Semiparametric regression methods for temporal processes subject to multiple sources of censoring

Process regression methodology is underdeveloped relative to the frequency with which pertinent data arise. In this article, the response-190 is a binary indicator process representing the joint event of being alive and remaining in a specific state. The process is indexed by time (e.g., time since diagnosis) and observed continuously. Data of this sort occur frequently in the study of chronic disease. A general area of application involves a recurrent event with non-negligible duration (e.g., hospitalization and associated length of hospital stay) and subject to a terminating event (e.g., death). We propose a semiparametric multiplicative model for the process version of the probability of being alive and in the (transient) state of interest. Under the proposed methods, the regression parameter is estimated through a procedure that does not require estimating the baseline probability. Unlike the majority of process regression methods, the proposed methods accommodate multiple sources of censoring. In particular, we derive a computationally convenient variant of inverse probability of censoring weighting based on the additive hazards model. We show that the regression parameter estimator is asymptotically normal, and that the baseline probability function estimator converges to a Gaussian process. Simulations demonstrate that our estimators have good finite sample performance. We apply our method to national end-stage liver disease data. The Canadian Journal of Statistics 48: 222–237; 2020 © 2019 Statistical Society of Canada     

A visualization method measuring the performance of biomarkers for guiding treatment decisions

Biomarkers that predict efficacy and safety for a given drug therapy become increasingly important for treatment strategy and drug evaluation in personalized medicine. Methodology for appropriately identifying and validating such biomarkers is critically needed, although it is very challenging to develop, especially in trials of terminal diseases with survival endpoints. The marker‐by‐treatment predictiveness curve serves this need by visualizing the treatment effect on survival as a function of biomarker for each treatment. In this article, we propose the weighted predictiveness curve (WPC). Based on the nature of the data, it generates predictiveness curves by utilizing either parametric or nonparametric approaches. Especially for nonparametric predictiveness curves, by incorporating local assessment techniques, it requires minimum model assumptions and provides great flexibility to visualize the marker‐by‐treatment relationship. WPC can be used to compare biomarkers and identify the one with the highest potential impact. Equally important, by simultaneously viewing several treatment‐specific predictiveness curves across the biomarker range, WPC can also guide the biomarker‐based treatment regimens. Simulations representing various scenarios are employed to evaluate the performance of WPC. Application on a well‐known liver cirrhosis trial sheds new light on the data and leads to discovery of novel patterns of treatment biomarker interactions. Copyright © 2015 John Wiley & Sons, Ltd.     

抗日文学光环掩盖下的文革

何顿的抗日题材长篇小说《来生再见》,其写作的重心不在抗日,而在文革;作家关注的不是历史,而是普通人在极端政治条件下人性的挣扎。生存环境险恶严酷的抗战时期,主人公黄抗日能够应用自己的生存哲学虎口脱身,回到家中安静地生活;但在文革的政治环境下,他却被逼得装疯、吃屎,家破人亡,生活、人格肢解得体无完肤。作品通过这种对比竖起了一座文革无字碑,形成对文革无言的控诉。     

A Note on the Large Sample Properties of Estimators Based on Generalized Linear Models for Correlated Pseudo‐observations

Pseudo‐values have proven very useful in censored data analysis in complex settings such as multi‐state models. It was originally suggested by Andersen et al., Biometrika, 90, 2003, 335 who also suggested to estimate standard errors using classical generalized estimating equation results. These results were studied more formally in Graw et al., Lifetime Data Anal., 15, 2009, 241 that derived some key results based on a second‐order von Mises expansion. However, results concerning large sample properties of estimates based on regression models for pseudo‐values still seem unclear. In this paper, we study these large sample properties in the simple setting of survival probabilities and show that the estimating function can be written as a U‐statistic of second order giving rise to an additional term that does not vanish asymptotically. We further show that previously advocated standard error estimates will typically be too large, although in many practical applications the difference will be of minor importance. We show how to estimate correctly the variability of the estimator. This is further studied in some simulation studies.     

Subgroup Analysis with Time‐to‐Event Data Under a Logistic‐Cox Mixture Model

Subgroup detection has received increasing attention recently in different fields such as clinical trials, public management and market segmentation analysis. In these fields, people often face time‐to‐event data, which are commonly subject to right censoring. This paper proposes a semiparametric Logistic‐Cox mixture model for subgroup analysis when the interested outcome is event time with right censoring. The proposed method mainly consists of a likelihood ratio‐based testing procedure for testing the existence of subgroups. The expectation–maximization iteration is applied to improve the testing power, and a model‐based bootstrap approach is developed to implement the testing procedure. When there exist subgroups, one can also use the proposed model to estimate the subgroup effect and construct predictive scores for the subgroup membership. The large sample properties of the proposed method are studied. The finite sample performance of the proposed method is assessed by simulation studies. A real data example is also provided for illustration.     

Collective versus Individual Effects in Survival Analysis of Multiple Failures

In survival analysis, we sometimes encounter data with multiple censored outcomes. Under certain scenarios, partial or even all covariates have ‘similar’ relative risks on the multiple outcomes in the Cox regression analysis. The similarity in covariate effects can be quantified using the proportionality of regression coefficients. Identifying the proportionality structure, or equivalently whether covariates have individual or collective effects, may have important scientific implications. In addition, it can lead to a smaller set of unknown parameters, which in turn results in more accurate estimation. In this article, we develop a novel approach for identifying the proportionality structure. Simulation shows the satisfactory performance of the proposed approach and its advantage over estimation under no assumed structure. We analyse three datasets to demonstrate the practical application of the proposed approach.     

Symmetrical Design of Experiment in Global Sensitivity Analysis Based on ANOVA High-dimensional Model Representation

This article reviews symmetrical global sensitivity analysis based on the analysis of variance of high-dimensional model representation. To overcome the computational difficulties and explore the use of symmetrical design of experiment (SDOE), two methods are presented. If the form of the objective function f is known, we use SDOE to estimate the symmetrical global sensitivity indices instead of Monte Carlo or quasi-Monte Carlo simulation. Otherwise, we use the observed values of the experiment to do symmetrical global sensitivity analysis. These methods are easy to implement and can reduce the computational cost. An example is given by symmetrical design of experiment.     

Unified multivariate survival model with a surviving fraction: an application to a Brazilian customer churn data

In this paper we propose a new lifetime model for multivariate survival data in presence of surviving fractions and examine some of its properties. Its genesis is based on situations in which there are m types of unobservable competing causes, where each cause is related to a time of occurrence of an event of interest. Our model is a multivariate extension of the univariate survival cure rate model proposed by Rodrigues et al. [37 J. Rodrigues, V.G. Cancho, M. de Castro, and F. Louzada-Neto, On the unification of long-term survival models, Statist. Probab. Lett. 79 (2009), pp. 753–759. doi: 10.1016/j.spl.2008.10.029[Crossref], [Web of Science ®] , [Google Scholar]]. The inferential approach exploits the maximum likelihood tools. We perform a simulation study in order to verify the asymptotic properties of the maximum likelihood estimators. The simulation study also focus on size and power of the likelihood ratio test. The methodology is illustrated on a real data set on customer churn data.     

Influence diagnostics for the Weibull-Negative-Binomial regression model with cure rate under latent failure causes

In this paper, we propose a flexible cure rate survival model by assuming that the number of competing causes of the event of interest follows the Negative Binomial distribution and the time to event follows a Weibull distribution. Indeed, we introduce the Weibull-Negative-Binomial (WNB) distribution, which can be used in order to model survival data when the hazard rate function is increasing, decreasing and some non-monotonous shaped. Another advantage of the proposed model is that it has some distributions commonly used in lifetime analysis as particular cases. Moreover, the proposed model includes as special cases some of the well-know cure rate models discussed in the literature. We consider a frequentist analysis for parameter estimation of a WNB model with cure rate. Then, we derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and present some ways to perform global influence analysis. Finally, the methodology is illustrated on a medical data.     

Graphical representation of survival curves in the presence of time-dependent categorical covariates with application to liver transplantation

Graphical representation of survival curves is often used to illustrate associations between exposures and time-to-event outcomes. However, when exposures are time-dependent, calculation of survival probabilities is not straightforward. Our aim was to develop a method to estimate time-dependent survival probabilities and represent them graphically. Cox models with time-dependent indicators to represent state changes were fitted, and survival probabilities were plotted using pre-specified times of state changes. Time-varying hazard ratios for the state change were also explored. The method was applied to data from the Adult-to-Adult Living Donor Liver Transplantation Cohort Study (A2ALL). Survival curves showing a ‘split’ at a pre-specified time t allow for the qualitative comparison of survival probabilities between patients with similar baseline covariates who do and do not experience a state change at time t. Time since state change interactions can be visually represented to reflect changing hazard ratios over time. A2ALL study results showed differences in survival probabilities among those who did not receive a transplant, received a living donor transplant, and received a deceased donor transplant. These graphical representations of survival curves with time-dependent indicators improve upon previous methods and allow for clinically meaningful interpretation.