properties of hazard based residuals and implications in model diagnostics abstract model diagnostic procedures in failure time models using hazard based residuals rely on the assumption that the residual vector closely resembles a random sample from a unit exponential distribution when the model holds this article formally investigates the validity of this critical assumption by deriving and examining the properties of parametrically semiparametrically and nonparametrically estimated residuals for complete and right censored data the joint distribution of the residual vector is characterized and the behavior of some tests for exponentiality when applied to the residuals is examined analytically and through monte carlo methods findings reveal that the critical assumption of approximate unit exponentiality of the residual vector may not be viable and consequently the model diagnostic procedures considered which revolve on checking the approximate unit exponentiality of the residual vector specifically hazard plotting and the use of spacings and total time on test stati

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

a generalization of the product limit estimator with an application to censored regression the product limit estimator ple and weighted empirical processes are two important ingredients of almost any censored regression analysis a link between them is provided by the generalized ples introduced in this paper these generalized ples are the product limit integrals of the empirical cumulative hazard function estimators in which weighted empirical processes are used to replace the standard empirical processes the weak convergence and some large sample approximations of the generalized ples are established as an application these generalized ples are used to define some minimum distance estimators which are shown to be asymptotically normal these estimators are qualitatively robust in some submodels an optimal choice of the weight matrix is the covariate matrix and some of these estimators are quite efficient at a few common survival distributions to implement these estimators some computational aspects are discussed and an algorithm is given from a real data example and some preliminary simulation results these estimators seem to be very competitive to and more robust than some more traditional estimators such as the buckley james estimator

extended weighted log rank estimating functions in censored regression abstract in the censored regression model some regression estimators are introduced using weighted integrals of the log rank estimating functions their limiting covariance matrices do not involve the error density and can be reliably estimated inference can then be easily obtained some of these estimators have high asymptotic efficiency at some important submodels some lack of fit tests are derived that require little extra computing time these tests are asymptotically normal under the model and consistent against certain monotone or convex model misspecifications numerical studies show that for some weight functions the estimators and tests perform well implementation of the proposed procedures is discussed and illustrated in a real data example

some scale estimators and lack of fit tests for the censored two sample accelerated life model some new scale estimators for the censored two sample accelerated life model are introduced they are zeros of some integrated weighted difference between the two cumulative hazard estimators these estimators are asymptotically normal the weight is chosen to result in estimators whose asymptotic variances do not involve the destiny functions and can be easily estimated this provides a fast and simple means of statistical inference in the censored two sample accelerated life model through investigating the asymptotic relative efficiency at some important censoring submodels and the finite example behaviors in various numerical studies we obtain some estimators with very competitive performance from the new class of scale estimators some lack of fit tests for the accelerated life model are also derived these tests are related to gill schumacher type tests and require little extra computing time once the estimator is obtained the estimators and tests are illustrated in two applications for a vaginal cancer data set for rats the effect of pretreatment regime was found to be well described by the two sample accelerated life model for a data set on progression of ovarian cancer it was found that the effect of grade of disease could not be described either by the two sample proportional hazards model or the two sample accelerated life model

a comparison of the bias in four versions of the product limit estimator summary the bias of the product limit estimator depends entirely on the method used to complete the estimator beyond the last observation when it is censored the bias has been investigated for the upper gill 1980 and lower efron 1967 bounds on these methods rather than using a completion method investigators in practice commonly truncate the estimator using data driven rules the bias under two common truncation rules are considered i truncating at the last observation if it is censored and ii truncating at the n l th order statistic a number of inequalities between these biases are derived and properties of the bias functions are proved this investigation shows

phase transitions and symmetry breaking in genetic algorithms with crossover in this paper we consider the role of the crossover operator in genetic algorithms specifically we study optimisation problems that exhibit many local optima and consider how crossover affects the rate at which the population breaks the symmetry of the problem as an example of such a problem we consider the subset sum problem in doing so we demonstrate a previously unobserved phenomenon whereby the genetic algorithm with crossover exhibits a critical mutation rate at which its performance sharply diverges from that of the genetic algorithm without crossover at this critical mutation rate the genetic algorithm with crossover exhibits a rapid increase in population diversity we calculate the details of this phenomenon on a simple instance of the subset sum problem and show that it is a classic phase transition between ordered and disordered populations finally we show that this critical mutation rate corresponds to the transition between the genetic algorithm accelerating or preventing symmetry breaking and that the critical mutation rate represents an optimum in terms of the balance of exploration and exploitation within the algorithm

finite sample pointwise confidence intervals for a survival distribution with right censored data we review and develop pointwise confidence intervals for a survival distribution with right censored data for small samples assuming only independence of censoring and survival when there is no censoring at each fixed time point the problem reduces to making inferences about a binomial parameter in this case the recently developed beta product confidence procedure bpcp gives the standard exact central binomial confidence intervals of clopper and pearson additionally the bpcp has been shown to be exact gives guaranteed coverage at the nominal level for progressive type ii censoring and has been shown by simulation to be exact for general independent right censoring in this paper we modify the bpcp to create a mid p version which reduces to the mid p confidence interval for a binomial parameter when there is no censoring we perform extensive simulations on both the standard and mid p bpcp using a method of moments implementation that enforces monotonicity over time all simulated scenarios suggest that the standard bpcp is exact the mid p bpcp like other mid p confidence intervals has simulated coverage closer to the nominal level but may not be exact for all survival times especially in very low censoring scenarios in contrast the two asymptotically based approximations have lower than nominal coverage in many scenarios this poor coverage is due to the extreme inflation of the lower error rates although the upper limits are very conservative both the standard and the mid p bpcp methods are available in our bpcp r package published 2016 this article is us government work and is in the public domain in the usa

phase transitions in sexual populations subject to stabilizing selection we show that a simple model of an evolving sexual population which dates back to some of the earliest work in theoretical population genetics exhibits an unexpected and previously unobserved phase transition between ordered and disordered states this behavior is not present in populations evolving asexually without recombination and is thus important in any comparison of sexual and asexual populations in order to calculate the details of the phase transition we use techniques from statistical physics we introduce the correlation of the population as the order parameter of the system and use maximum entropy inference to find the state of the population at any time

a partially parametric estimator of survival in the presence of randomly censored data many biological or medical experiments have as their goal to estimate the survival function of a specified population of subjects when the time to the specified event may be censored due to loss to follow up the occurrence of another event that precludes the occurrence of the event of interest or the study being terminated before the event of interest occurs this paper suggests an improvement of the kaplan meier product limit estimator when the censoring mechanism is random the proposed estimator treats the uncensored observations nonparametrically and uses a parametric model only for the censored observations one version of this proposed estimator always has a smaller bias and mean squared error than the product limit estimator an example estimating the survival function of patients enrolled in the ohio state university bone marrow transplant program is presented

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

on the small sample performance of efron s and of gill s version of the product limit estimator under nonproportional hazards various proposals have been made to extend the product limit estimator to survival times beyond the largest observation in case that observation is censored two extreme extensions are examined with respect to bias and mean squared error mse their quality depends considerably on the censoring constellation the mse of one extension appears to be robust against a wide variety of nonproportionalities of the hazard rates of the distributions of lifelength and time to censoring

small sample results for the kaplan meier estimator abstract whereas much is known about the asymptotic properties of the kaplan meier 1958 estimator kme of a survival function exact results for small samples have been difficult to obtain in this article we obtain an exact expression for the th moment 0 of the kme under a model of proportional hazards this enables us under proportional hazards to a study the bias of the kme and b compare the exact variance of the kme to its asymptotic variance

a k sample median test for censored data abstract a k sample median test for censored data is proposed the test is more sensitive to differences in median survival times than to differences in shape of the survival curves the asymptotic distribution of the test statistic is derived under both the null and the alternative hypotheses and its variance is shown to take a simple form the median test is compared to several other tests for censored data by computing asymptotic relative efficiencies and performing a monte carlo simulation under various conditions the procedure described is applied to data from a colorectal cancer clinical trial

accurate bootstrap confidence limits for the cumulative hazard and survivor functions under random censoring abstract in clinical trials and other settings confidence intervals for survival probabilities at a fixed point in time are often required typically such intervals are constructed on the cumulative hazard scale the quantiles required for computing these intervals are generally obtained using a first order normal theory approximation the appropriateness of such intervals for small sample sizes or under moderate to heavy censoring is suspect we demonstrate that significant improvement is possible for randomly censored data using the nonparametric bootstrap in particular using edgeworth expansion it is shown that the percentile t and bc a bootstrap methodologies based on the studentized nelson aalen estimator yield second order correct confidence limits for the cumulative hazard function at a fixed time point an explicit formula for the correction term of the edgeworth expansion is found easy to compute estimators for the components of the correction term are also found and lead to simple analytic

the quasispecies regime for the simple genetic algorithm with ranking selection we study the simple genetic algorithm with a ranking selection mechanism linear ranking or tournament we denote by the length of the chromosomes by m the population size by pc the crossover probability and by pm the mutation probability we introduce a parameter called the selection drift which measures the selection intensity of the fittest chromosome we show that the dynamics of the genetic algorithm depend in a critical way on the parameter 1 pc 1 pm if 1 then the genetic algorithm operates in a quasispecies regime an advantageous mutant invades a positive fraction of the population with probability larger than a constant p which does not depend on m we estimate next the probability of the occurrence of a catastrophe the whole population falls below a fitness level which was previously reached by a positive fraction of the population the asymptotic results suggest the following rules 1 pc 1 pm should be slightly larger than 1 pm should be of order 1 m should be larger than ln the running time should be of exponential order in m the first condition requires that pm pc ln these conclusions must be taken with great care they come from an asymptotic regime and it is a formidable task to understand the relevance of this regime for a real world problem at least we hope that these conclusions provide interesting guidelines for the practical implementation of the simple genetic algorithm

on complemented subspaces of non archimedean kothe spaces abstract the generalized power series spaces d f a r are the most known and important examples of nuclear kothe spaces we prove that every kothe montel space over a non archimedean field k has a complemented closed subspace isomorphic to a generalized power series space d f a r it follows that every non normable frechet space e that is not isomorphic to the product of a banach space and the space k n has a closed subspace isomorphic to a generalized power series space d f a r

estimating the median survival time summary two methods are proposed for setting confidence intervals for the median survival time it is shown how these are related to bootstrap methods for censored data and some numerical comparisons are presented in many medical follow up studies the survival experience of a group of patients is summarized by the product limit or kaplan meier estimate of the survival distribution this may follow an analysis of the relation between survival time and some explanatory variables by for example the proportional hazards model the median of the estimated survival distribution is sometimes a convenient summary statistic and may be preferred to the mean because it is less sensitive to long tails in the estimated survival distribution this paper is concerned with estimating the distribution of the estimated median and providing confidence intervals for the true median two methods are considered in 2 they are both based in different ways on generalizations of the solution for the uncensored case these methods turn out to be connected to two ways of extending bootstrap methods for use with censored data this connexion is discussed in 3 thinking about extensions of the bootstrap to censored data highlights the need for careful consideration of the role of the censoring mechanism and how it should be incorporated into the data analysis section 4 provides some examples and monte carlo simulations the work is closely related to that of efron 1981 and emerson 1981

on the calibration problem extended to nonlinear models the traditional calibration problem is concerned with estimating the unknown value of an explanatory variable x corresponding to an observed value of a response variable y that is assumed to be functionally related to x the problem for which y is related to x by a simple linear model has been discussed in the literature this paper is concerned with obtaining a confidence interval for an unknown value of x corresponding to a specified or fixed value of y where y and x are related through a known nonlinear function given a specified value y of a response variable y that is related to x through a known function linear or nonlinear a point estimate of xc can be found through the inverse function if the inverse exists or through an iterative search procedure two approaches are presented for determining a confidence interval for xc given a value y when the inverse function exists a confidence interval about xc can be obtained from the approximate distribution of kc which provides a symmetric confidence interval about xc confidence intervals based on the asymptotic distribution of f3 are not symmetric about kc which is particularly appropriate when considering nonlinear functions that have asymptotes the technique based on the distribution of f3 is more general because it does not depend on having a closed form of the inverse function a simulation study for sample sizes of 20 involving an exponential decay function indicates that both approaches attained the desired confidence coefficient a test procedure comparing two calibration points from different populations or treatment groups is presented a simulation study of sample sizes of 20 involving an exponential decay function indicates that the test procedure attains the desired level of significance with good power additional simulation studies may be necessary to determine the appropriateness of these techniques for different model types and or sample sizes an example from meat sciences research is presented demonstrating the techniques discussed

symmetric tests and confidence intervals for survival probabilities and quantiles of censored survival data we describe existing tests and introduce two new tests concerning the value of a survival function these tests may be used to construct a confidence interval for the survival probability at a given time or for a quantile of the survival distribution simulation studies show that error rates can differ substantially from their nominal values particularly at survival probabilities close to zero or one we recommend our new constrained bootstrap test for its good overall performance

the dynamics of a genetic algorithm for simple random ising systems abstract a formalism is presented for analysing genetic algorithms it is used to study a simple genetic algorithm consisting of selection mutation and crossover which is searching for the ground states of simple random ising spin systems a random field ideal paramagnet and a spin glass chain the formalism can also be applied to other population based search techniques and to biological models of micro evolution to make the problem tractable it is assumed that the population dynamics can be described by a few macroscopic order parameters and that the remaining microscopic degrees of freedom can be averaged out the macroscopic quantities that are used are the cumulants of the distribution of fitnesses or energies in the population a statistical mechanics model is presented which describes the population configuration in terms of the cumulants this is used to derive equations of motion for the cumulants predictions of the theory are compared with experiments and are shown to predict the average time to convergence and the average fitness of the final population accurately a simplified version of the equations is produced by keeping only leading nonlinear terms and truncating the cumulant expansion this is shown to give a novel description of the role of genetic operators in search e g it is argued that an important role of crossover is to reduce the skewness of the population

a note on confidence limits for quartiles with right censored data two new methods are proposed for constructing the confidence limits for quartiles the small sample behaviour of these two methods is compared with the jennison and turnbull modified brookmeyer crowley method at three quartiles the simulation study indicates that one of the new methods the smoothed modified reflected method is preferred over the other methods when the censoring rate is less than 40 per cent while the jennison and turnbull method is preferred for higher censoring the results for the upper quartile are similar to the median for the lower quartile with small sample and high censoring semi infinite intervals may often occur the correct practice is to permit the semi infinite intervals without modifying them since it is more informative and gives closer to nominal level coverage

nonparametwic confidence intervals for the median in the presence of right censoriilg a method is proposed for constructing nonpararnetric confidence intervals for the median of a survival distribution the method applies when survival data are subject to random right censoring the confidence interval is constructed by inverting a hypothesis test the test used being one that generalizes the binomial test to accommodate censoring a nonparametric estimate of the eventual failure time for each censored observation modifies the usual binomial test statistic the estimates are computed using the kaplan meier product limit estimate of the survival function a large simulation study indicates that the nonparametric method performs well for various survival distributions of different shapes two existing techniques that assume exponentiality perform well for exponential data they give good coverage probabilities with intervals that are shorter than those provided by the nonparametric approach the nonparametric intervals exhibit superior coverage probabilities when data are generated from nonexponential distributions this is the case for weibull data with both increasing and decreasing hazard functions the nonparametric construction is appropriate for samples of size 10 or greater with up to 50 censoring a monte carlo study supports the use of a binomial distribution to approximate the exact discrete distribution of the test statistic median survival time is often used for evaluation of the efficacy of a treatment for a chronic disease one would like to provide a confidence interval for the median as well as a point estimate when little is known about the shape of the survival distribution an interval is needed for which no particular parametric form for the distribution is assumed a nonparametric confidence interval for the median is easily formed when all observations are complete the problem increases in subtlety and complexity when incomplete or censored observations exist in this paper a method is proposed for constructing nonparametric confidence intervals for the median when observations may be right censored the distribution of survival time may be either discrete or continuous and it need not have finite moments the method does assume however that the censoring mechanism is noninformative in that censoring acts independently of survival time see lagakos 1979 in the absence of censoring the usual construction of a nonparametric confidence interval for the median inverts the sign test this test is based upon the number of failures that occur beyond the hypothesized value of the median the present paper generalizes the procedure to allow for right censoring by using the kaplan meier estimate of survival to approximate the number of failures beyond the hypothesized median confidence interval estimation when data are censored has received recent attention in

a simple hybrid variance estimator for the kaplan meier survival function in this paper we propose a hybrid variance estimator for the kaplan meier survival function this new estimator approximates the true variance by a binomial variance formula where the proportion parameter is a piecewise non increasing function of the kaplan meier survival function and its upper bound as described below also the effective sample size equals the number of subjects not censored prior to that time in addition we consider an adjusted hybrid variance estimator that modifies the regular estimator for small sample sizes we present a simulation study to compare the performance of the regular and adjusted hybrid variance estimators to the greenwood and peto variance estimators for small sample sizes we show that on average these hybrid variance estimators give closer variance estimates to the true values than the traditional variance estimators and hence confidence intervals constructed with these hybrid variance estimators have more nominal coverage rates indeed the greenwood and peto variance estimators can substantially underestimate the true variance in the left and right tails of the survival distribution even with moderately censored data finally we illustrate the use of these hybrid and traditional variance estimators on a data set from a leukaemia clinical trial

power series space representations of nuclear frechet spaces let e be a nuclear graded frechet space such that the norms satisfy inequalities 2 ik ckjl lk li ik l for all k let f beagradedfrechet space such that the dual extended real valued norms satisfy inequalities ii2 dkil lii lk l for all k and let a be a tame resp linearly tame linear map from f to e then there exists a tame resp linearly tame factorization of a through a power series space a 2 a in the case of a tame quotient map e ib tamely equivalent to a power series space of infinite type this applies in particular to the range of a tame resp linearly tame projection in a power series space a2o a in this case one does not need nuclearity it also applies to the tame spaces in the sense of the various implicit function theorems if they are nuclear they are tamely equivalent to power series spaces ao a the question whether certain frechet spaces have isomorphic representations as kothe sequence spaces has become more and more important on one hand by examples of mityagin zobin 28 djakov mityagin 2 and others it has become clear that in general even for the nuclear case a representation is not possible on the other hand the theory of operators in frechet spaces has developed tools which are more or less connected to such representations an important open problem is for instance whether complemented subspaces of nuclear k6the spaces always have a basis i e whether they are again isomorphic to k6the spaces see pelczyfiski 15 this is not even clear for the complemented subspaces of the space s or more generally of a power series space a a of infinite type except for special cases see 4 5 10 23 27 moreover in this case it is of interest to determine the continuity estimates of isomorphisms in particular to determine whether there are tame or linearly tame isomorphisms see 6 in the case of finite type power series spaces any complemented subspace is again a finite type power series space see mityagin 12 and mityagin henkin 13 the consequence of this for questions on the linearization of the basic constructions of complex analysis are presented in mityagin henkin 13 extensions and generalizations of the method of mityagin henkin have also been given in dubinsky 3 and krone 8 9 received by the editors march 20 1987 1980 mathematics subject classification 1 98 5 revision primary 46a45 46a 1 2 58c 1 5 1990 american mathematical society 0002 9947 90 1 00 25 per page

repeated confidence intervals for the median survival time summary we describe methods for the construction of a confidence interval for median survival time based on right censored data these methods are extended to the construction of repeated confidence intervals for the median based on accumulating data here the overall probability that all intervals contain the true median is guaranteed at a fixed level the use of repeated confidence intervals for median survival time in post marketing surveillance is discussed a confidence interval for median survival time provides a useful summary of the survival experience of a group of patients if confidence intervals are calculated repeatedly as data accumulates the probability that at least one interval fails to contain the median may be much higher than the error rate for a single interval and if these confidence intervals are used in a decision making process the probability of an incorrect decision increases accordingly jennison turnbull 1984 have proposed methods for calculating repeated confidence intervals appropriate to such situations similar ideas have also been discussed by lai 1984 in 2 we propose a new form of single sample nonparametric confidence interval this interval has asymptotically correct coverage probability and monte carlo simulations suggest it is superior to its competitors for small sample sizes repeated confidence intervals for the median are presented in 3 and their stnall sample size performance is assessed by monte carlo simulation an example of their use is given in 4 all the methods considered can easily be modified to give confidence intervals for other quantiles or for the survival probability at a fixed time

a confidence interval for the median survival time a nonparametric asymptotic confidence interval for the median survival time is developed for the case where data are subject to arbitrary right censoring this is accomplished by inverting a generalization of the sign test for censored data a simulation study shows that this nonparametric confidence interval performs well for a variety of underlying survival functions the procedure is applied to data from a clinical trial that compared f our dosage regimens of 5 uorouracil

approximate confidence intervals for probabilities of survival and quantiles in life table analysis for survival probabilities with censored data rothman 1978 journal of chronic diseases 31 557 560 has recommended the use of quadratic confidence limits based on the assumption that the product of the effective sample size at time t and the life table estimate of the survival probability past time t follows a binomial distribution this paper shows that the proposed confidence limits are asymptotically correct for continuous survival data these intervals as well as those based on the arcsine transformation the logit transformation and the log log transformation are compared by simulation to those based on greenwood s formula the usual method of interval estimation in life table analysis with large amounts of data the alternatives to the greenwood method all produce acceptable intervals on the basis of overall performance the intervals suggested by rothman are preferred for smaller samples any of these methods may be used to generate confidence sets for the median survival time or for any other quantile

accurate confidence limits for quantiles under random censoring in survival analysis estimates of median survival times in homogeneous samples are often based on the kaplan meier estimator of the survivor function confidence intervals for quantiles such as median survival are typically constructed via large sample theory or the bootstrap the former has suspect accuracy for small sample sizes under moderate censoring and the latter is computationally intensive in this paper improvements on so called test based intervals and reflected intervals cf slud byar and green 1984 biometrics 40 587 600 are sought using the edgeworth expansion for the distribution of the studentized nelson aalen estimator derived in strawderman and wells 1997 journal of the american statistical association 92 we propose a method for producing more accurate confidence intervals for quantiles with randomly censored data the intervals are very simple to compute and numerical results using simulated data show that our new test based interval outperforms commonly used methods for computing confidence intervals for small sample sizes and or heavy censoring especially with regard to maintaining specified coverage

a comparison of reflected versus test based confidence intervals for the median survival time based on censored data the small sample performance of some recently proposed nonparametric methods of constructing confidence intervals for the median survival time based on randomly right censored data is compared with that of two new methods most of these methods are equivalent for large samples all proposed intervals are either test based or reflected intervals in the sense defined in the paper coverage probabilities for the interval estimates were obtained by exact calculation for uncensored data and by stimulation for three life distributions and four censoring patterns in the range of situations studied test based methods often have less than nominal coverage while the coverage of the new reflected confidence intervals is closer to nominal although somewhat conservative and these intervals are easy to compute

survival estimation using splines a nonparametric maximum likelihood procedure is given for estimating the survivor function from right censored data it approximates the hazard rate by a simple function such as a spline with different approximations yielding different estimators a special case is that proposed by nelson 1969 journal of quality technology 1 27 52 and altshuler 1970 mathematical biosciences 6 1 11 the estimators are uniformly consistent and have the same asymptotic weak convergence properties as the kaplan meier 1958 journal of the american statistical association 53 457 481 estimator however in small and in heavily censored samples the simplest spline estimators have uniformly smaller mean squared error than do the kaplan meier and nelson altshuler estimators the procedure is extended to estimate the baseline hazard rate and regression coefficients in the cox 1972 journal of the royal statistical society series b 34 187 220 proportional hazards model and is illustrated using experimental carcinogenesis data

bootstrap type confidence intervals for quantiles of the survival distribution in this paper we outline and illustrate an easy to program method for analytically calculating both parametric and non parametric bootstrap type confidence intervals for quantiles of the survival distribution based on right censored data this new approach allows for the incorporation of covariates within the framework of parametric models the procedure is based upon the notion of fractional order statistics and is carried forth using a simple beta transformation of the estimated survival function parametric or non parametric it is the only direct method currently available in the sense that all other methods are based on inverting test statistics or employing confidence intervals for other survival quantities we illustrate that the new method has favourable coverage probabilities for median confidence intervals as compared to six other competing methods

two sample inference for median survival times based on one sample procedures for censored survival data abstract confidence intervals for median survival times are derived for censored survival data the intervals are obtained by using the quantiles of the kaplan meier product limit estimator and have the same pitman efficiency as the intervals found by inverting the sign test two sample tests and confidence intervals for the difference in median survival times are then developed based on the comparison of the one sample confidence intervals several methods for choosing the confidence coefficients of the corresponding one sample confidence intervals are developed the pitman efficiencies of these two sample tests are the same as that of the median test proposed by brookmeyer and crowley 1982a the procedures can also be used for the accelerated failure time model proportional hazard model and the behrens fisher problem nonparametric two sample inference procedures are useful in comparing the responses of treatment and control groups in medical follow up studies the data are usually subjected to cens

two sample quantile tests under general conditions summary a simple nonparametric two sample test for equality of a given collection of quantiles is developed which can be applied to a variety of empirical distribution functions including the kaplan meier estimator a self consistent estimator for doubly censored data and an estimator for repeated measures data the null hypothesis tested is that the quantiles are equal but other aspects of the distributions may diver between the two samples this procedure can also be applied to quantile testing in group sequential clinical trials with staggered patient entry a simple simulation study demonstrates that the moderate sample size properties of this procedure are reasonable

a correlation goodness of fit test for randomly censored data summary for testing a composite goodness of fit hypothesis with randomly censored data a correlation statistic which is an analogue of the shapiro francia statistic is presented the test for exponentiality in case of light censoring is asymptotically robust against departures from the koziol green model of random censorship the power of the test is compared with the total time on test procedure and the new better than used test using monte carlo simulation as an example the test is applied to some data with prostate cancer