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

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

stability and bifurcation for a delayed predator prey model and the effect of diffusion abstract we consider a predator prey system with one or two delays and a unique positive equilibrium e its dynamics are studied in terms of the local stability of e and of the description of the hopf bifurcation that is proven to exist as one of the delays taken as a parameter crosses some critical values we also consider a reaction diffusion system with neumann conditions resulting from adding one spatial variable and diffusion terms in the previous model the spectral and bifurcation analysis in the neighborhood of e now as a stationary point of this latter system is addressed and the results obtained for the case without diffusion are applied

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

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

spatiotemporal dynamics and spatial pattern in a diffusive intraguild predation model with delay effect abstract based on biological meaning a kind of diffusive intraguild predation igp resource ig prey and ig predator model with delay effect is investigated in this paper the model has holling type i functional response between resource ig prey and resource ig predator holling type ii functional response between ig prey and ig predator we first give sufficient conditions on the stability of possible nonnegative constant steady state solutions for the proposed model which give us a complete picture of the global dynamics then we investigate hopf bifurcation near the unique positive constant steady state solution by taking delay as bifurcation parameter and derive the hopf bifurcation threshold it is shown that the delay can induce three types of bistability node node bistability node cycle bistability and cycle cycle bistability periodic oscillations and irregular oscillations triggering spatiotemporal chaos in the diffusive igp model numerical simulations are performed to illustrate our theoretical results and suggest that delay can even trigger the emergence of self organised spatiotemporal patterns which evolve from spiral patterns to irregular spatial patterns via spatiotemporal hopf bifurcation in addition the impact of diffusion on the model s dynamics under certain time delay are also explored

global stability and hopf bifurcations of a beddington deangelis type predator prey system with diffusion and delays the dynamics of a diffusive predator prey system with the beddington deangelis functional response and two delays are considered by choosing the sum of two delays as a bifurcation parameter the stability of the constant equilibria and the existence of hopf bifurcations are investigated by analyzing the characteristic equations and the formulas determining the direction and the stability of the bifurcating periodic solutions are derived by using the center manifold and the normal form theory of partial functional differential equations particularly the sufficient conditions of the global stability of the positive equilibrium are given by the upper lower solutions method

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

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

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

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

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

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

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

global analysis of the predator prey system with beddington deangelis functional response abstract in this paper predator prey systems with beddington deangelis functional response are considered by using divergency criterion global stability is established provided the system possesses a positive locally asymptotically stable equilibrium

on the dynamics of predator prey models with the beddington deangelis functional response abstract the dynamics of predator prey models with the beddington deangelis functional response are analyzed primarily from the viewpoint of permanence uniform persistence the beddington deangelis functional response is similar to the holling type 2 functional response but contains an extra term describing mutual interference by predators both spatially homogeneous models based on ordinary differential equations and reaction diffusion models are considered criteria for permanence and for predator extinction are derived for systems without diffusion or with no flux boundary conditions criteria are derived for the existence of a globally stable coexistence equilibrium or alternatively for the existence of periodic orbits

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

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

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

dynamics of a diffusion reaction prey predator model with delay in prey effects of delay and spatial components abstract we study the complex dynamics of a monod haldane type predator prey interaction model that incorporates 1 a constant time delay in the prey growth and 2 diffusion in both prey and predator we provide the rigorous results of our system including the asymptotic stability of a positive equilibrium hopf bifurcation and the direction of hopf bifurcation and the stability of bifurcated periodic solutions we also perform numerical simulations on the effects of diffusion or and delay when the corresponding ode model has either a unique interior equilibrium with two interior attractors or two interior equilibria our theoretical and numerical results show that diffusion can either stabilize or destabilize the system large delay could destabilize the system and the combination of diffusion and delay could intensify the instability of the system moreover when the corresponding ode system has two interior equilibria diffusion or time delay in prey or both could lead to the extinction of predator our results may provide us useful biological insights on population managements for prey predator interaction systems

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

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

stability and hopf bifurcation for a delayed prey predator system with diffusion effects abstract this paper is concerned with a delayed lotka volterra prey predator system with diffusion effects and neumann boundary conditions the main purpose is to investigate the stability of spatially homogeneous positive equilibrium and give the explicit formulae determining the direction and stability of hopf bifurcation by linearizing the system at positive equilibrium and analyzing the associated characteristic equation the stability of positive equilibrium and the existence of hopf bifurcation are demonstrated by means of the normal form theory and the center manifold reduction for partial functional differential equations pfdes the direction and stability of periodic solutions occurring through hopf bifurcation are determined finally in order to verify our theoretical results some numerical simulations are also included

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

a 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

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

dynamics of nonlinear parabolic systems with time delays abstract the dynamics of a coupled system of semilinear parabolic equations with discrete time delays is investigated using the method of upper and lower solutions it is shown that if the reaction function in the system possesses a mixed quasimonotone property and the corresponding elliptic system has a pair of coupled upper and lower solutions then there is a monotone iteration process which yields a pair of quasisolutions of the elliptic system and the sector between the quasisolutions is an attractor of the delayed parabolic system under some additional conditions this sector is a global attractor and the solution of the parabolic system converges to a true solution of the elliptic system the same conclusions are obtained for a coupled system of parabolic ordinary equations with time delays applications are given to three model problems arising from ecology and nuclear engineering these model problems possess multiple steady state solutions and sufficient conditions are given to ensure the stability and instability of these solutions

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

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

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

implicit explicit time discretization coupled with finite element methods for delayed predator prey competition reaction diffusion system the main purpose of this paper is to develop the two step implicit explicit imex time discretization coupled with finite element methods for solving delayed predator prey competition reaction diffusion system finite element methods are used to discretize the space variables both imex two step one leg methods and imex linear two step methods are considered in time discretization where the nonlinear reaction part is discretized explicitly and the diffusion part is discretized implicitly the l 2 norm error estimates with handling the breaking points are derived these methods only require solving two independent linear systems with the same coefficient matrix at different time and avoid solving large scale systems of nonlinear algebraic equations thus the resulting schemes are efficient some numerical experiments are presented to confirm the theoretical results

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

stability and bifurcation in a delayed predator prey system with beddington deangelis functional response we consider a delayed predator prey system with beddington deangelis functional response the stability of the interior equilibrium will be studied by analyzing the associated characteristic transcendental equation by choosing the delay as a bifurcation parameter we show that hopf bifurcation can occur as the delay crosses some critical values the direction and stability of the hopf bifurcation are investigated by following the procedure of deriving normal form given by faria and magalhaes an example is given and numerical simulations are performed to illustrate the obtained results

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

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

observations sur le memoire precedent as mentioned in footnote 2 in the previous paper in private correspondence elie cartan made certain observations on the manuscript that ddk had sent him there seems to have been a lively exchange of letters and ideas between kosambi and cartan as the next paper also testifies the previous paper this note and a later paper by s s chern in the bulletin des sciences mathematiques 63 206 1939 form the basis of the kosambi cartan chern or kcc theory kosambi s contribution here is the short explanatory paragraph in english at the end although the paper is in french it seems more appropriate to include it here given the close relationship it bears to the preceding paper rather than in sect iii

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

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

normal forms and hopf bifurcation for partial differential equations with delays the paper addresses the computation of normal forms for some partial functional differential equations pfdes near equilibria the analysis is based on the theory previously developed for autonomous retarded functional differential equations and on the existence of center or other invariant manifolds as an illustration of this procedure two examples of pfdes where a hopf singularity occurs on the center manifold are considered

the effect of mutual interference between predators on a predator prey model with diffusion abstract we consider a diffusive predator prey model with beddington deangelis functional response under homogeneous dirichlet boundary conditions the effect of large k which represents the extent of mutual interference between predators is extensively studied by making use of the fixed point index theory we obtain a complete understanding of the existence uniqueness and stability of positive steady states when k is sufficiently large moreover we present some numerical simulations that supplement the analytic results in one dimension

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

systems of parabolic equations with continuous and discrete delays abstract in this paper we investigate the global existence and the dynamics of a coupled system of nonlinear parabolic equations where the nonlinear reaction function may depend on both continuous infinite or finite and discrete delays it is shown that if the reaction function is locally lipschitz continuous and the system possesses a pair of coupled upper and lower solutions then there exists a unique global solution to the system without any quasimonotone condition on the reaction function for systems with mixed quasimonotone reaction functions we use the monotone method to establish more dynamic property of the parabolic system in terms of the quasisolutions of the corresponding elliptic system this approach yields a global attractor of the parabolic system and under some additional conditions this attractor leads to the existence and asymptotic stability of a solution of the elliptic system application to three model problems in population dynamics and chemical reactions is given

a complete analysis of the global dynamics of a diffusive predator and toxic prey model considering many species can release toxic substances to protect themselves against predators a diffusive predator and toxic prey system with spatial heterogeneity in predator and prey populations has been investigated for this system we give a complete and rigorous analysis of the global dynamics with the boundedness globally asymptotical stability transcritical bifurcation hopf bifurcation and its direction and the stability of the bifurcating periodic solutions meanwhile we consider the effects of toxins produced by the prey on the dynamic behavior the consequence of the global stability of the coexistence equilibrium is that the toxin s intrinsic characteristic will not change the stability of the system irreversibly our results show that the toxin produced by the prey phytoplankton may be used as a bio control agent for the harmful algal bloom problems

kcc theory and geometry of the rikitake system the earth s magnetic field undergoes aperiodical reversals these can be explained by a simple two disc dynamo system rikitake system in this paper the rikitake system is studied based on a differential geometry theory of kosambi cartan chern the electrical and mechanical equations of motion are derived from faraday s law as well as from magnetohydrodynamic equations from the geometric theory the solution of the rikitake system can be regarded as a trajectory on the tangent bundle accordingly there exist five geometrical invariants in the rikitake system the third invariant as a torsion tensor can be expressed by mutual inductances as a result of electrical and mechanical interactions which cause the aperiodic magnetic reversal this aperiodic behaviour corresponds to a magnetohydrodynamic turbulent motion by a topological invariant such as chern simons number which expresses the interaction between the toroidal and poloidal currents this rikitake system is equivalent to other nonlinear dynamical systems thus chaotic behaviours of various nonlinear dynamical systems can be uniformly investigated by the five geometrical invariants and the topological invariant the chern simons number

geometrical unified theory of rikitake system and kcc theory abstract the rikitake system as nonlinear dynamical systems in geomagnetism can be studied based on the kcc theory and the unified field theory especially the behavior of the magnetic field of the rikitake system is represented in the electrical system projected from the electro mechanical unified system then the kcc invariants for the electrical and mechanical systems can be obtained the third invariant as the torsion tensor expresses the aperiodic behavior of the magnetic field moreover as a result of the projection a protrusion between the mechanical and electrical systems is represented by the euler schouten tensor this euler schouten tensor and the third invariant consist of the same mutual inductance therefore the aperiodic behavior of the magnetic field can be characterized by the protrusion between the electrical and mechanical systems