend tests a real example is used to illustrate the methods

characterization of domains of fractional powers of certain operators arising in elastic systems and applications with x a hilbert space where a the elastic operator and b the damping operator are closed operators in x with dense domains q a and 9 b respectively moreover a is throughout assumed to be self adjoint and strictly positive stimulated by two conjectures raised in crl the most general of which referred to the case lx f described below we have already studied the operators and sb defined respectively by

explicit solutions for constrained maximum likelihood estimators in survival sacrifice experiments summary regulatory agencies routinely base conclusions regarding carcinogenicity of compounds tested in long term animal studies on tests which are known to be biased under conditions of treatment lethality and tumour lethality the recognition of these biases has led to a variety of proposed approaches which rely on survival and sacrifice data williams portier 1992 derived analytic expressions for maximum likelihood estimators of the tumour incidence rate and discrete death rates based on a discrete multistate model a disadvantage of the proposed estimators was that they sometimes resulted in negative estimates of the tumour incidence rate in this paper explicit solutions for constrained estimators are derived under the imposition of boundary conditions for a study design with one or two interim sacrifices and a terminal sacrifice for study designs with more than two interim sacrifices alternative estimators of the tumour incidence rate and discrete death rates are developed heuristically by pooling data together from adjacent

effects of treatment induced mortality and tumor induced mortality on tests for carcinogenicity in small samples statistical tests of carcinogenicity are shown to have varying degrees of robustness to the effects of mortality mortality induced by two different mechanisms is studied mortality due to the tumor of interest and mortality due to treatment independent of the tumor the two most commonly used tests the life table test and the cochran armitage linear trend test are seen to be highly sensitive to increases in treatment lethality using small sample simulations increases in tumor lethality are seen to affect the performance of commonly used prevalence tests such as logistic regression a simple survival adjusted quantal response test appears to be the most robust of all the procedures considered

a quadrature rule of interpolatory type for cauchy integrals abstract we construct a quadrature rule of interpolatory type based on a trigonometric interpolation for cauchy integrals we obtain the same error bound o ann as hasegawa and torii math comp 56 1991 741 754 numerical examples are included to substantiate the performance of the present method

on the uniform convergence of gaussian quadrature rules for cauchy principal value integrals and their derivatives the convergence of the aforementioned quadrature rules for integrands possessing h6lder continuous derivatives of an appropriate order is proved to be uniform and not only pointwise the rate of convergence is also established and an application to the numerical solution of singular integral equations is made

numerical integration based on approximating splines abstract convergence results are proved for product integration rules based on approximating splines these results are both for bounded and unbounded integrands pointwise and uniform convergence results are proved for sequences of cauchy principal values of these approximating splines

on the evaluation of cauchy principal value integrals by rules based on quasi interpolating splines abstract in this paper we consider the numerical evaluation of one dimensional cauchy principal value integrals of the form 1 1 k x f x x d x 1 by rules obtained by subtracting out the singularity and then applying quadrature formulas based on quasi interpolating splines

optimal control of semilinear stochastic evolution equations the aim of this paper is to initiate a semigroup theory based approach to characterization of optimal markov controls for controlled semilinear stochastic evolution equations it may be recalled that markov controls are those that depend only on the current state at each time for finite dimensional controlled stochastic differential equations with a nondegenerate diffusion matrix this task is traditionally achieved through the hamilton jacobi bellman equation of dynamic programming associated with the problem and an accompanying verification theorem the latter states that an optimal markov control can be explicitly obtained by the pointwise minimization of a hamiltonian derivable from the solution of the hjb equation moreover any optimal markov control is obtainable in this manner

efficient estimation of the lifetime and disease onset distribution summary we study efficient nonparametric maximum likelihood estimation of the distribution of onset and lifetime associated with an irreversible disease that is only detectable at sacrifice or death we show that if the onset distribution is continuous then estimation of the lifetime distribution cannot be improved by using current status information on the time till onset in this case the kaplan meier estimator of the lifetime distribution is asymptotically efficient the nonparametric maximum likelihood estimator tries to use current status information on the time till onset but it is asymptotically equivalent to the kaplan meier estimator and it is outperformed by the latter in simulations the nonparametric maximum likelihood estimator of the onset distribution is shown to be an iteratively reweighted least squares estimator which can be computed with the weighted pool adjacent violators algorithm we show that it is unnecessary to estimate the weights iteratively since an initial estimate cannot be improved this insight leads to a simple explicit estimator which improves on the nonparametric maximum likelihood estimator of the onset distribution the results are verified with simulations and a data analysis example is provided

tumour incidence rate alternatives and the cause of death test for carcinogenicity summary lagakos louis 1988 and burnett krewski bleuer 1989 show that the cause ofdeath test of peto et al 1980 for carcinogenicity studies can be viewed as the approximate score test of a one dimensional joint hypothesis about tumour prevalences and the rates of death from tumour we relate this joint prevalence death rate hypothesis to hypotheses about differences in tumour incidence rates for two sample tests we show that when the control group tumour incidence is low when tumours are highly lethal or when the alternative is local the prevalence death rate family of alternatives is approximately equivalent to a proportional tumour incidence rate family more generally the prevalencedeath rate null hypothesis is always equivalent to a hypothesis of equal tumour incidence rates and each member of the family of prevalence death rate alternatives requires the tumour incidence rates not to cross using computer simulation we show that when the model does not hold the test of peto et al can be anti conservative and have poor power we discuss the model s implications for the interpretation of tests of regression hypotheses

on the use of covariates for rodent bioassay and screening experiments summary consider a three state compartmental model with an initial an absorbing and an intermediate state which may or may not be entered before absorption observable data are time to absorption and an indication of whether the intermediate state was entered but not the time of transition the transition rates characterizing the process are nonidentifiable without simplifying assumptions or additional information on the prevalence function defined as the time specific proportion of nonabsorbed individuals in the intermediate state our approach makes prevalence identifiable and easily estimable through the use of covariates combined with one or more random screens of the population the results are illustrated with pathology data from a rodent tumourigenicity experiment involving several random sacrifices

adaptive boundary and point control of linear stochastic distributed parameter systems an adaptive control problem for the boundary or the point control of a linear stochastic distributed parameter system is formulated and solved in this paper the distributed parameter system is modeled by an evolution equation with an infinitesimal generator for an analytic semigroup since there is boundary or point control the linear transformation for the control in the state equation is also an unbounded operator the unknown parameters in the model appear affinely in both the infinitesimal generator of the semigroup and the linear transformation of the control strong consistency is verified for a family of least squares estimates of the unknown parameters an ito formula is established for smooth functions of the solution of this linear stochastic distributed parameter system with boundary or point control the certainty equivalence adaptive control is shown to be self tuning by using the continuity of the solution of a stationary riccati equation as a function of parameters in a uniform operator topology for a quadratic cost functional of the state and the control the certainty equivalence control is shown to be self optimizing that is the family of average costs converges to the optimal ergodic cost some examples of stochastic parabolic problems with boundary control and a structurally damped plate with random loading and point control are described that satisfy the assumptions for the adaptive control problem solved in this paper

long term optimal investment strategies in the presence of adjustment costs we consider the problem of determining in a dynamical way the optimal capacity level of an investment project that operates within a random economic environment in particular we consider an investment project that yields payoff at a rate that depends on its installed capacity level and on a random economic indicator such as the price of the project s output commodity we model this economic indicator by means of a general one dimensional ergodic diffusion at any time the project s capacity level can be increased or decreased at given proportional costs the aim is to maximize an ergodic performance criterion that reflects the long term average payoff resulting from the project s management we solve this genuinely two dimensional stochastic control problem by constructing an explicit solution to an appropriate hamilton jacobi bellman equation and by fully characterizing an optimal investment strategy

model selection for the competing risks model with and without masking the competing risks model is useful in settings in which individuals or units may die or fail because of various causes it can also be the case that for some of the items the cause of failure is known only up to a subgroup of all causes in which case we say that the failure is group masked a widely used approach for competing risks data with and without masking involves the specification of cause specific hazard rates often because of the availability of likelihood methods for estimation and testing piecewise constant hazards are used the piecewise constant rates also offer model flexibility and computational convenience however for such piecewise constant hazard models the choice of the endpoints for each interval on which the hazards are constant is usually a subjective one in this article we discuss and propose the use of model selection methods that are data driven and automatic we compare three model selection procedures based on the minimum description length principle the bayes in

a class of rank test procedures for censored survival data summary a class of linear rank statistics is proposed for the k sample problem with rightcensored survival data the class contains as special cases the log rank test mantel 1966 cox 1972 and a test essentially equivalent to peto peto s 1972 generalization of the wilcoxon test martingale theory is used to establish asymptotic normality of test statistics under the null hypotheses considered and to derive expressions for asymptotic relative efficiencies under contiguous sequences of alternative hypotheses a class of distributions is presented which corresponds to the class of rank statistics in the sense that for each distribution there is a statistic with some optimal properties for detecting location alternatives from that distribution some monte carlo results are displayed which present small sample behaviour

a comparison of tumour incidence analyses applicable in single sacrifice animal experiments monte carlo methods are used to evaluate the operating characteristics of several trend tests for comparing incidence rates of occult tumours the candidate tests are applicable in long term animal experiments that have just one sacrifice time and no information on cause of death when survival decreases with dose and the tumour is lethal the tests that do not adjust for survival or that assume tumours are non lethal behave conservatively whereas the test that assumes tumours are rapidly lethal rejects the hypothesis of equal incidence rates too frequently the only test which consistently operates at the correct level is one that specifies a constant difference between the death rates for animals with and without the tumour surprisingly the test that specifies a constant ratio of these death rates often is conservative finally a test based on a simple modification of the unadjusted test which accounts for differential mortality by scaling down the size of the risk set performs reasonably well in many cases among the tests that operate at the proper level the constant risk difference test consistently exhibits high power across a wide range of situations

proportional hazards model for repeated measures with monotonic ordinal response in this paper we present a proportional hazards model to determine the effect of predictors on repeated measures data with ordinal response that is monotonic over time the model can handle both categorical and continuous predictors it naturally models the time spent in the response states the assumption of proportional hazards can be partially assessed if replicates individuals with identical covariate vectors are available censoring can be incorporated into the model although it does require additional modelling if the censoring is informative

tests for differences in tumor incidence based on animal carcinogenesis experiments abstract in animal carcinogenesis studies statistical methods that compare the production of occult tumors should compare tumor incidence rates in general the incidence rate cannot be identified even approximately without both survival and sacrifice information if information from frequent sacrifices is available however a function that approximates the incidence rate can be identified without assumptions about the relationship between tumor incidence and death some earlier proposals that based comparisons on tumor prevalence rates and other functions also compared tumor incidence rates under special conditions but these tests can be biased when the conditions are violated tests that compare functions approximating tumor incidence rates can be developed using survival sacrifice information but these tests may be seriously inefficient in special cases in which sacrifices are not necessary to identify the tumor incidence rate

nonparametric prevalence and mortality estimators for animal experiments with incomplete cause of death data abstract age specific prevalence and mortality estimators are important descriptors of disease development and the subsequent effects of a disease on longevity nonparametric maximum likelihood estimators for the prevalence and mortality functions are available for the case in which incidental and fatal occurrences of a disease can always be distinguished this article generalizes these methods to allow the role of a disease in causing death to be uncertain for a subset of the animals dying with the disease the proposed analysis makes no assumptions about the degree of disease lethality data from sacrificed animals can be incorporated easily although sacrifices are not necessary if a certain representativeness assumption holds no restrictions are imposed on the distribution of survival times but the prevalence function is held constant over time intervals for stabilization purposes variances are estimated by inverting the observed information matrix an em algorithm simplifies the analysis when the

spline product quadrature rules for cauchy singular integrals abstract in this paper product quadrature rules based on cubic spline interpolation are obtained for the numerical evaluation of cauchy singular integrals and an error bound is proposed some numerical examples that test the performance of the rules are given

regular solutions of second order stationary hamilton jacobi equations abstract we study a second order stationary hamilton jacobi equation in infinite dimension this equation is nonlinear and convex with respect to the first order term we use properties of the transition semigroup associated to the linear equation to write the hamilton jacobi equation in integral form and we prove existence uniqueness and regularity of a solution by the theory of maximal monotone operators we also prove that this solution is the pointwise limit of a uniformly bounded sequence of classical solutions of approximating problems finally the solution is the value function of the associated optimal stochastic control problem some examples are given

a penalized likelihood approach for a progressive three state model with censored and truncated data application to aids summary we consider the estimation of the intensity and survival functions for a continuous time progressive three state semi markov model with intermittently observed data the estimator of the intensity function is defined nonparametrically as the maximum of a penalized likelihood we thus obtain smooth estimates of the intensity and survival functions this approach can accommodate complex observation schemes such as truncation and interval censoring the method is illustrated with a study of hemophiliacs infected by hiv the intensity functions and the cumulative distribution functions for the time to infection and for the time to aids are estimated covariates can easily be incorporated into the model

piecewise polynomial quadratures for cauchy singular integrals in this paper we propose piecewise polynomial methods for the approximation of cauchy principal value integrals and develop a simple efficient and numerically stable algorithm for the evaluation of the weights of the resulting piecewise polynomial quadratures we present two examples to illustrate the advantages of these quadratures versus the gauss jacobi quadratures

adaptive control for semilinear stochastic systems an adaptive ergodic cost stochastic control problem for a partially known semilinear stochastic system in an infinite dimensional space is formulated and solved the solutions of the hamilton jacobi bellman equations for the discounted cost and the ergodic cost stochastic control problems require some special interpretations because they do not typically exist in the usual sense the solutions of the parameter dependent ergodic hamilton jacobi bellman equations are obtained from some corresponding discounted cost control problems as the discount rate tends to zero the solutions of the ergodic hamilton jacobi bellman equations are shown to depend continuously on the parameter a certainty equivalence adaptive control is given that is based on the optimal controls from the solutions of the ergodic hamilton jacobi bellman equations and a strongly consistent family of estimates of the unknown parameter this adaptive control is shown to achieve the optimal ergodic cost for the known system

nonparametric estimation of the distribution of time to onset for specific diseases in survival sacrifice experiments this paper concerns the analysis of an animal survival sacrifice experiment designed to investigate the incidence of a particular disease of interest the disease is assumed to be irreversible and detectable only at death for example by a necropsy each observation can be of one of three types i death caused by the disease ii death from a competing cause such as sacrifice with the disease present or iii death with the disease absent a two dimensional em algorithm is proposed for the nonparametric maximum likelihood estimation of the distributions of the time to onset and of the time to death from the disease these can be compared with nonparametric estimators recently proposed by kodell shaw and johnson 1982 biometrics 38 43 58 and by dinse and lagakos 1982 biometrics 38 921 932 a slight modification of the algorithm permits the construction of likelihood based interval estimates of quantiles of the distributions some extensions and generalizations are indicated

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

cubic splines and approximate solution of singular integral equations of concern here is the numerical solution of singular integral equations of cauchy type i e equations involving principal value integrals the unknown function is expressed as the product of an appropriate weight function and a cubic spline the problem is reduced to a system of linear algebraic equations which is solved for the approximate values of the function at the knots an estimate is provided for the maximum error of the approximate solution numerical results from the spline method are compared with those obtained using other methods

nonparametric estimation of stage occupation probabilities in a multistage model with current status data multistage models are used to describe individuals or experimental units moving through a succession of stages corresponding to distinct states e g healthy diseased diseased with complications dead the resulting data can be considered to be a form of multivariate survival data containing information about the transition times and the stages occupied traditional survival analysis is the simplest example of a multistage model where individuals begin in an initial stage say alive and move irreversibly to a second stage death in this article we consider general multistage models with a directed tree structure progressive models in which individuals traverse through stages in a possibly non markovian manner we construct nonparametric estimators of stage occupation probabilities and marginal cumulative transition hazards empirical calculations of these quantities are not possible due to the lack of complete data we consider current status information which represents a more severe form of censoring than the commonly used right censoring asymptotic validity of our estimators can be justified using consistency results for nonparametric regression estimators finite sample behavior of our estimators is studied by simulation in which we show that our estimators based on these limited data compare well with those based on complete data we also apply our method to a real life data set arising from a cardiovascular diseases study in taiwan

nonparametric estimation of the survival function when cause of death is uncertain summary a nonparametric estimator for the survival function accommodating censored survival times and uncertainty in the assignment of cause of death is proposed for example in a carcinogenicity experiment the data on each animal may consist of an observed age at death and some indication of the probability that the tumor type under study caused death an estimator of the net survival function for time to death due to the cause of interest is developed under certain assumptions the proposed estimator is consistent and asymptotically normally distributed monte carlo simulations were used to compare this estimator with the kaplan meier estimator forcing the cause of death to be specified with certainty as required by the kaplan meier estimator may result in substantial biases

homogenized dynamics of stochastic partial differential equations with dynamical boundary conditions a microscopic heterogeneous system under random influence is considered the randomness enters the system at physical boundary of small scale obstacles as well as at the interior of the physical medium this system is modeled by a stochastic partial differential equation defined on a domain perforated with small holes obstacles or heterogeneities together with random dynamical boundary conditions on the boundaries of these small holes

estimating features of a distribution from binomial data we propose estimators of previous termfeatures of the distributionnext term of an unobserved random variable w what is observed is previous termanext term sample of y v x where previous termanext term binary y equals one when w exceeds previous termanext term threshold v determined by experimental design and x are covariates potential applications include bioassay and destructive duration analysis our empirical application is referendum contingent valuation in resource economics where one is interested in previous termfeatures of the distributionnext term of values w willingness to pay placed by consumers on previous termanext term public good such as endangered species sample consumers with characteristics x are asked whether they favor with y 1 if yes and zero otherwise previous termanext term referendum that would provide the good at previous termanext term cost v specified by experimental design this paper provides estimators for quantiles and conditional on x moments of w under both nonparametric and semiparametric specifications

a note on nonparametric estimation of the distribution function from interval censored and truncated observations this paper is concerned with the nonparametric estimation of the distribution function f from interval censored and truncated data as discussed by turnbull it is observed that turnbun s characterization of f the maximum likelihood estimator of f is not applicable in general when the data are interval censored and truncated it is shown however that turnbull s characterization can be easily modified to obtain the appropriate characterization of f

a measure of tumorigenic potency incorporating dose response shape many researchers have considered the problem of ranking chemical agents based on their carcinogenic potency sawyer et al 1984 biometrics 40 27 40 proposed a carcinogenic potency estimate that incorporates both intercurrent mortality and background tumor rates since then many authors have either generalized the method outlined by sawyer et al or developed their own method based on a slightly different adjustment for treatment related changes in survival none of these methods however has estimated the shape of the dose response curve and incorporated such an estimate in potency estimation in this manuscript a measure of tumorigenic potency is proposed that utilizes the estimated shape of the dose response relationship in addition to estimated dose effects in order to rank chemicals on the basis of carcinogenic risk comparison of this new measure to that of sawyer et al is done using a large database of animal carcinogenicity experiments from the national cancer institute and the national toxicology program

nonparametric joint estimators for disease resistance and survival functions in survival sacrifice experiments the nonparametric estimators proposed in this paper simultaneously estimate the disease resistance function s t for the distribution of time to occurrence of disease and the survival function p t for the distribution of time to death caused by the disease the estimators are applicable to animal survival data when the disease of interest is irreversible and the cause of death of each animal can be determined diseases need not be classified as universally lethal or universally nonlethal and time to occurrence of the disease of interest need not be observable directly it is shown that the proposed estimators are maximum likelihood estimators under the condition that s t p t is monotonically decreasing application of the derived estimators is illustrated with experimental survival sacrifice data and results of a simulation study of the estimators performance are reported

sieve maximum likelihood regression analysis of dependent current status data current status data occur in contexts including demographic studies and tumorigenicity experiments in such cases each subject is observed only once and the failure time of interest is either left or right censored kalbfleisch prentice 2002 many methods have been developed for the analysis of such data huang 1996 sun 2006 most of which assume that the failure time and the observation time are independent completely or given covariates in this paper we present a sieve maximum likelihood approach for current status data when independence does not hold a copula model and monotone i splines are used and the asymptotic properties of the resulting estimators are established in particular the estimated regression parameters are shown to be semiparametrically efficient an illustrative example is provided

ergodic control of semilinear stochastic equations and the hamilton jacobi equation abstract in this paper we consider optimal control of stochastic semilinear equations with lipschitz continuous drift and cylindrical noise we show existence and uniqueness up to an additive constant of solutions to the stationary hamilton jacobi equation associated with the cost functional given by the asymptotic average per unit time cost as a consequence we find the optimizing controls given in the feedback form to obtain these results we prove also some new results on the transition semigroups of semilinear diffusion acting in the spaces of continuous function with the weighted sup norms and on the optimal control of semilinear diffusions for the discounted cost functional

age adjusted exact trend tests in the event of rare occurrences summary preclinical animal carcinogenicity studies are usually concerned with testing the statistical significance of a dose response relationship when the response consists of a rare event such as the development of a certain type of tumor exact statistical methods are often employed the exact randomization trend test based on the multivariate hypergeometric distribution is less powerful in the presence of treatment related risks other than the specified response particularly the loss of power becomes more pronounced when competing risks cause progressively higher mortality rates with increasing dose which is usual in practice an age adjusted form of the randomization test is proposed to adjust for this effect permutational distribution for peto s cause of death cod test is also explored and compared with its asymptotic counterpart by simulation the use of cod information has been a controversial issue due to the subjectivity in the pathologists determinations as well as for economic reasons the proposed age adjusted exact test does not require cod and it is shown to compare favorably to the cod tests via an extensive monte carlo simulation applications of the methods to two real data sets are included

inference based on the em algorithm for the competing risks model with masked causes of failure summary in this paper we propose inference methods based on the em algorithm for estimating the parameters of a weakly parameterised competing risks model with masked causes of failure and second stage data with a carefully chosen definition of complete data the maximum likelihood estimation of the cause specific hazard functions and of the masking probabilities is performed via an em algorithm both the e and m steps can be solved in closed form under the full model and under some restricted models of interest we illustrate the flexibility of the method by showing how grouped data and tests of common hypotheses in the literature on missing cause of death can be handled the method is applied to a real dataset and the asymptotic and robustness properties of the estimators are investigated through simulation

on the existence and uniqueness of the maximum likelihood estimate of a vector valued parameter in fixed size samples the maximum likelihood estimate is shown to exist and to be unique if a twice continuously differentiable likelihood function is constant on the boundary of the parameter space and if the hessian matrix is negative definite whenever the gradient vector vanishes the condition of constancy on the boundary cannot be completely removed cf tarone and gruenhage 1975 the theory is illustrated with several examples

quadrature formula for approximating the singular integral of cauchy type with unbounded weight function on the edges new quadrature formulas qfs for evaluating the singular integral si of cauchy type with unbounded weight function on the edges is constructed the construction of the qfs is based on the modification of discrete vortices method mmdv and linear spline interpolation over the finite interval 1 1 it is proved that the constructed qfs converge for any singular point x not coinciding with the end points of the interval 1 1 numerical results are given to validate the accuracy of the qfs the error bounds are found to be of order o h a lnh and o h lnh in the classes of functions h a 1 1 and c 1 1 1 respectively

second order hamilton jacobi equations in hilbert spaces and stochastic boundary control the paper is concerned with fully nonlinear second order hamilton jacobi bellman isaacs equations of elliptic type in separable hilbert spaces which have unbounded first and second order terms the viscosity solution approach is adapted to the equations under consideration and the existence and uniqueness of viscosity solutions are proved a stochastic optimal control problem driven by a parabolic stochastic pde with control of dirichlet type on the boundary is considered it is proved that the value function of this problem is the unique viscosity solution of the associated hamilton jacobi bellman equation

stationary hamilton jacobi equations in hilbert spaces and applications to a stochastic optimal control problem we study an infinite horizon stochastic control problem associated with a class of stochastic reaction diffusion systems with coefficients having polynomial growth the hamiltonian is assumed to be only locally lipschitz continuous so that the quadratic case can be covered we prove that the value function v corresponding to the control problem is given by the solution of the stationary hamilton jacobi equation associated with the state system to this purpose we write the hamilton jacobi equation in integral form and by using the smoothing properties of the transition semigroup relative to the state system and the theory of m dissipative operators we show that it admits a unique solution moreover the value function v is obtained as the limit of minima for some approximating control problems which admit unique optimal controls and states

maximum principle for an optimal control problem associated to a spde with nonlinear boundary conditions abstract we study a control problem where the state equation is a nonlinear partial differential equation of the calculus of variation in a bounded domain perturbed by noise we allow the control to act on the boundary and set boundary conditions which result in a stochastic differential equation for the trace of the solution on the boundary this work provides necessary and sufficient conditions of optimality in the form of a maximum principle we also provide a result of existence for the optimal control in the case where the control acts linearly

estimating tumor incidence rates in animal carcinogenicity experiments tumor incidence is the primary measure of carcinogenesis this article focuses on estimating time dependent incidence rates in animal experiments with few sacrifices when the context of observation is known for none or all of the animals dying with the tumor of interest previous results are obtained under relaxed assumptions the link with existing semiparametric and nonparametric procedures based on latent failure times is exploited by using these methods to compute maximum likelihood estimates of the incidence rates without introducing latent random variables nonparametric estimators that are appropriate when all contexts of observation are known are generalized to the case in which the contexts of observation are unknown for a subset of the tumor bearing animals

convergence results for piecewise linear quadratures for cauchy principal value integrals etablissement des conditions de convergence simple et uniforme des quadratures lineaires par morceaux pour les integrales a valeur principale de cauchy

current status and right censored data structures when observing a marker at the censoring time we study nonparametric estimation with two types of data structures in the first data structure n i i d copies of c n c are observed where n is a finite state counting process jumping at time variables of interest and c a random monitoring time in the second data structure n i i d copies of c t i t c n c t are observed where n is a counting process with a final jump at time t e g death this data structure includes observing right censored data on t and a marker variable at the censoring time in these data structures easy to compute estimators namely weighted pool adjacent violator estimators for the marginal distributions of the unobservable time variables and the kaplan meier estimator for the time t till the final observable event are available these estimators ignore seemingly important information in the data in this paper we prove that at many continuous data generating distributions the ad hoc estimators yield asymptotically efficient estimators of formula see text estimable parameters

analysis of competing risks survival data when some failure types are missing we propose a method to analyse competing risks survival data when failure types are missing for some individuals our approach is based on a standard proportional hazards structure for each of the failure types and involves the solution to estimating equations we present consistent and asymptotically normal estimators of the regression coefficients and related score tests an appealing feature is that individuals with known failure types make the same contributions as they would to a standard proportional hazards analysis contributions of individuals with unknown failure types are weighted according to the probability that they failed from the cause of interest efficiency and robustness are discussed results are illustrated with data from a breast cancer trial

a nonparametric test for current status data with unequal censoring nonparametric tests for the comparison of different treatments based on current status data are proposed for this problem most methods proposed in the literature require that observation times on all subjects follow the same distribution in other words censoring distributions are identical between the treatment groups in this paper we focus on the situation where the censoring distributions may be different for subjects in different treatment groups and the test that can take this unequal censoring into account is given the asymptotic distribution of the test proposed is derived the method proposed is applied to data arising from a tumorigenicity experiment

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

ergodic boundary point control of stochastic semilinear systems a controlled markov process in a hilbert space and an ergodic cost functional are given for a control problem that is solved where the process is a solution of a parameter dependent semilinear stochastic differential equation and the control can occur only on the boundary or at discrete points in the domain the linear term of the semilinear differential equation is the infinitesimal generator of an analytic semigroup the noise for the stochastic differential equation can be distributed boundary and point some ergodic properties of the controlled markov process are shown to be uniform in the control and the parameter the existence of an optimal control is verified to solve the ergodic control problem the optimal cost is shown to depend continuously on the system parameter

survival with competing risks and masked causes of failures consider a life testing situation in which systems are subject to failure from independent competing risks the hazards of various risks are proportional to each other when a failure occurs immediate i e stage 1 procedures are used in an attempt to reach a definitive diagnosis if a diagnosis is not reached this phenomenon is called masking stage 2 procedures such as failure analysis or autopsy provide definitive diagnosis for a small sample of the masked cases this paper shows how stage 1 and stage 2 information can be combined to provide statistical inference about a survival functions of the individual risks b the proportions of failures associated with individual risks and c probability for a specified masked case that each of the masked competing risks is responsible for the failure

regression analysis of a disease onset distribution using diagnosis data we consider methods for estimating the effect of a covariate on a disease onset distribution when the observed data structure consists of right censored data on diagnosis times and current status data on onset times amongst individuals who have not yet been diagnosed dunson and baird 2001 biometrics 57 306 403 approached this problem using maximum likelihood under the assumption that the ratio of the diagnosis and onset distributions is monotonic nondecreasing as an alternative we propose a two step estimator an extension of the approach of van der laan jewell and petersen 1997 biometrika 84 539 554 in the single sample setting which is computationally much simpler and requires no assumptions on this ratio a simulation study is performed comparing estimates obtained from these two approaches as well as that from a standard current status analysis that ignores diagnosis data results indicate that the dunson and baird estimator outperforms the two step estimator when the monotonicity assumption holds but the reverse is true when the assumption fails the simple current status estimator loses only a small amount of precision in comparison to the two step procedure but requires monitoring time information for all individuals in the data that motivated this work a study of uterine fibroids and chemical exposure to dioxin the monotonicity assumption is seen to fail here the two step and current status estimators both show no significant association between the level of dioxin exposure and the hazard for onset of uterine fibroids the two step estimator of the relative hazard associated with increasing levels of exposure has the least estimated variance amongst the three estimators considered

use of historical controls in time adjusted trend tests for carcinogenicity we develop a method for incorporating historical control information into time adjusted tests for dose effects in carcinogenicity studies after discretizing the time scale we use a multinomial distribution to model the number of animals dying with tumor in each interval data from past studies are used to estimate the parameters characterizing the prior a score test derived from the resulting dirichlet multinomial generalizes the test of tarone 1982 biometrics 38 215 220 and reduces in the limit to the log rank test in the case of a diffuse prior the methodology is illustrated with data from a study of the fire retardant 2 2 bis bromomethyl 1 3 propanediol