contrasting treatment specific survival using double robust estimators in settings where a randomized trial is infeasible observational data are frequently used to compare treatment specific survival the average causal effect ace can be used to make inference regarding treatment policies on patient populations and a valid ace estimator must account for imbalances with respect to treatment specific covariate distributions one method through which the ace on survival can be estimated involves appropriately averaging over cox regression based fitted survival functions a second available method balances the treatment specific covariate distributions through inverse probability of treatment weighting and then contrasts weighted nonparametric survival function estimators because both methods have their advantages and disadvantages we propose methods that essentially combine both estimators the proposed methods are double robust in the sense that they are consistent if at least one of the two working regression models i e logistic model for treatment and cox model for death hazard is correct the proposed methods involve estimating the ace with respect to restricted mean survival time defined as the area under the survival curve up to some prespecified time point we derive and evaluate asymptotic results through simulation we apply the proposed methods to estimate the ace of donation after cardiac death kidney transplantation with the use of data obtained from multiple centers in the netherlands

an extended hazard model with longitudinal covariates summary in clinical trials and other medical studies it has become increasingly common to observe an event time of interest and longitudinal covariates simultaneously in the literature joint modelling approaches have been employed to analyze both survival and longitudinal processes and to investigate their association early attention has mostly been placed on developing adaptive and flexible longitudinal processes based on a prespecified survival model most commonly the cox proportional model in this paper we propose a general class of semi parametric hazard regres

on the cox model with time varying regression coefficients in the analysis of censored failure time observations the standard cox proportional hazards model assumes that the regression coefficients are time invariant often these parameters vary over time and the temporal covariate effects on the failure time are of great interest in this article following previous work of cai and sun we propose a simple estimation procedure for the cox model with time varying coefficients based on a kernel weighted partial likelihood approach we construct pointwise and simultaneous confidence intervals for the regression parameters over a properly chosen time interval via a simple resampling technique we derive a prediction method for future patients survival with any specific set of covariates building on the estimates for the time varying coefficients we also consider the mixed case and present an estimation procedure for time independent parameters in the model furthermore we show how to use an integrated function of the estimate for a specific regression coeffic

joint modelling of accelerated failure time and longitudinal data summary the accelerated failure time model is an attractive alternative to the cox model when the proportionality assumption fails to capture the relationship between the survival time and longitudinal covariates several complications arise when the covariates are measured intermittently at different time points for different subjects possibly with measurement errors or measurements are not available after the failure time joint modelling of the failure time and longitudinal data offers a solution to such complications we explore the joint modelling approach under the accelerated failure time assumption when covariates are assumed to follow a linear mixed effects model with measurement errors the procedure is based on maximising the joint likelihood function with random effects treated as missing data a monte carlo em algorithm is used to estimate all the unknown parameters including the unknown baseline hazard function the performance of the proposed procedure is checked in simulation studies a case study of reproductive egg laying data for female mediterranean fruit flies and their relationship to longevity demonstrate the effectiveness of the new procedure

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

restricted mean survival time for interval censored data restricted mean survival time rmst evaluates the mean event free survival time up to a prespecified time point it has been used as an alternative measure of treatment effect owing to its model free structure and clinically meaningful interpretation of treatment benefit for right censored data in clinical trials another type of censoring called interval censoring may occur if subjects are examined at several discrete time points and the survival time falls into an interval rather than being exactly observed the missingness of exact observations under interval censored cases makes the nonparametric measure of treatment effect more challenging employing the linear smoothing technique to overcome the ambiguity we propose a new model free measure for the interval censored rmst as an alternative to the commonly used log rank test we further construct a hypothesis testing procedure to assess the survival difference between two groups simulation studies show that the bias of our proposed interval censored rmst estimator is negligible and the testing procedure delivers promising performance in detecting between group difference with regard to size and power under various configurations of survival curves the proposed method is illustrated by reanalyzing two real datasets containing interval censored observations

on the restricted mean survival time curve in survival analysis for a study with an event time as the endpoint its survival function contains all the information regarding the temporal stochastic profile of this outcome variable the survival probability at a specific time point say t however does not transparently capture the temporal profile of this endpoint up to t an alternative is to use the restricted mean survival time rmst at time t to summarize the profile the rmst is the mean survival time of all subjects in the study population followed up to t and is simply the area under the survival curve up to t the advantages of using such a quantification over the survival rate have been discussed in the setting of a fixed time analysis in this article we generalize this approach by considering a curve based on the rmst over time as an alternative summary to the survival function inference for instance based on simultaneous confidence bands for a single rmst curve and also the difference between two rmst curves are proposed the latter is informative for evaluating two groups under an equivalence or noninferiority setting and quantifies the difference of two groups in a time scale the proposal is illustrated with the data from two clinical trials one from oncology and the other from cardiology

non permutation flow shop scheduling with order acceptance and weighted tardiness model the problem of non permutation flow shop scheduling with order acceptance the model is transformed to linear mip that is optimally solved by commercial solver theorems that are favorable for developing algorithms are presented an efficient two phase genetic algorithm tp ga is proposed the heuristic yields high quality non permutation solutions this paper studies the non permutation solution for the problem of flow shop scheduling with order acceptance and weighted tardiness fss oawt we formulate the problem as a linear mixed integer programming lmip model that can be optimally solved by ampl cplex for small sized problems in addition a non linear integer programming nip model is presented to design heuristic algorithms a two phase genetic algorithm tp ga is developed to solve the problem of medium and large sizes based on the nip model the properties of fss oawt are investigated and several theorems for permutation and non permutation optimum are provided the performance of the tp ga is studied through rigorous computational experiments using a large number of numeric instances the lmip model is used to demonstrate the differences between permutation and non permutation solutions to the fss oawt problem the results show that a considerably large portion of the instances have only an optimal non permutation schedule e g 43 3 for small sized and the proposed tp ga algorithms are effective in solving the fss oawt problems of various scales small medium and large with both permutation and non permutation solutions

variance estimation when using inverse probability of treatment weighting iptw with survival analysis propensity score methods are used to reduce the effects of observed confounding when using observational data to estimate the effects of treatments or exposures a popular method of using the propensity score is inverse probability of treatment weighting iptw when using this method a weight is calculated for each subject that is equal to the inverse of the probability of receiving the treatment that was actually received these weights are then incorporated into the analyses to minimize the effects of observed confounding previous research has found that these methods result in unbiased estimation when estimating the effect of treatment on survival outcomes however conventional methods of variance estimation were shown to result in biased estimates of standard error in this study we conducted an extensive set of monte carlo simulations to examine different methods of variance estimation when using a weighted cox proportional hazards model to estimate the effect of treatment we considered three variance estimation methods i a naive model based variance estimator ii a robust sandwich type variance estimator and iii a bootstrap variance estimator we considered estimation of both the average treatment effect and the average treatment effect in the treated we found that the use of a bootstrap estimator resulted in approximately correct estimates of standard errors and confidence intervals with the correct coverage rates the other estimators resulted in biased estimates of standard errors and confidence intervals with incorrect coverage rates our simulations were informed by a case study examining the effect of statin prescribing on mortality 2016 the authors statistics in medicine published by john wiley sons ltd

efficient estimation of the distribution of quality adjusted survival time quality of life is an important aspect in evaluation of clinical trials of chronic diseases such as cancer and aids quality adjusted survival analysis is a method that combines both the quantity and quality of a patient s life into one single measure in this paper we discuss the efficiency of weighted estimators for the distribution of quality adjusted survival time using the general representation theorem for missing data processes we are able to derive an estimator that is more efficient than the one proposed in zhao and tsiatis 1997 biometrika 84 339 348 simulation experiments are conducted to assess the small sample properties of this estimator and to compare it with the semiparametric efficiency bound the value of this estimator is demonstrated from an application of the method to a data set obtained from a breast cancer clinical trial

on permutation tests for comparing restricted mean survival time with small sample from randomized trials between group comparison based on the restricted mean survival time rmst is getting attention as an alternative to the conventional logrank hazard ratio approach for time to event outcomes in randomized controlled trials rcts the validity of the commonly used nonparametric inference procedure for rmst has been well supported by large sample theories however we sometimes encounter cases with a small sample size in practice where we cannot rely on the large sample properties generally the permutation approach can be useful to handle these situations in rcts however a numerical issue arises when implementing permutation tests for difference or ratio of rmst from two groups in this article we discuss the numerical issue and consider six permutation methods for comparing survival time distributions between two groups using rmst in rcts setting we conducted extensive numerical studies and assessed type i error rates of these methods our numerical studies demonstrated that the inflation of the type i error rate of the asymptotic methods is not negligible when sample size is small and that all of the six permutation methods are workable solutions although some permutation methods became a little conservative no remarkable inflation of the type i error rates were observed we recommend using permutation tests instead of the asymptotic tests especially when the sample size is less than 50 per arm

on dynamical properties of general dynamical systems and differential inclusions abstract let f be a general dynamical system defined on a complete locally compact metric space x we give a slightly improved version of the lyapunov characterization of asymptotic stability in one of our previous works and provide a short self contained proof for the existence of arbitrarily small positively invariant neighborhoods of compact asymptotically stable sets in the present context based on these results we prove that the uniform attractors of f are connected and are stable with respect to perturbations under appropriate conditions we are also interested in the dynamical properties of differential inclusion x t f x t on r m first we show that if no solutions of the system blow up in finite future time then its reachable mapping f is a general dynamical system then we discuss some asymptotic stability properties of the system in particular we prove that if there exists a nonempty compact connected subset m of r m such that m attracts a neighborhood of itself then the system has a connected uniform attractor a we also prove that a is stable with respect to both internal and external perturbations more precisely we prove that when 0 is sufficiently small the perturbed system x t con f x t b 1 b 1 has a connected uniform attractor a moreover h a a 0 as 0 where h is the hausdorff distance in r m

nonparametric survival analysis with time dependent covariate effects a penalized partial likelihood approach techniques are developed for nonparametric analysis of data under a cox regression like model permitting time dependent covariate effects determined by a regression function beta 0 t estimators resulting from maximization of an appropriate penalized partial likelihood are shown to exist and a computational approach is outlined weak uniform consistency with a rate of convergence and pointwise asymptotic normality of the estimators are established under regularity conditions a consistent estimator of a common baseline hazard function is presented and used to construct a consistent estimator of the asymptotic variance of the estimator of the regression function extensions to multiple covariates general relative risk functions and time dependent covariates are discussed

regression models for the restricted residual mean life for right censored and left truncated data the hazard ratios resulting from a cox s regression hazards model are hard to interpret and to be converted into prolonged survival time as the main goal is often to study survival functions there is increasing interest in summary measures based on the survival function that are easier to interpret than the hazard ratio the residual mean time is an important example of those measures however because of the presence of right censoring the tail of the survival distribution is often difficult to estimate correctly therefore we consider the restricted residual mean time which represents a partial area under the survival function given any time horizon and is interpreted as the residual life expectancy up to of a subject surviving up to time t we present a class of regression models for this measure based on weighted estimating equations and inverse probability of censoring weighted estimators to model potential right censoring furthermore we show how to extend the models and the estimators to deal with delayed entries we demonstrate that the restricted residual mean life estimator is equivalent to integrals of kaplan meier estimates in the case of simple factor variables estimation performance is investigated by simulation studies using real data from danish monitoring cardiovascular risk factor surveys we illustrate an application to additive regression models and discuss the general assumption of right censoring and left truncation being dependent on covariates copyright 2017 john wiley sons ltd

on estimation of partially linear transformation models we study a general class of partially linear transformation models which extend linear transformation models by incorporating nonlinear covariate effects in survival data analysis a new martingale based estimating equation approach consisting of both global and kernel weighted local estimation equations is developed for estimating the parametric and nonparametric covariate effects in a unified manner we show that with a proper choice of the kernel bandwidth parameter one can obtain the consistent and asymptotically normal parameter estimates for the linear effects asymptotic properties of the estimated nonlinear effects are established as well we further suggest a simple resampling method to estimate the asymptotic variance of the linear estimates and show its effectiveness to facilitate the implementation of the new procedure an iterative algorithm is developed numerical examples are given to illustrate the finite sample performance of the procedure supplementary materials are available online

large sample behaviour of the product limit estimator on the whole line weak convergence results are proved for the product limit estimator on the whole line applications are given to confidence band construction estimation of mean lifetime and to the theory of q functions the results are obtained using stochastic calculus and in probability linear bounds for empirical processes

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

stabilities in multi valued dynamical systems abstract for the study of the various stabilities in multi valued dynamical systems we obtain some necessary and sufficient conditions of the notions of stability and lyapunov stability and investigate the connection between the concepts of attractions and the suitable versions of limit sets also we consider the notion of characteristic 0 in multi valued dynamical systems and obtain necessary and sufficient conditions for the concept of characteristic 0

some diagnostic methods for cox regression models through hazard smoothing in this paper some graphical methods are proposed for evaluating the fit of cox regression models in survival analysis the simplest procedure proposed is to estimate the baseline hazard separately within subgroups by applying kernel based smoothing to standard cumulative hazard estimates the different estimates should be the same to within sampling variability when the model is correct a modification of this procedure gives a direct way of calculating smooth estimates of hazard ratios over time a further modification gives estimates of ratios as a function of a continuous covariate and time the methods are applied to data taken from a clinical trial of adjuvant therapy for breast cancer

analysis of restricted mean survival time for length biased data summary in clinical studies with time to event outcomes the restricted mean survival time rmst has attracted substantial attention as a summary measurement for its straightforward clinical interpretation when the data are subject to length biased sampling which is frequently encountered in observational cohort studies existing methods to estimate the rmst are not applicable in this article we consider nonparametric and semiparametric regression methods to estimate the rmst under the setting of length biased sampling to assess the covariate effects on the rmst a semiparametric regression model that directly relates the covariates and the rmst is assumed based on the model we develop unbiased estimating equations to obtain consistent estimators of covariate effects by properly adjusting for informative censoring and length bias stochastic process theories are used to establish the asymptotic properties of the proposed estimators we investigate the finite sample performance through simulations and illustrate the methods by analyzing a prevalent cohort study of dementia in canada

a note on linear rank tests and gill and schumacher s tests of proportionality summary gill schumacher 1987 assess proportionality of hazards in the two sample case by comparing two generalized linear rank tests with different weights they consider the difference of the two linear rank statistics under proportionality the expected value of this difference is zero and its variance may be estimated the purpose of this note is to show that one can perform a similar procedure within the traditional regression setting the procedure has the advantage of generalizability to multi sample or continuous data and is computable using existing regression programs

checking the cox model with cumulative sums of martingale based residuals summary this paper presents a new class of graphical and numerical methods for checking the adequacy of the cox regression model the procedures are derived from cumulative sums of martingale based residuals over follow up time and or covariate values the distributions of these stochastic processes under the assumed model can be approximated by zero mean gaussian processes each observed process can then be compared both visually and analytically with a number of simulated realizations from the approximate null distribution these comparisons enable the data analyst to assess objectively how unusual the observed residual patterns are special attention is given to checking the functional form of a covariate the form of the link function and the validity of the proportional hazards assumption an omnibus test consistent against any model misspecification is also studied the proposed techniques are illustrated with two real data sets

adjusted kaplan meier estimator and log rank test with inverse probability of treatment weighting for survival data estimation and group comparison of survival curves are two very common issues in survival analysis in practice the kaplan meier estimates of survival functions may be biased due to unbalanced distribution of confounders here we develop an adjusted kaplan meier estimator akme to reduce confounding effects using inverse probability of treatment weighting iptw each observation is weighted by its inverse probability of being in a certain group the akme is shown to be a consistent estimate of the survival function and the variance of the akme is derived a weighted log rank test is proposed for comparing group differences of survival functions simulation studies are used to illustrate the performance of akme and the weighted log rank test the method proposed here outperforms the kaplan meier estimate and it does better than or as well as other estimators based on stratification the akme and the weighted log rank test are applied to two real examples one is the study of times to reinfection of sexually transmitted diseases and the other is the primary biliary cirrhosis pbc study

asymptotic stability in general dynamical systems general dynamical systems are used to describe multivalued contingent differential equations 5 18 191 differential equations without uniqueness 21 control systems l 5 8 9 11 14 231 and functional differential equations 131 alternative names for general dynamical systems are used in the literature among them are set valued dynamical systems 114 dispersive dynamical systems 22 and dynamical polysystems l pelczar 15 and sobanski 20 among others in the polish school considered the so called generalized pseudo dynamical systems which are basically generated dynamical systems without any continuity assumptions on the attainability maps before going further in our analysis let us pause for a moment to give the definition of a general dynamical system that will be used here

restricted mean life with adjustment for covariates abstract although the mean is the most widely used measure of location in comparing two distributions its use is essentially precluded in the presence of substantial censoring typical in survival analysis of medical therapies to accommodate censoring irwin 1949 proposed estimation of the expectation of life restricted to a time t using the actuarial estimator of the survival function in this article we examine the restricted mean as an index for comparing survival in two groups and then extend the method to incorporate covariates into the analysis for this purpose it is convenient to depart slightly from the actuarial approach and to consider piecewise exponential models asymptotic properties are explored and the assumption of piecewise exponentiality is shown to be rather mild as departures from the model have a relatively small effect on estimation of the restricted mean the methodology is illustrated using published data from a study conducted by the radiation therapy oncology group rtog

a nonparametric test to compare survival distributions with covariate adjustment summary the analysis of covariance is a technique that is used to improve the power of a k sample test by adjusting for concomitant variables if the end point is the time of survival and some observations are right censored the score statistic from the cox proportional hazards model is the method that is most commonly used to test the equality of conditional hazard functions in many situations however the proportional hazards model assumptions are not satisfied specifically the relative risk function is not time invariant or represented as a log linear function of the covariates we propose an asymptotically valid k sample test statistic to compare conditional hazard functions which does not require the assumption of proportional hazards a parametric specification of the relative risk function or randomization of group assignment simulation results indicate that the performance of this statistic is satisfactory the methodology is demonstrated on a data set in prostate cancer

diagnostic plots to reveal functional form for covariates in multiplicative intensity models abstract we show how plots based on the residuals from a proportional hazards model may be used to reveal the correct functional form for covariates in the model a smoothed plot of the martingale residues was suggested for this purpose by therneau grambsch and fleming 1990 biometrika 77 147 160 however its consistency required that the covariates be independent they also noted that the plot could be biased for large covariate effects we introduce two refinements which overcome these difficulties the first is based on a ratio of scatter plot smooths where the numerator is the smooth of the observed count plotted against the covariate and the denominator is a smooth of the expected count this is related to the arjas goodness of fit plot 1988 journal of the american statistical association 83 204 212 the second technique smooths the martingale residuals divided by the expected count using expected count as a weight this latter approach is related to a glm partial residual plot as well as to the iterative methods of hastie and tibshirani 1990 biometrics 46 1005 1016 and gentleman and crowley 1991 biometrics 47 1283 1296 applications to survival data sets are given

two branch and bound algorithms for the permutation flow shop problem abstract the objective of this paper is to present two exact methods for the permutation flow shop problem the first method is based on immediate selections and optimal adjustments of heads and tails the second method consists in recursively enumerating jobs potentially processed first inputs and jobs which would be processed last outputs on machines it is found that this second method gives better results than the first however the first method becomes more efficient when initial heads and tails are added

on the empirical choice of the time window for restricted mean survival time the t year mean survival or restricted mean survival time rmst has been used as an appealing summary of the survival distribution within a time window 0 t rmst is the patient s life expectancy until time t and can be estimated nonparametrically by the area under the kaplan meier curve up to t in a comparative study the difference or ratio of two rmsts has been utilized to quantify the between group difference as a clinically interpretable alternative summary to the hazard ratio the choice of the time window 0 t may be prespecified at the design stage of the study based on clinical considerations on the other hand after the survival data have been collected the choice of time point t could be data dependent the standard inferential procedures for the corresponding rmst which is also data dependent ignore this subtle yet important issue in this paper we clarify how to make inference about a random parameter moreover we demonstrate that under a rather mild condition on the censoring distribution one can make inference about the rmst up to t where t is less than or even equal to the largest follow up time either observed or censored in the study this finding reduces the subjectivity of the choice of t empirically the proposal is illustrated with the survival data from a primary biliary cirrhosis study and its finite sample properties are investigated via an extensive simulation study

estimating subject specific survival functions under the accelerated failure time model summary we use the semiparametric accelerated failure time model to predict the survival function and its related quantities for future subjects with a given set of covariates we derive the large sample distribution for the subject specific cumulative hazard function estimate we then propose a simple resampling technique for constructing pointwise confidence intervals and simultaneous bands for the corresponding survival function and its quantile function over a properly selected time interval the new proposals are illustrated with the mayo primary biliary cirrhosis data

score tests for homogeneity of regression effect in the proportional hazards model a simple model containing the proportional hazards regression model as a special case is presented the purpose of the model is to provide a framework in which specific alternatives to the proportional hazards assumption may be tested rank invariant score tests for linear quadratic or exponential trends can for instance all be undertaken within this framework in the case of the two sample problem the required calculations are shown to take a particularly simple form special consideration is given to the two sample case in which there is an inversion of the regression effect i e where the hazard functions cross at some given point both of the motivating examples are concerned with this problem computational aspects are relatively straightforward and some discussion on this is provided

causal inference on the difference of the restricted mean lifetime between two groups summary when comparing survival times between two treatment groups it may be more appropriate to compare the restricted mean lifetime i e the expectation of lifetime restricted to a time l rather than mean lifetime in order to accommodate censoring when the treatments are not assigned to patients randomly as in observational studies we also need to account for treatment imbalances in confounding factors in this article we propose estimators for the difference of the restricted mean lifetime between two groups that account for treatment imbalances in prognostic factors assuming a proportional hazards relationship large sample properties of our estimators based on martingale theory for counting processes are also derived simulation studies were conducted to compare these estimators and to assess the adequacy of the large sample approximations our methods are also applied to an observational database of acute coronary syndrome patients from duke university medical center to estimate the treatment effect on the restricted mean lifetime over 5 years

decomposition of number of life years lost according to causes of death we study the competing risks model and show that the cause j cumulative incidence function integrated from 0 to has a natural interpretation as the expected number of life years lost due to cause j before time this is analogous to the restricted mean lifetime which is the survival function integrated from 0 to it is discussed how the number of years lost may be related to subject specific explanatory variables in a regression model based on pseudo observations and the method is exemplified using data from a bone marrow transplantation study finally inclusion of standard mortality rates is discussed copyright 2013 john wiley sons ltd

a consistent estimator for the distribution of quality adjusted survival time summary quality adjusted survival analysis is a new approach to therapy evaluation in clinical trials it has received much attention recently because of its ability to take patients quality of life into consideration in this paper we present a method that enables us to calculate the survival distribution of quality adjusted lifetime using martingale theory for counting processes we can show that our estimator is asymptotically consistent normally distributed and its asymptotic variance estimate can be obtained analytically simulation experiments are conducted to compare our estimator with the true underlying distribution for two cases that are of practical importance

calibrating parametric subject specific risk estimation for modern evidence based medicine decisions on disease prevention or management strategies are often guided by a risk index system for each individual the system uses his her baseline information to estimate the risk of experiencing a future disease related clinical event such a risk scoring scheme is usually derived from an overly simplified parametric model to validate a model based procedure one may perform a standard global evaluation via for instance a receiver operating characteristic analysis in this article we propose a method to calibrate the risk index system at a subject level specifically we developed point and interval estimation procedures for t year mortality rates conditional on the estimated parametric risk score the proposals are illustrated with a dataset from a large clinical trial with post myocardial infarction patients

a clinical trial design using the concept of proportional time using the generalized gamma ratio distribution traditional methods of sample size and power calculations in clinical trials with a time to event end point are based on the logrank test and its variations cox proportional hazards ph assumption or comparison of means of 2 exponential distributions of these sample size calculation based on ph assumption is likely the most common and allows adjusting for the effect of one or more covariates however when designing a trial there are situations when the assumption of ph may not be appropriate additionally when it is known that there is a rapid decline in the survival curve for a control group such as from previously conducted observational studies a design based on the ph assumption may confer only a minor statistical improvement for the treatment group that is neither clinically nor practically meaningful for such scenarios a clinical trial design that focuses on improvement in patient longevity is proposed based on the concept of proportional time using the generalized gamma ratio distribution simulations are conducted to evaluate the performance of the proportional time method and to identify the situations in which such a design will be beneficial as compared to the standard design using a ph assumption piecewise exponential hazards assumption and specific cases of a cure rate model a practical example in which hemorrhagic stroke patients are randomized to 1 of 2 arms in a putative clinical trial demonstrates the usefulness of this approach by drastically reducing the number of patients needed for study enrollment

sample size and power for the weighted log rank test and kaplan meier based tests with allowance for nonproportional hazards asymptotic distributions under alternative hypotheses and their corresponding sample size and power equations are derived for nonparametric test statistics commonly used to compare two survival curves test statistics include the weighted log rank test and the wald test for difference in or ratio of kaplan meier survival probability percentile survival and restricted mean survival time accrual survival and loss to follow up are allowed to follow any arbitrary continuous distribution we show that schoenfeld s equation often used by practitioners to calculate the required number of events for the unweighted log rank test can be inaccurate even when the proportional hazards ph assumption holds in fact it can mislead one to believe that 1 1 is the optimal randomization ratio rr when actually power can be gained by assigning more patients to the active arm meaningful improvements to schoenfeld s equation are made the present theory should be useful in designing clinical trials particularly in immuno oncology where nonproportional hazards are frequently encountered we illustrate the application of our theory with an example exploring optimal rr under ph and a second example examining the impact of delayed treatment effect a companion r package npsurvss is available for download on cran

asymptotic properties of a general class of nonparametric tests for survival analysis many of the popular nonparametric test statistics for censored survival data used in two sample s sample trend and single continuous covariate situations are special cases of a general statistic differing only in the choice of covariate based label and weight function formulated in terms of counting processes and martingales this general statistic standardized by the square root of its consistent variance estimator is shown to be asymptotically normal under the null hypothesis and under a sequence of contiguous hazard alternatives that includes both relative and excess risk models

testing causal effects in observational survival data using propensity score matching design time to event data are very common in observational studies unlike randomized experiments observational studies suffer from both observed and unobserved confounding biases to adjust for observed confounding in survival analysis the commonly used methods are the cox proportional hazards ph model the weighted logrank test and the inverse probability of treatment weighted cox ph model these methods do not rely on fully parametric models but their practical performances are highly influenced by the validity of the ph assumption also there are few methods addressing the hidden bias in causal survival analysis we propose a strategy to test for survival function differences based on the matching design and explore sensitivity of the p values to assumptions about unmeasured confounding specifically we apply the paired prentice wilcoxon ppw test or the modified ppw test to the propensity score matched data simulation studies show that the ppw type test has higher power in situations when the ph assumption fails for potential hidden bias we develop a sensitivity analysis based on the matched pairs to assess the robustness of our finding following rosenbaum s idea for nonsurvival data for a real data illustration we apply our method to an observational cohort of chronic liver disease patients from a mayo clinic study the ppw test based on observed data initially shows evidence of a significant treatment effect but this finding is not robust as the sensitivity analysis reveals that the p value becomes nonsignificant if there exists an unmeasured confounder with a small impact

regression by local fitting methods properties and computational algorithms abstract local regression is a procedure for estimating regression surfaces by the local fitting of linear or quadratic functions of the independent variables in a moving fashion that is analogous to how a moving average is computed for a time series the advantage of the methodology over the global fitting of parametric functions of the independent variables by least squares the current paradigm in regression studies is that a much wider class of regression functions can be estimated without distortion in this paper we discuss the methods their statistical properties and computational algorithms

goodness of fit analysis for the cox regression model based on a class of parameter estimators abstract in this article we propose a class of estimation functions for the vector of regression parameters in the cox proportional hazards model with possibly time dependent covariates by incorporating the weight functions commonly used in weighted log rank tests into the partial likelihood score function the resulting estimators behave much like the conventional maximum partial likelihood estimator in that they are consistent and asymptotically normal when the cox model is inappropriate however the estimators with different weight functions generally converge to nonidentical constant vectors for example the magnitude of the parameter estimator using the kaplan meier survival estimator as the weight function will be stochastically larger than that of the maximum partial likelihood estimator if covariate effects diminish over time such facts motivate us to develop goodness of fit methods for the cox regression model by comparing parameter estimators with different weight functions under the assume

balance diagnostics for comparing the distribution of baseline covariates between treatment groups in propensity score matched samples the propensity score is a subject s probability of treatment conditional on observed baseline covariates conditional on the true propensity score treated and untreated subjects have similar distributions of observed baseline covariates propensity score matching is a popular method of using the propensity score in the medical literature using this approach matched sets of treated and untreated subjects with similar values of the propensity score are formed inferences about treatment effect made using propensity score matching are valid only if in the matched sample treated and untreated subjects have similar distributions of measured baseline covariates in this paper we discuss the following methods for assessing whether the propensity score model has been correctly specified comparing means and prevalences of baseline characteristics using standardized differences ratios comparing the variance of continuous covariates between treated and untreated subjects comparison of higher order moments and interactions five number summaries and graphical methods such as quantile quantile plots side by side boxplots and non parametric density plots for comparing the distribution of baseline covariates between treatment groups we describe methods to determine the sampling distribution of the standardized difference when the true standardized difference is equal to zero thereby allowing one to determine the range of standardized differences that are plausible with the propensity score model having been correctly specified we highlight the limitations of some previously used methods for assessing the adequacy of the specification of the propensity score model in particular methods based on comparing the distribution of the estimated propensity score between treated and untreated subjects are uninformative

estimating differences in restricted mean lifetime using observational data subject to dependent censoring in epidemiologic studies of time to an event mean lifetime is often of direct interest we propose methods to estimate group e g treatment specific differences in restricted mean lifetime for studies where treatment is not randomized and lifetimes are subject to both dependent and independent censoring the proposed methods may be viewed as a hybrid of two general approaches to accounting for confounders specifically treatment specific proportional hazards models are employed to account for baseline covariates while inverse probability of censoring weighting is used to accommodate time dependent predictors of censoring the average causal effect is then obtained by averaging over differences in fitted values based on the proportional hazards models large sample properties of the proposed estimators are derived and simulation studies are conducted to assess their finite sample applicability we apply the proposed methods to liver wait list mortality data from the scientific registry of transplant recipients

proportional hazards tests and diagnostics based on weighted residuals summary nonproportional hazards can often be expressed by extending the cox model to include time varying coefficients e g for a single covariate the hazard function for subject i is modelled as exp fl t zi t a common example is a treatment effect that decreases with time we show that the function 3 t can be directly visualized by smoothing an appropriate residual plot also many tests of proportional hazards including those of cox 1972 gill schumacher 1987 harrell 1986 lin 1991 moreau o quigley mesbah 1985 nagelkerke oosting hart 1984 o quigley pessione 1989 schoenfeld 1980 and wei 1984 are related to time weighted score tests of the proportional hazards hypothesis and can be visualized as a weighted least squares line fitted to the residual plot

adjusted restricted mean survival times in observational studies in observational studies with censored data exposure outcome associations are commonly measured with adjusted hazard ratios from multivariable cox proportional hazards models the difference in restricted mean survival times rmsts up to a pre specified time point is an alternative measure that offers a clinically meaningful interpretation several regression based methods exist to estimate an adjusted difference in rmsts but they digress from the model free method of taking the area under the survival function we derive the adjusted rmst by integrating an adjusted kaplan meier estimator with inverse probability weighting ipw the adjusted difference in rmsts is the area between the two ipw adjusted survival functions in a monte carlo type simulation study we demonstrate that the proposed estimator performs as well as two regression based approaches the ancova type method of tian et al and the pseudo observation method of andersen et al we illustrate the methods by reexamining the association between total cholesterol and the 10 year risk of coronary heart disease in the framingham heart study

a branch and bound algorithm with fuzzy inference for a permutation flowshop scheduling problem abstract this paper considers an m machine permutation flowshop scheduling problem of minimizing the makespan this classical scheduling problem is still important in modern manufacturing systems and is well known to be intractable i e np hard in fact branch and bound algorithms developed so far for this problem have not come to solve large scale problem instances with over a hundred jobs in order to improve the performance of branch and bound algorithms this paper proposes a new dominance relation by which the search load could be reduced and notices that it is based on a sufficient precondition this suggests that the dominance relation holds with high possibility even if the precondition approximately holds thus being more realistic the branch and bound algorithm proposed here takes advantage of this possibility for obtaining an optimal solution as early as possible in the branch and bound search for this purpose this paper utilizes membership functions in the context of the fuzzy inference extensive numerical experiments that were executed through monte carlo simulations and benchmark tests show that the developed branch and bound algorithm can solve 3 machine problem instances with up to 1000 jobs with probability of over 99 and 4 machine ones with up to 900 jobs with over 97

martingale based residuals for survival models summary graphical methods based on the analysis of residuals are considered for the setting of the highly used cox 1972 regression model and for the andersen gill 1982 generalization of that model we start with a class of martingale based residuals as proposed by barlow prentice 1988 these residuals and or their transforms are useful for investigating the functional form of a covariate the proportional hazards assumption the leverage of each subject upon the estimates of 13 and the lack of model fit to a given subject 1 1 model consider a set of n independent subjects such that the counting process ni ni t t o for the ith subject in the set indicates the number of observed events experienced over time t the sample paths of the ni are step functions with jumps of size 1 and with ni 0 0 we assume that the intensity function for ni t is given by yi t da t zi t yi t ep z t dao t 1 where yi t is a 0 1 process indicating whether the ith subject is a risk at time t 13 is a vector of regression coefficients zi t is a p dimensional vector of covariate processes and ao is the baseline cumulative hazard function several familar survival models fit into this framework the andersen gill 1982 generalization of the cox 1972 model arises when ao t is completely unspecified the further restriction that yi t 1 until the first event or censoring and is 0 thereafter yields the cox model the parametric form ao t t yields a poisson model or an exponential if restricted to a single event per subject and ao t tp a weibull model our attention will focus primarily on the andersen gill and cox models however the

a simple test for goodness of fit of cox s proportional hazards model cox s proportional hazards model for survival analysis 1972 has gained widespread attention from both applied and theoretical statisticians and is central to most work on survival analysis to verify the assumption of proportional hazards underlying the model several methods have recently been put forward cox 1979 schoenfeld 1980 andersen 1982 kalbfleisch and prentice 1980 these methods consist either of graphical techniques designed so as to visualize departures from the proportional hazards ph assumption or of formal tests based on parameterizing the interaction between covariates and time in this paper a simple test statistic is proposed for detecting departures from the ph assumption the proposed test is computationally and conceptually straightforward expressions for the first two moments of the test statistic are presented

restricted mean life with covariates modification and extension of a useful survival analysis method abstract karrison has presented a method for covariate adjusted comparison of two groups with respect to survival when the group effect is expected to not be of proportional hazards form this article describes a simplified procedure for implementing karrison s basic approach along with an extended version designed to achieve robustness against misspecification in the underlying analytical model a simulation study of these techniques is presented and the techniques are illustrated with an example taken from karrison

confidence bands for survival functions with censored data a comparative study consider the problem of obtaining simultaneous confidence bands for the survival function s x when the data are arbitrarily right censored the usual pointwise confidence intervals based on greenwood s variance formula can be adapted to yield a large sample confidence band this band has in a certain sense equal precision at each point of s x it is compared with the censored versions of the kolmogorov band and the renyi band the comparisons are made in terms of the widths and the adequacy of large sample approximations and are carried out under various censoring models and degrees of censoring the bands are illustrated by applying them to data from a mechanical switch life test

double robust semiparametric estimator for differences in restricted mean lifetimes in observational studies restricted mean lifetime is often of direct interest in epidemiologic studies involving censored survival times differences in this quantity can be used as a basis for comparing several groups for example transplant surgeons nephrologists and of course patients are interested in comparing posttransplant lifetimes among various types of kidney transplants to assist in clinical decision making as the factor of interest is not randomized covariate adjustment is needed to account for imbalances in confounding factors in this report we use semiparametric theory to develop an estimator for differences in restricted mean lifetimes although accounting for confounding factors the proposed method involves building working models for the time to event and coarsening mechanism i e group assignment and censoring we show that the proposed estimator possesses the double robust property i e when either the time to event or coarsening process is modeled correctly the estimator is consistent and asymptotically normal simulation studies are conducted to assess its finite sample performance and the method is applied to national kidney transplant data

some efficient heuristic methods for the flow shop sequencing problem abstract in this paper the best heuristic methods known up to now are compared to solve the flow shop sequencing problem and we improve the complexity of the best one next this problem is applied to taboo search a new technique to solve combinatorial optimization problems and computational experiments are reported finally a parallel taboo search algorithm is presented and experimental results show that this heuristic allows very good speed up

robust alternatives to ancova for estimating the treatment effect via a randomized comparative study in comparing two treatments via a randomized clinical trial the analysis of covariance ancova technique is often utilized to estimate an overall treatment effect the ancova is generally perceiv

testing goodness of fit for proportional hazards model with censored observations abstract a numerical omnibus test of fit for the two sample proportional hazards model is proposed for randomly censored observations the test is derived from cox s partial likelihood and does not need a dummy time dependent covariate or any partition of the time axis consistency of the test is established examples are provided for illustration

a computational study with a new algorithm for the three machine permutation flow shop problem with release times abstract we consider the three machine permutation flow shop scheduling problem with release times where the objective is to minimize the maximum completion time a special solvable case is found for the f 2 r j c max problem which sharpens the boundary between easy and hard cases and can be used to compute a tight lower bound for our problem two dominance rules are generalized and applied to generating initial schedules directing the search strategy and decomposing the problem into smaller ones the branch and bound algorithm proposed here combines an adaptive branching rule with a fuzzy search strategy to narrow the search tree and lead the search to an optimal solution as early as possible our extensive numerical experiments have led to a classification of easy vs hard problems dependent only on the relative size of the release times the algorithm has quickly solved approximately 90 of the hardest test problem instances with up to 200 jobs and 100 of the large problems classified as easy

martingale difference residuals as a diagnostic tool for the cox model the proportional hazards model makes two major assumptions the hazard ratio is constant over time and the relationship between the hazard and continuous covariates is log linear methods exist for checking and relaxing each of these assumptions but in both cases the methods rely on the other assumption being true problems can occur if neither of the assumptions is appropriate or even if only one of the assumptions is appropriate but it is not known which we propose a new kind of residual for checking the two assumptions simultaneously the smoothed residuals provide a flexible estimate of the hazard ratio which may deviate from the standard proportional hazards model by having a time dependent hazard ratio transformed covariates or both the methods are illustrated using data from the medical research council s myeloma trials

double inverse weighted estimation of cumulative treatment effects under nonproportional hazards and dependent censoring in medical studies of time to event data nonproportional hazards and dependent censoring are very common issues when estimating the treatment effect a traditional method for dealing with time dependent treatment effects is to model the time dependence parametrically limitations of this approach include the difficulty to verify the correctness of the specified functional form and the fact that in the presence of a treatment effect that varies over time investigators are usually interested in the cumulative as opposed to instantaneous treatment effect in many applications censoring time is not independent of event time therefore we propose methods for estimating the cumulative treatment effect in the presence of nonproportional hazards and dependent censoring three measures are proposed including the ratio of cumulative hazards relative risk and difference in restricted mean lifetime for each measure we propose a double inverse weighted estimator constructed by first using inverse probability of treatment weighting iptw to balance the treatment specific covariate distributions then using inverse probability of censoring weighting ipcw to overcome the dependent censoring the proposed estimators are shown to be consistent and asymptotically normal we study their finite sample properties through simulation the proposed methods are used to compare kidney wait list mortality by race

regression calibration in semiparametric accelerated failure time models summary in large cohort studies it often happens that some covariates are expensive to measure and hence only measured on a validation set on the other hand relatively cheap but error prone measurements of the covariates are available for all subjects regression calibration rc estimation method prentice 1982 biometrika 69 331 342 is a popular method for analyzing such data and has been applied to the cox model by wang et al 1997 biometrics 53 131 145 under normal measurement error and rare disease assumptions in this article we consider the rc estimation method for the semiparametric accelerated failure time model with covariates subject to measurement error asymptotic properties of the proposed method are investigated under a two phase sampling scheme for validation data that are selected via stratified random sampling resulting in neither independent nor identically distributed observations we show that the estimates converge to some well defined parameters in particular unbiased estimation is feasible under additive normal measurement error models for normal covariates and under berkson error models the proposed method performs well in finite sample simulation studies we also apply the proposed method to a depression mortality study

on dynamical stability in general dynamical systems this paper is concerned with dynamical stability of general dynamical systems we discuss invariance properties of some limit sets investigate connections between various notions and definitions related to stability and attraction properties and establish existence results for invariant uniform attractors we also give a characterization of asymptotic stability of general dynamical systems via uniformly unbounded lyapunov functions