testing against ordered alternatives for censored survival data in animal carcinogenesis experiments or comparative clinical trials where the r groups correspond to increasing dosages of an agent or an increasing number of additional modalities and the primary outcome is time to a certain event e g tumor occurrence death t ordered alternatives of the form h1 s1 s2 sr where si t pr ti t is the survival function for group are of special interest using the counting process formulation of the problem and generalizing earlier results we show that the class of all two sample weighted logrank statistics can be extended to test specifically for ordered alternatives ordered versions of the gehan wilcoxon unweighted logrank and peto prentice wilcoxon tests are investigated in detail asymptotic relative efficiencies under lehmann and scale alternatives are evaluated analytically and numerically among these three tests and against tarone s trend test 1975 for weibull gamma and lognormal survival distributions effects of censoring and unequa

stability and size dependency of cauchy born hypothesis in three dimensional applications abstract the cauchy born hypothesis cb provides a hierarchical approach in the molecular theory of crystal elasticity to relate the continuum and atomic deformations this kinematic theory has been extensively used as the constitutive law of continuum regions in multi scale models in these models the fine scale is proposed to describe the real behavior of crystalline structure wherever the continuum description fails the main objective of this article is to investigate the stability and size dependency of cb hypothesis in three dimensional applications by direct comparison of information between atomistic and continuous description of a medium the sutton chen many body potential is used for the gold metal to consider the real metallic behavior in numerical simulations two failure criteria are introduced in the strain and stress domains the validity surfaces are derived for the cauchy born hypothesis and the size effect of specimens is investigated on the convergency of results it is shown that the gold crystal deforms homogeneously inside the validity surface in which the material is elastic and the cb has remained valid it is observed that although the deformation is inhomogeneous and the cb is invalid outside the validity surface the crystalline structure may exhibit elastic or plastic behavior in this region moreover it is numerically shown that the size dependency of validity surface decreases with the increase of the size of specimens these observations are meticulously investigated by loading and unloading several cubic specimens using molecular dynamics simulation

harnack inequalities and discrete continuous error estimates for a chain of atoms with two body interactions we consider deformations in r 3 of an infinite linear chain of atoms where each atom interacts with all others through a two body potential we compute the effect of an external force applied to the chain at equilibrium the positions of the particles satisfy an euler lagrange equation for large classes of potentials we prove that every solution is well approximated by the solution of a continuous model we establish an error estimate between the discrete and the continuous solution based on a harnack lemma of indepen dent interest finally we apply our results to some lennard jones potentials

overall properties of a discrete membrane with randomly distributed defects a prototype for variational percolation problems with surface energies is considered the description of the macroscopic properties of a two dimensional discrete membrane with randomly distributed defects in the spirit of the weak membrane model of blake and zisserman quadratic springs that may break at a critical length of the elongation after introducing energies depending on suitable independent identically distributed random variables this is done by exhibiting an equivalent continuum energy computed using convergence geometric measure theory and percolation arguments we show that below a percolation threshold the effect of the defects is negligible and the continuum description is given by the dirichlet integral while above that threshold an additional griffith fracture term appears in the energy which depends only on the defect probability through the chemical distance on the weak cluster of defects

power of the mantel haenszel and other tests for discrete or grouped time to event data under a chained binomial model power for time to event analyses is usually assessed under continuous time models often however times are discrete or grouped as when the event is only observed when a procedure is performed wallenstein and wittes biometrics 1993 describe the power of the mantel haenszel test for discrete life tables under their chained binomial model for specified vectors of event probabilities over intervals of time herein the expressions for these probabilities are derived under a piecewise exponential model allowing for staggered entry and losses to follow up radhakrishna biometrics 1965 showed that the mantel haenszel test is maximally efficient under the alternative of a constant odds ratio and derived the optimal weighted test under other alternatives lachin biostatistical methods the assessment of relative risks 2011 describes the power function of this family of weighted mantel haenszel tests prentice and gloeckler biometrics 1978 describe a generalization of the proportional hazards model for grouped time data and the corresponding maximally efficient score test their test is also shown to be a weighted mantel haenszel test and its power function is likewise obtained there is trivial loss in power under the discrete chained binomial model relative to the continuous time case provided that there is a modest number of periodic evaluations relative to the case of homogeneity of odds ratios there can be substantial loss in power when there is substantial heterogeneity of odds ratios especially when heterogeneity occurs early in a study when most subjects are at risk but little loss in power when there is heterogeneity late in a study

effective cohesive behavior of layers of interatomic planes a simple model of cleavage in brittle crystals consists of a layer of material containing n atomic planes separating in accordance with an interplanar potential under the action of an opening displacement prescribed on the boundary of the layer the problem addressed in this work concerns the characterization of the constrained minima of the energy en of the layer as a function of as n becomes large these minima determine the effective or macroscopic cohesive law of the crystal the main results presented in this communication are i the computation of the limit e0 of en as n ii the characterization of the minimum values of e0 as a function of the macroscopic opening displacement iii a proof of uniform convergence of the minima of en for the case of nearest neighbor interactions and iv a proof of uniform convergence of the derivatives of en or tractions in the same case the scaling on which the present convergence analysis is based has the effect of separating the bulk and surface contributions to the energy it differs crucially from other scalings employed in the past in that it renders both contributions of the same order

rank based inference for the accelerated failure time model summary a broad class of rank based monotone estimating functions is developed for the semiparametric accelerated failure time model with censored observations the corresponding estimators can be obtained via linear programming and are shown to be consistent and asymptotically normal the limiting covariance matrices can be estimated by a resampling technique which does not involve nonparametric density estimation or numerical derivatives the new estimators represent consistent roots of the non monotone estimating equations based on the familiar weighted log rank statistics simulation studies demonstrate that the proposed methods perform well in practical settings two real examples are provided

maximum of the weighted kaplan meier tests with application to cancer prevention and screening trials summary a class of maximum weighted kaplan meier test statistics is described where the weight functions are chosen from a family of smooth functions the investigated test statistic is robust and sensitive to a variety of alternatives that are often observed in cancer prevention and screening trials a simulation study is performed to compare the size and power properties between the proposed test statistics and some existing ones we illustrate the procedure using data from a clinical trial of a breast cancer screening program

a sharper bonferroni procedure for multiple tests of significance summary a simple procedure for multiple tests of significance based on individual p values is derived this simple procedure is sharper than holm s 1979 sequentially rejective procedure both procedures contrast the ordered p values with the same set of critical values holm s procedure rejects an hypothesis only if its p value and each of the smaller p values are less than their corresponding critical values the new procedure rejects all hypotheses with smaller or equal p values to that of any one found less than its critical value

a consistency adjusted alpha adaptive strategy for sequential testing in a clinical trial with two clinically important endpoints each of which can fully characterize a treatment benefit to support an efficacy claim by itself a minimum degree of consistency in the findings is expected otherwise interpretation of study findings can be problematic clinical trial literature contains examples where lack of consistency in the findings of clinically relevant endpoints led to difficulties in interpreting study results the aim of this paper is to introduce this consistency concept at the study design stage and investigate the consequences of its implementation in the statistical analysis plan the proposed methodology allows testing of hierarchically ordered endpoints to proceed as long as a pre specified consistency criterion is met in addition while an initial allocation of the alpha level is specified for the ordered endpoints at the design stage the methodology allows the alpha level allocated to the second endpoint to be adaptive to the findings of the first endpoint in addition the methodology takes into account the correlation between the endpoints in calculating the significance level and the power of the test for the next endpoint the proposed consistency adjusted alpha adaptive strategy caaas is very general several of the well known multiplicity adjustment approaches arise as special cases of this strategy by appropriate selection of the consistency level and the form of alpha adaptation function we discuss control of the type i error rate as well as power of the proposed methodology and consider its application to clinical trial data

signed rank tests for censored matched pairs abstract i consider the problem of testing bivariate symmetry in matched pair experiments where the observations are subject to univariate censoring thus the observable random variables are given by y 1 y 2 and 1 2 where y j min x j c and j i x j c j 1 2 here x 1 x 2 is a random pair of partially observable lifetimes and c is a fixed or random censoring variable the hypothesis to be tested is that x 1 x 2 and x 2 x 1 have the same distribution following woolson and lachenbruch 1980 i consider censored data generalizations of signed rank tests such as the sign signed wilcoxon and signed normal scores tests i derive the asymptotic distribution of these test statistics under fixed and contiguous alternatives the efficiencies of the signed rank tests are considered in a log linear model and compared with efficiencies of the paired prentice wilcoxon and log rank tests

sequential monitoring of survival data with the wilcoxon statistic when a spending function is used in sequential data monitoring of a clinical trial it is important to know the information fraction at the times of interim analysis in a maximum duration designed study the information fraction is unknown when data are monitored and it has to be estimated the modified wilcoxon statistic developed by peto and peto and modified by prentice is often used to compare two survival curves in a clinical trial we give guidelines for estimating the information fraction in a maximum duration trial when this statistic is employed when there is a relatively low event rate or the survival time is approximately exponential the information fraction for the peto peto prentice wilcoxon statistic is very close to that of the popular logrank statistic in other cases it would be helpful to estimate the information fraction as a function of elapsed calendar time we discuss both group sequential and continuous monitoring

unobserved covariates in the two sample comparison of survival times a maximin efficiency robust test in analysing a clinical trial with the logrank test the hazards between the two groups are usually assumed to be proportional nevertheless this hypothesis is no longer valid with unobserved covariates as a consequence there is a loss of power of the logrank test for testing the null hypothesis h 0 of no treatment effect we propose a test suited for taking into account unobserved covariates the proposed approach is based on a proportional hazard frailty model whereby the omitted covariates are considered as an unobserved frailty variable the procedure is as follows in a first step the weighted logrank test optimal for testing h 0 against a general proportional hazard frailty model is obtained and its specialization for a gamma frailty variable is derived in a second step the proposed test is obtained by combining the maximin efficiency robustness principle and the gamma frailty distribution properties simulation studies investigate the power properties of the test for different frailty distributions a breast cancer clinical trial is analysed as an example the proposed test might be recommended rather than the logrank for practical situations in which one expects heterogeneity related to omitted covariates

asymptotic properties of censored linear rank tests a conjecture of prentice is established which states that for censored linear rank test exact scores based on conditional expectations can be replaced by approximate scores obtained by evaluating the score function at an estimate of the survival function we show that under minimal conditions asymptotically equivalent tests are obtained when either the kaplan meier altshuler or moment estimator of the survival function is used asymptotic normality is also established for a general random censorship model under the null hypothesis and for contiguous alternatives this is used to calculate efficacies and when the censoring times are i i d an expression for the asymptotic relative efficiency is given which is a natural generalization of the one for classical uncensored linear rank tests 1 introduction prentice 1978 has constructed a general class of linear rank tests for a regression model with censored data his approach was to specify a score function for a classical linear rank test in the absence of censoring chernoff and savage 1958 hajek and sidak 1967 to construct all possible rankings of the unobserved uncensored values which were consistent with observed censored sample and then to assign to each observation the average of all possible scores it could have received in the absence of censoring giving equal weighting to each possible uncensored ranking except for a few special scoring functions notably logarithmic or power law scores these averages are unwieldy when there is appreciable censoring and prentice suggested that asymptotically equivalent tests might arise if the score function was evaluated at some suitable estimate of the survivor function this is well known to be true for uncensored data but requires further justification when censoring is present because the estimate of the survivor function is more complicated in this work we show that prentice s conjecture is true under minimal conditions and also we show that it remains true if prentice s moment estimator of the survivor function is replaced by either the kaplan meier estimator or altshuler s estimator asymptotic normality of these tests is established under a random censorship model for the null hypothesis and contiguous alternatives by martingale methods this is used to compute efficacies for a general random censorship model and asymptotic relative efficiencies for i i d potential censoring times where fully efficient linear rank tests exist asymptotic normality for general alternatives has been established in cuzick 1982 by more complicated methods

accelerated hazards regression model and its adequacy for censored survival data summary the accelerated hazards regression model is introduced to study the relationship between survival times and covariates through a scale change between hazard functions the model is also compared with several other popular classes of regression models for censored survival data in statistical literature test statistics are proposed and studied to assess the model s adequacy actual data from a randomized clinical trial of biodegradable carmustine polymer for treatment of brain cancer are analyzed to demonstrate the potential application of the regression model and the proposed test statistics

rank tests and a one sample logrank test for comparing observed survival data to a standard population for cox s proportional hazards model test procedures are described for the comparison of randomly right censored observed and expected standard population survival data it is observed that the class of linear rank tests proposed by prentice 1978 biometrika 65 167 179 may be employed to test regression hypotheses in this one sample setting in order to compare globally the observed and expected survival data the one sample limit of mantel s logrank test is formally derived the statistic derived is identical to one proposed from a diflerent viewpoint by breslow 1975 intemational statistical review 43 45 58 throughout it is assumed that the standard population survival function is a continuous function of time and that the survival or censoring time for each study sample individual is exact and is not grouped into categories

conditional rank tests for the two sample problem under random censorship for the two sample problem with randomly censored data there exists a general asymptotic theory of rank statistics which are functionals of stochastic integrals with respect to certain empirical martingales in the present paper a conditional counterpart of this theory is developed the conditional martingales are versions of the original ones reduced to the unit interval having their jumps at fixed lattice points the resulting conditional tests are strictly distribution free under the null hypothesis of randomness if the censoring distributions in both samples are equal and are asymptotically equivalent to their unconditional counterparts even if the censoring distributions are different simulations for linear rank statistics and kolmogorov smirnov type statistics show superiority of the conditional versions over their unconditional counterparts with respect to size and robustness under unequal censoring in both samples at the same time the power of the conditional and unconditional tests is very similar in most cases

two sample goodness of fit tests for additive risk models with censored observations summary the additive risk model assumes that the hazard function associated with a set of covariates is the sum of the baseline hazard function and the regression function of covariates we propose two different test procedures for checking the adequacy of two sample additive risk models for randomly censored observations one is based on the martingale residuals and the other on the difference between weighted estimators of the excess risk the test statistics are shown to be asymptotically normal under appropriate regularity conditions and consistent under any model misspecifications finally two real examples are provided along with results of a simulation study

the energy of some microscopic stochastic lattices we introduce a notion of energy for some microscopic stochastic lattices such lattices are broad generalizations of simple periodic lattices for which the question of the definition of an energy was examined in a series of previous works 14 18 note that slightly more general deterministic geometries were also considered in 6 these lattices are involved in the modelling of materials whose microscopic structure is a perturbation in a sense made precise in the article of the periodic structure of a perfect crystal the modelling considered here is either a classical modelling where the sites of the lattice are occupied by ball like atomic systems that interact by pair potentials or a quantum modelling where the sites are occupied by nuclei equipped with an electronic structure spread all over the ambient space the corresponding energies for the infinite stochastic lattices are derived consistently with truncated systems of finite size by application of a thermodynamic limit process subsequent works 7 8 will be devoted to the macroscopic limits of the energies of such microscopic lattices thereby extending to a stochastic context the results of 4 5 such convergences in a stochastic setting in dimension 1 have been studied in 21 22 we will also study in 8 some variants and extensions of the stationary setting presented here

a chi squared goodness of fit test for randomly censored data abstract in this article procedures analogous to karl pearson s well known chi squared goodness of fit test for a simple null hypothesis are developed under the random censorship model it is shown that one straightforward analog of pearson s statistic is diminished in applicability due to the form of its limiting distribution this leads to the development of an asymptotically exact test based on a wald type statistic with a chi squared limiting null distribution this test is compared and contrasted theoretically and via a simulation with akritas test with respect to significance levels asymptotic local powers and finite sample powers the general conclusions from the simulation study are that the proposed test usually achieves the desired significance levels when the probability of observing a censored or an uncensored value in the last interval is not small whereas akritas test tends to be a bit anticonservative on the other hand akritas test is more powerful than the proposed test in a model

survival trees by goodness of split abstract a tree based method for censored survival data is developed based on maximizing the difference in survival between groups of patients represented by nodes in a binary tree the method includes a pruning algorithm with optimal properties analogous to the classification and regression tree cart pruning algorithm uniform convergence of the estimates of the conditional cumulative hazard and survival functions is discussed and an example is given to show the utility of the algorithm for developing prognostic classifications for patients

weighted kaplan meier statistics a class of distance tests for censored survival data a class of statistics based on the integrated weighted difference in kaplan meier estimators is introduced for the two sample censored data problem with positive weight functions these statistics are intuitive for and sensitive against the alternative of stochastic ordering the standard weighted log rank statistics are not always sensitive against this alternative particularly if the hazard functions cross qualitative comparisons are made between the weighted log rank statistics and these weighted kaplan meier wkm statistics a statement of null asymptotic distribution theory is given and the choice of weight function is discussed in some detail results from small sample simulation studies indicate that these statistics compare favorably with the log rank procedure even under the proportional hazards alternative and may perform better than it under the crossing hazards alternative

geometry of batalin vilkovisky quantization the geometry ofp manifolds odd symplectic manifolds andsp manifolds p manifolds provided with a volume element is studied a complete classification of these manifolds is given this classification is used to prove some results about batalin vilkovisky procedure of quantization in particular to obtain a very general result about gauge independence of this procedure

rank based estimating equations with general weight for accelerated failure time models an induced smoothing approach the induced smoothing technique overcomes the difficulties caused by the non smoothness in rank based estimating functions for accelerated failure time models but it is only natural when the estimating function has gehan s weight for a general weight the induced smoothing method does not provide smooth estimating functions that can be easily evaluated we propose an iterative induced smoothing procedure for general weights with the estimator from gehan s weight initial value the resulting estimators have the same asymptotic properties as those from the non smooth estimating equations with the same weight their variances are estimated with an efficient resampling approach that avoids solving estimating equations repeatedly the methodology is generalized to incorporate an additional weight to accommodate missing data and various sampling schemes in a numerical study the proposed estimators were obtained much faster without losing accuracy in comparison to those from non smooth estimating equations and the variance estimators provided good approximation of the variation in estimation the methodology was applied to two real datasets the first one from an adolescent depression study and the second one from a cancer study with missing covariates by design the implementation is available in an r package aftgee

estimation and testing in a two sample generalized odds rate model abstract the generalized odds ratio for a survival variable t is defined as t t c c 1 1 sc t sc t for c 0 and log s t for c 0 where s t pr t t this ratio coincides with the integrated hazard for c 0 and the odds ratio for c 1 when the distribution of t depends on a covariate vector we assume that conditionally on the covariates log t t c is linear in the covariates this model is a generalization of the proportional hazard model phm which has an interpretation both as a phm with random nuisance effects clayton and cuzick 1986 and as a proportional odds rate model with the odds rate defined from the response times of series systems harrington and fleming 1982 and bickel 1986a considered rank tests for this semiparametric model clayton and cuzick 1986 considered estimation we use the odds rate representation to define a class of estimates of the proportionality parameter in the two sample case we show that the estimates are consistent and asymptotica

a general class of semiparametric transformation frailty models for nonproportional hazards survival data we propose a semiparametrically efficient estimation of a broad class of transformation regression models for non proportional hazards data classical transformation models are to be viewed from a frailty model paradigm and the proposed method provides a unified approach that is valid for both continuous and discrete frailty models the proposed models are shown to be flexible enough to model long term follow up survival data when the treatment effect diminishes over time a case for which the proportional hazards or proportional odds assumption is violated or a situation in which a substantial proportion of patients remains cured after treatment estimation of the link parameter in frailty distribution considered to be unknown and possibly dependent on a time independent covariates is automatically included in the proposed methods the observed information matrix is computed to evaluate the variances of all the parameter estimates our likelihood based approach provides a natural way to construct simple statistics for testing the proportional hazards and proportional odds assumptions for usual survival data or testing the short term and long term effects for survival data with a cure fraction simulation studies demonstrate that the proposed inference procedures perform well in realistic settings applications to two medical studies are provided

maximum weighted partial likelihood estimators for the cox model new estimators for cox regression that maximize a weighted version of the partial likelihood are considered their asymptotic properties on the model are sketched estimators with bounded influence curves are identified and shown to have good asymptotic relative efficiency the results of a small simulation study are included the estimators are applied to a well known data set the possible influence of an outlying observation on the cox estimator can be of any magnitude individuals who survive longest have a high potential of being influential in analogy with weighted linear rank tests we introduce estimators of the regression coefficients that maximize a weighted partial likelihood for instance by using weights proportional to the number at risk one obtains a wilcoxon type estimator this estimator has bounded influence provided the covariate space is compact and in a wide variety of situations its asymptotic relative efficiency is at least as good as that of the wilcoxon test asymptotic prop

sample size calculation for cluster randomization trials with a time to event endpoint cluster randomization trials randomize groups called clusters of subjects called subunits between intervention arms and observations are collected from each subject in this case subunits within each cluster share common frailties so that the observations from subunits of each cluster tend to be correlated oftentimes the outcome of a cluster randomization trial is a time to event endpoint with censoring in this article we propose a closed form sample size formula for weighted rank tests to compare the marginal survival distributions between intervention arms under cluster randomization with possibly variable cluster sizes extensive simulation studies are conducted to evaluate the performance of our sample size formula under various design settings real study examples are taken to demonstrate our method

cohomological structure in soliton equations and jacobian varieties on etudie la structure des orbites du systeme dynamique definie par la hierarchie kp totale on montre que chaque orbite est localement isomorphe a un certain groupe de cohomologie associe a une algebre commutative le systeme dynamique kp restreint a chaque orbite determine un systeme dynamique de mouvements lineaires sur lui par rapport a la structure lineaire du groupe de cohomologie

a comparison of estimated proportional hazards models and regression trees we present examples of the usage of regression trees for censored response via two real world datasets one a rheumatoid arthritis survival study and the other a hip replacement study and draw comparisons with the results of cox proportional hazards modelling the two methods pursue different goals motivation of the tree techniques is the desire to extract meaningful prognostic groups while the proportional hazards model enables assessment of the impact of risk factors the methods are thus complementary for the arthritis study the two techniques corroborate one another although the flavour of the conclusions derived differ for the hip replacement study however the regression tree approach reveals structure that would not emerge from a routine proportional hazards analysis we also discuss the treatment of data analytic issues such as the handling of missing values and influence in the presence of non uniform censoring

parametric models for accelerated and long term survival a comment on proportional hazards the cox proportional hazards model cph is routinely used in clinical trials but it may encounter serious difficulties with departures from the proportional hazards assumption even when the departures are not readily detected by commonly used diagnostics we consider the gamel boag gb model a log normal model for accelerated failure in which a proportion of subjects are long term survivors when the cph model is fit to simulated data generated from this model the results can range from gross overstatement of the effect size to a situation where increasing follow up may cause a decline in power we implement a fitting algorithm for the gb model that permits separate covariate effects on the rapidity of early failure and the fraction of long term survivors when effects are detected by both the cph and gb methods the attribution of the effect to long term or short term survival may change the interpretation of the data we believe these examples motivate more frequent use of parametric survival models in conjunction with the semi parametric cox proportional hazards model

the odd origin of gerstenhaber brackets batalin vilkovisky operators and master equations using five basic principles we treat gerstenhaber lie brackets batalin vilkovisky bv operators and master equations appearing in mathematical and physical contexts in a unified way the different contexts for this are given by the different types of feynman graphs that underlie the particular situation two of the maxims we bring forth are 1 that extending to the non connected graphs gives a commutative multiplication forming a part of the bv structure and 2 that there is a universal odd twist that unifies and explains seemingly ad hoc choices of signs and is responsible for the bv operator being a differential our treatment results in uniform general theorems these allow us to prove new results and recover and connect many constructions that have appeared independently throughout the literature the more general point of view also allows us to disentangle the necessary from the circumstantial

two sample asymptotically distribution free tests for incomplete multivariate observations abstract asymptotically distribution free tests for equality of two multivariate distributions based on censored observations are proposed by choosing appropriate test scores we obtain the multivariate versions of the gehan and log rank tests an important application of the proposed tests is in the area in which multiple observations are collected on study subjects some of whom may have missing observations the patterns of missing observations are allowed to differ for the two groups to be compared these tests are particularly useful for longitudinal studies for example the analysis of repeated measurements and growth curves real examples are also provided for illustration

parametric versus non parametric methods for estimating cure rates based on censored survival data if a patient s failure time is incorrectly recorded as being too early the correction will lower the plateau of the kaplan meier curve and hence the associated estimated cure rate implications of this counter intuitive observation are discussed in addition a parametric approach based on the gompertz distribution to the problem of cure rate estimation is presented

a generalization of the weibull distribution with application to the analysis of survival data abstract the weibull distribution which is frequently used for modeling survival data is embedded in a larger family obtained by introducing an additional shape parameter this generalized family not only contains distributions with unimodal and bathtub hazard shapes but also allows for a broader class of monotone hazard rates furthermore the distributions in this family are analytically tractable and computationally manageable the modeling and analysis of survival data using this family is discussed and illustrated in terms of a lifetime dataset and the results of a two arm clinical trial

key multiplicity issues in clinical drug development much progress has been made over the past decade with the development of novel methods for addressing increasingly more complex multiplicity problems arising in confirmatory phase iii clinical trials this includes traditional problems with a single source of multiplicity for example analysis of multiple endpoints or dose placebo contrasts in addition more advanced problems with several sources of multiplicity have attracted attention in clinical drug development these problems include two or more families of objectives such as multiple endpoints evaluated at multiple dose levels or in multiple patient populations this paper provides a review of concepts that play a central role in defining and solving multiplicity problems error rate definitions and introduces main classes of multiple testing procedures widely used in clinical trials nonparametric semiparametric and parametric procedures the paper also presents recent advances in multiplicity research including gatekeeping procedures for clinical trials with multiple sets of objectives the concepts and methods introduced in the paper are illustrated using several case studies on the basis of real clinical trials software implementation of commonly used multiple testing and gatekeeping procedures is discussed copyright 2012 john wiley sons ltd

modelling tumour biology progression relationships in screening trials there has been some recent work in the statistical literature for modelling the relationship between tumour biology properties and tumour progression in screening trials while non parametric methods have been proposed for estimation of the tumour size distribution at which metastatic transition occurs their asymptotic properties have not been studied in addition no testing or regression methods are available so that potential confounders and prognostic factors can be adjusted for we develop a unified approach to non parametric and semi parametric analysis of modelling tumour size metastasis data in this article an association between the models considered by previous authors with survival data structures is discussed based on this relationship we develop non parametric testing procedures and semi parametric regression methodology of modelling the effect of size of tumour on the probability at which metastatic transitions occur in two situations asymptotic properties of these estimators are provided the proposed methodology is applied to data from a screening study in lung cancer

the versatility of function indexed weighted log rank statistics abstract two sample weighted log rank statistics are used in the presence of right censoring to test whether failure times from two populations have different survival distributions kosorok has showed that large families of these statistics form stochastic processes indexed by weight functions and that these function indexed statistics can be used to construct versatile test procedures simultaneously sensitive to a wide array of both ordered hazards and stochastic ordering alternatives the complexity of the asymptotic distribution of these statistics precludes obtaining p values through analytical means in this article we develop a monte carlo method for accurately obtaining these p values and we evaluate the moderate sample size properties of this method and compare the power of function indexed statistics with previously developed weighted log rank tests these statistics are also examined in a data analysis of the beta blocker heart attack trial bhat the results of this article demonstrate that

a two sample censored data rank test for acceleration a score test for the null hypothesis of proportional hazards against rank regression alternatives is proposed as a complement to the logrank test for comparing censored survival curves the test statistic has an asymptotic normal distribution that is independent of the logrank distribution under the null hypothesis and its power is good against acceleration alternatives i e with crossing hazards where the logrank test fails monte carlo studies indicate that its small sample properties are comparable to those of the logrank and ranksum procedures

a method for determining groups in multiple survival curves survival analysis includes a wide variety of methods for analyzing time to event data one basic but important goal in survival analysis is the comparison of survival curves between groups several nonparametric methods have been proposed in the literature to test for the equality of survival curves for censored data when the null hypothesis of equality of curves is rejected leading to the clear conclusion that at least one curve is different it can be interesting to ascertain whether curves can be grouped or if all these curves are different from each other a method is proposed that allows determining groups with an automatic selection of their number the validity and behavior of the proposed method was evaluated through simulation studies the applicability of the proposed method is illustrated using real data software in the form of an r package has been developed implementing the proposed method

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

convergence analysis of a quasi continuum approximation for a two dimensional material without defects in many applications materials are modeled by a large number of particles or atoms where any particle can interact with any other the computational cost is very high since the number of atoms is huge recently much attention has been paid to a so called quasi continuum qc method which is a mixed atomistic continuum model the qc method uses an adaptive finite element framework to effectively integrate the majority of the atomistic degrees of freedom in regions where there is no serious defect however numerical analysis of this method is still in its infancy in this paper we will conduct a convergence analysis of the qc method in the case when there is no defect we will also remark on the case when the defect region is small the difference between our analysis and conventional analysis is that our exact atomistic solution is not a solution of a continuous partial differential equation but a discrete lattice scale solution which is not approximately related to any conventional partial differential equation

quantum open closed homotopy algebra and string field theory we reformulate the algebraic structure of zwiebach s quantum open closed string field theory in terms of homotopy algebras we call it the quantum open closed homotopy algebra qocha which is the generalization of the open closed homotopy algebra ocha of kajiura and stasheff the homotopy formulation reveals new insights about deformations of open string field theory by closed string backgrounds in particular deformations by maurer cartan elements of the quantum closed homotopy algebra define consistent quantum open string field theories

repeated significance testing for a general class of statistics used in censored survival analysis abstract the asymptotic joint distribution of a class of sequentially computed statistics used in survival analysis is derived when the individuals under study enter serially and are subject to random loss to follow up these results are used for constructing repeated significance tests over real time

accelerated failure time regression models with a regression model of surviving fraction an application to the analysis of permanent employment in japan abstract accelerated failure time regression models with an additional regression model for the surviving fraction are proposed for the analysis of events that may never occur regardless of censoring for some people in the population risk set the models attempt to estimate simultaneously the effects of covariates on the acceleration deceleration of the timing of a given event and the surviving fraction that is the proportion of the population for which the event never occurs the extended family of the generalized gamma distribution is used for the accelerated failure time regression model the logistic function is used for the regression model of the surviving fraction the models are applied to the data of interfirm job mobility in japan to assess variability in permanent employment among white collar and blue collar employees in firms of different sizes independent from their variability in the timing of interfirm job separations

inference for a family of survival models encompassing the proportional hazards and proportional odds models for survival data regression the cox proportional hazards model is the most popular model but in certain situations the cox model is inappropriate various authors have proposed the proportional odds model as an alternative yang and prentice recently presented a number of easily implemented estimators for the proportional odds model here we show how to extend the methods of yang and prentice to a family of survival models that includes the proportional hazards model and proportional odds model as special cases the model is defined in terms of a box cox transformation of the survival function indexed by a transformation parameter this model has been discussed by other authors and is related to the harrington fleming g family of tests and to frailty models we discuss inference for the case where is known and the case where must be estimated we present a simulation study of a pseudo likelihood estimator and a martingale residual estimator we find that the methods perform reasonably we apply our model to a real data set copyright 2005 john wiley sons ltd

atomic to continuum passage for nanotubes a discrete saint venant principle and error estimates we consider general infinite nanotubes of atoms in mathbb r 3 where each atom interacts with all the others through a two body potential at the equilibrium the positions of the atoms satisfy a euler lagrange equation when there are no exterior forces and for a suitable geometry a particular family of nanotubes is the set of perfect nanotubes at the equilibrium when exterior forces are applied on the nanotube we compare the nanotube to nanotubes of the previous family in part i of the paper this quantitative comparison is formulated in our first main result as a discrete saint venant principle as a corollary we also give a liouville classification result our saint venant principle can be derived for a large class of potentials including the lennard jones potential when the perfect nanotubes at the equilibrium are stable the approach is designed to be applicable to nanotubes that can have general shapes like for instance carbon nanotubes or dna under the oversimplified assumption that all the atoms are identical in part ii of the paper we derive from our saint venant principle a macroscopic mechanical model for general nanotubes we prove that every solution is well approximated by the solution of a continuum model involving stretching and twisting but no bending we establish error estimates between the discrete and the continuous solution more precisely we give two error estimates one at the microscopic level and one at the macroscopic level

supremum versions of the log rank and generalized wilcoxon statistics abstract considerable progress has been made in generalizing to censored data hypothesis tests based on rank statistics the most commonly used generalizations are the log rank test statistic which extends the savage exponential scores statistic cox 1972 mantel 1966 and the generalized wilcoxon statistics gehan 1965 peto and peto 1972 gill 1980 showed that in the two sample problem the asymptotic efficiency properties of the savage and wilcoxon statistics are maintained in censored data by the log rank and peto and peto wilcoxon statistics respectively when censoring is the same in both samples heuristics and simulations have implied that some recently proposed supremum statistics closely related to these two popular linear rank statistics can be used to construct tests that provide good power against a much wider range of nonlocal alternatives see e g fleming and harrington 1981 fleming o brien o fallon and harrington 1980 gill 1980 schumacher 1984 in this article we consider n

supersymmetry and localization we study conditions under which an odd symmetry of the integrand leads to localization of the corresponding integral over a super manifold we also show that in many cases these conditions guarantee exactness of the stationary phase approximation of such integrals

two dimensional topological gravity and equivariant cohomology the analogy between topological string theory and equivariant cohomology for differentiable actions of the circle group on manifolds has been widely remarked on one of our aims in this paper is to make this analogy precise we show that topological string theory is the derived functor of semi relative cohomology just as equivariant cohomology is the derived functor of basic cohomology that homological algebra finds a place in the study of topological string theory should not surprise the reader granted that topological string theory is the conformal field theorist s algebraic topology

controlling alpha in a clinical trial the case for secondary endpoints regardless of whether a statistician believes in letting a data set speak for itself through nominal p values or believes in strict alpha conservation the interpretation of experiments which are negative for the primary endpoint but positive for secondary endpoints is the source of some angst the purpose of this paper is to apply the notion of prospective alpha allocation in clinical trials to this difficult circumstance an argument is presented for differentiating between the alpha for the experiment experimental alpha or e and the alpha for the primary endpoint primary alpha or p and notation is presented which succinctly describes the findings of a clinical trial in terms of its conclusions capping e at 0 10 and p at 0 05 conserves sample size and preserves consistency with the strength of evidence for the primary endpoint of clinical trials in addition a case is presented for the well defined circumstances in which a trial which did not reject the null hypothesis for the primary endpoint but does reject the null hypothesis for at least one of the secondary endpoints may be considered positive in a manner consistent with conservative alpha management

a geometrically regularized gradient damage model with energetic equivalence abstract aiming to bridge the gap between damage and fracture mechanics for modeling localized failure in solids this paper addresses a novel geometrically regularized gradient damage model with energetic equivalence for cracking evolution with the free energy potential defined as usual in terms of the local strain and damage fields the constitutive relations are derived consistently from the standard framework of thermodynamics upon the sharp crack topology geometrically regularized by the damage localization band with a length scale the ensuing energetic equivalence naturally yields the damage evolution law of gradient type and the associated boundary condition of neumann type compared to other gradient damage models no extra assumptions like the nonlocal energy residual and insulation condition are introduced moreover the damage gradient physically accounting for microscopic nonlocal interactions is fully dissipative as expected in line with the unified phase field theory recently proposed by the author wu 2017 during failure processes the material behavior is uniquely characterized by two constitutive functions i e the degradation function defining the free energy potential of the bulk and the geometric function regularizing the sharp crack topology in particular optimal constitutive functions defining an equivalent cohesive zone model of general softening laws are postulated with the involved parameters calibrated from standard material properties the proposed model is numerically implemented into the multi field finite element method and applied to several benchmark tests of concrete under mode i and mixed mode failure it is found that the incorporated length scale can be regarded either a numerical parameter or a material property for the former considered in this work the length scale has negligible if not no effects on the global responses so long as the sharp crack topology and the damage field of high gradients within the localization band are well resolved furthermore the localization bandwidth does not exhibit spurious widening but rather it approaches to a finite value proportional to the length scale comparison between the numerical and experimental results regarding the curve of load versus displacement and crack path confirms validity of the proposed gradient damage model for characterizing localized failure in quasi brittle solids

variational formulation of softening phenomena in fracture mechanics the one dimensional case we show that discrete models of atoms subject to nearest neighbour non linear interactions approximate continua allowing for softening and fracture a detailed study of local minima and stationary points is carried out scale effects are discussed

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

weighted mean survival test statistics a class of distance tests for censored survival data a class of test statistics is introduced which is sensitive against the alternative of stochastic ordering in the two sample censored data problem the test statistics for evaluating a cumulative weighted difference in survival distributions are developed while taking into account the imbalances in base line covariates between two groups this procedure can be used to test the null hypothesis of no treatment effect especially when base line hazards cross and prognostic covariates need to be adjusted the statistics are semiparametric not rank based and can be written as integrated weighted differences in estimated survival functions where these survival estimates are adjusted for covariate imbalances the asymptotic distribution theory of the tests is developed yielding test procedures that are shown to be consistent under a fixed alternative the choice of weight function is discussed and relies on stability and interpretability considerations an example taken from a clinical trial for acquired immune deficiency syndrome is presented

biometrika centenary survival analysis although papers relating to survival analysis have appeared in biometrika since the very first issue the current emphasis on the topic in this journal is fairly new especially as it relates to applications in biostatistics this survey traces the development of survival analysis throughout the twentieth century as reflected in the pages of biometrika focusing primarily on work published since 1980

comparing two samples extensions of the t rank sum and log rank tests abstract i consider the problem of testing that two populations are identical with respect to the distribution of a continuous variable against the alternative that values tend to be larger in one population i observe that the t rank sum and log rank tests are insensitive for a large class of alternatives that may be expected to occur commonly in practice propose a criterion for identifying this problem in a particular data set and propose corresponding extensions of the conventional methods the proposed methods should be useful for both identifying and interpreting group differences

asymptotic behaviour of a pile up of infinite walls of edge dislocations we consider a system of parallel straight edge dislocations and we analyse its asymptotic behaviour in the limit of many dislocations the dislocations are represented by points in a plane and they are arranged in vertical walls each wall is free to move in the horizontal direction the system is described by a discrete energy depending on the one dimensional horizontal positions x i 0 of the n walls the energy contains contributions from repulsive pairwise interactions between all walls a global shear stress forcing the walls to the left and a pinned wall at x 0 that prevents the walls from leaving through the left boundary we study the behaviour of the energy as the number of walls n tends to infinity and characterise this behaviour in terms of convergence there are five different cases depending on the asymptotic behaviour of the single dimensionless parameter n corresponding to beta n ll 1 n 1 n ll beta n ll 1 and beta n gg 1 and the two critical regimes n 1 n and n 1 as a consequence we obtain characterisations of the limiting behaviour of stationary states in each of these five regimes the results shed new light on the open problem of upscaling large numbers of dislocations we show how various existing upscaled models arise as special cases of the theorems of this paper the wide variety of behaviour suggests that upscaled models should incorporate more information than just dislocation densities this additional information is encoded in the limit of the dimensionless parameter n

rank tests for clustered survival data when dependent subunits are randomized in clustered survival data subunits within each cluster share similar characteristics so that observations made from them tend to be positively correlated in clinical trials the correlated subunits from the same cluster are often randomized to different treatment groups in this case the variance formulas of the standard rank tests such as the logrank gehan wilcoxon or prentice wilcoxon proposed for independent samples need to be adjusted for intracluster correlations both within and between treatment groups for testing equality of marginal survival distributions in this paper we derive a general form of simple variance formulas of the rank tests when subunits from the same cluster are randomized into different treatment groups extensive simulation studies are conducted to investigate small sample performance of the variance formulas we compare our non parametric rank tests based on the adjusted variances with one from a shared frailty model which is an optimal semi parametric testing procedure when the intracluster correlations within and between groups are the same

the problem of a covariate time qualitative interaction in a survival study we introduce a test for the equality of two survival distributions against the specific alternative of crossing hazards although this kind of alternative is somewhat rare designing a test specifically aimed at detecting such departures from the null hypothesis in this direction leads to powerful procedures upon which we can call in those few cases where such departures are suspected furthermore the proposed test and an approximate version of the test are seen to suffer only moderate losses in power when compared with their optimal counterparts should the alternative be one of proportional hazards our interest in the problem is motivated by clinical studies on the role of acute graft versus host disease as a risk factor in leukemic children and we discuss the analysis of this study in detail the model we use in this work is a special case of the one introduced by anderson and senthilselvan 1982 applied statistics 31 44 51 we propose overcoming an inferential problem stemming from their model by using the methods of davies 1977 biometrika 64 247 254 1987 biometrika 74 33 43 backed up by resampling techniques we also look at an approach relying directly on resampling techniques the distributional aspects of this approach under the null hypothesis are interesting but practically its behaviour is such that its use cannot be generally recommended outlines of the necessary asymptotic theory are presented and for this we use the tools of martingale theory

extension of adaptive alpha allocation methods for strong control of the family wise error rate with recent advancements in clinical trial design and the availability of rigorous statistical methods that provide strong control of the family wise type i error rate for multiple testing of hypotheses it is now common for sponsors to design clinical trials with prospectively specified multiple testing of hypotheses of both primary and secondary endpoints and with the intent to obtain labeling claims for secondary endpoints one of these recent advancements in multiple testing techniques is the adaptive alpha allocation approach 4a proposed by li and mehrotra statistics in medicine 2008 27 5377 5391 which groups the hypotheses into two families on the basis of perceived trial power and allows the significance level for the second family to be set adaptively on the basis of the largest observed p value in the first family we introduce a class of flexible functions that generalize the 4a procedure and can lead to relatively more powerful test statistics in the case when the test statistics are correlated we introduce well defined functions to calculate the significance level for the second family the numerical computation for our methods is straightforward making application in practice easy copyright 2012 john wiley sons ltd

analysis of three dimensional crack initiation and propagation using the extended finite element method an erratum has been published for this article in international journal for numerical methods in engineering 2005 63 8 1228 we present a new formulation and a numerical procedure for the quasi static analysis of three dimensional crack propagation in brittle and quasi brittle solids the extended finite element method xfem is combined with linear tetrahedral elements a viscosity regularized continuum damage constitutive model is used and coupled with the xfem formulation resulting in a regularized crack band version of xfem the evolving discontinuity surface is discretized through a c0 surface formed by the union of the triangles and quadrilaterals that separate each cracked element in two the element s properties allow a closed form integration and a particularly efficient implementation allowing large scale 3d problems to be studied several examples of crack propagation are shown illustrating the good results that can be achieved copyright 2005 john wiley sons ltd

cauchy born rule and the stability of crystalline solids static problems we study the connection between atomistic and continuum models for the elastic deformation of crystalline solids at zero temperature we prove under certain sharp stability conditions that the correct nonlinear elasticity model is given by the classical cauchy born rule in the sense that elastically deformed states of the atomistic model are closely approximated by solutions of the continuum model with stored energy functionals obtained from the cauchy born rule the analysis is carried out for both simple and complex lattices and for this purpose we develop the necessary tools for performing asymptotic analysis on such lattices our results are sharp and they also suggest criteria for the onset of instabilities of crystalline solids

procedures for comparing samples with multiple endpoints summary five procedures are considered for the comparison of two or more multivariate samples these procedures include a newly proposed nonparametric rank sum test and a generalized least squares test also considered are the following tests ordinary least squares hotelling s p and a bonferroni per experiment error rate approach applications are envisaged in which each variable represents a qualitatively different measure of response to treatment the null hypothesis of no treatment difference is tested with power directed towards alternatives in which at least one treatment is uniformly better than the others in all simulations the nonparametric procedure provided relatively good power and accurate control over the size of the test and is recommended for general use alternatively the generalized least squares procedure may also be useful with normally distributed data in moderate or large samples a convenient expression for this procedure is obtained and its asymptotic relative efficiency with respect to the ordinary least squares test is evaluated clinical trials are often conducted for the purpose of evaluating the relative efficacy of two or more modes of therapy when the therapies are administered to independent groups and efficacy is measured on the basis of a single response variable appropriate parametric and nonparametric one way analysis of variance anova procedures and their properties are well known often however efficacy is measured by more than one variable although univariate methods for assessing each characteristic individually are useful in this setting there is often the additional need for a single overall objective probability statement that addresses the question of whether or not the experimental therapy is efficacious this need is particularly acute when the medical question is controversial and the sample size is small although a large literature exists on the comparison of multivariate samples the procedures tend to be infrequently used in practice as pointed out by meier 1975 p 523 the standard analysis for the comparison of two multivariate samples which is based on hotelling s t2 statistic addresses somewhat the wrong question and consequently has very poor power for the alternatives of primary interest specifically the t2 procedure addresses the question are one or more of the treatments different making no distinction between variables that change favorably and variables that change unfavorably a second approach would be to assign per experiment error rates to each of the univariate tests by using bonferroni s inequality i e by multiplying each univariate p value by the number of variables studied the desired overall probability statement is then given by the minimum of the per experiment univariate p values although this approach may be useful in some settings it may lack power for alternatives in which most or all measures of efficacy are improved this will be of particular concern when the number k of endpoints studied is large relative to sample size in fact statistical significance will not be possible in some instances this problem will be exacerbated when the measures of efficacy are highly

monotone estimating equations for censored data the monotone class rank test based estimating equations for regression models with right censored data is considered we introduce an estimator which is a solution of a monotone estimating equation that is an extension of the gehan test the estimator is easy to derive sqrt n consistent and asymptotically normal under minimal conditions all monotone estimating equations are characterized and a simulation study which shows that our suggested procedure performs well is included

tests for location with k samples and censored data summary tests which are specific for location are developed in the k sample situation with right censored data the tests are based on general estimating functions and do not require full parametric assumptions for large samples but in general they are not based only on ranks one class of tests allows shapes to differ in the k populations and includes as a special case the median test of brookmeyer crowley 1982 if the distributions are assumed to differ at most in location modified tests are suggested in which survival function estimates are obtained by pooling the data from all samples prentice s 1978 median test with minor modifications is included in this class

sample size calculation for the weighted rank statistics with paired survival data this paper introduces a sample size calculation method for the weighted rank test statistics with paired two sample survival data our sample size formula requires specification of joint survival and censoring distributions for modelling the distribution of paired survival variables we may use a paired exponential survival distribution that is specified by the marginal hazard rates and a measure of dependency also in most trials randomizing paired subjects the subjects of each pair are accrued and censored at the same time over an accrual period and an additional follow up period so that the paired subjects have a common censoring time under these practical settings the design parameters include type i and type ii error probabilities marginal hazard rates under the alternative hypothesis correlation coefficient accrual period or accrual rate and follow up period if pilot data are available we may estimate the survival distributions from them but we specify the censoring distribution based on the specified accrual trend and the follow up period planned for the new study through simulations the formula is shown to provide accurate sample sizes under practical settings real studies are taken to demonstrate the proposed method

a two sample test with interval censored data via multiple imputation interval censored data arise naturally in large scale panel studies where subjects can only be followed periodically and the event of interest can only be recorded as having occurred between two examination times in this paper we consider the problem of comparing two interval censored samples we propose to impute exact failure times from interval censored observations to obtain right censored data then apply existing techniques such as harrington and fleming s g rho tests to imputed right censored data to appropriately account for variability a multiple imputation algorithm based on the approximate bayesian bootstrap abb is discussed through simulation studies we find that it performs well the advantage of our proposal is its simplicity to implement and adaptability to incorporate many existing two sample comparison techniques for right censored data the method is illustrated by reanalysing the breast cosmesis study data set

semiclassical approximation in batalin vilkovisky formalism the geometry of supermanifolds provided with aq structure i e with an odd vector fieldq satisfying q q 0 ap structure odd symplectic structure and ans structure volume element or with various combinations of these structures is studied the results are applied to the analysis of the batalin vilkovisky approach to the quantization of gauge theories in particular the semiclassical approximation in this approach is expressed in terms of reidemeister torsion

a comparison of tests of the difference in the proportion of patients who are cured we compared by simulation the likelihood ratio wald and score tests based on a mixture model similar to that proposed by farewell 1982 biometrics 38 1041 1046 and a simple nonparametric test based on the plateau value of the product limit estimate for testing the difference in cured proportions between two groups the parametric tests obtained their asymptotic properties even in small samples provided that one could assume equal failure rates in the two groups otherwise good agreement with predictions required that essentially all potential failures had been observed the comparative properties of the parametric tests depended on whether the population survival functions crossed with the power of the wald test as good as or better than the others in the common situation when the survival functions do not cross however its size was sometimes less than nominal the score test was often not defined and is therefore of limited value the product limit test often performed as well as the parametric tests and despite being biased in some circumstances may be a useful alternative to these especially in small samples when some potential failures have not been observed

survivorship analysis when cure is a possibility a monte carlo study parametric survivorship analyses of clinical trials commonly involves the assumption of a hazard function constant with time when the empirical curve obviously levels off one can modify the hazard function model by use of a gompertz or weibull distribution with hazard decreasing over time some cancer treatments are thought to cure some patients within a short time of initiation then instead of all patients having the same hazard decreasing over time a biologically more appropriate model assumes that an unknown proportion 1 pi have constant high risk whereas the remaining proportion pi have essentially no risk this paper discusses the maximum likelihood estimation of pi and the power curves of the likelihood ratio test monte carlo studies provide results for a variety of simulated trials empirical data illustrate the methods

two sample tests based on cumulative incidence functions from coherent systems summary suppose that n1 and n2 independent copies of a coherent system composed of m components operate in two different environments all copies are monitored until their failure the data consist of the lifetimes of all the components which fail before the system and the time to failure of the system which also is the censoring time for the components not yet failed in this paper we propose a class of tests based on the incidence functions of the component failures obtained from the above data for the equality of the joint distributions of the component lifetimes without assuming either the independence of the components within a system or the knowledge of the structure function of the system the test statistics have asymptotically a chi squared distribution with m degrees of freedom results of some simulation studies exhibit the closeness of the approximation of the null distribution and the power of these tests for certain coherent structures

grassmannian and string theory the infinite dimensional grassmannian manifold contains moduli spaces of riemann surfaces of all genera this well known fact leads to a conjecture that non perturbative string theory can be formulated in terms of the grassmannian we present new facts supporting this hypothesis in particular it is shown that grassmannians can be considered as generalized moduli spaces this statement permits us to define corresponding string amplitudes at least formally one can conjecture that it is possible to explain the relation between non perturbative and perturbative string theory by means of localization theorems for equivariant cohomology this conjecture is based on the characterization of moduli spaces relevant to string theory as sets consisting of points with large stabilizers in certain groups acting on the grassmannian we describe an involution on the grassmannian that could be related to s duality in string theory