a large sample study of cox s regression model strong consistency and asymptotic normality are established for the maximum partial likelihood estimate of the regression parameter in cox s regression model estimates are also derived for the underlying cumulative hazard function and survival distribution we establish the asymptotic normality of these estimates and calculate the limiting variances

cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

branching index sum rules for simple lie algebras let l and l0 be a simple lie algebra and its sub lie algebra respectively then a given irreducible representation of l decomposes into a direct sum of irreducible components of l0 which is called the branching rule the general dynkin indices introduced earlier satisfy many sum rules for the branching rule these are found to be strong enough to uniquely determine the branching rule for many cases we have studied the sum rules are especially useful for cases of exceptional lie algebras

fast recursion formula for weight multiplicities the purpose of this note is to describe and prove a fast recursion formula for computing multiplicities of weights of finite dimensional representations of simple lie algebras over c until now information about weight multiplicities for all but some special cases 1 2 has had to be found from the recursion formulas of freudenthal 3 or racah 4 typically these formulas become too laborious to use for hand computations for ranks 5 and dimensions 1 0 0 and for ranks 10 and dimensions 10 on a large computer 5 6 with the proposed method the multiplicities can routinely be calculated even by hand for dimensions far exceeding these as an example we present a summary of calculations 7 of all multiplicities in the first sixteen irreducible representations of es let be a semisimple lie algebra over c with root system a and weyl group w relative to a cartan subalgebra let a be the positive roots with respect to some ordering and ii at a the set of simple roots let q and p be the root and weight lattices respectively spanning the real vector space f c if x c p we denote by x the set of dominant elements of x relative to n let m be an irreducible module with highest weight a and weight system 2 an important feature of the approach is the direct determination of 2 without computing outside the dominant chamber since every w orbit is represented by one weight x 2 of the same multiplicity it suffices to compute such x s the recursion formula for computing the multiplicities is a modification proposition 4 of the freudenthal formula in which the weyl group has been exploited to collapse it as much as possible after describing the procedure we present the e example finally the necessary proofs are given

characterization of best model based predictors in survey sampling on presente des conditions necessaires et suffisantes d optimalite d un predicteur lineaire arbitraire

omnibus tests for comparison of competing risks with adjustment for covariate effects summary this article develops omnibus tests for comparing cause specific hazard rates and cumulative incidence functions at specified covariate levels confidence bands for the difference and the ratio of two conditional cumulative incidence functions are also constructed the omnibus test is formulated in terms of a test process given by a weighted difference of estimates of cumulative cause specific hazard rates under cox proportional hazards models a simulation procedure is devised for sampling from the null distribution of the test process leading to graphical and numerical techniques for detecting significant differences in the risks the approach is applied to a cohort study of type specific hiv infection rates

absolute risk regression for competing risks interpretation link functions and prediction in survival analysis with competing risks the transformation model allows different functions between the outcome and explanatory variables however the model s prediction accuracy and the interpretation of parameters may be sensitive to the choice of link function we review the practical implications of different link functions for regression of the absolute risk or cumulative incidence of an event specifically we consider models in which the regression coefficients have the following interpretation the probability of dying from cause d during the next t years changes with a factor exp for a one unit change of the corresponding predictor variable given fixed values for the other predictor variables the models have a direct interpretation for the predictive ability of the risk factors we propose some tools to justify the models in comparison with traditional approaches that combine a series of cause specific cox regression models or use the fine gray model we illustrate the methods with the use of bone marrow transplant data

sample size formula for proportional hazards modelling of competing risks to test the effect of a therapeutic or prognostic factor on the occurrence of a particular cause of failure in the presence of other causes the interest has shifted in some studies from the modelling of the cause specific hazard to that of the subdistribution hazard we present approximate sample size formulas for the proportional hazards modelling of competing risk subdistribution considering either independent or correlated covariates the validity of these approximate formulas is investigated through numerical simulations two illustrations are provided a randomized clinical trial and a prospective prognostic study

the effect of sampling design and response mechanism on multivariate regression based predictors abstract a general regression procedure for the prediction of a vector of population means in situations of nonresponse is proposed the multivariate treatment of the prediction problem is not computationally complicated and allows the borrowing of information from one target variable to the other even when both variables are subject to nonresponse the predictors are optimal under a general model that specifies the first and second moments of the joint distribution of the survey variables the effects of the sampling design and response mechanism on the properties of the predictors are investigated and appropriate modifications and bias corrections that use the sample inclusion probabilities are proposed the performance of the predictors is illustrated empirically and compared with that of other predictors using simulated and real data data collected in governmental and other large scale surveys is almost always incomplete typical causes for the incompleteness of the data are delays in attaining part

a class of k sample tests for comparing the cumulative incidence of a competing risk in this paper for right censored competing risks data a class of tests developed for comparing the cumulative incidence of a particular type of failure among different groups the tests are based on comparing weighted averages of the hazards of the subdistribution for the failure type of interest asymptotic results are derived by expressing the statistics in terms of counting processes and using martingale central limit theory it is proposed that weight functions very similar to those for the g p tests from ordinary survival analysis be used simulation results indicate that the asymptotic distributions provide adequate approximations in moderate sized samples

bias robust estimation in finite populations using nonparametric calibration a standard problem in sample survey inference is that of predicting the finite population total h of a function h y of a random variable y the model based approach to this problem first defines a working model for y and then predicts h by estimating its expectation under conditional on the sample values of y this approach leads to biased predictions if is incorrect we explore an automatic solution to this misspecification bias that uses nonparametric regression to define a robust but inefficient predictor of h and then calibrates this predictor for its bias under an application to prediction of the finite population distribution function of a population of australian beef farms is presented

ignorable and informative designs in survey sampling inference summary the role of the sample selection mechanism in a model based approach to finite population inference is examined when the data analyst has only partial information on the sample design then a design which is ignorable when known fully may become informative conditions under which partially known designs can be ignored are established and examined for some standard designs the results are illustrated by an example used by scott 1977

confidence bands for cumulative incidence curves under the additive risk model in the context of competing risks the cumulative incidence function is often used to summarize the cause specific failure time data as an alternative to the proportional hazards model the additive risk model is used to investigate covariate effects by specifying that the subject specific hazard function is the sum of a baseline hazard function and a regression function of covariates based on such a formulation we present an approach to constructing simultaneous confidence intervals for the cause specific cumulative incidence function of patients with given risk factors a melanoma data set is used for the purpose of illustration

balanced samples and robust bayesian inference in finite population sampling summary bayesian inference in finite populations uses probability models at two stages i to describe relationships among population units and ii to express uncertainty concerning the values of parameters appearing at stage i here we consider the bayes posterior distribution of the population total when a multivariate normal regression model is used at stage i with a diffuse prior distribution on the regression coefficients we study the situation where the stage i model is in error because an important regressor is omitted and we show that in balanced samples such errors do not affect the posterior distribution cases where the covariance matrix contains an unknown scale parameter or is itself misspecified are also considered

prediction of cumulative incidence function under the proportional hazards model in the presence of dependent competing risks in survival analysis the cox model can be utilized to examine the covariate effects on the cause specific hazard function for the failure type of interest for this situation the cumulative incidence function provides an intuitively appealing summary curve for marginal probabilities of this particular event in this paper we show how to construct confidence intervals and bands for such a function under the cox model for future patients with certain covariates our proposals are illustrated with data from a prostate cancer trial

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

conditional coverage properties of finite population confidence intervals abstract standardized errors t v 1 2 were calculated for both ratio and regression estimators in each of 10 000 simple random samples of n 32 from each of six populations using four different variance estimators graphs show how the percentage of intervals t 1 96 v 1 2 that fail to contain t changes as a function of the average value of the auxiliary variable in the sample they reveal that a intervals using the variance estimators from standard linear regression theory were hopelessly unreliable b intervals using the conventional finite population variance estimators showed a striking excess of failures in badly balanced samples and c none of the four variance estimators produced satisfactory confidence intervals in populations arising from badly skewed prediction models

some tests for comparing cumulative incidence functions and cause specific hazard rates abstract we consider the competing risks problem with the available data in the form of times and causes of failure in many practical situations e g in reliability testing it is important to know whether two risks are equal or whether one is more serious than the other we propose some distribution free tests for comparing cumulative incidence functions and cause specific hazard rates against ordered alternatives without making any assumptions on the nature of dependence between the risks both the censored and the uncensored cases are studied the performance of the proposed tests is assessed in a simulation study as an illustration we compare the risks of two types of cancer mortality thymic lymphoma and reticulum cell carcinoma in a strain of laboratory mice

on the use of cause specific failure and conditional failure probabilities examples from clinical oncology data abstract nonparametric maximum likelihood estimation of the probability of failing from a particular cause by time t in the presence of other acting causes i e the cause specific failure probability is discussed a commonly used incorrect approach is to take 1 minus the kaplan meier km estimator 1 km whereby patients who fail of extraneous causes are treated as censored observations examples showing the extent of bias in using the 1 km approach are presented using clinical oncology data this bias can be quite large if the data are uncensored or if a large percentage of patients fail from extraneous causes prior to the occurrence of failures from the cause of interest each cause specific failure probability is mathematically defined as a function of all of the cause specific hazards therefore nonparametric estimates of the cause specific failure probabilities may not be able to identify categorized covariate effects on the cause specific hazards these effects would be correctly identified

second and fourth indices of plethysms the direct product of several copies of a representation decomposes into a direct sum of components each with a definite permutation symmetry the decomposition of any of the components into a direct sum of irreducible representations is the computation of a plethysm the decomposition is often simply effected when the dimension and its analogs the second and fourth indices of the plethysm are known the paper contains formulas for second and fourth indices of many specific plethysms as well as a prescription for the general plethysm the same formula is valid for the plethysm based on any finite representation of any semisimple lie algebra applications are illustrated by decomposition of all plethysms of degree 3 based on the e8 representation of dimension 3875 all fourth degree e8 scalars are enumerated

saddlepoint approximations in resampling methods summary saddlepoint approximations are shown to be easy to use and accurate in a variety of simple bootstrap and randomization applications examples include mean estimation ratio estimation two sample comparisons and autoregressive estimation

the weighted residual technique for estimating the variance of the general regression estimator of the finite population total summary the paper deals with design based estimation of the variance of the general regression estimator of the finite population total the usual taylor linearization variance estimator is an expression in the design weighted regression residuals in many applications the resulting expression is counterintuitive from a model based standpoint the improved variance estimator in this paper attaches another simple weight called g weight to each individual residual this new variance estimator i gives valid design based confidence intervals ii is nearly unbiased uiider a suitably chosen regression model and iii works well for conditional inference examples are given

optimality of royall s predictor under a gaussian superpopulation model summary this note shows that under the assumption of a gaussian superpopulation model with a general symmetric and positive definite covariance matrix the model based predictor of royall 1976 is the unbiased minimum mean squared error predictor of the total of a given finite population this somewhat anticipated result is a generalization of recent published work in which it was derived under more restrictive assumptions

an evaluation of model dependent and probability sampling inferences in sample surveys abstract in this paper we are concerned with inferences from a sample survey to a finite population we contrast inferences that are dependent on an assumed model with inferences based on the randomization induced by the sample selection plan randomization consistency for finite population estimators is defined and adopted as a requirement of probability sampling a numerical example is examined to illustrate the dangers in the use of model dependent estimators even when the model is apparently consonant with the sample data the paper concludes with a summary of principles that we believe should guide the practitioner of sample surveys of finite populations

likelihood based confidence intervals for functions of many parameters summary methods described first by madansky 1965 and revived more recently by cox oakes 1984 pp 51 2 are extended to incorporate the calculation of likelihood based confidence intervals for functions of many parameters examples involving failure time data are used to illustrate the techniques this paper concerns the derivation of confidence intervals for complicated functions of many binomial parameters examples include the probability of being in response function introduced by temkin 1978 and the cumulative incidence functions that arise in the context of multivariate failure time data with competing risks although point estimates of these summary functions are available their standard errors given by the multivariate 8 method may be algebraically complicated so that confidence intervals may not always be easily obtained in 2 of this paper we describe a likelihood based solution to the problem of deriving 1 a confidence intervals for complicated functions of many parameters because the intervals are based directly on the likelihood function they are invariant under 1 1 transformations of the parameters the description of the solution is set in the context of k independent binomial samples since the two examples presented in 3 arise in this context however the method does not appear to be intrinsically limited by the binomial framework and could yield useful results in many other parametric and nonparametric settings

semiparametric models for cumulative incidence functions in analyses of time to failure data with competing risks cumulative incidence functions may be used to estimate the time dependent cumulative probability of failure due to specific causes these functions are commonly estimated using nonparametric methods but in cases where events due to the cause of primary interest are infrequent relative to other modes of failure nonparametric methods may result in rather imprecise estimates for the corresponding subdistribution in such cases it may be possible to model the cause specific hazard of primary interest parametrically while accounting for the other modes of failure using nonparametric estimators the cumulative incidence estimators so obtained are simple to compute and are considerably more efficient than the usual nonparametric estimator particularly with regard to interpolation of cumulative incidence at early or intermediate time points within the range of data used to fit the function more surprisingly they are often nearly as efficient as fully parametric estimators we illustrate the utility of this approach in the analysis of patients treated for early stage breast cancer

methods for bounding the marginal survival distribution for time to event data with many potential failure types one cannot uniquely determine the distribution of time to a specific event type or marginal survival distribution in the case where event types are mutually exclusive in this paper we discuss several methods for estimating functions that bound the non identifiable marginal survival distribution in the competing risks problem we compute and compare bounds for data simulated from two bivariate survival distributions results show that the methods provide a suitable estimate of the marginal survival probability when one has specified dependence correctly data from a large clinical trial for breast cancer illustrate the methods

inference for cumulative incidence quantiles via parametric and nonparametric approaches in survival analysis a point estimate and confidence interval for median survival time have been frequently used to summarize the survival curve however such quantile analyses on competing risks data have not been widely investigated in this paper we propose parametric inferences for quantiles from the cumulative incidence function and develop parametric confidence intervals for quantiles in addition we study a simplified method of inference for the nonparametric approach we compare the parametric and nonparametric inferences in empirical studies simulation studies show that the procedures perform well with parametric analyses yielding smaller mean square error when the model is not too badly misspecified we illustrate the methods with data from a breast cancer clinical trial copyright 2011 john wiley sons ltd

estimating the occurrence rate for prevalent survival data in competing risks models abstract the problem of interest is the estimation of occurrence probabilities based on prevalent data in competing risks models in the literature the development of nonparametric methods has relied heavily on the independent competing risks assumption the primary purpose of this article is to establish a statistical framework without excluding the possibility of dependence among competing risks this is done through the use of crude hazard functions the crude hazard functions not only are estimable regardless of whether the competing risks are independent but also are mathematically more tractable in this article we show that there is a one to one correspondence between the crude hazard functions and the occurrence probabilities the general inversion formulas for the occurrence probabilities are presented from which various representations can be derived under different sampling techniques maximum likelihood estimators are derived using these representations for nonparametric and length bias dat

precision estimation in sample survey inference a criterion for choice between variance estimators summary we advocate the mean squared error of predicted squared error as a universal criterion for the choice between variance estimators in sample survey inference the predictive nature of the measure rewards variance estimators adapted to the amount of information in the actual sample this makes the new measure more satisfactory than the simpler mean squared error of the variance estimator the criterion turns out to be the same for design based as for model based inference and may also be used for comparison between the design and model based theoretical variances the theory is exemplified for the ratio estimator by a study of six variance estimators suggested in the literature these calculations are primarily made under a proportional regression model but consideration is also paid to model robustness three of the six estimators are shown to be inferior to the three others which are approximately equivalent

on the asymptotic distribution of ratio and regression estimators we give a formal derivation of the asymptotic normality of ratio and regression estimators of a finite population total for simple random sampling and for sampling with probability proportional to aggregate size the results are all well known and widely used of course but a rigorous development spelling out relatively simple sufficient conditions under which the standard results are valid does not seem to be available at present

a note on bayesian least squares inference for finite population models abstract this note presents some distribution free results for incorporating prior information in finite population models the formulas given are based on modifications of existing bayesian least squares estimation results and require only the specification of first and second moments of the distributions involved

nonparametric estimation of bivariate failure time associations in the presence of a competing risk most research on the study of associations among paired failure times has either assumed time invariance or been based on complex measures or estimators little has accommodated competing risks this paper targets the conditional cause specific hazard ratio henceforth called the cause specific cross ratio a recent modification of the conditional hazard ratio designed to accommodate competing risks data estimation is accomplished by an intuitive non parametric method that localizes kendall s tau time variance is accommodated through a partitioning of space into bins between which the strength of association may differ inferential procedures are developed small sample performance is evaluated and the methods are applied to the investigation of familial association in dementia onset

on conditioning for model based inference in survey sampling summary a discontinuity of sampling distribution inference between a prediction problem and an estimation problem in model based survey sampling is discussed the problem is resolved by conditioning on an appropriate ancillary within a curved exponential family framework the ignorability of the sampling design for inference is discussed

kaplan meier marginal or conditional probability curves in summarizing competing risks failure time data in the context of competing risks the kaplan meier estimator is often unsuitable for summarizing failure time data we discuss some alternative descriptive methods including marginal probability and conditional probability estimators two sample test statistics are also presented

estimation of the adjusted cause specific cumulative probability using flexible regression models for the cause specific hazards in competing risks setting we account for death according to a specific cause and the quantities of interest are usually the cause specific hazards cshs and the cause specific cumulative probabilities a cause specific cumulative probability can be obtained with a combination of the cshs or via the subdistribution hazard here we modeled the csh with flexible hazard based regression models using b splines for the baseline hazard and time dependent td effects we derived the variance of the cause specific cumulative probabilities at the population level using the multivariate delta method and showed how we could easily quantify the impact of a covariate on the cumulative probability scale using covariate adjusted cause specific cumulative probabilities and their difference we conducted a simulation study to evaluate the performance of this approach in its ability to estimate the cumulative probabilities using different functions for the cause specific log baseline hazard and with or without a td effect in the scenario with td effect we tested both well specified and misspecified models we showed that the flexible regression models perform nearly as well as the nonparametric method if we allow enough flexibility for the baseline hazards moreover neglecting the td effect hardly affects the cumulative probabilities estimates of the whole population but impacts them in the various subgroups we illustrated our approach using data from people diagnosed with monoclonal gammopathy of undetermined significance and provided the r code to derive those quantities as an extension of the r package mexhaz

biometrika centenary sample surveys summary despite karl pearson s stated aim that the evolutionist has to become in the widest sense of the words a registrar general for all forms of life the papers published in biometrika on sample surveys have been mainly theoretical and do not start to appear until the 1940s there has been little work on sampling in the life sciences with the exception of capture recapture methods the major areas have been in variable probability designs the foundations of inference for finite populations analytic surveys and the role of selection mechanisms in inference in recent years the work on survey analysis has been the outcome of an interaction between sample selection mechanisms and mainstream theory with interesting consequences for both areas

branching rules for irreducible representations of e8 into d8 the branching rules for irreducible representations of e8 into d8 are calculated using the knowledge of the kronecker products for those two algebras tables of kronecker products for both e8 and d8 algebras are also included

estimating a finite population mean from unequal probability samples abstract two approaches to estimating a finite population mean from unequal probability samples are contrasted in the prediction approach a model is specified for the population values and is used to predict the nonsampled values in the generalized regression approach the horvitz thompson estimator of the population mean is modified to allow the introduction of covariate information sarndal 1980 generalized regression estimates have the desirable property of asymptotic design consistency which is not always enjoyed by estimates in the prediction class however it is suggested that the prediction approach is the more principled method of estimation if asymptotic design consistency is a desirable property in a given application then only models that yield asymptotically design consistent prediction estimates should be used two classes of models with this property are suggested namely fixed and random effects models that allow a separate intercept for subclasses of the population indexed by the pr

character calculations for semisimple lie algebras a recursive method for calculation of characters of semisimple lie algebras is outlined by slight modifications algorithms are obtained for the computation of weight multiplicities kronecker products and branching rules as well as symmetrized kronecker powers

the prediction approach to robust variance estimation in two stage cluster sampling abstract robust statistics are derived for estimating the error variance when a finite population total or a ratio of totals is estimated from a two stage cluster sample in which the first stage sampling fraction is small the analysis is based on prediction superpopulation models that allow for very general correlation structure within clusters results are obtained for when all cluster sizes are known and for when sizes are known only for sample clusters ratio regression and mean of ratios statistics are in the class of population total estimators considered

smooth semi nonparametric snp estimation of the cumulative incidence function this paper presents a novel approach to estimation of the cumulative incidence function in the presence of competing risks the underlying statistical model is specified via a mixture factorization of the joint distribution of the event type and the time to the event the time to event distributions conditional on the event type are modeled using smooth semi nonparametric densities one strength of this approach is that it can handle arbitrary censoring and truncation while relying on mild parametric assumptions a stepwise forward algorithm for model estimation and adaptive selection of smooth semi nonparametric polynomial degrees is presented implemented in the statistical software r evaluated in a sequence of simulation studies and applied to data from a clinical trial in cryptococcal meningitis the simulations demonstrate that the proposed method frequently outperforms both parametric and nonparametric alternatives they also support the use of ad hoc asymptotic inference to derive confidence intervals an extension to regression modeling is also presented and its potential and challenges are discussed 2017 the authors statistics in medicine published by john wiley sons ltd

the finite population linear regression estimator and estimators of its variance an empirical study abstract the usual variance estimator for the linear regression estimator of a finite population total is examined under some prediction superpopulation models its bias is compared with that of the least squares variance estimator also described are three bias robust alternatives one of which is the jackknife variance estimator the theoretical results are supported by an empirical study in which simple and restricted random samples as well as some purposive nonrandom samples are drawn from six real populations the results illustrate the need for prediction models and the inadequacy of randomization per se in providing a theoretical framework for robust inferences

applications of crude incidence curves crude incidence curves display the cumulative number of failures of interest as a function of time with competing causes of failure they are distinct from cause specific incidence curves that treat secondary types of failures as censored observations after briefly reviewing their definition and estimation we present five applications of crude incidence curves to show their utility in a broad range of studies in some of these applications it is helpful to model survival time distributions with use of two different time metameters for example time from diagnosis and age of the patient we describe how one can incorporate published vital statistics into the models when secondary types of failure correspond to common causes of death

poststratification and conditional variance estimation poststratification estimation is a technique used in sample surveys to improve efficiency of estimators survey weights are adjusted to force the estimated numbers of units in each of a set of estimation cells to be equal to known population totals the resulting weights are then used in forming estimates of means or totals of variables collected in the survey for example in a household survey the estimation cells may be based on age race sex categories of individuals and the known totals may come from the most recent population census although the variance of a poststratified estimator can be computed over all possible sample configurations inferences made conditionally on the achieved sample configuration are desirable theory and a simulation study using data from the u s current population survey are presented to study both the conditional bias and variance of the poststratified estimator of a total the linearization balanced repeated replication and jackknife variance estimators are also exa

comparing the small sample performance of several variance estimators under competing risks we examine several variance estimators for cumulative incidence estimators that have been proposed over time some of which are derived from asymptotic martingale or counting process theory and some of which are developed from the moments of the multinomial distribution there is little published work comparing these variance estimators largely because the variance estimators are algebraically complex and difficult to interpret and all but one have yet to be programmed for a standard statistical package through simulation and application to real data we compare the performance of six variance estimators in relation to each other and the bootstrap in order to confirm earlier reports of their performance and to provide future direction toward their application we find that the multinomial moment based estimators have performance close to that of the bootstrap and are quite accurate for estimating the variance even in samples of 20 subjects all but one of the martingale theory based estimators tend to perform poorly in small samples tending to either overestimate or underestimate the empirical variance in samples of fewer than 100 subjects

estimates of absolute cause specific risk in cohort studies in this paper we study methods for estimating the absolute risk of an event c1 in a time interval t1 t2 given that the individual is at risk at t1 and given the presence of competing risks we discuss some advantages of absolute risk for measuring the prognosis of an individual patient and some difficulties of interpretation for comparing two treatment groups we also discuss the importance of the concept of absolute risk in evaluating public health measures to prevent disease variance calculations permit one to gauge the relative importance of random and systematic errors in estimating absolute risk efficiency calculations were also performed to determine how much precision is lost in estimating absolute risk with a nonparametric approach or with a flexible piecewise exponential model rather than a simple exponential model and other calculations indicate the extent of bias that arises with the simple exponential model when that model is invalid such calculations suggest that the more flexible models will be useful in practice simulations confirm that asymptotic methods yield reliable variance estimates and confidence interval coverages in samples of practical size

does simple random sampling provide adequate balance une etude empirique montre que sous un echantillonnage aleatoire simple les intervalles de confiance du total peuvent avoir des probabilites de recouvrement conditionnelles qui sont imposantes de facon persistante lorsque la taille de l echantillon croit

an em based semi parametric mixture model approach to the regression analysis of competing risks data we consider a mixture model approach to the regression analysis of competing risks data attention is focused on inference concerning the effects of factors on both the probability of occurrence and the hazard rate conditional on each of the failure types these two quantities are specified in the mixture model using the logistic model and the proportional hazards model respectively we propose a semi parametric mixture method to estimate the logistic and regression coefficients jointly whereby the component baseline hazard functions are completely unspecified estimation is based on maximum likelihood on the basis of the full likelihood implemented via an expectation conditional maximization ecm algorithm simulation studies are performed to compare the performance of the proposed semi parametric method with a fully parametric mixture approach the results show that when the component baseline hazard is monotonic increasing the semi parametric and fully parametric mixture approaches are comparable for mildly and moderately censored samples when the component baseline hazard is not monotonic increasing the semi parametric method consistently provides less biased estimates than a fully parametric approach and is comparable in efficiency in the estimation of the parameters for all levels of censoring the methods are illustrated using a real data set of prostate cancer patients treated with different dosages of the drug diethylstilbestrol

modelling multivariate failure time associations in the presence of a competing risk there has been much research on analysing multivariate failure times but little that has accommodated failures that arise in the presence of a competing failure process this paper studies the problem of describing associations among times to such failures it proposes a modified conditional hazard ratio measure of association that is tailored to competing risks data develops frailty models and a nonparametric method for describing the proposed measure and contrasts estimation by proposed methods with the standard of treating competing risks as independently censoring failure times due to targeted causes the methods are investigated on simulated and real data

quasi linear bayes estimation in stratified finite populations in this paper a bayesian least squares approximation is proposed for descriptive inference in a finite population when a categorical auxiliary variable is known a hierarchical model ii analysis of variance is assumed the solution consists of a projection on the vector of group totals and on the between and within sums of squares the approximation can be seen as a normal approximation of the joint distribution of the statistic and of the parameter of interest conditional on two discrete variables these denote attribution to one group and selection in the sample the main consequence of the conditioning is that conjectures about non normality can be taken into account the solution is compared with others that have been published

outlier resistant alternatives to the ratio estimator abstract many techniques have been suggested to lower the impact of outliers on sample survey estimates outliers can be downweighted by winsorization that is by replacing extreme data points by a data dependent or a predetermined value before calculating estimates another approach is to reduce the weight of outliers from the inverse sampling fraction to 1 in the estimation of population characteristics in this article the problem of estimating the population mean using auxiliary information in the presence of outliers is considered a resistant version of the ratio estimator is introduced it is constructed with a m or a gm estimator of the slope of the regression model through the origin which is implicitly called on when considering the ratio estimator the asymptotic biases and asymptotic variances of the proposed alternatives to the ratio estimator are calculated with respect to the randomization of the sampling plan the selection of a resistant estimator is seen to involve a trade off betwee

simultaneously model unbiased design unbiased estimation this paper proposes a class of inferential procedures incorporating both design and estimation elements that yield estimates of means that are simultaneously model unbiased and design unbiased classical regression procedures yield conditionally unbiased estimators for the mean conditioning on the model and choice of observation points in contrast design based methods yield estimators that are unconditionally unbiased on matter what the form of the underlying model variance properties of the proposed class are examined and applications to bioavailability water quality from mine run off and finite population regression estimation are considered the proposed procedures perform well especially in the typical case where a model is only approximately correct

methods of inference for estimates of absolute risk derived from population based case control studies the absolute risk is the probability of developing a given disease over a specified time interval given age and risk factors gail et al 1989 journal of the national cancer institute 81 1879 1888 obtained point estimates from population based case control data by combining relative risk estimates from the case control data and composite incidence estimates from the cohort data they also obtained variance estimates but they only took into account the variability in estimating relative risks in this paper we present variance estimates that take into account all components of variability namely the variance of relative risk estimates and of baseline incidence estimates as well as the covariance between the two the latter term being obtained by using implicit delta method arguments benichou and gail 1989 the american statistician 43 41 44 simulations demonstrate the validity of such variance estimates as well as of corresponding confidence intervals these methods are applied to a population based case control study of breast cancer

estimating distribution functions from survey data summary a simple method for estimating population distribution functions and associated quantiles from sample survey data is described and some asymptotic theory for it presented the method assumes a model based approach to survey estimation and allows auxiliary population information to be directly incorporated into the estimation process monte carlo results comparing the proposed method with conventional design based methods are given these suggest that the model based approach offers significant gains when the auxiliary population information is linearly related to the survey variables of interest

an empirical study of the ratio estimator and estimators of its variance abstract this paper reports results from an empirical study of the ratio estimator for a finite population total from each of six real populations 1 000 simple random samples 1 000 restricted random samples and three nonrandom samples of size 32 are drawn performance of the ratio estimator and of five estimators of its variance is compared with theoretical results generated using a prediction superpopulation models and b probability sampling distributions the results presented graphically show that theory based on prediction models can reveal relationships that are essential in making inferences but that are concealed in probability sampling analyses

median estimation in the presence of auxiliary information summary this paper deals with the estimation under simple random sampling of a finite population median in the presence of an auxiliary variable an estimator which is a simple modification of the ratio estimator for the mean is studied along with two other proposed estimators derived from a different approach these estimators are applicable in situations where only the population median or a grouped frequency distribution of the auxiliary variable is known on the basis of the asymptotic properties derived and some simulation results the efficiencies of these estimators are compared it is shown that the two estimators proposed unlike that obtained from modifying the ratio estimator always dominate the sample median in mean squared error and that their efficiencies depend directly on the probability of concordance rather than on the validity of a linearity assumption between the survey variable and the auxiliary variable when the linearity assumption is approximately satisfied the three estimators are seen to have comparable efficiencies while the modified ratio estimator is found to be quite sensitive to departures from the linearity assumnption