本文提出了一种群体平均加性子分布风险模型，用于评估协变量对累积发生函数的边际效应，并分析存在竞争风险的相关失效时间数据。该方法通过纳入由目标事件之外的竞争事件导致的潜在相关删失，对群体平均加性风险模型进行了拓展。在假设独立工作相关结构的前提下，本文概述了一种用于估计回归系数的估计方程方法，并提出了一种新的三明治方差估计量。该三明治方差估计量同时考虑了失效时间之间和删失时间之间的相关性，且对每个聚类内未知依赖结构的错误设定具有稳健性。我们进一步开发了拟合优度检验，用于评估整体模型及每个协变量的子分布风险加性结构的适用性。本文通过模拟研究考察了所提方法在有限样本下的性能，并利用STrategies to Reduce Injuries and Develop confidence in Elders（STRIDE，减少老年人伤害并提升信心策略）试验的数据对方法进行了实例演示。
英文摘要：
A population-averaged additive subdistribution hazards model is proposed to assess the marginal effects of covariates on the cumulative incidence function and to analyze correlated failure time data subject to competing risks. This approach extends the population-averaged additive hazards model by accommodating potentially dependent censoring due to competing events other than the event of interest. Assuming an independent working correlation structure, an estimating equations approach is outlined to estimate the regression coefficients and a new sandwich variance estimator is proposed. The proposed sandwich variance estimator accounts for both the correlations between failure times and between the censoring times, and is robust to misspecification of the unknown dependency structure within each cluster. We further develop goodness-of-fit tests to assess the adequacy of the additive structure of the subdistribution hazards for the overall model and each covariate. Simulation studies are conducted to investigate the performance of the proposed methods in finite samples. We illustrate our methods using data from the STrategies to Reduce Injuries and Develop confidence in Elders (STRIDE) trial.
Competing risks data arise frequently in clinical trials. When the proportional subdistribution hazard assumption is violated or two cumulative incidence function (CIF) curves cross, rather than comparing the overall treatment effects, researchers may be interested in focusing on a comparison of clinical utility at some fixed time points. This paper extend a series of tests that are constructed based on a pseudo-value regression technique or different transformation functions for CIFs and their variances based on Gaynor's or Aalen's work, and the differences among CIFs at a given time point ar…
The generalization performance of a risk prediction model can be evaluated by its calibration, which measures the agreement between predicted and observed outcomes on external validation data. Here, methods for assessing the calibration of discrete time-to-event models in the presence of competing risks are proposed. The methods are designed for the class of discrete subdistribution hazard models, which directly relate the cumulative incidence function of one event of interest to a set of covariates. Simulation studies show that the methods are strong tools for calibration assessment even in s…
An individualized risk prediction model that dynamically updates the probability of a clinical event from a specific cause is valuable for physicians to be able to optimize personalized treatment strategies in real-time by incorporating all available information collected over the follow-up. However, this is more complex and challenging when competing risks are present, because it requires simultaneously updating the overall survival and the cumulative incidence functions (CIFs) while adjusting for the time-dependent covariates and time-varying covariate effects. In this study, we developed a …
Many time-to-event studies are complicated by the presence of competing risks. Such data are often analyzed using Cox models for the cause specific hazard function or Fine-Gray models for the subdistribution hazard. In practice regression relationships in competing risks data with either strategy are often complex and may include nonlinear functions of covariates, interactions, high-dimensional parameter spaces and nonproportional cause specific or subdistribution hazards. Model misspecification can lead to poor predictive performance. To address these issues, we propose a novel approach to fl…
In this paper we introduce the subdistribution beta-Stacy process, a novel Bayesian nonparametric process prior for subdistribution functions useful for the analysis of competing risks data. In particular, we i) characterize this process from a predictive perspective by means of an urn model with reinforcement, ii) show that it is conjugate with respect to right-censored data, and iii) highlight its relations with other prior processes for competing risks data. Additionally, we consider the subdistribution beta-Stacy process prior in a nonparametric regression model for competing risks data wh…
In many applications of survival data analysis, the individuals are treated in different medical centres or belong to different clusters defined by geographical or administrative regions. The analysis of such data requires accounting for between-cluster variability. Ignoring such variability would impose unrealistic assumptions in the analysis and could affect the inference on the statistical models. We develop a novel parametric mixed-effects general hazard (MEGH) model that is particularly suitable for the analysis of clustered survival data. The proposed structure generalises the mixed-effe…
For the analysis of clustered survival data, two different types of models that take the association into account, are commonly used: frailty models and copula models. Frailty models assume that conditional on a frailty term for each cluster, the hazard functions of individuals within that cluster are independent. These unknown frailty terms with their imposed distribution are used to express the association between the different individuals in a cluster. Copula models on the other hand assume that the joint survival function of the individuals within a cluster is given by a copula function, e…
In clinical and epidemiological studies, hazard ratios are often applied to compare treatment effects between two groups for survival data. For competing risks data, the corresponding quantities of interest are cause-specific hazard ratios (cHRs) and subdistribution hazard ratios (sHRs). However, they both have some limitations related to model assumptions and clinical interpretation. Therefore, we recommend restricted mean time lost (RMTL) as an alternative that is easy to interpret in a competing risks framework. Based on the difference in restricted mean time lost (RMTLd), we propose a new …
In this work, we propose a new Bayesian spatial homogeneity pursuit method for survival data under the proportional hazards model to detect spatially clustered patterns in baseline hazard and regression coefficients. Specially, regression coefficients and baseline hazard are assumed to have spatial homogeneity pattern over space. To capture such homogeneity, we develop a geographically weighted Chinese restaurant process prior to simultaneously estimate coefficients and baseline hazards and their uncertainty measures. An efficient Markov chain Monte Carlo (MCMC) algorithm is designed for our p…
In this paper, we discuss causal inference on the efficacy of a treatment or medication on a time-to-event outcome with competing risks. Although the treatment group can be randomized, there can be confoundings between the compliance and the outcome. Unmeasured confoundings may exist even after adjustment for measured co- variates. Instrumental variable (IV) methods are commonly used to yield consistent estimations of causal parameters in the presence of unmeasured confoundings. Based on a semi-parametric additive hazard model for the subdistribution hazard, we pro- pose an instrumental variab…
This paper discusses endogenous treatment models with duration outcomes, competing risks and random right censoring. The endogeneity issue is solved using a discrete instrumental variable. We show that the competing risks model generates a non-parametric quantile instrumental regression problem. The cause-specific cumulative incidence, the cause-specific hazard and the subdistribution hazard can be recovered from the regression function. A distinguishing feature of the model is that censoring and competing risks prevent identification at some quantiles. We characterize the set of quantiles for…
Many research questions involve time-to-event outcomes that can be prevented from occurring due to competing events. In these settings, we must be careful about the causal interpretation of classical statistical estimands. In particular, estimands on the hazard scale, such as ratios of cause specific or subdistribution hazards, are fundamentally hard to be interpret causally. Estimands on the risk scale, such as contrasts of cumulative incidence functions, do have a causal interpretation, but they only capture the total effect of the treatment on the event of interest; that is, effects both th…
Causal identification of treatment effects for infectious disease outcomes in interconnected populations is challenging because infection outcomes may be transmissible to others, and treatment given to one individual may affect others' outcomes. Contagion, or transmissibility of outcomes, complicates standard conceptions of treatment interference in which an intervention delivered to one individual can affect outcomes of others. Several statistical frameworks have been proposed to measure causal treatment effects in this setting, including structural transmission models, mediation-based partne…
We consider variable selection in competing risks regression for multi-center data. Our research is motivated by deceased donor kidney transplants, from which recipients would experience graft failure, death with functioning graft (DWFG), or graft survival. The occurrence of DWFG precludes graft failure from happening and therefore is a competing risk. Data within a transplant center may be correlated due to a latent center effect, such as varying patient populations, surgical techniques, and patient management. The proportional subdistribution hazard (PSH) model has been frequently used in th…
Clustered competing risks data are commonly encountered in multicenter studies. The analysis of such data is often complicated due to informative cluster size, a situation where the outcomes under study are associated with the size of the cluster. In addition, cause of failure is frequently incompletely observed in real-world settings. To the best of our knowledge, there is no methodology for population-averaged analysis with clustered competing risks data with informative cluster size and missing causes of failure. To address this problem, we consider the semiparametric marginal proportional …
Survival models incorporating random effects to account for unmeasured heterogeneity are being increasingly used in biostatistical and applied research. Specifically, unmeasured covariates whose lack of inclusion in the model would lead to biased, inefficient results are commonly modelled by including a subject-specific (or cluster-specific) frailty term that follows a given distribution (e.g. Gamma or log-Normal). Despite that, in the context of parametric frailty models little is known about the impact of misspecifying the baseline hazard, the frailty distribution, or both. Therefore, our ai…
This paper develops two orthogonal contributions to scalable sparse regression for competing risks time-to-event data. First, we study and accelerate the broken adaptive ridge method (BAR), an $\ell_0$-based iteratively reweighted $\ell_2$-penalization algorithm that achieves sparsity in its limit, in the context of the Fine-Gray (1999) proportional subdistributional hazards (PSH) model. In particular, we derive a new algorithm for BAR regression, named cycBAR, that performs cyclic update of each coordinate using an explicit thresholding formula. The new cycBAR algorithm effectively avoids fit…
Dependent survival data arise in many contexts. One context is clustered survival data, where survival data are collected on clusters such as families or medical centers. Dependent survival data also arise when multiple survival times are recorded for each individual. Frailty models is one common approach to handle such data. In frailty models, the dependence is expressed in terms of a random effect, called the frailty. Frailty models have been used with both Cox proportional hazards model and the accelerated failure time model. This paper reviews recent developments in the area of frailty mod…
Clustered observations are ubiquitous in controlled and observational studies and arise naturally in multi-centre trials or longitudinal surveys. We present a novel model for the analysis of clustered observations where the marginal distributions are described by a linear transformation model and the correlations by a joint multivariate normal distribution. The joint model provides an analytic formula for the marginal distribution. Owing to the richness of transformation models, the techniques are applicable to any type of response variable, including bounded, skewed, binary, ordinal, or survi…
