Use of log−log survival function in modeling time-covariate interactions in Cox regression

Plotting of log−log survival functions against time for different categories or combinations of categories of covariates is perhaps the easiest and most commonly used graphical tool for checking proportional hazards (PH) assumption. One problem in the utilization of the technique is that the covariates need to be categorical or made categorical through appropriate grouping of the continuous covariates. Subjectivity in the decision making on the basis of eye-judgment of the plots and frequent inconclusiveness arising in situations where the number of categories and/or covariates gets larger are among other limitations of this technique. This paper proposes a non-graphical (numerical) test of the PH assumption that makes use of log−log survival function. The test enables checking proportionality for categorical as well as continuous covariates and overcomes the other limitations of the graphical method. Observed power and size of the test are compared to some other tests of its kind through simulation experiments. Simulations demonstrate that the proposed test is more powerful than some of the most sensitive tests in the literature in a wide range of survival situations. An example of the test is given using the widely used gastric cancer data.     

Men's Participation in Family Planning Decisions in Kenya

At the beginning of the 1930's Sweden had one of the lowest reproduction rates in Europe, and a decline in population was regarded as imminent. Since then, however, developments have shown a different trend and the natural increase has become higher, the fears about a decrease in population thus being considerably lessened or entirely removed.     

A generalization of the compound rayleigh distribution: using a bayesian method on cancer survival times

In this paper the generalized compound Rayleigh model, exhibiting flexible hazard rate, is high¬lighted. This makes it attractive for modelling survival times of patients showing characteristics of a random hazard rate. The Bayes estimators are derived for the parameters of this model and some survival time parameters from a right censored sample. This is done with respect to conjugate and discrete priors on the parameters of this model, under the squared error loss function, Varian's asymmetric linear-exponential (linex) loss function and a weighted linex loss function. The future survival time of a patient is estimated under these loss functions. A Monte Carlo simu¬lation procedure is used where closed form expressions of the estimators cannot be obtained. An example illustrates the proposed estimators for this model.     

Sourcing with Deferred Payment and Inspection under Supplier Product Adulteration Risk

We study the deferred payment and inspection mechanisms for mitigating supplier product adulteration, with endogenous procurement decision and general defect discovery process. We first derive the optimal deferred payment contract, which reveals that either entire or partial deferral can arise, depending on the moral hazard severity and the information accumulation rate. Because of the supplier's incentive to adulterate, the optimal procurement quantity under deferred payment generally is smaller than the first‐best quantity. We then investigate the inspection mechanism and characterize the equilibrium. We find that under the inspection mechanism, the optimal procurement quantity is no less than the first best. A comparison between these two mechanisms shows that the deferred payment mechanism generally can outperform the inspection mechanism when either the market size is small or the profit margin is low. However, we find that these two mechanisms can also be complementary, for which we characterize a necessary condition.     

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.