a proportional hazards model for interval censored failure time data this paper develops a method for fitting the proportional hazards regression model when the data contain left right or interval censored observations results given for testing the hypothesis of a zero regression coefficient lead to a generalization of the log rank test for comparison of several survival curves the method is used to analyze data from an animal tumorigenicity study and also a clinical trial

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

a multiple imputation approach to cox regression with interval censored data we propose a general semiparametric method based on multiple imputation for cox regression with interval censored data the method consists of iterating the following two steps first from finite interval censored but not right censored data exact failure times are imputed using tanner and wei s poor man s or asymptotic normal data augmentation scheme based on the current estimates of the regression coefficient and the baseline survival curve second a standard statistical procedure for right censored data such as the cox partial likelihood method is applied to imputed data to update the estimates through simulation we demonstrate that the resulting estimate of the regression coefficient and its associated standard error provide a promising alternative to the nonparametric maximum likelihood estimate our proposal is easily implemented by taking advantage of existing computer programs for right censored data

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

on the continuous differentiability of inter spike intervals of synaptically connected cortical spiking neurons in a neuronal network we derive conditions for continuous differentiability of inter spike intervals isis of spiking neurons with respect to parameters decision variables of an external stimulating input current that drives a recurrent network of synaptically connected neurons the dynamical behavior of individual neurons is represented by a class of discontinuous single neuron models we report here that isis of neurons in the network are continuously differentiable with respect to decision variables if 1 a continuously differentiable trajectory of the membrane potential exists between consecutive action potentials with respect to time and decision variables and 2 the partial derivative of the membrane potential of spiking neurons with respect to time is not equal to the partial derivative of their firing threshold with respect to time at the time of action potentials our theoretical results are supported by showing fulfillment of these conditions for a class of known bidimensional spiking neuron models

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

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

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

inference based on imputed failure times for the proportional hazards model with interval censored data abstract we propose an approach to the proportional hazards model for interval censored data in which parameter estimates are obtained by solving estimating equations that are the partial likelihood score equations for the full data proportional hazards model averaged over all rankings of imputed failure times consistent with the observed censoring intervals imputed failure times are generated using a parametric estimate of the baseline distribution the parameters of the baseline distribution are estimated simultaneously with the proportional hazards regression parameters although a parametric form for the baseline distribution must be specified simulation studies show that the method performs well even when the baseline distribution is misspecified the estimating equations are solved using monte carlo techniques we present a recursive stochastic approximation scheme that converges to the zero of the estimating equations the solution has a random error that is asymptotically normally distributed w

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

bifurcation analysis of a general class of nonlinear integrate and fire neurons in this paper we define a class of formal neuron models being computationally efficient and biologically plausible i e able to reproduce a wide range of behaviors observed in in vivo or in vitro recordings of cortical neurons this class includes for instance two models widely used in computational neuroscience the izhikevich and the brette gerstner models these models consist of a 4 parameter dynamical system we provide the full local bifurcation diagram of the members of this class and show that they all present the same bifurcations an andronov hopf bifurcation manifold a saddle node bifurcation manifold a bogdanov takens bifurcation and possibly a bautin bifurcation i e all codimension two local bifurcations in a two dimensional phase space except the cusp among other global bifurcations this system shows a saddle homoclinic bifurcation curve we show how this bifurcation diagram generates the most prominent cortical neuron behaviors this study leads us to introduce a new neuron mode

nonsmooth dynamics in spiking neuron models large scale studies of spiking neural networks are a key part of modern approaches to understanding the dynamics of biological neural tissue one approach in computational neuroscience has been to consider the detailed electrophysiological properties of neurons and build vast computational compartmental models an alternative has been to develop minimal models of spiking neurons with a reduction in the dimensionality of both parameter and variable space that facilitates more effective simulation studies in this latter case the single neuron model of choice is often a variant of the classic integrate and fire model which is described by a nonsmooth dynamical system in this paper we review some of the more popular spiking models of this class and describe the types of spiking pattern that they can generate ranging from tonic to burst firing we show that a number of techniques originally developed for the study of impact oscillators are directly relevant to their analysis particularly those for treating grazing bifurcations importantly we highlight one particular single neuron model capable of generating realistic spike trains that is both computationally cheap and analytically tractable this is a planar nonlinear integrate and fire model with a piecewise linear vector field and a state dependent reset upon spiking we call this the pwl if model and analyse it at both the single neuron and network level the techniques and terminology of nonsmooth dynamical systems are used to flesh out the bifurcation structure of the single neuron model as well as to develop the notion of liapunov exponents we also show how to construct the phase response curve for this system emphasising that techniques in mathematical neuroscience may also translate back to the field of nonsmooth dynamical systems the stability of periodic spiking orbits is assessed using a linear stability analysis of spiking times at the network level we consider linear coupling between voltage variables as would occur in neurobiological networks with gap junction coupling and show how to analyse the properties existence and stability of both the asynchronous and synchronous states in the former case we use a phase density technique that is valid for any large system of globally coupled limit cycle oscillators whilst in the latter we develop a novel technique that can handle the nonsmooth reset of the model upon spiking finally we discuss other aspects of neuroscience modelling that may benefit from further translation of ideas from the growing body of knowledge on nonsmooth dynamics

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

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

a log rank test for equivalence of two survivor functions summary we consider a hypothesis testing problem in which the alternative states that the vertical distance between the underlying survivor functions nowhere exceeds some prespecified bound 6 0 under the assumption of proportional hazards this hypothesis is shown to be logically equivalent to the statement i 1 log l c where d denotes the regression coefficient associated with the treatment group indicator and c is a simple strictly increasing function of 5 the testing procedure proposed consists of carrying out in terms of d i e the standard cox likelihood estimator of the uniformly most powerful level a test for a suitable interval hypothesis about the mean of a gaussian distribution with fixed variance the computation of the critical constant of this test is very easy in practice since it admits a representation as the root of the ath quantile of a noncentral chi square distribution with a single degree of freedom

a local likelihood proportional hazards model for interval censored data we discuss the use of local likelihood methods to fit proportional hazards regression models to right and interval censored data the assumed model allows for an arbitrary smoothed baseline hazard on which a vector of covariates operates in a proportional manner and thus produces an interpretable baseline hazard function along with estimates of global covariate effects for estimation we extend the modified em algorithm suggested by betensky lindsey ryan and wand we illustrate the method with data on times to deterioration of breast cosmeses and hiv 1 infection rates among haemophiliacs

laguerre polynomials and the inverse laplace transform using discrete data abstract we consider the problem of finding a function defined on 0 from a countable set of values of its laplace transform the problem is severely ill posed we shall use the expansion of the function in a series of laguerre polynomials to convert the problem in an analytic interpolation problem then using the coefficients of lagrange polynomials we shall construct a stable approximation solution error estimate is given numerical results are produced

rank based inference in the proportional hazards model for interval censored data summary a marginal likelihood approach to fitting the proportional hazards model to interval censored or grouped data is proposed this approach maximises a likelihood that is the sum over all rankings of the data that are consistent with the observed censoring intervals as in the usual proportional hazards model the method does not require specification of the baseline hazard function the score equations determining the maximum marginal likelihood estimator can be written as the expected value of the score of the usual proportional hazards model with respect to a certain distribution of rankings a gibbs sampling scheme is given to generate rankings from this distribution and stochastic approximation is used to solve the score equations simulation results under various censoring schemes give point estimates that are close to estimates obtained using actual failure times

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

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

the inverse laplace transform and analytic pseudo differential operators abstract by comparing the laplace transform l with the differential operatord we obtain a formula for the inverse laplace transform l 1 1 v 1 cos d v l wherevis a unitary transformation operator this helps us obtain an explicit spectral representation of l some applications of the above relation are discussed

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

a generalized linear integrate and fire neural model produces diverse spiking behaviors for simulations of neural networks there is a trade off between the size of the network that can be simulated and the complexity of the model used for individual neurons in this study we describe a generalization of the leaky integrate and fire model that produces a wide variety of spiking behaviors while still being analytically solvable between firings for different parameter values the model produces spiking or bursting tonic phasic or adapting responses depolarizing or hyperpolarizing after potentials and so forth the model consists of a diagonalizable set of linear differential equations describing the time evolution of membrane potential a variable threshold and an arbitrary number of firing induced currents each of these variables is modified by an update rule when the potential reaches threshold the variables used are intuitive and have biological significance the model s rich behavior does not come from the differential equations which are linear but rather from complex update rules this single neuron model can be implemented using algorithms similar to the standard integrate and fire model it is a natural match with event driven algorithms for which the firing times are obtained as a solution of a polynomial equation

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

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

complex variable and regularization methods of inversion of the laplace transform in this paper three methods are derived for approximating f given its laplace transform g on 0 oo i e fo f t exp st dt g s assuming that g e l 0 oo the first method is based on a sinc like rational approximation of 9 the second on a sinc solution of the integral equation fo0 f t exp st dt g s via standard regularization and the third method is based on first converting fo0 f t exp st dt g s to a convolution integral over r and then finding a sinc approximation to f via the application of a special regularization procedure to solve the fourier transform problem we also obtain bounds on the error of approximation which depend on both the method of approximation and the regularization parameter

semiparametric regression analysis of interval censored data summary we propose a semiparametric approach to the proportional hazards regression analysis of interval censored data an em algorithm based on an approximate likelihood leads to an m step that involves maximizing a standard cox partial likelihood to estimate regression coefficients and then using the breslow estimator for the unknown baseline hazards the e step takes a particularly simple form because all incomplete data appear as linear terms in the complete data log likelihood the algorithm of turnbull 1976 journal of the royal statistical society series b38 290 295 is used to determine times at which the hazard can take positive mass we found multiple imputation to yield an easily computed variance estimate that appears to be more reliable than asymptotic methods with small to moderately sized data sets in the right censored survival setting the approach reduces to the standard cox proportional hazards analysis while the algorithm reduces to the one suggested by clayton and cuzick 1985 applied statistics34 148 156 the method is illustrated on data from the breast cancer cosmetics trial previously analyzed by finkelstein 1986 biometrics42 845 854 and several subsequent authors

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

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

neural dynamics bifurcations and firing rates in a quadratic integrate and fire model with a recovery variable i deterministic behavior we study the dynamics of a quadratic integrate and fire model of a single compartment neuron with a slow recovery variable as input current and parameters describing timescales recovery variable and postspike reset change analysis of a codimension 2 bifurcation reveals that the domain of attraction of a stable hyperpolarized rest state interacts subtly with reset parameters which reposition the system state after spiking we obtain explicit approximations of instantaneous firing rates for fixed values of the recovery variable and use the averaging theorem to obtain asymptotic firing rates as a function of current and reset parameters along with the different phase plane geometries these computations provide explicit tools for the interpretation of different spiking patterns and guide parameter selection in modeling different cortical cell types

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

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

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

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

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

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

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

importance of the cutoff value in the quadratic adaptive integrate and fire model the quadratic adaptive integrate and fire model izhikevich 2003 2007 is able to reproduce various firing patterns of cortical neurons and is widely used in large scale simulations of neural networks this model describes the dynamics of the membrane potential by a differential equation that is quadratic in the voltage coupled to a second equation for adaptation integration is stopped during the rise phase of a spike at a voltage cutoff value vc or when it blows up subsequently the membrane potential is reset and the adaptation variable is increased by a fixed amount we show in this note that in the absence of a cutoff value not only the voltage but also the adaptation variable diverges in finite time during spike generation in the quadratic model the divergence of the adaptation variable makes the system very sensitive to the cutoff changing vc can dramatically alter the spike patterns furthermore from a computational viewpoint the divergence of the adaptation variable implies that the time steps for numerical simulation need to be small and adaptive however divergence of the adaptation variable does not occur for the quartic model touboul 2008 and the adaptive exponential integrate and fire model brette gerstner 2005 hence these models are robust to changes in the cutoff value

maximum likelihood estimation in semiparametric regression models with censored data summary semiparametric regression models play a central role in formulating the effects of covariates on potentially censored failure times and in the joint modelling of incomplete repeated measures and failure times in longitudinal studies the presence of infinite dimensional parameters poses considerable theoretical and computational challenges in the statistical analysis of such models we present several classes of semiparametric regression models which extend the existing models in important directions we construct appropriate likelihood functions involving both finite dimensional and infinite dimensional parameters the maximum likelihood estimators are consistent and asymptotically normal with efficient variances we develop simple and stable numerical techniques to implement the corresponding inference procedures extensive simulation experiments demonstrate that the inferential and computational methods proposed perform well in practical settings applications to three medical studies yield important new insights we conclude that there is no reason theoretical or numerical not to use maximum likelihood estimation for semiparametric regression models we discuss several areas that need further research

the bad truth about laplace s transform inverting the laplace transform is a paradigm for exponentially ill posed problems for a class of operators including the laplace transform we give forward and inverse formulae that have fast implementations using the fast fourier transform these formulae lead easily to regularized inverses whose effects on noise and filtered data can be precisely described our results give cogent reasons for the general sense of dread most mathematicians feel about inverting the laplace transform

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

a practical approach to computing power for generalized linear models with nominal count or ordinal responses data analysts facing study design questions on a regular basis could derive substantial benefit from a straightforward and unified approach to power calculations for generalized linear models many current proposals for dealing with binary ordinal or count outcomes are conceptually or computationally demanding limited in terms of accommodating covariates and or have not been extensively assessed for accuracy assuming moderate sample sizes here we present a simple method for estimating conditional power that requires only standard software for fitting the desired generalized linear model for a non continuous outcome the model is fit to an appropriate expanded data set using easily calculated weights that represent response probabilities given the assumed values of the parameters the variance covariance matrix resulting from this fit is then used in conjunction with an established non central chi square approximation to the distribution of the wald statistic alternatively the model can be re fit under the null hypothesis to approximate power based on the likelihood ratio statistic we provide guidelines for constructing a representative expanded data set to allow close approximation of unconditional power based on the assumed joint distribution of the covariates relative to prior proposals the approach proves particularly flexible for handling one or more continuous covariates without any need for discretizing we illustrate the method for a variety of outcome types and covariate patterns using simulations to demonstrate its accuracy for realistic sample sizes

on the simulation of nonlinear bidimensional spiking neuron models bidimensional spiking models are garnering a lot of attention for their simplicity and their ability to reproduce various spiking patterns of cortical neurons and are used particularly for large network simulations these models describe the dynamics of the membrane potential by a nonlinear differential equation that blows up in finite time coupled to a second equation for adaptation spikes are emitted when the membrane potential blows up or reaches a cutoff i the precise simulation of the spike times and of the adaptation variable is critical for it governs the spike pattern produced and is hard to compute accurately because of the exploding nature of the system at the spike times we thoroughly study the precision of fixed time step integration schemes for this type of model and demonstrate that these methods produce systematic errors that are unbounded as the cutoff value is increased in the evaluation of the two crucial quantities the spike time and the value of the adaptation variable at this time precise evaluation of these quantities therefore involves very small time steps and long simulation times in order to achieve a fixed absolute precision in a reasonable computational time we propose here a new algorithm to simulate these systems based on a variable integration step method that either integrates the original ordinary differential equation or the equation of the orbits in the phase plane and compare this algorithm with fixed time step euler scheme and other more accurate simulation algorithms