on the existence of weak solutions of perturbated systems with critical growth sur un domaine borne de r n on considere le probleme de dirichlet pour le systeme elliptique a u g u f sur et u 0 ou a u est un operateur quasi lineaire et la perturbation g u depend de u et de d u on etudie des conditions suffisantes sur a u et sur g u pour l existence de solutions faibles

statistical inference with data dependent treatment allocation rules abstract in comparing two treatments with dichotomous responses the randomized play the winner rule wei and durham 1978 tends to assign more study subjects to the better treatment for ethical reasons this property is desirable for studies on human subjects the randomized play the winner rule which is a modification of zelen s play the winner rule zelen 1969 is not deterministic and is less vulnerable to experimental bias than other adaptive designs recently this design has been used in a trial to evaluate extracorporeal membrane oxygenation ecmo for treating newborns with respiratory failures at the university of michigan in this article exact conditional exact unconditional and approximate confidence intervals for the treatment difference are studied from a frequentist point of view with the randomized play the winner rule for small and moderate sized trials the exact unconditional procedures perform much better than the conditional ones because of the adaptive nature of the designs

bayesian random effects meta analysis of trials with binary outcomes methods for the absolute risk difference and relative risk scales when conducting a meta analysis of clinical trials with binary outcomes a normal approximation for the summary treatment effect measure in each trial is inappropriate in the common situation where some of the trials in the meta analysis are small or the observed risks are close to 0 or 1 this problem can be avoided by making direct use of the binomial distribution within trials a fully bayesian method has already been developed for random effects meta analysis on the log odds scale using the bugs implementation of gibbs sampling in this paper we demonstrate how this method can be extended to perform analyses on both the absolute and relative risk scales within each approach we exemplify how trial level covariates including underlying risk can be considered data from 46 trials of the effect of single dose ibuprofen on post operative pain are analysed and the results contrasted with those derived from classical and bayesian summary statistic methods the clinical interpretation of the odds ratio scale is not straightforward the advantages and flexibility of a fully bayesian approach to meta analysis of binary outcome data considered on an absolute risk or relative risk scale are now available

simultaneous confidence intervals for comparing binomial parameters summary to compare proportions with several independent binomial samples we recommend a method of constructing simultaneous confidence intervals that uses the studentized range distribution with a score statistic it applies to a variety of measures including the difference of proportions odds ratio and relative risk for the odds ratio a simulation study suggests that the method has coverage probability closer to the nominal value than ad hoc approaches such as the bonferroni implementation of wald or exact small sample pairwise intervals it performs well even for the problematic but practically common case in which the binomial parameters are relatively small for the difference of proportions the proposed method has performance comparable to a method proposed by piegorsch 1991 biometrics 47 45 52

frequentist performance of bayesian confidence intervals for comparing proportions in 2 2 contingency tables this article investigates the performance in a frequentist sense of bayesian confidence intervals cis for the difference of proportions relative risk and odds ratio in 2 x 2 contingency tables we consider beta priors logit normal priors and related correlated priors for the two binomial parameters the goal was to analyze whether certain settings for prior parameters tend to provide good coverage performance regardless of the true association parameter values for the relative risk and odds ratio we recommend tail intervals over highest posterior density hpd intervals for invariance reasons to protect against potentially very poor coverage probabilities when the effect is large it is best to use a diffuse prior and we recommend the jeffreys prior otherwise with relatively small samples bayesian cis using more informative even uniform priors tend to have poorer performance than the frequentist cis based on inverting score tests which perform uniformly quite well for these parameters

a note on design when response has an exponential family distribution summary some simple design problems are considered when responses have an exponential family distribution with the difference between treatment groups in the canonical parameter being the objective of study it is shown that normal theory conclusions apply to a possibly surprising extent the loss from randomizing followed by subsequent stratification is the equivalent of one observation per stratum for binary data heterogeneity has to be quite large before failure to stratify induces serious loss whereas unnecessary use of a matched pair design is fully efficient asymptotically

non linear elliptic and parabolic equations involving measure data in this paper we prove the existence of solutions for equations of the type div a du f in a bounded open set u 0 on where a is a possibly non linear function satisfying some coerciveness and monotonicity assumptions and f is a bounded measure we also consider the equation div a du g u f in u 0 on with f l1 or f m u u 0 and the parabolic equivalent of the first elliptic equation

asymptotics in response adaptive designs generated by a two color randomly reinforced urn this paper illustrates asymptotic properties for a response adaptive design generated by a two color randomly reinforced urn model the design considered is optimal in the sense that it assigns patients to the best treatment with probability converging to one an approach to show the joint asymptotic normality of the estimators of the mean responses to the treatments is provided in spite of the fact that allocation proportions converge to zero and one results on the rate of convergence of the number of patients assigned to each treatment are also obtained finally we study the asymptotic behavior of a suitable test statistic

solvability of perturbed elliptic equations with critical growth exponent for the gradient sur un domaine borne cr n on considere le probleme de dirichlet a u g u f u 0 ou a u t 1 n 1 d i a i x u d u definit un operateur pseudomonotone d un espace de sobolev h 0 1 p dans son espace dual et la perturbation g u g x u d u satisfait une condition de croissance

bayesian analysis for a single 2 x 2 table the simple comparison of two binomial populations is frequently of interest in epidemiology when the domains are large for small domains however there are no exact methods except fisher s exact test a basic problem therefore is to compare two populations by assessing the difference between the proportions of individuals who possess a characteristic in the first and second populations when there is prior information we take the proportions to have independent conjugate beta distributions with known parameters thereby facilitating a bayesian analysis we consider bayesian inference on functions of the proportions and the three most common scalar measures used in epidemiology and health services research namely relative risk odds ratio and attributable risk we develop the highest density regions both exact and approximate for relative risk odds ratio and attributable risk in addition we consider the bayes factor for testing whether the model with a common proportion holds rather than one with distinct proportions using data from the population based worcester heart attack study we apply our methodology to study gender differences in the therapeutic management of patients with acute myocardial infarction ami by selected demographic and clinical characteristics the bayes factor the approximate and exact intervals generally suggest that there are no substantial differences in the pharmacologic management of males and females hospitalized with ami

adaptive biased coin designs for skewing the allocation proportion in clinical trials with normal responses response adaptive designs are used in phase iii clinical trial for skewing the allocation pattern towards the better treatments we use optimum design theory to derive adaptive designs when the responses are normally distributed the performance of the designs is studied with respect to the loss and the proportion of allocation to different treatments the adaptive design does not affect inference

existence results for some quasilinear parabolic equations on considere le probleme de cauchy pour une equation dont la partie principale est un operateur parabolique quasilineaire le terme non lineaire additionnel a au plus une croissance quadratique par rapport au gradient de la solution on demontre l existence d une solution bornee faible sous des hypotheses de regularite minimales en supposant l existence d une sous solution et d une supersolution pour le probleme

shift invariant target in allocation problems we provide a template for finding target allocation proportions in optimal allocation designs where the target will be invariant for both shifts in location and scale of the response distributions one possible application of such target allocation proportions is to carry out a response adaptive allocation while most of the existing designs are invariant for any change in scale of the underlying distributions they are not location invariant in most of the cases first we indicate this serious flaw in the existing literature and illustrate how this lack of location invariance makes the performance of the designs very poor in terms of allocation for any drastic change in location such as the changes from degrees centigrade to degrees fahrenheit we illustrate that unless a target allocation is location invariant it might lead to a completely irrelevant and useless target for allocation then we discuss how such location invariance can be achieved for general continuous responses we illustrate the proposed method using some real clinical trial data we also indicate the possible extension of the procedure for more than two treatments at hand and in the presence of covariates

holder continuity of the inverse ofp laplacian abstract in this note we study the inverse operator p 1ofp lapalcian on a bounded domain rn we show that p 1 w 1 p w1 p0 is holder continuous and is a compact operator fromv q s tow1 p0 s 0 p q p the conjugate of critical sobolev exponent as an application we study existence of positive solutions of two nonlinear elliptic equations

lower semicontinuity of functionals via the concentration compactness principle in this paper we show the weak lower semicontinuity of some classes of functionals using the concentration compactness principle of p l lions these functionals involve an integral term and we do not know whether it can be handled by the de giorgi theorem the semicontinuity result allows us to prove several existence results for quasilinear elliptic equations

legendrian fronts for affine varieties in this article we study weinstein structures endowed with a lefschetz fibration in terms of the legendrian front projection first we provide a systematic recipe for translating from a weinstein lefschetz bifibration to a legendrian handlebody then we present several new applications of this technique to symplectic topology this includes the detection of flexibility and rigidity for several families of weinstein manifolds and the existence of closed exact lagrangian submanifolds in particular we prove that the koras russell cubic is stein deformation equivalent to c3 and we verify the affine parts of the algebraic mirrors of two weinstein 4 folds

confidence intervals for an effect size measure based on the mann whitney statistic part 2 asymptotic methods and evaluation several asymptotic confidence interval methods for u mn the mann whitney u statistic divided by the product of the two sample sizes are developed and evaluated alongside published methods novel methods derived from gaussian and beta models perform well though overall a modification of the hanley mcneil approach method 5 in this evaluation performed better and is recommended for calculating confidence intervals for u mn for continuously distributed data

the hierarchical logistic regression model for multilevel analysis abstract a hierarchical logistic regression model is proposed for studying data with group structure and a binary response variable the group structure is defined by the presence of micro observations embedded within contexts macro observations and the specification is at both of these levels at the first micro level the usual logistic regression model is defined for each context the same regressors are used in each context but the micro regression coefficients are free to vary over contexts at the second level the micro coefficients are treated as functions of macro regressors an empirical bayes estimation procedure is proposed for estimating the micro and macro coefficients explicit formulas are provided that are computationally feasible for large scale data analyses these include an algorithm for finding the maximum likelihood estimates of the covariance components representing within and between macro equation error variability the methodology is applied to world fertility survey data

optimum biased coin designs for sequential clinical trials with prognostic factors patients in a clinical trial arrive sequentially and are assigned to one of t treatments this assignment should maintain a balance between the numbers receiving each treatment yet should be sufficiently random to avoid any suspicion of conscious or unconscious cheating to balance these requirements efron 1971 introduced biased coin designs for the comparison of two treatments in which allocation of the treatment is determined probabilistically but with a bias towards the underrepresented treatment one disadvantage of efron s scheme is that it does not include balance over covariates or prognostic factors which may affect the response of the patient to the treatment biased coin schemes which do force balance over both treatments and prognostic factors are given by pocock simon 1975 and efron 1980 the properties of the designs have been elucidated by numerical studies and they are now being increasingly used in clinical trials reviews of the literature and discussions of the practical implications of the designs are given by pocock 1979 and simon 1979 however the designs suffer from the disadvantage that they rely on arbitrary functions to achieve the desired balance the procedures thus lack a firm theoretical framework an alternative approach in the presence of prognostic factors begg iglewicz 1980 uses optimum design theory to suggest a deterministic design criterion which is then modified for computational convenience in this paper i use optimum design theory to provide a procedure of the biased coin type for an arbitrary number of treatments in the presence or absence of prognostic factors this has the theoretical advantage of obviating dependence on a series of arbitrary functions the necessary optimum design theory is presented in 2 and in 3 applied to biased coin experiments the simplest case that of two treatments in the absence of prognostic factors is studied in 4 the extension to three or more treatments is in 5 followed in 6 by the allowance for prognostic factors although in the biased coin designs allocation of treatments is made probabilistically the results of the paper can be used for the sequential construction of da optimum designs in which randomization is not introduced by the experimenter all the designs mentioned so far are sequential but not adaptive in the useful distinction made by pericchi 1981 they are data dependent but not outcomedependent each allocation depends on the previous allocations and prognostic factors

regularizing effect for some p laplacian systems abstract we study existence and regularity of weak solutions for the following p laplacian system p u a 1 u r 2 u f u w 0 1 p p u r w 0 1 p where is an open bounded subset of r n n 2 p v div v p 2 v is the p laplacian operator for 1 p n a 0 r 1 0 p 1 and f belongs to a suitable lebesgue space in particular we show how the coupling between the equations in the system gives rise to a regularizing effect producing the existence of finite energy solutions

inference for proportions in a 2 x 2 contingency table hpd or not hpd highest posterior density intervals are common in bayesian inference but as noted by agresti and min 2005 biometrics 61 515 523 they are not invariant under transformations agresti and min suggested central or tail intervals as preferable in the context of the relative risk and odds ratio a modification to this is proposed for extreme outcomes as invariance is maintained when replacing central intervals by one sided intervals bayes laplace priors for the binomial parameters appear preferable here compared to jeffreys priors contrary to agresti and min s suggestion based on frequentist coverage

bias and loss the two sides of a biased coin the paper assesses biased coin designs for sequential treatment allocation in clinical trials comparisons emphasise the importance of considering randomness as well as treatment balance which are calculated as bias and loss in the numerical examples the responses are assumed normally distributed perhaps after transformation and balance is required over a set of covariates the effect of covariate distribution on the properties of five allocation rules is investigated with an emphasis on methods of comparison which also apply to other forms of response the concept of admissibility shows that the widely used minimisation rule is outperformed by atkinson s rule derived from the theory of optimum experimental design we present a simplified form of this rule for this rule the ability to guess the next treatment allocation decreases with study size for the other rules it is constant

local lipschitz continuity of the inverse of the fractional p laplacian holder type continuity and continuous dependence of solutions to associated parabolic equations on bounded domains let p 1 s 0 1 and rn an arbitrary bounded open set in the first part we consider the inverse s p p s 1 of the fractional p laplace operator p s with the dirichlet boundary condition we show that in the singular case p 1 2 the operator s p is locally lipschitz continuous on l and that global lipschitz continuity cannot be achieved we use this result to show that in the case n sp if 2nn 2s p 2 0 q npn sp 2 and are small constants then the nonlinear problem psu u qu u npn sp 2u hin u 0 on rn has at least one weak solution in the second part of the paper we prove that the operator p s generates a nonlinear submarkovian semigroup ss p t t 0 on l2 if p 2 and sp 0 such that for every t 0 and u v lq q 2 we have ss p t u ss p t v l c s t s u v lq s where s s and s are explicit constants depending only on n s p q

frequentist performance of bayesian inference with response adaptive designs in controlled clinical trials where minimizing treatment failures is crucial response adaptive designs are attractive competitors to 1 1 randomized designs for comparing the success rates 1 and 2 of two treatments in these designs each new treatment assignment depends on previous outcomes through some predefined rule here play the winner pw randomized play the winner rpw drop the loser generalized drop the loser and doubly adaptive biased coin designs are considered for new treatment assignments as frequentist inference relies on complex sampling distributions in those designs we investigate how bayesian inference based on two independent beta prior distributions performs from a frequentist point of view performance is assessed through coverage probabilities of interval estimation procedures power and minimization of failure count it is shown that bayesian inference can be favorably compared to frequentist procedures where the latter are available the power of response adaptive designs is generally very close to the power of 1 1 randomized design however failure count savings are generally small except for the pw and doubly adaptive biased coin designs in particular ranges of the true success rates the rpw assignment rule has the worst performance while pw generalized drop the loser or doubly adaptive biased coin designs may outperform other designs depending on different particular ranges of the true success rates copyright 2010 john wiley sons ltd

asymptotic properties of covariate adjusted response adaptive designs response adaptive designs have been extensively studied and used in clinical trials however there is a lack of a comprehensive study of response adaptive designs that include covariates despite their importance in clinical trials because the allocation scheme and the estimation of parameters are affected by both the responses and the covariates covariate adjusted response adaptive cara designs are very complex to formulate in this paper we overcome the technical hurdles and lay out a framework for general cara designs for the allocation of subjects to k 2 treatments the asymptotic properties are studied under certain widely satisfied conditions the proposed cara designs can be applied to generalized linear models two important special cases the linear model and the logistic regression model are considered in detail

invariants of contact structures from open books in this note we define three invariants of contact structures in terms of open books supporting the contact structures these invariants are the support genus which is the minimal genus of a page of a supporting open book for the contact structure the binding number which is the minimal number of binding components of a supporting open book for the contact structure with minimal genus pages and the norm which is minus the maximal euler characteristic of a page of a supporting open book

comparative analysis of two rates in this paper we examine comparative analysis of rates with a view to each of the usual comparative parameters rate difference rd rate ratio rr and odds ratio or and with particular reference to first principles for rd and rr we show the prevailing statistical practices to be rather poor we stress the need for restricted estimation of variance in the chi square function underlying interval estimation and also point estimation and hypothesis testing for rr analysis we propose a chi square formulation analogous to that for rd and thus one which obviates the present practice of log transformation and its associated use of taylor series approximation of the variance as for or analysis we emphasize that the chi square function introduced by cornfield for unstratified data and extended by gart to the case of stratified analysis is based on the efficient score and thus embodies its optimality properties we provide simulation results to evince the better performance of the proposed parameter constrained procedures over the traditional ones

non autonomous perturbations for a class of quasilinear elliptic equations on r abstract this paper is concerned with the existence of two positive solutions for a class of quasilinear elliptic equations on r involving the p laplacian with a non autonomous perturbation the first solution is obtained as a local minimum in a neighborhood of 0 and the second one by a mountain pass argument the special features of the problem here is the complex structure of the linear part which in particular oblige to work into the space w 1 p r then one faces problems in the convergence of the sequences of derivatives u n u

bayesian adaptive biased coin designs for clinical trials with normal responses des schemas adaptatifs sont utilises dans des essais cliniques de phase iii pour biaiser l attribution des traitements en faveur des meilleurs nous utilisons la theorie des schemas optimaux pour etablir une procedure bayesienne de tirage au sort biaise pour des schemas sequentiels avec reponses continues la performance de ces schemas adaptatifs est etudiee a la fois numeriquement et theoriquement des proprietes importantes sont la perte et la proportion de sujets alloues au meilleur traitement

multi objective optimal designs in comparative clinical trials with covariates the reinforced doubly adaptive biased coin design the present paper deals with the problem of allocating patients to two competing treatments in the presence of covariates or prognostic factors in order to achieve a good trade off among ethical concerns inferential precision and randomness in the treatment allocations in particular we suggest a multipurpose design methodology that combines efficiency and ethical gain when the linear homoscedastic model with both treatment covariate interactions and interactions among covariates is adopted the ensuing compound optimal allocations of the treatments depend on the covariates and their distribution on the population of interest as well as on the unknown parameters of the model therefore we introduce the reinforced doubly adaptive biased coin design namely a general class of covariate adjusted response adaptive procedures that includes both continuous and discontinuous randomization functions aimed to target any desired allocation proportion the properties of this proposal are described both theoretically and through simulations

properties of biased coin designs in sequential clinical trials martingale methods and the martingale invariance principle are used to derive central limit theorems and related results for biased coin designs of the kind previously studied by efron wei and many others the results are applied to the study of selection bias the method is developed for the simplest two treatment case and then extended first to the case of several treatments and secondly to the case of two treatments with prognostic factors

asymptotic properties of adaptive designs for clinical trials with delayed response for adaptive clinical trials using a generalized friedman s urn design we derive the limiting distribution of the urn composition under staggered entry and delayed response the stochastic delay mechanism is assumed to depend on both the treatment assigned and the patient s response a very general setup is employed with k treatments and l responses when l k 2 one example of a generalized friedman s urn design is the randomized playthe winner rule an application of this rule occurred in a clinical trial of depression which had staggered entry and delayed response we show that maximum likelihood estimators from such a trial have the usual asymptotic properties

bayesianly justifiable and relevant frequency calculations for the applied statistician a common reaction among applied statisticians is that the bayesian statistician s energies in an applied problem must be directed at the a priori elicitation of one model specification from which an optimal design and all inferences follow automatically by applying bayes s theorem to calculate conditional distributions of unknowns given knowns i feel however that the applied bayesian statistician s tool kit should be more extensive and include tools that may be usefully labeled frequency calculations three types of bayesianly justifiable and relevant frequency calculations are presented using examples to convey their use for the applied statistician

a new exact and more powerful unconditional test of no treatment effect from binary matched pairs we consider the problem of testing for a difference in the probability of success from matched binary pairs starting with three standard inexact tests the nuisance parameter is first estimated and then the residual dependence is eliminated by maximization producing what i call an e m p value the e m p value based on mcnemar s statistic is shown numerically to dominate previous suggestions including partially maximized p values as described in berger and sidik 2003 statistical methods in medical research 12 91 108 the latter method however may have computational advantages for large samples

optimal results for parabolic problems arising in some physical models with critical growth in the gradient respect to a hardy potential abstract we deal with the following parabolic problem u t u u p u x 2 f u 0 in 0 t u x t 0 on 0 t u x 0 u 0 x x where r n n 3 is a bounded regular domain such that 0 or r n p 1 0 and f 0 u 0 0 are in a suitable class of functions there are deep differences with respect to the heat equation 0 the main features in the paper are the following if 0 there exists a critical exponent p such that for p p there is no nontrivial local solution p is optimal in the sense that if p p there exists solution for suitable data if we consider the cauchy problem i e r n we find the same phenomenon about the critical power p as above moreover there exists a fujita type exponent f p in the sense that independently of the initial datum for 1 p f any solution blows up in a finite time respect to an integral norm this is a major difference with respect to the heat equation 0

confidence intervals for the ratio of two binomial proportions sometimes the ratio of two binomial proportions is the parameter of major interest for instance as the risk ratio in a two group cohort study fleiss 1973 or as the likelihood ratio for a diagnostic test procedure mcneill keeler and adelstein 1975 let x and y be independent binomial variates based on sample sizes m and n and parameters p and p2 respectively let 0 pm p2 we consider the construction of confidence intervals for 0 santner and snell 1980 have proposed a nonanalytical procedure which guarantees a lower bound on the confidence coefficient of the 1 a interval for 0 their algorithm is usable for small m and n but may produce conservative intervals in 2 an analytical method for obtaining approximate confidence intervals for 0 is proposed and compared to the one recommended by katz et al 1978

confidence intervals for a ratio of two independent binomial proportions several large sample confidence intervals for the ratio of independent binomial proportions are compared in terms of exact coverage probability and width a non iterative approximate bayesian interval is derived and its frequency properties are superior to all of the non iterative confidence intervals considered the approximate bayesian interval which is very easy to compute has performance characteristics that are very similar to the computationally intensive score method two sample size determination formulas are presented one for desired absolute precision and the other for desired relative precision

on inferences from wei s biased coin design for clinical trials wei 1988 analyzed data from a clinical trial in which an urn sampling model was used to allocate patients to treatments the trial resulted in 11 patients being allocated to the experimental treatment all successes and with one patient allocated to the control treatment a failure wei analyzed these data using a randomization algorithm and concluded that the results were almost significant at p 0 051 he asserted that an analysis which ignored the design and presumed complete randomization leads to a p value of 0 001 in fact if a more conventional analysis is used in which both margins are fixed then this leads to p 0 083 fisher s exact test if complete randomization is assumed if the urn sampling allocation is taken into account much more conservative inferences are obtained an analysis which conditions on both margins leads to p 028 while one which conditions on the observed sequence of responses and the observed treatment totals leads to p 0 62 these serious discrepancies are discussed in addition to the inappropriateness of biased coin design and small sample sizes in important medical trials

the p dirichlet to neumann operator with applications to elliptic and parabolic problems abstract in this paper we investigate the dirichlet to neumann operator associated with second order quasi linear operators of p laplace type for 1 p which acts on the boundary of a bounded lipschitz domain in r d for d 2 we establish well posedness and holder continuity with uniform estimates of weak solutions of some elliptic boundary value problems involving the dirichlet to neumann operator by employing these regularity results of weak solutions of elliptic problems we show that the semigroup generated by the negative dirichlet to neumann operator on l q enjoys an l q c 0 smoothing effect and the negative dirichlet to neumann operator on the set of continuous functions on the boundary of the domain generates a strongly continuous and order preserving semigroup moreover we establish convergence in large time with decay rates of all trajectories of the semigroup and in the singular case 1 e 2 d d 2 p 2 for some e 0 we give upper estimates of the finite time of extinction

pseudo score confidence intervals for parameters in discrete statistical models we propose pseudo score confidence intervals for parameters in models for discrete data the confidence interval is obtained by inverting a test that uses a pearson chi squared statistic to compare fitted values for the working model with fitted values of the model when a parameter of interest takes various fixed values for multinomial models the pseudo score method simplifies to the score method when the model is saturated and otherwise it is asymptotically equivalent to score and likelihood ratio test based inferences for cases in which ordinary score methods are impractical such as when the likelihood function is not an explicit function of model parameters the pseudo score method is feasible we illustrate the method for four such examples generalizations of the method are also presented for future research including inference for complex sampling designs using a quasilikelihood pearson statistic that compares fitted values for two models relative to the variance of the observations under the simpler model

optimality variability power we provide a theoretical template for the comparison of response adaptive randomization procedures for clinical trials using a taylor expansion of the noncentrality parameter of the usual chi squared test for binary responses we show explicitly the relationship among the target allocation proportion the bias of the randomization procedure from that target and the variability induced by the randomization procedure we also generalize this relationship for more than two treatments under various multivariate alternatives this formulation allows us to directly evaluate and compare different response adaptive randomization procedures and different target allocations in terms of power and expected treatment failure rate without relying on simulation for k 2 treatments we compare four response adaptive randomization procedures and three target allocations based on multiple objective optimality criteria we conclude that the drop the loser rule and the doubly adaptive biased coin design are clearly super

conditioning in 2 2 tables two by two tables arise in a number of diverse settings in biomedical research including analysis of data from a clinical trial with a binary outcome and gating methods in flow cytometry to separate antigen specific immune responses from general immune responses these applications offer interesting challenges concerning what we should really be conditioning on the total number of events the number of events in the control condition etc we give several biostatistics examples to illustrate the complexities of analyzing what appear to be simple data

adaptive designs for normal responses with prognostic factors summary adaptive designs are often used in clinical trials to force balance in sequential allocation of patients between two or more competitive treatments sometimes from ethical considerations the goal may be to allocate a larger number of patients to the better treatment in the course of the trial in the present paper we consider patients who are heterogeneous with respect to some prognostic factors and assume that the response from each patient is a continuous variable we consider a normal linear model and provide an allocation design with due attention to the prognostic factors the loss of efficiency incurred by using a balanced design is also indicated issues of inference based on adaptive allocation are also discussed finally a guideline is provided for the appropriate choice of the design parameters

exact two sample permutation tests based on the randomized play the winner rule in comparing two treatments in a clinical trial the randomized play the winner rule tends to assign more study subjects to the better treatment it is applicable when patients have delayed responses to treatments it is not deterministic and is less vulnerable to experimental bias than other adaptive designs in this paper an efficient algorithm is provided to construct exact permutation tests for testing the equality of the two treatments with the randomized play the winner rule the test procedure is illustrated with a real life example the example shows that the design used in the trial should not be ignored in the analysis