a nonparametric mixture model for cure rate estimation summary nonparametric methods have attracted less attention than their parametric counterparts for cure rate analysis in this paper we study a general nonparametric mixture model the proportional hazards assumption is employed in modeling the effect of covariates on the failure time of patients who are not cured the em algorithm the marginal likelihood approach and multiple amputations are employed to estimate parameters of interest in the model this model extends models and improves estimation methods proposed by other researchers it also extends cox s proportional hazards regression model by allowing a proportion of event free patients and investigating covariate effects on that proportion the model and its estimation method are investigated by simulations an application to breast cancer data including comparisons with previous analyses using a parametric model and an existing nonparametric model by other researchers confirms the conclusions from the parametric model but not those from the existing nonparametric model

a semiparametric approach for the two sample comparison of survival times with long term survivors summary in the two sample comparison of survival times with long term survivors the overall difference between the two distributions reflects differences occurring in early follow up for susceptible subjects and in long term follow up for nonsusceptible subjects in this setting we propose statistics for testing i no overall ii no short term and iii no long term difference between the two distributions to be compared the statistics are derived as follows a semiparametric model is defined that characterizes a short term effect and a long term effect by approximating this model about no difference in early survival a time dependent proportional hazards model is obtained the statistics are obtained from this working model the asymptotic distributions of the statistics for testing no overall or no short term effects are ascertained while that of the statistic for testing no long term effect is valid only when the short term effect is small simulation studies investigate the power properties of the proposed tests for different configurations the results show the interesting behavior of the proposed tests for situations where a short term effect is expected an example investigating the impact of progesterone receptors status on local tumor relapse for patients with early breast cancer illustrates the use of the proposed tests

planning the size of survival time clinical trials with allowance for stratification approximate allocation designs for comparing two survival distributions are considered and compared with the exact solution the influence of incorporating covariates by stratification accrual and follow up duration on trial size and power is investigated the bernstein and lagakos design is suited for exponential survival due to its generality and allowance for stratification while the freedman design is convenient for distribution free survival in view of its simplicity with other specifications fixed the saving in sample size becomes minimal as the accrual period or post accrual follow up time units expand above three required sample size also increases dramatically when the number of strata exceeds three

the asymptotic properties of nonparametric tests for comparing survival distributions the asymptotic distribution under alternative hypotheses is derived for a class of statistics used to test the equality of two survival distributions in the presence of arbitrary and possibly unequal right censoring the test statistics include equivalents to the log rank statistic the modified wilcoxon statistic and the class of rank invariant test procedures introduced by peto peto when there are equal censoring distributions and the hazard functions are proportional the sample size formula for the f test used to compare exponential samples is shown to be valid for the log rank test in certain situations the power of the log rank test falls as the amount of censoring decreases

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

sample size formulae for two stage randomized trials with survival outcomes two stage randomized trials are growing in importance in developing adaptive treatment strategies i e treatment policies or dynamic treatment regimes usually the first stage involves randomization to one of the several initial treatments the second stage of treatment begins when an early nonresponse criterion or response criterion is met in the second stage nonresponding subjects are re randomized among second stage treatments sample size calculations for planning these two stage randomized trials with failure time outcomes are challenging because the variances of common test statistics depend in a complex manner on the joint distribution of time to the early nonresponse criterion or response criterion and the primary failure time outcome we produce simple albeit conservative sample size formulae by using upper bounds on the variances the resulting formulae only require the working assumptions needed to size a standard single stage randomized trial and in common settings are only mildly conservative these sample size formulae are based on either a weighted kaplan meier estimator of survival probabilities at a fixed time point or a weighted version of the log rank test

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

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

sparse linear discriminant analysis by thresholding for high dimensional data in many social economical biological and medical studies one objective is to classify a subject into one of several classes based on a set of variables observed from the subject because the probability distribution of the variables is usually unknown the rule of classification is constructed using a training sample the well known linear discriminant analysis lda works well for the situation where the number of variables used for classification is much smaller than the training sample size because of the advance in technologies modern statistical studies often face classification problems with the number of variables much larger than the sample size and the lda may perform poorly we explore when and why the lda has poor performance and propose a sparse lda that is asymptotically optimal under some sparsity conditions on the unknown parameters for illustration of application we discuss an example of classifying human cancer into two classes of leukemia based on a set of 7 129 genes and a training sample of size 72 a simulation is also conducted to check the performance of the proposed method

properties of proportional hazards score tests under misspecified regression models the effects are investigated of misspecifying a proportional hazards regression model on the associated partial likelihood score test for comparing two randomized treatments in the presence of covariates the asymptotic efficiency of the proportional hazards score test relative to the optimal partial likelihood test declines slowly as the hazard functions for the two treatments deviate from proportionality the efficiency can be very low when the hazard functions cross or differ only at large survival times misspecification of the functional form of the regression portion of a proportional hazards model introduces a quantitative treatment covariate interaction in the situations that we examine based on a binary covariate this misspecification usually results in only a minor drop in efficiency the omission of a covariate that is balanced across treatments has a negligible effect on the size of the score test but can substantially reduce power when the covariate effect is strong the loss of power from mismodeling a balanced covariate is usually small

consistency of trace norm minimization regularization by the sum of singular values also referred to as the trace norm is a popular technique for estimating low rank rectangular matrices in this paper we extend some of the consistency results of the lasso to provide necessary and sufficient conditions for rank consistency of trace norm minimization with the square loss we also provide an adaptive version that is rank consistent even when the necessary condition for the non adaptive version is not fulfilled

goodness of fit tests for the cure rate in a mixture cure model summary we consider models for time to event data that allow that an event e g a relapse of a disease never occurs for a certain percentage p of the population called the cure rate we suppose that these data are subject to random right censoring and we model the data using a mixture cure model in which the survival function of the uncured subjects is left unspecified the aim is to test whether the cure rate p as a function of the covariates satisfies a certain parametric model to do so we propose a test statistic that is inspired by a goodness of fit test for a regression function due to hardle mammen 1993 we show that the statistic is asymptotically normally distributed under the null hypothesis that the model is correctly specified and under local alternatives a bootstrap procedure is proposed to implement the test the good performance of the approach is confirmed with simulations for illustration we apply the test to data on the times between first and second births

sequential linear rank tests for two sample censored survival data under extremely general patterns of patient arrival allocation to treatment and loss to follow up in randomized clinical trial settings the sequentially computed logrank statistic mantel 1966 is shown under the null hypothesis of identically distributed lifetimes to have exactly uncorrelated increments and is shown via rebolledo s 1980 martingale invariance principle to satisfy a functional central limit theorem justifying sequential logrank tests of jones and whitehead 1979 generalizations are made to other twosample rank tests for censored survival data and practical applicability to real randomized clinical trials is discussed

matrix discriminant analysis with application to colorimetric sensor array data with the rapid development of nano technology a colorimetric sensor array csa that is referred to as an optical electronic nose has been developed for the identification of toxicants unlike traditional sensors that rely on a single chemical interaction csa can measure multiple chemical interactions by using chemo responsive dyes the color changes of the chemo responsive dyes are recorded before and after exposure to toxicants and serve as a template for classification the color changes are digitalized in the form of a matrix with rows representing dye effects and columns representing the spectrum of colors thus matrix classification methods are highly desirable in this article we develop a novel classification method matrix discriminant analysis mda which is a generalization of linear discriminant analysis lda for the data in matrix form by incorporating the intrinsic matrix structure of the data in discriminant analysis the proposed method can improve csa s sensitivity and more impor

reliability based code search algorithms for maximum likelihood decoding of block codes efficient code search maximum likelihood decoding algorithms based on reliability information are presented for binary linear block codes the codewords examined are obtained via encoding the information set utilized for encoding comprises the positions of those columns of a generator matrix g of the code which for a given received sequence constitute the most reliable basis for the column space of g substantially reduced computational complexity of decoding is achieved by exploiting the ordering of the positions within this information set the search procedures do not require memory the codeword to be examined is constructed from the previously examined codeword according to a fixed rule consequently the search algorithms are applicable to codes of relatively large size they are also conveniently modifiable to achieve efficient nearly optimum decoding of particularly large codes

inefficiency of randomization methods that balance on stratum margins and improvements with permuted blocks and a sequential method stratified permuted blocks randomization is commonly applied in clinical trials but other randomization methods that attempt to balance treatment counts marginally for the stratification variables are able to accommodate more stratification variables when the analysis stratifies on the cells formed by crossing the stratification variables these other randomization methods yield treatment effect estimates with larger variance than does stratified permuted blocks when it is truly necessary to balance the randomization on many stratification variables it is shown how this inefficiency can be improved by using a sequential randomization method where the first level balances on the crossing of the strata used in the analysis and further stratification variables fall lower in the sequential hierarchy copyright 2012 john wiley sons ltd

what price kaplan meier summary the asymptotic efficiency of the kaplan meier product limit estimator relative to the maximum likelihood estimator of a parametric survival function is examined under a random censoring model

a relationship between two forms of linear rank procedures for censored data summary this paper gives a useful relationship between two popular classes of linear rank statistics for arbitrarily right censored data the relationship allows a linear rank procedure with certain optimal properties to be transformed into the form of a procedure having established asymptotic properties under proportional hazards alternatives

reduced rank regression via adaptive nuclear norm penalization we propose an adaptive nuclear norm penalization approach for low rank matrix approximation and use it to develop a new reduced rank estimation method for high dimensional multivariate regression the adaptive nuclear norm is defined as the weighted sum of the singular values of the matrix and it is generally non convex under the natural restriction that the weight decreases with the singular value however we show that the proposed non convex penalized regression method has a global optimal solution obtained from an adaptively soft thresholded singular value decomposition the method is computationally efficient and the resulting solution path is continuous the rank consistency of and prediction estimation performance bounds for the estimator are established for a high dimensional asymptotic regime simulation studies and an application in genetics demonstrate its efficacy

grassmannian packings from operator reed muller codes this paper introduces multidimensional generalizations of binary reed muller codes where the codewords are projection operators and the corresponding subspaces are widely separated with respect to the chordal distance on grassmannian space parameters of these grassmannian packings are derived and a low complexity decoding algorithm is developed by modifying standard decoding algorithms for binary reed muller codes the subspaces are associated with projection operators determined by pauli matrices appearing in the theory of quantum error correction and this connection with quantum stabilizer codes may be of independent interest the grassmannian packings constructed here find application in noncoherent wireless communication with multiple antennas where separation with respect to the chordal distance on grassmannian space guarantees closeness to the channel capacity it is shown that the capacity of the noncoherent multiple input multiple output mimo channel at both low and moderate signal to noise ratio snr under the constraint that only isotropically distributed unitary matrices are used for information transmission is closely approximated by these packings

sample size planning of two arm superiority and noninferiority survival studies with discrete follow up in clinical trials using lifetime as primary outcome variable it is more the rule than the exception that even for patients who are failing in the course of the study survival time does not become known exactly since follow up takes place according to a restricted schedule with fixed possibly long intervals between successive visits in practice the discreteness of the data obtained under such circumstances is plainly ignored both in data analysis and in sample size planning of survival time studies as a framework for analyzing the impact of making no difference between continuous and discrete recording of failure times we use a scenario in which the partially observed times are assigned to the points of the grid of inspection times in the natural way evaluating the treatment effect in a two arm trial fitting into this framework by means of ordinary methods based on cox s relative risk model is shown to produce biased estimates and or confidence bounds whose actual coverage exhibits marked discrepancies from the nominal confidence level not surprisingly the amount of these distorting effects turns out to be the larger the coarser the grid of inspection times has been chosen as a promising approach to correctly analyzing and planning studies generating discretely recorded failure times we use large sample likelihood theory for parametric models accommodating the key features of the scenario under consideration the main result is an easily implementable representation of the expected information and hence of the asymptotic covariance matrix of the maximum likelihood estimators of all parameters contained in such a model in two real examples of large scale clinical trials sample size calculation based on this result is contrasted with the traditional approach which consists of applying the usual methods for exactly observed failure times copyright 2017 john wiley sons ltd

statistical behavior and consistency of classification methods based on convex risk minimization we study how closely the optimal bayes error rate can be approximately reached using a classification algorithm that computes a classifier by minimizing a convex upper bound of the classification error function the measurement of closeness is characterized by the loss function used in the estimation we show that such a classification scheme can be generally regarded as a nonmaximum likelihood conditional in class probability estimate and we use this analysis to compare various convex loss functions that have appeared in the literature furthermore the theoretical insight allows us to design good loss functions with desirable properties another aspect of our analysis is to demonstrate the consistency of certain classification methods using convex risk minimization this study sheds light on the good performance of some recently proposed linear classification methods including boosting and support vector machines it also shows their limitations and suggests possible improvements

a direct approach to sparse discriminant analysis in ultra high dimensions summary sparse discriminant methods based on independence rules such as the nearest shrunken centroids classifier tibshirani et al 2002 and features annealed independence rules fan fan 2008 have been proposed as computationally attractive tools for feature selection and classification with high dimensional data a fundamental drawback of these rules is that they ignore correlations among features and thus could produce misleading feature selection and inferior classification we propose a new procedure for sparse discriminant analysis motivated by the least squares formulation of linear discriminant analysis to demonstrate our proposal we study the numerical and theoretical properties of discriminant analysis constructed via lasso penalized least squares our theory shows that the method proposed can consistently identify the subset of discriminative features contributing to the bayes rule and at the same time consistently estimate the bayes classification direction even when the dimension can grow faster than any polynomial order of the sample size the theory allows for general dependence among features simulated and real data examples show that lassoed discriminant analysis compares favourably with other popular sparse discriminant proposals

the power of the mantel haenszel test for grouped failure time data the mantel haenszel test for grouped failure time data mhf test compares the distribution of failure times in two cohorts followed for an interval of time when the data are collected in discrete subintervals this paper derives approximations to the power of the mantel haenszel test for arbitrary failure time distributions in the presence of censoring the approximations are appropriate for both equal and nonequal odds ratios in the constituent tables and can be used for arbitrary subdivisions of time four approximations are proposed they differ from each other according to whether the parameter measuring treatment effect is an odds ratio or a difference in proportions and whether the survival distributions are calculated under the null or alternative hypothesis in addition we demonstrate that when the hazards are constant increasing the number of subintervals often produces only a negligible increase in the power of the mhf test on the other hand for arbitrary hazards and nonconstant hazard ratios the choice of frequency and actual times of measurement can have important effects on power finally the paper presents simple expressions for power under exponential failure and censoring models

a comparison of the power of two tests for qualitative interactions qualitative or crossover interactions arise when a new treatment compared with a control treatment is beneficial in some subsets of patients and harmful in other subsets we present a new range test for crossover interactions and compare it with the likelihood ratio test developed by gail and simon the range test has greater power when the new treatment is harmful in only a few subsets whereas the likelihood ratio test has greater power when the new treatment is harmful in several subsets we provide power tables for both tests to facilitate sample size calculations for designing experiments to detect qualitative interactions and for interpreting the results of clinical trials

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

near shannon limit and low peak to average power ratio turbo block coded ofdm in this paper we present an advanced solution for the long standing problem of large peak to average power ratio papr in orthogonal frequency division multiplexing ofdm systems although the design of low papr codewords has been extensively studied and the existence of asymptotically good codes with low papr is also proven still no code has been constructed to satisfy all requirements the main goal of the paper is to develop a coding scheme that not only generates low papr codewords but it also performs relatively close to the shannon limit we achieve this goal by implementing a time frequency turbo block coded ofdm in this scheme we design the frequency domain component to have a tightly bounded papr the time domain component code is designed to obtain good performance while the decoding algorithm has reasonable complexity through comparative performance evaluation we show that utilizing the proposed method we achieve considerable improvement in terms of papr while we slightly loose the performance compared to capacity achieving codes with similar overall block length

optimal soft decision block decoders based on fast hadamard transform an approach for efficient utilization of fast hadamard transform in decoding binary linear block codes is presented computational gain is obtained by employing various types of concurring codewords and memory reduction is also achieved by appropriately selecting rows for the generator matrix the availability of these codewords in general and particularly in some of the most frequently encountered codes is discussed

a simple estimator for a shared frailty regression model summary we propose a simple estimation procedure for a proportional hazards frailty regression model for clustered survival data in which the dependence is generated by a positive stable distribution inferences for the frailty parameter can be obtained by using output from cox regression analyses the computational burden is substantially less than that of the other approaches to estimation the large sample behaviour of the estimator is studied and simulations show that the approximations are appropriate for use with realistic sample sizes the methods are motivated by studies of familial associations in the natural history of diseases their practical utility is illustrated with sib pair data from beaver dam wisconsin

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

sample size considerations for the evaluation of prognostic factors in survival analysis when the role of a new prognostic factor is investigated careful planning of an appropriate study is required this includes an assessment of the power of the study in terms of sample sizes an adequate analysis of the independent prognostic effect of a new factor has to be adjusted for the existing standard factors with survival time as endpoint this will usually be done with the cox proportional hazards model sample size and power formulae in survival analysis have been developed by schoenfeld for randomized treatment comparisons in the analysis of prognostic factors the covariates included are expected to be correlated with the factor of primary interest in this situation the existing sample size and power formulae are not valid and may not be applied in this paper schoenfeld s formula is first extended to the situation where a correlated factor is included in the analysis the validity of the resulting approximate asymptotic formula is investigated for its asymptotic behaviour by numerical integration and for its finite behaviour by simulation second an approximate formula for sample size and power is provided to detect an interaction between the interesting and a second correlated factor this extends the formula for independent effects finally the approach is illustrated by an example on the prognostic impact of dna ploidy and other factors in advanced ovarian cancer

effects of mismodelling and mismeasuring explanatory variables on tests of their association with a response variable we consider three commonly used statistical tests for assessing the association between an explanatory variable and a measured binary or survival time response variable and investigate the loss in efficiency from mismodelling or mismeasuring the explanatory variable with respect to mismodelling we examine the consequences of using an incorrect dose metameter in a test for trend of mismodelling a continuous explanatory variable and of discretizing a continuous explanatory variable we also examine the consequences of classification errors for a discrete explanatory variable and of measurement errors for a continuous explanatory variable for all three statistical tests the asymptotic relative efficiency are corresponding to each type of mis specification equals the square of the correlation between the correct and fitted form of the explanatory variable this result is evaluated numerically for the different types of mis specification to provide insight into the selection of tests the interpretation of results and the design of studies where the correct explanatory variable cannot be measured exactly

sample size calculations for ordered categorical data many clinical trials yield data on an ordered categorical scale such as very good good moderate poor under the assumption of proportional odds such data can be analysed using techniques of logistic regression in simple comparisons of two treatments this approach becomes equivalent to the mann whitney test in this paper sample size formulae consistent with an eventual logistic regression analysis are derived the influence on efficiency of the number and breadth of categories will be examined effects of misclassification and of stratification are discussed and examples of the calculations are given

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

regularized matrix regression modern technologies are producing a wealth of data with complex structures for instance in two dimensional digital imaging flow cytometry and electroencephalography matrix type covariates frequently arise when measurements are obtained for each combination of two underlying variables to address scientific questions arising from those data new regression methods that take matrices as covariates are needed and sparsity or other forms of regularization are crucial owing to the ultrahigh dimensionality and complex structure of the matrix data the popular lasso and related regularization methods hinge on the sparsity of the true signal in terms of the number of its non zero coefficients however for the matrix data the true signal is often of or can be well approximated by a low rank structure as such the sparsity is frequently in the form of low rank of the matrix parameters which may seriously violate the assumption of the classical lasso we propose a class of regularized matrix regression methods based on spectral regularization a highly efficient and scalable estimation algorithm is developed and a degrees of freedom formula is derived to facilitate model selection along the regularization path superior performance of the method proposed is demonstrated on both synthetic and real examples

soft decision decoding of reed muller codes a simplified algorithm soft decision decoding is considered for general reed muller rm codes of length n and distance d used over a memoryless channel a recursive decoding algorithm is designed and its decoding threshold is derived for long rm codes the algorithm has complexity of order nlnn and corrects most error patterns of the euclidean weight of order radicn lnn instead of the decoding threshold radicd 2 of the bounded distance decoding also for long rm codes of fixed rate r the new algorithm increases 4 pi times the decoding threshold of its hard decision counterpart

l2rm low rank linear regression models for high dimensional matrix responses the aim of this article is to develop a low rank linear regression model to correlate a high dimensional response matrix with a high dimensional vector of covariates when coefficient matrices have

generalized low density parity check codes based on hadamard constraints in this paper we consider the design and analysis of generalized low density parity check gldpc codes in awgn channels the gldpc codes are specified by a bipartite tanner graph as with standard ldpc codes but with the single parity check constraints replaced by general coding constraints in particular we consider imposing hadamard code constraints at the check nodes for a low rate approach termed ldpc hadamard codes we introduce a low complexity message passing based iterative soft input soft output siso decoding algorithm which employs the a posteriori probability app fast hadamard transform fht for decoding the hadamard check codes at each decoding iteration the achievable capacity with the gldpc codes is then discussed a modified ldpc hadamard code graph is also proposed we then optimize the ldpc hadamard code ensemble using a low complexity optimization method based on approximating the density evolution by a one dimensional dynamic system represented by an extrinsic mutual information transfer exit chart simulation results show that the optimized ldpc hadamard codes offer better performance in the low rate region than low rate turbo hadamard codes but also enjoy a fast convergence rate a rate 0 003 ldpc hadamard code with large block length can achieve a bit error rate ber performance of 10 5 at 1 44 db which is only 0 15 db away from the ultimate shannon limit 1 592 db and 0 24 db better than the best performing low rate turbo hadamard codes

cure rate models power of the logrank and generalized wilcoxon tests this paper reports the results of simulations that compare the power of the logrank and generalized wilcoxon tests in situations where the cure rate model is appropriate

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

sample size formula for the proportional hazards regression model a formula is derived for determining the number of observations necessary to test the equality of two survival distributions when concomitant information is incorporated this formula should be useful in designing clinical trials with a heterogeneous patient population schoenfeld 1981 biometrika 68 316 319 derived the asymptotic power of a class of statistics used to test the equality of two survival distributions that result is extended to the case where concomitant information is available for each individual and where the proportional hazards model holds the loss of efficiency caused by ignoring concomitant variables is also computed

investigating maximum power losses in survival studies with nonstratified randomization in studies with nonstratified randomization imbalances may occur which lead to power loss we investigate how much power may be lost at worst that is with small but nonnegligible probability the situation considered is a two treatment trial with censored survival data and three to five strata we also derive asymptotic results as the sample size and or number of strata increase in addition we consider how much a projected sample size needs to be increased to be confident at a certain probability level that the intended power will be retained conditionally on the unbalanced configuration

sample size determination for comparing more than two survival distributions we examine the asymptotic properties of the tarone and ware and harrington and fleming classes of test statistics under alternative hypotheses when there are comparisons between more than two survival distributions in the presence of arbitrary right censoring when we assume equal censoring distributions across treatment groups and proportional hazards we derive the sample size formula for testing the equality of k 2 survival distributions using the logrank test this work extends schoenfeld s derivation for comparing two survival distributions and also generalizes the results of makuch and simon we also derive the sample size formula for testing monotone dose response using tarone s trend test we then investigate the practicality of the formula in various situations by presenting empirical power with use of monte carlo simulations in addition with stratification present we derive the sample size formula for the stratified logrank test which is an extension of palta and amini

bayesian model selection analysis of a survival model with a surviving fraction we describe a methodology for model comparison in a bayesian framework as applied to survival with a surviving fraction this is illustrated using a case study of a randomized and controlled clinical trial investigating time until recurrence of depression posterior distributions are simulated using metropolis within gibbs markov chain methods models reflecting the effects of covariates on the log odds of being in the surviving fraction the log of the hazard rate as well as both and neither are compared bayes factors for comparing the models are obtained by using the bridge sampling method of calculating normalizing constants

on the optimum bit orders with respect to the state complexity of trellis diagrams for binary linear codes it was shown earlier that for a punctured reed muller rm code or a primitive bch code which contains a punctured rm code of the same minimum distance as a large subcode the state complexity of the minimal trellis diagrams is much greater than that for an equivalent code obtained by a proper permutation of the bit positions the problem of finding a permutation of the bit positions for a given code that minimizes the state complexity of its minimal trellis diagram is related to the generalized hamming weight hierarchy of a code and it is shown that for rm codes the standard binary order of bit positions is optimum at every bit position with respect to the state complexity of a minimal trellis diagram by using a theorem due to v k wei 1991 the state complexity of the trellis diagram for the extended and permuted 64 24 bch code is discussed

effects of mid point imputation on the analysis of doubly censored data doubly censored data arise in some cohort studies of the aids incubation period because the time of infection may be known only up to an interval defined by two successive screening tests for hiv antibody a simple analytic approach is to impute the infection time by the mid point of the interval and then apply standard survival techniques for right censored data the objective of this paper is to investigate the statistical properties of such a mid point imputation approach we investigated the asymptotic bias of the kaplan meier estimate coverage probabilities of associated confidence intervals bias in hazard ratio and the size of the logrank test we show that the statistical properties of mid point imputation depend strongly on the underlying distributions of infection times and the incubation periods and the width of the interval between screening tests in the absence of treatment the median incubation period of hiv infection is approximately 10 years and we conclude that for this situation mid point imputation is a reasonable procedure for interval widths of 2 years or less

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

a log rank type test to compare net survival distributions in population based cancer studies it is often interesting to compare cancer survival between different populations however in such studies the exact causes of death are often unavailable or unreliable net survival methods were developed to overcome this difficulty net survival is the survival that would be observed if the disease under study was the only possible cause of death the pohar perme estimator ppe is a nonparametric consistent estimator of net survival in this article we present a log rank type test for comparing net survival functions as estimated by ppe between several groups we put the test within the counting process framework to introduce the inverse probability weighting procedure as required by the ppe we built a stratified version to control for categorical covariates that affect the outcome we performed simulation studies to evaluate the performance of this test and worked an application on real data

weighted logrank tests to detect a transient improvement in survivorship summary in investigating whether an intervention has an effect on survival we exploit the flexibility of weighted logrank tests for constructing optimal tests sensitive to specified patterns of changes in the ratios or differences of the hazards as a function of time the tests presented seem appropriate if either the intervention on trial imposes changes in life style such as a diet modification or an exercise regimen or if the effect of therapy itself is limited in duration such as in the case of drugs for aids that may induce drug resistant viruses for such problems we postulate no difference between the hazards of the two groups initially increased discrepancies as time goes on and an eventual leveling off of the discrepancies in hazards perhaps due to compliance problems or to adoption of the behavior change under study by individuals in the control group we suggest a quadratic weight function for such problems and show how to evaluate the power of the proposed tests as well as their efficiency relative to other logrank tests other uses of quadratic weight functions for example for evaluating effects with lag times and for some parametric procedures are also described additive and multiplicative models are presented and both discrete and continuous times are considered

efficiency of two sample tests via the restricted mean survival time for analyzing event time observations in comparing two treatments with the event time observations the hazard ratio hr estimate is routinely used to quantify the treatment difference however this model dependent estimate may be difficult to interpret clinically especially when the proportional hazards ph assumption is violated an alternative estimation procedure for treatment efficacy based on the restricted means survival time or t year mean survival time t mst has been discussed extensively in the statistical and clinical literature on the other hand a statistical test via the hr or its asymptotically equivalent counterpart the logrank test is asymptotically distribution free in this article we assess the relative efficiency of the hazard ratio and t mst tests with respect to the statistical power under various ph and non ph models theoretically and empirically when the ph assumption is valid the t mst test performs almost as well as the hr test for non ph models the t mst test can substantially outperform its hr counterpart on the other hand the hr test can be powerful when the true difference of two survival functions is quite large at end but not the beginning of the study unfortunately for this case the hr estimate may not have a simple clinical interpretation for the treatment effect due to the violation of the ph assumption

a road to classification in high dimensional space the regularized optimal affine discriminant for high dimensional classification it is well known that naively performing the fisher discriminant rule leads to poor results due to diverging spectra and noise accumulation therefore researchers proposed independence rules to circumvent the diverging spectra and sparse independence rules to mitigate the issue of noise accumulation however in biological applications there are often a group of correlated genes responsible for clinical outcomes and the use of the covariance information can significantly reduce misclassification rates in theory the extent of such error rate reductions is unveiled by comparing the misclassification rates of the fisher discriminant rule and the independence rule to materialize the gain based on finite samples a regularized optimal affine discriminant road is proposed road selects an increasing number of features as the regularization relaxes further benefits can be achieved when a screening method is employed to narrow the feature pool before hitting the road an efficient constrained coordinate descent algorithm ccd is also developed to solve the associated optimization problems sampling properties of oracle type are established simulation studies and real data analysis support our theoretical results and demonstrate the advantages of the new classification procedure under a variety of correlation structures a delicate result on continuous piecewise linear solution path for the road optimization problem at the population level justifies the linear interpolation of the ccd algorithm

estimating regression parameters using linear rank tests for censored data a class of estimates for regression parameters in a linear model with right censored data is proposed these estimates are derived by using linear rank tests for right censored data as estimating equations they are shown to be consistent and asymptotically normal with covariance matrix for which estimates are proposed efficient estimates within this class are derived together with conditions when they are fully efficient 0 introduction the problem of estimating regression coefficients using ranks has received much attention in the literature for uncensored data and the results are summarized very nicely in hettmansperger 1984 there has also been some work with censored data for the two sample problem specifically louis 1981 considered estimation of a scale change between two distributions with the use of a log rank test whereas wei and gail 1983 generalize to other linear rank tests as well we shall consider the general problem of multiple linear regression and show how linear rank tests can be used as estimating equations the resulting linear rank estimates will be shown to be asymptotically normal with variances that can be estimated consistently we shall also look at the efficiency of these estimates under various situations

comparing sample size formulae for trials with unbalanced allocation using the logrank test this paper compares the sample size formulae given by schoenfeld freedman hsieh and shuster for unbalanced designs freedman s formula predicts the highest power for the logrank test when the sample size ratio of the two groups equals the reciprocal of the hazard ratio the other three formulae predict highest powers when sample sizes in the two groups are equal results of monte carlo simulations performed for the power of the logrank test with various sample size ratios show that the power curve of the logrank test is almost flat between a sample size ratio of one and a sample size ratio close to the reciprocal of the hazard ratio an equal sample size allocation may not maximize the power of the logrank test monte carlo simulations also show that under an exponential model when the sample size ratio is toward the reciprocal of the hazard ratio freedman s formula predicts more accurate powers schoenfeld s formula however seems best for predicting powers with equal sample size

conditionally cycle free graphical models for coset codes conditionally cycle free graphical models i e cyclic graphical models which become cycle free after conditioning on a subset of the hidden variables are constructed for coset codes following the description of a general construction procedure examples of a number of families of codes including first order reed muller rm and the delsarte goethals codes are provided for which the proposed procedure yields optimal soft in soft out siso decoding algorithms that are less complex than the best known trellis based algorithms in the case of the first order rm codes which have a recursive coset construction the optimal siso decoding algorithm that results when the proposed construction is applied repeatedly is denoted recursive coset representation rcr decoding connections are made between rcr decoding and existing algorithms that exploit fast hadamard transforms finally the utility of the proposed decoding algorithms are supported by a practically motivated application the construction of serially concatenated codes that have high rates and low error floors extended hamming codes are proposed as outer codes in such constructions with efficient decoding employing the siso algorithms developed herein

simple map decoding of first order reed muller and hamming codes a maximum a posteriori map probability decoder of a block code minimizes the probability of error for each transmitted symbol separately the standard way of implementing map decoding of a linear code is the bahl cocke jelinek raviv bcjr algorithm which is based on a trellis representation of the code the complexity of the bcjr algorithm for the first order reed muller rm 1 codes and hamming codes is proportional to n sup 2 where n is the code s length in this correspondence we present new map decoding algorithms for binary and nonbinary rm 1 and hamming codes the proposed algorithms have complexities proportional to q sup 2 n log sub q n where q is the alphabet size in particular for the binary codes this yields complexity of order n log n

a class of tests for the equality of k cause specific hazard rates in a competing risks model a class of asymptotically distribution free tests for the equality of the k risks in a competing risks model is considered the tests can be derived by martingale theory or by a marginal likelihood approach when the risks are dependent the quantities to be compared would be the cause specific hazard rates or equivalently the pseudosurvivor functions related to the cause specific hazard rates this class of tests allows one to compare k risks simultaneously for k 2 is able to handle possibly right censored data and is extremely simple to apply choices of the optimal weight functions leading to the locally most powerful rank tests for a general class of semiparametric alternative hypotheses are discussed the performances of the tests are studied by simulation under various alternative hypotheses

reed muller codes for random erasures and errors this paper studies the parameters for which binary reed muller rm codes can be decoded successfully on the binary erasure channel and binary symmetry channel and in particular when can they achieve capacity for these two classical channels necessarily this paper also studies the properties of evaluations of multivariate gf 2 polynomials on the random sets of inputs for erasures we prove that rm codes achieve capacity both for very high rate and very low rate regimes for errors we prove that rm codes achieve capacity for very low rate regimes and for very high rates we show that they can uniquely decode at about the square root of the number of errors at capacity the proofs of these four results are based on different techniques which we find interesting in their own right in particular we study the following questions about e m r the matrix whose rows are the truth tables of all the monomials of degree leq r in m variables what is the most resp least number of random columns in e m r that define a submatrix having full column rank resp full row rank with high probability we obtain tight bounds for very small resp very large degrees r which we use to show that rm codes achieve capacity for erasures in these regimes our decoding from random errors follows from the following novel reduction for every linear code c of sufficiently high rate we construct a new code c obtained by tensorizing c such that for every subset s of coordinates if c can recover from erasures in s then c can recover from errors in s specializing this to the rm codes and using our results for erasures imply our result on the unique decoding of the rm codes at high rate finally two of our capacity achieving results require tight bounds on the weight distribution of rm codes we obtain such bounds extending the recent bounds from constant degree to linear degree polynomials

doubly generalized ldpc codes over the awgn channel in this paper the design of doubly generalized low density parity check dgldpc codes is proposed this approach generalizes the structure of ldpc codes at both check and variable nodes the performance of dgldpc codes over the awgn channel is analyzed using exit charts combined with differential evolution optimization this analysis provides thresholds for dgldpc codes that are better than that of ldpc and gldpc codes with the same maximum variable degree these theoretical thresholds are verified via simulations furthermore dgldpc codes exhibit a lower error floor compared with their ldpc and gldpc counterparts

relative efficiency of the log rank test within a multiplicative intensity model summary for large sample clinical trials with independent individuals randomly allocated to two treatment groups in which survival times follow a log linear multiplicative intensity model with treatment group as one covariate this paper calculates the asymptotic relative efficiency of the log rank test for treatment effect as compared with the optimal score test the method is to exhibit the failure hazard intensity not of proportional hazards form obtained by ignoring all covariates other than treatment group the efficiency formulae are illustrated in two examples and estimation from data of the loss of efficiency is illustrated for two clinical trial datasets

projecting the standard error of the kaplan meier estimator clinical studies in which a major objective is to produce kaplan meier estimates of survival probabilities should be designed to produce those estimates with a desired prespecified precision as measured by their standard errors by considering the peto and greenwood formulae for the estimated standard error of the kaplan meier estimate and replacing their constituents with expected values based on the study s design parameters formulae for projected standard errors can be produced these formulae are shown through simulations to be quite accurate

sample size determination for comparing several survival curves with unequal allocations ahnn and anderson derived sample size formulae for unstratified and stratified designs assuming equal allocation of subjects to three or more treatment groups we generalize the sample size formulae to allow for unequal allocation in addition we define the overall probability of death to be equal to one minus the censored proportion for the stratified design this definition also leads to a slightly different definition of the non centrality parameter than that of ahnn and anderson for the stratified case assuming proportional hazards sample sizes are determined for a prespecified power significance level hazard ratios allocation of subjects to several treatment groups and known censored proportion in the proportional hazards setting three cases are considered 1 exponential failures exponential censoring 2 exponential failures uniform censoring and 3 weibull failures assuming same shape parameter for all groups uniform censoring in all three cases of the unstratified case it is assumed that the censoring distribution is the same for all of the treatment groups for the stratified log rank test it is assumed the same censoring distribution across the treatment groups and the strata further formulae have been developed to provide approximate powers for the test based upon the first two or first four moments of the asymptotic distribution we observe the following two major findings based on the simulations first the simulated power of the log rank test does not depend on the censoring mechanism second for a significance level of 0 05 and power of 0 80 the required sample size n is independent of the censoring pattern moreover there is very close agreement between the exact asymptotic and simulated powers when a sequence of alternatives is close to the null hypothesis two moment and four moment power series approximations also yield powers in close agreement with the exact asymptotic power with unequal allocations our simulations show that the empirical powers are consistently above the target value of prespecified power of 0 80 when 50 per cent of the patients are allocated to the treatment group with the smallest hazard

matrix linear discriminant analysis we propose a novel linear discriminant analysis lda approach for the classification of high dimensional matrix valued data that commonly arises from imaging studies motivated by the equivalence

designing cancer immunotherapy trials with random treatment time lag effect in some clinical settings such as the cancer immunotherapy trials a treatment time lag effect may be present and the lag duration possibly vary from subject to subject an efficient study design and analysis procedure should not only take into account the time lag effect but also consider the individual heterogeneity in the lag duration in this paper we present a generalized piecewise weighted logrank gpw logrank test designed to account for the random time lag effect while maximizing the study power with respect to the weights based on the proposed test both analytic and numeric approaches are developed for the sample size and power calculation asymptotic properties are derived and finite sample efficiency is evaluated in simulations compared with the standard practice ignoring the delayed effect the proposed design and analysis procedures are substantially more efficient when a random lag is expected further compared with the existing methods by xu et al considering the fixed time lag effect the proposed approaches are significantly more robust when the lag model is misspecified an r package delayedeffect design is developed for implementation

issues of efficiency in combining proportions of deaths from several clinical trials the mantel haenszel test provides a straightforward method to combine results from several clinical trials when only summary information such as the proportion of deaths is available for each trial more efficient tests such as the stratified logrank test should be used if the survival and censoring times are known for all individuals but in practice the cost and effort of obtaining this information may be prohibitive the purpose of this paper is to derive a general expression for the asymptotic relative efficiency are of the mantel haenszel test with respect to the stratified logrank test and to compute the are in situations which are likely to be of practical interest the results show that under realistic assumptions about the survival distribution losses to follow up and duration of accrual the are frequently exceeds 80 per cent an example is given to show the usefulness of the approach when combining proportions of deaths from several cancer clinical trials

sequential monitoring of clinical trials the role of information and brownian motion sequential monitoring has been a topic of major interest in clinical trials methodology over the past two decades this paper presents a unified conceptual framework for sequential monitoring that covers a wide variety of monitoring procedures in a wide variety of clinical trial settings the central elements of this framework consist of a suitable concept of statistical information and a scheme for using this concept as a basis for summarizing the accumulating results of a trial in a standardized form through a stochastic process that can be shown to approximate classical brownian motion the ideas are developed in a simple step by step fashion and illustrated by several practical examples

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

reduced lists of error patterns for maximum likelihood soft decoding a method whereby a substantially reduced family of error patterns called survivors may be created for maximum likelihood soft decoding is introduced the family of survivor depends on the received word a decoder based on this approach first forms the survivors then scores them rather than obtaining the survivors by online elimination of error patterns the use of predetermined lists that represent all families of survivors is proposed

maximum likelihood methods for cure rate models with missing covariates we propose maximum likelihood methods for parameter estimation for a novel class of semiparametric survival models with a cure fraction in which the covariates are allowed to be missing we allow the covariates to be either categorical or continuous and specify a parametric distribution for the covariates that is written as a sequence of one dimensional conditional distributions we propose a novel em algorithm for maximum likelihood estimation and derive standard errors by using louis s formula louis 1982 journal of the royal statistical society series b 44 226 233 computational techniques using the monte carlo em algorithm are discussed and implemented a real data set involving a melanoma cancer clinical trial is examined in detail to demonstrate the methodology

three classes of censored data rank tests strengths and weaknesses under censoring summary nonparametric tests are useful when definite parametric alternatives are not available the behaviour under censoring of extensions of the tests is used to delineate three distinct classes of censored data rank tests asymptotically efficient approximately distribution free and approximately unbiased section 2 gives qualitative comparisons 3 gives some representative numerical comparisons the pitman efficiencies approximated by lee desu gehan 1975 from simulations with 50 observations in each group are shown to agree with asymptotic calculations 1 weighted log rank tests it is assumed that two samples of randomly censored observations are available that is that the true lifetimes yij have cumulative distribution functions f y i oj for j 1 n i i 1 2 that the censoring times cij have cumulative distribution functions h y i of and that the observable quantities are xij min yij c and dij xij yij where a denotes the indicator function of the set a it is assumed that 01 0 that f t 1 0 is continuous in 0 and that the null hypothesis is 61 02 0 the true value of 02 will be denoted by 0 and the functions f t i 0 and h t i 0 will be abbreviated to f and h survival distributions will be denoted by a bar so that f t 1 f t the hazard rates of f and f t 10 will be denoted by a and ao respectively the test statistics studied are functions of di t the number of deaths observed before time t in the ith sample ri t the number at risk at time t in the ith sample and aj an estimator of the cumulative hazard function for the ith sample these functions are defined formally by n i n i