survival models for heterogeneous populations derived from stable distributions summary a new three parameter family of distributions on the positive numbers is proposed it includes the stable distributions on the positive numbers the gamma the degenerate and the inverse gaussian distributions the family is characterized by the laplace transform from which moments convolutions infinite divisibility unimodality and other properties are derived the density is complicated but a simple saddlepoint approximation is provided weibull and gompertz distributions are naturally mixed over some of the distributions the family is natural exponential in one of the parameters the distributions are relevant for application as frailty distributions in life table methods for heterogeneous populations desirable properties of such distributions are discussed as an example survival after myocardial infarction is considered

bayesian computation for nonhomogeneous poisson processes in software reliability abstract a unified approach to the nonhomogeneous poisson process in software reliability models is given this approach models the epochs of failures according to a general order statistics model or to a record value statistics model their corresponding point processes can be related to the nonhomogeneous poisson processes for example the goel okumoto the musa okumoto the duane and the cox lewis processes bayesian inference for the nonhomogeneous poisson processes is studied the gibbs sampling approach sometimes with data augmentation and with the metropolis algorithm is used to compute the bayes estimates of credible sets mean time between failures and the current system reliability model selection based on a predictive likelihood is studied a numerical example with a real software failure data set is given

a general class of parametric models for recurrent event data the general class of models proposed by pena and hollander for recurrent event data is considered under a fully parametric specification of the baseline hazard rate function and under the two cases where the model does and does not incorporate frailty components estimators of model parameters are presented and their finite and asymptotic properties are ascertained for the asymptotic properties the results of borgan concerning maximum likelihood estimators in counting process models are used to obtain weak convergence to gaussian distributions of estimators however the required regularity conditions are reformulated into conditions involving gap times which make it more feasible to obtain explicit theoretical expressions of asymptotic covariances the procedures are applied to fit the general class of models with a parametric baseline hazard rate function to a dataset on hydraulic subsystems of load haul dump machines in mining

hierarchical poisson regression modeling abstract the poisson model and analyses here feature nonexchangeable gamma distributions although exchangeable following a scale transformation for individual parameters with standard deviations proportional to means a relatively uninformative prior distribution for the shrinkage values eliminates the ill behavior of maximum likelihood estimators of the variance components when tested in simulation studies the resulting procedure provides better coverage probabilities and smaller risk than several other published rules and thus works well from bayesian and frequentist perspectives alike the computations provide fast accurate density approximations to individual parameters and to structural regression coefficients the computer program is publicly available through statlib

empirical bayes estimation of the reliability of nuclear power plant emergency diesel generators for a binomial sampling model using pass fail data and a beta prior distribution parametric empirical bayes peb point and credibility interval estimates are provided for the time and diesel average emergency diesel generator edg reliability to load run on demand at 63 u s commercial nuclear power stations for a geometric sampling model and a beta prior distribution similar estimates of the time dependent edg average reliability are also obtained for four plants this is an expository article that introduces seven practical steps involving both model validation and inference in applying modern peb methods it also illustrates some important advantages of using industry wide data to make inferences on individual items

bivariate survival models induced by frailties abstract when two observed survival times depend via a proportional hazards model on the same unobserved variable called a frailty this common dependence induces an association between the observed times this article considers the class of bivariate survival distributions that can arise in this way extends it to allow negative association and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter a cross ratio function easily estimated even from censored data is the key to both the characterization results and inferential procedures and diagnostic plots that are introduced and illustrated by real examples the models considered are the natural counterpart for survival data of the latent variable models that have long been used in factor analysis for continuous data or in latent structure analysis for binary data the main distinguishing feature of survival data is the possibility of censoring which makes the standard methods difficu

analysis of multi type recurrent events in longitudinal studies application to a skin cancer prevention trial we consider the statistical modeling and analysis of replicated multi type point process data with covariates such data arise when heterogeneous subjects experience repeated events or failures which may be of several distinct types the underlying processes are modeled as nonhomogeneous mixed poisson processes with random subject and fixed covariate effects the method of maximum likelihood is used to obtain estimates and standard errors of the failure rate parameters and regression coefficients score tests and likelihood ratio statistics are used for covariate selection a graphical test of goodness of fit of the selected model is based on generalized residuals measures for determining the influence of an individual observation on the estimated regression coefficients and on the score test statistic are developed an application is described to a large ongoing randomized controlled clinical trial for the efficacy of nutritional supplements of selenium for the prevention of two types of skin cancer

pre testing for linear restrictions in a regression model with spherically symmetric disturbances abstract in this paper we derive the exact risk under quadratic loss of pre test estimators of the prediction vector and of the error variance of a linear regression model with spherically symmetric disturbances the pre test in question is one of the validity of a set of exact linear restrictions on the model s coefficient vector we demonstrate how the known results for the model with normal disturbances can be extended to this broader case we also show that the critical value of unity results in a minimum of the risk of the pre test estimator of the error variance to illustrate the results we assume multivariate student t regression disturbances and numerically evaluate the derived expressions

estimation of the error variance after a preliminary test of homogeneity in a regression model with spherically symmetric disturbances abstract in this paper we consider the risk under quadratic loss of an estimator of the error variance after a pre test for homogeneity of the variances in the two sample linear regression model we investigate the effects on risk of assuming normal disturbances when in fact the error distribution is spherically symmetric we also broaden the standard assumption that the never pool variance estimators are based on the least squares principle to illustrate the results numerically we consider two families of variance mixing distributions one of which results in multivariate student t disturbances our results show that in some situations we should always pre test even if the error variances are equal and we provide the optimal test critical value the evaluations also show that using the least squares technique to form the never pool estimators may not always be the preferred strategy

tests for an increasing trend in the intensity of a poisson process a power study abstract this article concerns a comparison of several tests for testing the hypothesis of a constant intensity against the alternative of an increasing intensity function in a nonhomogeneous poisson process nhpp the study includes the well known laplace test statistic the most powerful test for the shape parameter in a poisson process with weibull intensity the likelihood ratio test against arbitrary nhpp alternatives two nonparametric tests for trends based on kendall s tau and spearman s rho and a test based on an f statistic the powers of the tests are determined by monte carlo simulation against alternatives that are increasing at an exponential rate a power rate weibull intensity and a logarithmic rate alternatives that are step functions with one jump are also considered in a few cases the exact powers are also obtained analytically

convergence of fourth order compact difference schemes for three dimensional convection diffusion equations we consider a dirichlet boundary value problem for the three dimensional convection diffusion equations with constant coefficients in the unit cube a high order compact finite difference scheme is constructed on a 19 point stencil using the steklov averaging operators we prove that the finite difference scheme converges in discrete w 2 m omega norm with the convergence rate o h s m where the real parameter s satisfies the condition max 1 5 m s le m 4 m 0 1 2 and the exact solution belongs to the sobolev space w 2 s omega

confidence interval procedures for the weibull process with applications to reliability growth the weibull process a nonhomogeneous poisson process with intensity r t t 1 is considered as a stochastic model for the duane 1964 reliability growth postulate under this model the mean time between failure mtbf for the system at time t is given by m t r t 1 small sample and asymptotic confidence intervals on m t are discussed for failure and time truncated testing tabled values to compute the confidence intervals and numercial examples illustrating these procedures are presented

nonparametric estimation with recurrent event data the problem of nonparametric estimation for the distribution function governing the time to occurrence of a recurrent event in the presence of censoring is considered we derive nelson aalen and kaplan meier type estimators for the distribution function and establish their respective finite sample and asymptotic properties we allow for random observation periods for each subject under study and explicitly account for the informative sum quota nature of the data accrual scheme these allowances complicate technical matters considerably and in particular invalidate the direct use of martingale methods consistency and weak convergence of our estimators are obtained by extending an approach due to sellke who considered a single renewal process i e recurrent events on a single subject observed over an infinite time period a useful feature of the present analysis is that strong parallels are drawn to the usual single event setting providing a natural route toward developing extensions that involve

on the analysis of life tables for dependent observations applying methods assuming independence when observations are positively correlated means that confidence intervals become too short and significance levels of statistical tests are less extreme this paper discusses elements of life table analysis based on the standard product limit estimator and a modified greenwood formula for its variance to be used for dependent observations an application from oral surgery is given erroneously assuming independence in the analysis of a life table could have serious consequences it is demonstrated in a simulation study that the confidence levels can be much too low the proposed modification of the greenwood formula for the variance of the estimated survival function most often results in confidence levels not too much below the required level using the upper bound for the variance will give conservative confidence intervals but also larger standard errors averaging individual group survival curves should only be considered for situations with large groups

markov chains for exploring posterior distributions several markov chain methods are available for sampling from a posterior distribution two important examples are the gibbs sampler and the metropolis algorithm in addition several strategies are available for constructing hybrid algorithms this paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues on the theoretical side results from the theory of general state space markov chains can be used to obtain convergence rates laws of large numbers and central limit theorems for estimates obtained from markov chain methods these theoretical results can be used to guide the construction of more efficient algorithms for the practical use of markov chain methods standard simulation methodology provides several variance reduction techniques and also give guidance on the choice of sample size and allocation

the statistical analysis of failure time data preface 1 introduction 1 1 failure time data 1 2 failure time distributions 1 3 time origins censoring and truncation 1 4 estimation of the survivor function 1 5 comparison of survival curves 1 6 generalizations to accommodate delayed entry 1 7 counting process notation bibliographic notes exercises and complements 2 failure time models 2 1 introduction 2 2 some continuous parametric failure time models 2 3 regression models 2 4 discrete failure time models bibliographic notes exercises and complements 3 inference in parametric models and related topics 3 1 introduction 3 2 censoring mechanisms 3 3 censored samples from an exponential distribution 3 4 large sample likelihood theory 3 5 exponential regression 3 6 estimation in log linear regression models 3 7 illustrations in more complex data sets 3 8 discrimination among parametric models 3 9 inference with interval censoring 3 10 discussion bibliographic notes exercises and complements 4 relative risk cox regression models 4 1 introduction 4 2 estimation of beta 4 3 estimation of the baseline hazard or survivor function 4 4 inclusion of strata 4 5 illustrations 4 6 counting process formulas 4 7 related topics on the cox model 4 8 sampling from discrete models bibliographic notes exercises and complements 5 counting processes and asymptotic theory 5 1 introduction 5 2 counting processes and intensity functions 5 3 martingales 5 4 vector valued martingales 5 5 martingale central limit theorem 5 6 asymptotics associated with chapter 1 5 7 asymptotic results for the cox model 5 8 asymptotic results for parametric models 5 9 efficiency of the cox model estimator 5 10 partial likelihood filtration bibliographic notes exercises and complements 6 likelihood construction and further results 6 1 introduction 6 2 likelihood construction in parametric models 6 3 time dependent covariates and further remarks on likelihood construction 6 4 time dependence in the relative risk model 6 5 nonnested conditioning events 6 6 residuals and model checking for the cox model bibliographic notes exercises and complements 7 rank regression and the accelerated failure time model 7 1 introduction 7 2 linear rank tests 7 3 development and properties of linear rank tests 7 4 estimation in the accelerated failure time model 7 5 some related regression models bibliographic notes exercises and complements 8 competing risks and multistate models 8 1 introduction 8 2 competing risks 8 3 life history processes bibliographic notes exercises and complements 9 modeling and analysis of recurrent event data 9 1 introduction 9 2 intensity processes for recurrent events 9 3 overall intensity process modeling and estimation 9 4 mean process modeling and estimation 9 5 conditioning on aspects of the counting process history bibliographic notes exercises and complements 10 analysis of correlated failure time data 10 1 introduction 10 2 regression models for correlated failure time data 10 3 representation and estimation of the bivariate survivor function 10 4 pairwise dependency estimation 10 5 illustration australian twin data 10 6 approaches to nonparametric estimation of the bivariate survivor function 10 7 survivor function estimation in higher dimensions bibliographic notes exercises and complements 11 additional failure time data topics 11 1 introduction 11 2 stratified bivariate failure time analysis 11 3 fixed study period survival studies 11 4 cohort sampling and case control studies 11 5 missing covariate data 11 6 mismeasured covariate data 11 7 sequential testing with failure time endpoints 11 8 bayesian analysis of the proportional hazards model 11 9 some analyses of a particular data set bibliographic notes exercises and complements glossary of notation appendix a some sets of data appendix b supporting technical material bibliography author index subject index

restricted least squares pre test ols and stein rule estimators risk comparisons under model misspecification abstract the predictive squared error risk behavior of a restricted least squares estimator rls pre test estimator pt and stein rule sr estimator are each compared to the behavior of the ols estimator when relevant variables are omitted risk superiority conditions dependent on prior constraint error and this model specification error in a two dimensional parameter space are exhibited among the consequences of this model misspecification it is found that i perfectly correct prior constraints do not ensure risk superiority of any of the alternatives to ols ii the risk difference between ols and pt is no longer bounded and iii the sr no longer dominates ols the usefulness of risk superiority hypothesis tests based on the doubly non centralf distribution is examined

theoretical explanation of observed decreasing failure rate pooled data on the times of successive failures of the air conditioning system of a fleet of jet airplanes seemed to indicate that the life distribution had a decreasing failure rate more refined analysis showed that the failure distribution for each airplane separately was exponential but with a different failure rate using the theorem that a mixture of distributions each having a non increasing failure rate e g a mixture of exponential distributions itself has a non increasing failure rate the apparent decreasing failure rate of the pooled air conditioning life distribution was satisfactorily explained the present study has implications in other areas where an observed decreasing failure rate may well be the result of mixing exponential distributions having different parameters

statistical analysis of repeated events forming renewal processes for each of several individuals a sequence of repeated events forming a renewal process is observed up to some censoring time the object is to estimate the average interevent time over the population of individuals as well as the variation of interevent times within and between individuals medical motivation comes from gastroenterology and concerns the occurrence of certain cyclic movements in the small bowel during the fasting state two statistical models are considered one is the standard variance component model adapted to censored data and the other is a recent intensity based model with a random proportionality factor representing interindividual variation these models are applied to the motility data and their advantages are discussed the intensity based model allows simple empirical bayes estimation of the expected interevent times for an individual in the presence of censoring

a note on pooling variances abstract the estimation of variance in the normal distribution is studied under statistical inference based on conditional specification when there are two samples available for estimating the variance and it is not certain whether the two samples are from the same population the experimenter usually uses a test to resolve the uncertainty when the test is not significant the samples are pooled to obtain a pooled estimator otherwise the individual sample variance is used the bias and mean squared error of such a preliminary test estimator are studied it is shown that the preliminary test estimator has a smaller mean squared error than the usual unbiased estimator when the level of significance for the preliminary test is appropriately chosen

hierarchical generalized linear models we consider hierarchical generalized linear models which allow extra error components in the linear predictors of generalized linear models the distribution of these components is not restricted to be normal this allows a broader class of models which includes generalized linear mixed models we use a generalization of henderson s joint likelihood called a hierarchical or h likelihood for inferences from hierarchical generalized linear models this avoids the integration that is necessary when marginal likelihood is used under appropriate conditions maximizing the h likelihood gives fixed effect estimators that are asymptotically equivalent to those obtained from the use of marginal likelihood at the same time we obtain the random effect estimates that are asymptotically best unbiased predictors an adjusted profile h likelihood is shown to give the required generalization of restricted maximum likelihood for the estimation of dispersion components a scaled deviance test for the goodness of fit a model selection criterion for choosing between various dispersion models and a graphical method for checking the distributional assumption of random effects are proposed the ideas of quasi likelihood and extended quasi likelihood are generalized to the new class we give examples of the poisson gamma binomial beta and gamma inverse gamma hierarchical generalized linear models a resolution is proposed for the apparent difference between population averaged and subject specific models a unified framework is provided for viewing and extending many existing methods

fixed width output analysis for markov chain monte carlo markov chain monte carlo is a method of producing a correlated sample to estimate features of a target distribution through ergodic averages a fundamental question is when sampling should stop that is at what point the ergodic averages are good estimates of the desired quantities we consider a method that stops the simulation when the width of a confidence interval based on an ergodic average is less than a user specified value hence calculating a monte carlo standard error is a critical step in assessing the simulation output we consider the regenerative simulation and batch means methods of estimating the variance of the asymptotic normal distribution we give sufficient conditions for the strong consistency of both methods and investigate their finite sample properties in various examples

robust empirical bayes analyses of event rates a collection of i similar items generates point event histories for example machines experience failures or operators make mistakes suppose the intervals between events are modeled as iid exponential i or the counts as poisson i t i for the ith item furthermore so as to represent between item variability each individual rate parameter i is presumed drawn from a fixed super population with density g being a vector parameter a parametric empirical bayes peb setup for g specified alternatively as log student t n or gamma we exhibit the results of numerical procedures for estimating superpopulation parameters ll and for describing pooled estimates of the individual rates i obtained via bayes s formula three data sets are analyzed and convenient explicit approximate formulas are furnished for i estimates in the student t case the individual estimates are seen to have a robust quality

natural exponential families with quadratic variance functions statistical theory the normal poisson gamma binomial negative binomial and nefghs distributions are the six univariate natural exponential families nef with quadratic variance functions qvf this sequel to morris 1982 treats certain statistical topics that can be handled within this unified nef qvf formulation including unbiased estimation bhattacharyya and cramer rao lower bounds conditional distributions and moments quadratic regression conjugate prior distributions moments of conjugate priors and posterior distributions empirical bayes and g 2 minimax marginal distributions and their moments parametric empirical bayes and characterizations

a class of multivanate failure time distributions summary a class of continuous multivariate lifetime distributions is proposed the dependence between individuals in a group is modelled by a group specific quantity which can be interpreted as an unobserved covariate common to the individuals in the group and assumed to follow a positive stable distribution it is possible to include covariates in the model and discuss whether the dependence is still present after specific covariates are taken into account if the conditional hazards are proportional then the hazards in the marginal distributions are also proportional but with different constants of proportionality also the hazard for the minimum in a group is proportional to the marginal hazards if the conditional distributions given the group quantity are weibull then the marginal distributions are also weibull this class can be used to test the hypothesis of independence of litter mates in the proportional hazards model

some graphical displays and marginal regression analyses for recurrent failure times and time dependent covariates abstract recurrent event time data are common in medical research examples include infections in aids patients and seizures in epilepsy patients in this context as well as in the more usual context of a single failure time variable time dependent covariates are frequently of interest we suggest some rate functions that might be displayed when analyzing recurrent failure time data or when the effect of a categorical time dependent covariate is of interest estimators of these functions are provided along with two sample test statistics a new approach to regression modeling of these data is suggested and contrasted with existing methods our methods do not require that an explicit model be formulated for the probabilistic association between failure times within an individual this is in line with the currently popular generalized estimating equation approach to longitudinal data if the nature of such associations is known or is of particular interest then alternative methods may be appropriate

on the convergence of difference schemes for the approximation of solutionsu w m 2 m 0 5 of elliptic equations with mixed derivatives the paper deals with such estimates of the rate of convergence of difference methods which are compatible with the smoothness of the exact solutionu w 2 m m 0 5 of elliptic equations with mixed derivatives the error in the norm of the discrete sobolev spacew 2 s denoting the set of grid points is shown to be of the ordero h m s 0 s m

discretization of continuous markov chains and markov chain monte carlo convergence assessment abstract we show that continuous state space markov chains can be rigorously discretized into finite markov chains the idea is to subsample the continuous chain at renewal times related to small sets that control the discretization once a finite markov chain is derived from the markov chain monte carlo output general convergence properties on finite state spaces can be exploited for convergence assessment in several directions our choice is based on a divergence criterion derived from kemeny and snell which is first evaluated on parallel chains with a stopping time and then implemented more efficiently on two parallel chains only using birkhoff s pointwise ergodic theorem for stopping rules the performance of this criterion is illustrated on three standard examples

a general family of distributions for longitudinal dependence with special reference to event histories event histories play an increasingly important role in medical studies examples include times between recurrences of tumours as with bladder cancer and between repeated infections as with chronic granulotomous disease a general method for generating new distributions is proposed by introducing an intensity function into a density this procedure yields as special cases several distributions already proposed in the literature the families of distributions based on the pareto distribution are of particular interest for event history analysis because of their relationship to the laplace transform of a gamma distribution they can yield multivariate distributions with longitudinal serial dependence by a procedure similar to updating in the kalman filter and with uniform dependence in a similar way to copulas for longitudinal dependence several such updating procedures are proposed

the gamma frailty poisson model for the nonparametric estimation of panel count data summary in this article we study nonparametric estimation of the mean function of a counting process with panel observations we introduce the gamma frailty variable to account for the intracorrelation between the panel counts of the counting process and construct a maximum pseudo likelihood estimate with the frailty variable three simulated examples are given to show that this estimation procedure while preserving the robustness and simplicity of the computation improves the efficiency of the nonparametric maximum pseudo likelihood estimate studied in wellner and zhang 2000 annals of statistics28 779 814 a real example from a bladder tumor study is used to illustrate the method

minorization conditions and convergence rates for markov chain monte carlo abstract general methods are provided for analyzing the convergence of discrete time general state space markov chains such as those used in stochastic simulation algorithms including the gibbs sampler the methods provide rigorous a priori bounds on how long these simulations should be run to give satisfactory results results are applied to two models of the gibbs sampler a bivariate normal model and a hierarchical poisson model with gamma conditionals the methods use the notion of minorization conditions for markov chains

the total time on test plot and the cumulative total time on test statistic for a counting process results on the total time on test plot are usually obtained on the assumption that the number of events to be observed is fixed in advance here it is shown that the same large sample results hold when the number of events is random if a simple condition is satisfied

nonparametric and semiparametric trend analysis for stratified recurrence times summary recurrent event data are frequently encountered in longitudinal follow up studies when the occurrences of multiple events are considered as the major outcomes suppose that the recurrent events are of the same type and the variable of interest is the recurrence time between successive events in many applications the distributional pattern of recurrence times can be used as an index for the progression of a disease such a distributional pattern is important for understanding the natural history of a disease or for confirming long term treatment effect in this article we discuss and define the comparability of recurrence times nonparametric and semiparametric methods are developed for testing trend of recurrence time distributions and estimating trend parameters in regression models the construction of the methods is based on comparable recurrence times from stratified data a real data example is presented to illustrate the use of methodology

smooth goodness of fit tests for composite hypothesis in hazard based models consider a counting process n t t j with compensator process a t t j where a t 0 t y s 0 s ds y t t j is an observable predictable process and 0 is an unknown hazard rate function a general procedure for extending neyman s smooth goodness of fit test for the composite null hypothesis h 0 0 c 0 r q is proposed and developed the extension is obtained by embedding c in the class a k whose members are of the form 0 exp t x r k where 1 k t is a vector of observable random processes satisfying certain regularity conditions the tests are based on quadratic forms of the statistic 0 t s dm s where m t n t 0 t y s 0 s ds and is a restricted maximum likelihood estimator of asymptotic properties of the test statistics are obtained under a sequence of local alternatives and the asymptotic local powers of the tests are examined the effect of estimating by is ascertained and the problem of choosing the process is discussed the procedure is illustrated by developing tests for testing that 0 belongs to i the class of constant hazard rates and ii the class of weibull hazard rates with particular emphasis on the random censorship model simulation results concerning the achieved levels and powers of the tests are presented and the procedures are applied to three data sets that have been considered in the literature

a technique for estimating marginal posterior densities in hierarchical models using mixtures of conditional densities abstract a technique called quantile integration is proposed for the estimation of marginal posterior densities arising in bayesian models having hierarchical representations the method is based on approximating marginal densities as mixtures of conditional densities where the conditioning variables are selected deterministically from the mixing distributions the form of the approximation makes it easy to implement and the resulting approximations are computationally efficient to obtain the technique leads to particularly simple approximations for the predictive and posterior densities in kalman filter or state space models and specific formulas are provided for the special case in which innovations belong to location scale families other applications include a hierarchical empirical bayes model for poisson rates and a hierarchical linear model with exchangeable regression parameters and unknown variance components

parametric empirical bayes inference theory and applications abstract this article reviews the state of multiparameter shrinkage estimators with emphasis on the empirical bayes viewpoint particularly in the case of parametric prior distributions some successful applications of major importance are considered recent results concerning estimates of error and confidence intervals are described and illustrated with data

shorter communication evaluating tests for increasing intensity of a poisson process the problem of testing the hypothesis of a constant intensity against the alternative of an increasing intensity function in a nonhomogeneous poisson process is studied and six wellknown tests are considered three of the six are shown to have desirable power function properties whereas the other three do not have the properties in fact the tests without the desirable properties should not be used nor should any nonparametric test be used

estimation of trends in the scram rate at nuclear power plants an important task of the u s nuclear regulatory commission is to examine annual operating data from the nation s population of nuclear power plants for trends over time we are interested here in trends in the scram rate at 66 commercial nuclear power plants based on annual observed scram data from 1984 1993 for an assumed poisson distribution on the number of unplanned scrams a gamma prior and an appropriate hyperprior a parametric empirical bayes peb approximation to a full hierarchical bayes formulation is used to estimate the scram rate for each plant for each year the peb estimated prior and posterior distributions are then subsequently smoothed over time using an exponentially weighted moving average the results indicate that such bidirectional shrinkage is quite useful for identifying reliability trends over time

nonparametric k sample tests with panel count data we study the nonparametric k sample test problem with panel count data the asymptotic normality of a smooth functional of the nonparametric maximum pseudolikelihood estimator wellner zhang 2000 is established under some mild conditions we construct a class of easy to implement nonparametric tests for comparing mean functions of k populations based on this asymptotic normality we conduct various simulations to validate and compare the tests the simulations show that the tests perform quite well and generally have good power to detect differences among the mean functions the method is illustrated with a real life example

on the convergence of finite difference schemes for parabolic equations with variable coefficients we study the convergence of the finite difference schemes for the first initial boundary value problem for linear second order parabolic equations with variable coefficients using the bilinear version of the bramble hilbert lemma we obtain estimate of convergence in discretew 2 1 1 2 norm compatible with the smoothness of generalized solutionu w 2 2 q 1 3 and coefficients of equation

order statistic properties random generation and goodness of fit testing for a minimal repair model abstract we present properties of statistics arising from the block borges and savits age dependent minimal repair model these properties are analogous to the order statistic properties in homogeneous poisson processes these properties are exploited to obtain an algorithm for generating a realization from the minimal repair model and for testing hypothesis concerning the initial distribution function or hazard function of the repair model

a comparison of frailty models for multivariate survival data this paper reviews some of the main approaches to the analysis of multivariate censored survival data such data typically have correlated failure times the correlation can be a consequence of the observational design for example with clustered sampling and matching or it can be a focus of interest as in genetic studies longitudinal studies of recurrent events and other studies involving multiple measurements we assume that the correlation between the failure or survival times can be accounted for by fixed or random frailty effects we then compare the performance of conditional and mixture likelihood approaches to estimating models with these frailty effects in censored bivariate survival data we find that the mixture methods are surprisingly robust to misspecification of the frailty distribution the paper also contains an illustrative example on the times to onset of chest pain brought on by three endurance exercise tests during a drug treatment trial of heart patients

the accelerated gap times model summary this paper develops a new semiparametric model for the effect of covariates on the conditional intensity of a recurrent event counting process the model is a transparent extension of the accelerated failure time model for univariate survival data estimation of the regression parameter is motivated by semiparametric efficiency considerations extending the class of weighted log rank estimating functions originally proposed in prentice 1978 and subsequently studied in detail by tsiatis 1990 and ritov 1990 a novel rank based one step estimator for the regression parameter is proposed an aalen type estimator for the baseline intensity function is obtained asymptotics are handled with empirical process methods and finite sample properties are studied via simulation finally the new model is applied to the bladder tumour data of byar 1980

design of clinical trials for recurrent events with periodic monitoring this paper presents a design for randomized clinical trials in which incomplete data are collected on the occurrence of potentially recurrent events through periodic monitoring in particular events are assumed to arise according to a point process but information is available at the times of monitoring only if one or more events has occurred since the preceding monitoring point the event process is modelled via a piecewise poisson process and a proportional rates model is introduced to represent the difference in event rates between treatment groups the design was developed on the basis of a wald type test derived from the generalized estimating equations of liang and zeger biometrika 73 13 22 1986 robustification of the variance of the estimator of the treatment effect was considered under a random effects model with a semi parametric mixture distribution the design was adopted to address issues which arose in an osteoporosis trial conducted in japan

a sample reuse method for accurate parametric empirical bayes confidence intervals abstract parametric empirical bayes methods of point estimation for a vector of unknown parameters date to the landmark paper of james and stein 1961 the usual approach is to use the mean of the estimated posterior distribution of each parameter where the estimation of the prior parameters hyperparameters is accomplished through the marginal distribution of the data while point estimates computed this way usually perform well interval estimates based on the estimated posterior called naive eb intervals are not they fail to account for the variability in the estimation of the hyperparameters generally resulting in sub nominal coverage probability in the eb sense defined in morris 1983a in this paper we extend the work of carlin and gelfand 1989 who proposed a conditional bias correction method for developing eb intervals which corrects the deficiencies in the naive intervals we show how bias correction can be implemented in general via a type iii parametric bootstrap procedure a sample reuse method first employed by laird and louis 1987

derandomizing variance estimators one may consider a discrete event simulation as a markov chain evolving on a suitably rich state space one way that regenerative cycles may be constructed for general state space markov chains is to generate auxiliary coin flip random variables at each transition with a regeneration occurring if the coin flip results in a success the regenerative cycles are therefore randomized with respect to the sequence of states visited by the markov chain the point estimator for a steady state performance measure does not depend on the cycle structure of the chain but the variance estimator that defines the width of a confidence interval for the performance measure does this implies that the variance estimator is randomized with respect to the visited states we show how to derandomize the variance estimator through the use of conditioning a new variance estimator is obtained that is consistent and has lower variance than the standard estimator

repeated events and total time on test we adopt the total time on test procedure to investigate monotone time trends in the intensity in a repeated event setting the correct model is assumed to be a proportional hazards model with a random effect to account for dependence within subjects the method offers a simple routine for testing relevant hypotheses for recurrent event processes without making distributional assumptions about the frailty such assumptions may severely affect conclusions concerning regression coefficients and cause bias in the estimated heterogeneity the method is illustrated by re analyzing danish registry data and a long term swiss clinical study on recurrence in affective disorder

evaluating tests for increasing intensity of a poisson process the problem of testing the hypothesis of a constant intensity against the alternative of an increasing intensity function in a nonhomogeneous poisson process is studied and six wellknown tests are considered three of the six are shown to have desirable power function properties whereas the other three do not have the properties in fact the tests without the desirable properties should not be used nor should any nonparametric test be used unbiasedness

some simple robust methods for the analysis of recurrent events nelson discussed a method of estimating the cumulative mean function for identically distributed processes of recurrent events we show that a similar approach can be used with more general models including regression the key idea is to use point estimates based on poisson models and to develop robust variance estimates that are valid more generally the methods are illustrated on reliability and warranty data

nonparametric estimation of the bivariate survival function with an application to vertically transmitted aids summary in this paper we propose a nonparametric estimator of the bivariate survival function when the two durations are subject to right censoring we consider the situation where the duration variables are successive and are always observed in a particular order and the censoring mechanism bears on their sum rather than on each separately thus if they are correlated the second duration is right censored by a dependent variable a nonparametric maximum likelihood estimator is derived that takes the dependent censoring into account we also derive the asymptotic variance of the estimator and show how it can be estimated the methods are applied on a vertically acquired mother to child transmission aids data set the first duration corresponds to the hiv incubation period and the second to the period of aids

two likelihood based semiparametric estimation methods for panel count data with covariates we consider estimation in a particular semiparametric regression model for the mean of a counting process with panel count data the basic model assumption is that the conditional mean function of the counting process is of the form efn t jzg exp fl t z 0 t where z is a vector of covariates and 0 is the baseline mean function the panel count observation scheme involves observation of the counting processn for an individual at a random number k of random time points both the number and the locations of these time points may difier across individuals we study semiparametric maximum pseudo likelihood and maximum likelihood estimators of the unknown parameters fl0 0 derived on the basis of a nonhomogeneous poisson process assumption the pseudo likelihood estimator is fairly easy to compute while the maximum likelihood estimator poses more challenges from the computational perspective we study asymptotic properties of both estimators assuming that the proportional mean model holds but dropping the poisson process assumption used to derive the estimators in particular we establish asymptotic normality for the estimators of the regression parameter fl0 under appropriate hypotheses the results show that our estimation procedures are robust in the sense that the estimators converge to the truth regardless of the underlying counting process

analysis of dependent survival data applied to lifetimes of amalgam fillings when studying lifetimes of amalgam fillings one is faced with the fact that each patient may contribute multiple survival data this creates a dependence problem and some methods for solving it are presented here analysis for individual patients with simple approaches for combining data is discussed first then a parametric frailty model is applied to analyse variation within and between patients the results are presented in the form of an empirical bayes estimate for each patient

the optimal size of a preliminary test of linear restrictions in a misspecified regression model abstract when the choice of estimator for the coefficients in a linear regression model is determined by the outcome of a prior test of the validity of restrictions on the model it is well known that a minimax risk regret criterion leads to the simple rule that the optimal critical value for the preliminary test is approximately two in value regardless of the degrees of freedom we show that this result no longer holds in the likely event that relevant regressors are excluded from the model at the outset

bayesian computations for a class of reliability growth models in this article we consider the development and analysis of both attribute and variable data reliability growth models from a bayesian perspective we begin with an overview of a bayesian attribute data reliability growth model and illustrate how this model can be extended to cover the variable data growth models as well bayesian analysis of these models requires inference over ordered regions and even though closed form results for posterior quantities can be obtained in the attribute data case variable data models prove difficult in general when the number of test stages gets large computations become burdensome and more importantly the results may become inaccurate due to computational difficulties we illustrate how the difficulties in the posterior and predictive analyses can be overcome using markov chain monte carlo methods we illustrate the implementation of the proposed models by using examples from both attribute and variable reliability growth data

a linear regression model for the analysis of life times a linear model is suggested for the influence of covariates on the intensity function this approach is less vulnerable than the cox model to problems of inconsistency when covariates are deleted or the precision of covariate measurements is changed a method of non parametric estimation of regression functions is presented this results in plots that may give information on the change over time in the influence of covariates a test method and two goodness of fit plots are also given the approach is illustrated by simulation as well as by data from a clinical trial of treatment of carcinoma of the oropharynx

approximate bayesian inference in conditionally independent hierarchical models parametric empirical bayes models abstract we consider two stage models of the kind used in parametric empirical bayes peb methodology calling them conditionally independent hierarchical models we suppose that there are k units which may be experimental subjects cities study centers etcetera at the first stage the observation vectors yi for units i 1 k are independently distributed with densities p yi i or more generally p yi i at the second stage the unit specific parameter vectors i are iid with densities p i the peb approach proceeds by regarding the second stage distribution as a prior and noting that if were known inference about could be based on its posterior since is not known the simplest peb methods estimate the parameter by maximum likelihood or some variant and then treat as if it were known to be equal to this estimate although this procedure is sometimes satisfactory a well known defect is that it neglects the uncertainty due to the estimation of in this article w

further results on the non parametric linear regression model in survival analysis this paper gives further developments of a non parametric linear regression model in survival analysis three subjects are studied first martingale residuals originally developed for the cox model are introduced for our linear model their theory is developed and they are shown to be useful for judging goodness of fit the second focus of the paper is on the use of bootstrap replications to judge which features of the cumulative regression plots are likely to reflect real phenomena and not merely random variation in particular this is applied to judging whether the effect of a covariate disappears over time a problem for which no formal test exists the third subject is density type or kernel estimation of the regression functions themselves this might give more direct information than the cumulative plots the approaches are illustrated by data from a clinical trial of carcinoma of the oropharynx and by survival times of grafts in renal patients

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

some new tests of the power law process the power law process plp is often used to model failure data from repairable systems and its adequacy is tested with goodness of fit tests such as the cramer von mises test no single test however can be sensitive to all possible deviations from the plp exact tests that are powerful against some departures from the plp of particular interest to practitioners are derived heuristically the computation of their p values is described and their use is illustrated with examples one test is a modified version of the laplace test for trend another a modification of greenwood s test for clustering it is shown that these tests can be derived as score tests which ensures that they are powerful for large samples

life table methods for heterogeneous populations distributions describing the heterogeneity taking account of heterogeneity between the individuals in population based mortality studies is important a systematic way of describing heterogeneity is by an unobserved quantity called frailty entering the hazard multiplicatively until now most studies have used a gamma distributed frailty which is mathematically convenient for example the distribution among survivors is also gamma this paper shows that several other distributions have equally simple properties the main example being the inverse gaussian distribution consequences of the different distributions are examined the inverse gaussian makes the population homogeneous with time whereas for the gamma the relative heterogeneity is constant

autocorrelation pre testing in the linear model estimation testing and prediction abstract this paper explores by means of a monte carlo experiment the consequences of autocorrelation pre testing on estimation hypothesis testing and prediction in the linear regression model with first order autoregressive disturbances we find that overall pre testing is preferable to pure ols regression techniques and generally compares favourably with the strategy of always correcting for possible autocorrelation more surprising findings include the degree to which the regression matrix affects the relative performance of the various strategies and the degree to which the familiar ols based t test can lose power in the presence of autocorrelation

semi nonparametric maximum likelihood estimation on developpe une approche basee sur une innovation due a phillips 1983 sur les approximations des fonctions de densite

testing for monotone trend in recurrent event processes tests for the presence of monotone trends in recurrent event processes have been proposed and studied by many authors however a general concept of trend is elusive and the dependence of the behavior of tests on the assumed definitions of no trend and trend and on the observation periods for the processes has been largely ignored we discuss these issues and study them through analytical results and simulation studies the article also presents robust tests for trend across multiple processes extends them to deal with interval censored event times and compares them and other well known trend tests with respect to the issues mentioned

modelling memory processes and internet response times weibull or power law abstract the weibull distribution is proposed as a model for response times theoretical support is offered by classical results for extreme value distributions fits of the weibull distribution to response time data in different contexts show that this distribution and the exponential distribution on small time scales perform better than the often suggested power law and logarithmic function this study suggests that the power law can be viewed as an approximation at neural level for the aggregate strength of superposed memory traces that have different decay rates in distinct parts of the brain as we predict this view does not find support at the level of induced response processes the distinction between underlying and induced processes might also be considered in other fields such as engineering biology and physics

estimation of current reliability in a duane based reliability growth model in this article i investigate the statistical inference concerning the current field stage reliability of a reliability growth model the model assuming a step intensity structure evolves from the physical consideration of the duane learning curve property and incorporates the effect of a testanalyze and fix program that is typically undertaken in a developmental testing program both exact and large sample distributional results are derived for the maximum likelihood and the least squares estimators of the current intensity under the assumption that the step intensity model represents the reality i provide an assessment of the extent of misspecification when the widely used power law process model is fit to the failure data of a system experiencing recurrent failures extensive simulation results are carried out to supplement the theoretical findings an illustration with a dataset is provided as a demonstration of the application of the inference results

an analysis for menstrual data with time varying covariates this paper concerns the analysis of menstrual data in particular methodology to identify variables that contribute to the variability of menstrual cycles both within and between women the basis for the proposed methodology is a parameterization of the mean length of a menstrual cycle conditional upon the past cycles and covariates this approach accommodates the length bias and censoring commonly found in menstrual data data from a longitudinal study of menstrual patterns and other variables among lese women of the ituri forest zaire illustrate the methodology a small simulation illustrates the bias caused by incorrectly deleting the censored cycles

on the construction and analysis of high order locally conservative finite volume type methods for one dimensional elliptic problems locally conservative finite volume type methods based on continuous piecewise polynomial functions of degree r ge 2 are introduced and analyzed in the context of indefinite elliptic problems in one space dimension the new methods extend and generalize the classical finite volume method based on piecewise linear functions we derive a priori error estimates in the l2 h1 and l infty norm and discuss superconvergence effects for the error and its derivative explicit residual based a posteriori error bounds in the l2 and energy norm are also derived we compute the experimental order of convergence and show the results of an adaptive algorithm based on the a posteriori error estimates

regeneration in markov chain samplers abstract markov chain sampling has recently received considerable attention in particular in the context of bayesian computation and maximum likelihood estimation this article discusses the use of markov chain splitting originally developed for the theoretical analysis of general state space markov chains to introduce regeneration into markov chain samplers this allows the use of regenerative methods for analyzing the output of these samplers and can provide a useful diagnostic of sampler performance the approach is applied to several samplers including certain metropolis samplers that can be used on their own or in hybrid samplers and is illustrated in several examples

semiparametric regression for the mean and rate functions of recurrent events the counting process with the cox type intensity function has been commonly used to analyse recurrent event data this model essentially assumes that the underlying counting process is a time transformed poisson process and that the covariates have multiplicative effects on the mean and rate function of the counting process recently pepe and cai and lawless and co workers have proposed semiparametric procedures for making inferences about the mean and rate function of the counting process without the poisson type assumption in this paper we provide a rigorous justification of such robust procedures through modern empirical process theory furthermore we present an approach to constructing simultaneous confidence bands for the mean function and describe a class of graphical and numerical techniques for checking the adequacy of the fitted mean rate model the advantages of the robust procedures are demonstrated through simulation studies an illustration with multiple infection data taken from a clinical study on chronic granulomatous disease is also provided

nonparametric estimation of a recurrent survival function abstract recurrent event data are frequently encountered in studies with longitudinal designs let the recurrence time be the time between two successive recurrent events recurrence times can be treated as a type of correlated survival data in statistical analysis in general because of the ordinal nature of recurrence times statistical methods that are appropriate for standard correlated survival data in marginal models may not be applicable to recurrence time data specifically for estimating the marginal survival function the kaplan meier estimator derived from the pooled recurrence times serves as a consistent estimator for standard correlated survival data but not for recurrence time data in this article we consider the problem of how to estimate the marginal survival function in nonparametric models a class of nonparametric estimators is introduced the appropriateness of the estimators is confirmed by statistical theory and simulations simulation and analysis from schizophrenia data are pre