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

on fujita s spectrum conjecture abstract we prove fujita s spectrum conjecture on the discreteness of pseudo effective thresholds for polarized varieties

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

balanced line bundles on fano varieties a conjecture of batyrev and manin relates arithmetic properties of varieties with ample anticanonical class to geometric invariants in particular counting functions defined by metrized ample line bundles and the corresponding asymptotics of rational points of bounded height are interpreted in terms of cones of effective divisors and certain thresholds with respect to these cones this framework leads to the notion of balanced line bundles whose counting functions conjecturally capture generic distributions of rational points we investigate balanced line bundles in the context of the minimal model program with special regard to the classification of fano threefolds

varieties with too many rational points we investigate fano varieties defined over a number field that contain subvarieties whose number of rational points of bounded height is comparable to the total number on the variety

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

on the birational automorphisms of varieties of general type we show that the number of birational automorphisms of a variety of general type x is bounded by c vol x kx where c is a constant that only depends on the dimension of x

cubic unipotent arthur parameters and multiplicities of square integrable automorphic forms l g f g a ld g f g a lcont g f g a into the direct sum of its discrete spectrum and its continuous spectrum the theory of eisenstein series reduces the description of lcont g f g a to that of the discrete spectrum of certain reductive subgroups of g and thus the basic question is the understanding of the discrete spectrum ld g f g a the discrete spectrum has a further orthogonal decomposition

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

vector bundles of rank 2 and linear systems on algebraic surfaces let s be a smooth complex algebraic surface and let l be a divisor on s it is well known that the linear system il ksi where ks is the canonical divisor plays an important role in understanding the geometry of s several authors see for example 8 11 studied various properties of this system our paper treats the same subject but the point of view is different from the works mentioned above the philosophy underlying our approach is almost classical points on s more generally effective 0 cycles in special position with respect to il ksi see definition below contain information about the geometry of s this point of view was recently revived in 5 also 10 in fact this paper contains the technique of going from the effective 0 cycle z in special position with respect to il ksi to the geometry of s for the sake of completeness we give a definition and state a theorem which can be found in 5 10

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

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

automorphic forms with degenerate fourier coefficients the main theme of this paper is that singular automorphic forms on classical groups are given by theta series liftings we establish several inequalities relating the automorphic multiplicities of a given representation and that of its abstract theta lift our methods allow one to lift noncuspidal square integrable automorphic forms when the dual pair involved is in the stable range in this way we construct new families of singular automorphic forms many of which are clearly unipotent in fact starting from one dimensional representations and repeating the procedure of lifting in the stable range one may obtain all automorphic forms which are quadratic unipotent in the sense of moeglin

general elephants of three fold divisorial contractions the theory of minimal models has enriched the study of higher dimensional algebraic geometry see 10 and 12 for a variety with mild singularities this theory produces another variety which possesses good properties after finite elementary transformations called divisorial contractions and flips since mori completed this program in dimension three in 17 it has become desirable to study three folds explicitly this paper aims to complete the explicit study of three fold divisorial contractions whose exceptional divisors contract to gorenstein points after the papers 7 and 8 reid pointed out that general elements in the anti canonical systems of threefolds have at worst du val singularities in appropriate situations involving contractions of extremal faces this has become known as the general elephant conjecture the papers 19 21 and 22 support it with affirmative answers for fano threefolds with singularities and this approach has settled the problem of the existence of three fold flips in 11 and 17 our main theorem is that this conjecture holds for our divisorial contractions

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

calculation of carcinogenic potency from long term animal carcinogenesis experiments an index of carcinogenic potency for chemicals tested in chronic animal experiments is described by analogy with the well known lethal dose 50 ld50 of quantal bioassay a tumorigenic dose 50 td50 may be defined in the absence both of tumors in the control group and of intercurrent deaths as that daily dose of chemical which gives 50 of the test animals tumors by some fixed age tumors in the control zero dose group are handled exactly as for the ld50 and intercurrent deaths are handled by life table methods nonparametric procedures are developed for estimating the td50 and for constructing confidence intervals these are based on likelihoods which assume that the tumor hazard is linear in dose

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

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

on the geometry of thin exceptional sets in manin s conjecture manin s conjecture predicts the rate of growth of rational points of a bounded height after removing those lying on an exceptional set we study whether the exceptional set in manin s conjecture is a thin set using the minimal model program and boundedness of log fano varieties

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

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

sieving rational points on varieties an upper bound sieve for rational points on suitable varieties isdeveloped together with applications tocounting rational points in thin sets to local solubility in families and to the notion of friable rational pointswith respect to divisors in the special case of quadrics sharper estimates areobtained by developing a version of the selberg sieve for rational points

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

optimal designs for dose response models with restricted design spaces in dose response studies the dose range is often restricted due to concerns over drug toxicity and or efficacy we present restricted and unrestricted interval locally optimal designs with respect to a very general class of optimality criteria for estimating the underlying dose response curve the underlying curve belongs to a diversified set of link functions suitable for the dose response studies and having a common canonical form these include the fundamental binary response models the logit and the probit as well as the skewed versions of these models the results are illustrated through the re design of a dose ranging trial conducted at the merck research laboratories zeng and zhu 1997 this work is a generalization of the results of dai and zhu 2002 in terms of the design interval the underlying dose response curve and the optimality criterion

order restricted dose related trend tests methods of isotonic regression are proposed to increase the power of common trend tests in situations where a monotonicity constraint is imposed upon the dose response function isotonic versions of cochran armitage type trend tests for binary response data are developed and the bootstrap method is used in finding the empirical distributions of the test statistics and their critical values the isotonic likelihood ratio test with a survival adjustment is also proposed this survival adjustment can be applied to the likelihood ratio test for either the order restricted or unrestricted parameter cases to achieve the isotonic modifications an amalgamation algorithm is applied when the observed dose response is non monotonic a monte carlo simulation study comparing these trend tests shows the advantages of the isotonic modifications and survival adjustment by applying the proposed methods to data from a toxicology and carcinogenesis study conducted as part of the national toxicology program the effect of ci pigment red 23 is investigated

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

construction of discrete series for classical p adic groups in this paper the authors complete the classification of irreducible square integrable representations of classical p adic groups assuming a natural assumption which is expected to hold in general this classification implies a parameterization of irreducible tempered representations of these groups and it implies a classification of the non unitary duals of these groups modulo cuspidal data

etale fundamental groups of kawamata log terminal spaces flat sheaves and quotients of abelian varieties given a quasiprojective variety x with only kawamata log terminal singularities we study the obstructions to extending finite etale covers from the smooth locus xreg of x to x itself a simplified version of our main results states that there exists a galois cover y x ramified only over the singularities of x such that the etale fundamental groups of y and of yreg agree in particular every etale cover of yreg extends to an etale cover of y as a first major application we show that every flat holomorphic bundle defined on yreg extends to a flat bundle that is defined on all of y as a consequence we generalize a classical result of yau to the singular case every variety with at worst terminal singularities and with vanishing first and second chern class is a finite quotient of an abelian variety as a further application we verify a conjecture of nakayama and zhang describing the structure of varieties that admit polarized endomorphisms

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

an age adjusted bootstrap based poly k test the assumption of an asymptotic normal distribution of some test statistics may be invalid in certain dose response trend tests for instance the survival adjusted cochran armitage test known as the poly k test is asymptotically standard normal under the null hypothesis however the asymptotic normality is not valid if there is a deviation from the tumour onset distribution that is assumed in this test or if the competing risks survival rates differ across groups we develop an age adjusted bootstrap based method to assess the significance of assumed asymptotic normal tests for animal carcinogenicity data the proposed method differs from conventional bootstrap methods in the aspect of preserving the mortality rate in each dose group under the null hypothesis of equal tumour incidence rates among the groups we investigate an empirical distribution of the poly 3 p3 trend test statistic using the proposed age adjusted bootstrap based method and compare it with the p3 test statistic referenced to the assumed standard normal distribution a simulation study is conducted to evaluate the robustness of these tests to various weibull family tumour onset distributions the proposed method is applied to national toxicology program data sets to evaluate a dose related trend of a test substance on the incidence of neoplasms

order restricted inference for multivariate binary data with application to toxicology in many applications researchers collect multivariate binary response data under two or more naturally ordered experimental conditions in such situations one is often interested in using all binary outcomes simultaneously to detect an ordering among the experimental conditions to make such comparisons we develop a general methodology for testing for the multivariate stochastic order between k 2 multivariate binary distributions our proposed test uses order restricted estimators which according to our simulation study are more efficient than the unrestricted estimators in terms of their mean squared error we compared the power of the proposed test with that of several alternative tests including procedures that combine individual univariate tests for order such as union intersection tests and a bonferroni based test we also compared the proposed test with an unrestricted hotelling t2 type test our simulations suggest that the proposed method competes well with these alternatives the gain i

a canonical bundle formula a higher dimensional analogue of kodaira s canonical bundle formula is obtained as applications we prove that the log canonical ring of a klt pair with 3is finitely generated and that there exists an effectively computable natural number m such that mk x induces the iitaka fibering for every algebraic threefold x with kodaira dimension 1

tests for order restrictions in binary data in this article a general procedure is presented for testing for equality of k independent binary response probabilities against any given ordered alternative the proposed methodology is based on an estimation procedure developed in hwang and peddada 1994 annals of statistics 22 67 93 and can be used for a very broad class of order restrictions the procedure is illustrated through application to two data sets that correspond to three commonly encountered order restrictions simple tree order simple order and down turn order

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

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