Massive sized survival datasets are becoming increasingly prevalent with the development of the healthcare industry. Such datasets pose computational challenges unprecedented in traditional survival analysis use-cases. A popular way for coping with massive datasets is downsampling them to a more manageable size, such that the computational resources can be afforded by the researcher. Cox proportional hazards regression has remained one of the most popular statistical models for the analysis of survival data to-date. This work addresses the settings of right censored and possibly left truncated data with rare events, such that the observed failure times constitute only a small portion of the overall sample. We propose Cox regression subsampling-based estimators that approximate their full-data partial-likelihood-based counterparts, by assigning optimal sampling probabilities to censored observations, and including all observed failures in the analysis. Asymptotic properties of the proposed estimators are established under suitable regularity conditions, and simulation studies are carried out to evaluate the finite sample performance of the estimators. We further apply our procedure on UK-biobank colorectal cancer genetic and environmental risk factors.
Data-adaptive gene and pathway-based tests forrare-variant associations with survival outcomes
Medical College of Wisconsin（威斯康星医学院）；German Cancer Research Center (DKFZ)（德国癌症研究中心）；University of Leicester（莱斯特大学）；Instituto de Investigación Sanitaria de Santiago de Compostela（圣地亚哥-德孔波斯特拉卫生研究所）；Fundación Pública Galega de Medicina Xenómica（加利西亚公共基因组医学基金会）；Biomedical Network on Rare Diseases (CIBERER)（罕见病生物医学网络）；Icahn School of Medicine at Mount Sinai（西奈山伊坎医学院）；Cross Cancer Institute, University of Alberta（阿尔伯塔大学交叉癌症研究所）；University of Manchester（曼彻斯特大学）；Ghent University / Ghent University Hospital（根特大学/根特大学医院）
Efficient Poisson Subsampling for the Partially Linear Additive Cox Model
Nankai University（南开大学）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；University of Chinese Academy of Sciences（中国科学院大学）；Changchun University of Technology（长春工业大学）；Liaoning University（辽宁大学）；University of Connecticut（康涅狄格大学）；Tianjin University（天津大学）
The Cox regression model is a popular model for analyzing the relationship between a covariate and a survival endpoint. The standard Cox model assumes a constant covariate effect across the entire covariate domain. However, in many epidemiological and other applications, the covariate of main interest is subject to a threshold effect: a change in the slope at a certain point within the covariate domain. Often, the covariate of interest is subject to some degree of measurement error. In this paper, we study measurement error correction in the case where the threshold is known. Several bias corr…
Combining patient-level data from clinical trials can connect rare phenomena with clinical endpoints, but statistical techniques applied to a single trial may become problematical when trials are pooled. Estimating the hazard of a binary variable unevenly distributed across trials showcases a common pooled database issue. We studied how an unevenly distributed binary variable can compromise the integrity of fixed and random effects Cox proportional hazards models. We compared fixed effect and random effects Cox proportional hazards models on a set of simulated datasets inspired by a 17-trial p…
In epidemiology, identifying the effect of exposure variables in relation to a time-to-event outcome is a classical research area of practical importance. Incorporating propensity score in the Cox regression model, as a measure to control for confounding, has certain advantages when outcome is rare. However, in situations involving exposure measured with moderate to substantial error, identifying the exposure effect using propensity score in Cox models remains a challenging yet unresolved problem. In this paper, we propose an estimating equation method to correct for the exposure misclassifica…
The rapid development of computing power and efficient Markov Chain Monte Carlo (MCMC) simulation algorithms have revolutionized Bayesian statistics, making it a highly practical inference method in applied work. However, MCMC algorithms tend to be computationally demanding, and are particularly slow for large datasets. Data subsampling has recently been suggested as a way to make MCMC methods scalable on massively large data, utilizing efficient sampling schemes and estimators from the survey sampling literature. These developments tend to be unknown by many survey statisticians who tradition…
Prevalent cohort sampling is commonly used to study the natural history of a disease when the disease is rare or it usually takes a long time to observe the failure event. It is known, however, that the collected sample in this situation is not representative of the target population which in turn leads to biased sample risk sets. In addition, when survival times are subject to censoring, the censoring mechanism is informative. In this paper, I propose a pseudo-partial likelihood estimation method for estimating parameters in the Cox proportional hazards model with right-censored and biased sa…
Authentic Multinational Federated Time-to-Event Analyses Among People with HIV in Latin America
Vanderbilt University Medical Center（范德堡大学医学中心）；Pontificia Universidad Católica de Chile（智利天主教 Pontificia 大学）；Instituto Nacional de Infectologia Evandro Chagas, Fundação Oswaldo Cruz (INI-Fiocruz)（Evandro Chagas 国家传染病研究所，奥斯瓦尔多·克鲁兹基金会）；Instituto Nacional de Ciencias Médicas y Nutrición Salvador Zubirán（萨尔瓦多·祖比兰国家医学与营养科学研究所）；Johns Hopkins University（约翰斯·霍普金斯大学）；Vanderbilt University（范德堡大学）；Fundación Huésped（Huésped 基金会）；University of Pennsylvania（宾夕法尼亚大学）
We propose an extension of the regular Cox's proportional hazards model which allows the estimation of the probabilities of rare events. It is known that when the data are heavily censored at the upper end of the survival distribution, the estimation of the tail of the survival distribution is not reliable. To estimate the distribution beyond the last observed data, we suppose that the survival data are in the domain of attraction of the Fréchet distribution conditionally to covariates. Under this condition, by the Fisher-Tippett-Gnedenko theorem, the tail of the baseline distribution can be a…
Conventional methods for analyzing composite endpoints in clinical trials often only focus on the time to the first occurrence of all events in the composite. Therefore, they have inherent limitations because the individual patients' first event can be the outcome of lesser clinical importance. To overcome this limitation, the concept of the win ratio (WR), which accounts for the relative priorities of the components and gives appropriate priority to the more clinically important event, was examined. For example, because mortality has a higher priority than hospitalization, it is reasonable to…
Memorial Sloan-Kettering Cancer Center（纪念斯隆-凯特琳癌症中心）；Weill Cornell Medicine（威尔康奈尔医学院）；Erasmus Medical Center-Rotterdam（伊拉斯谟医学中心-鹿特丹）
Unlike common cancers, such as those of the prostate and breast, tumor grading in rare cancers is difficult and largely undefined because of small sample sizes, the sheer volume of time needed to undertake on such a task, and the inherent difficulty of extracting human-observed patterns. One of the most challenging examples is intrahepatic cholangiocarcinoma (ICC), a primary liver cancer arising from the biliary system, for which there is well-recognized tumor heterogeneity and no grading paradigm or prognostic biomarkers. In this paper, we propose a new unsupervised deep convolutional autoenc…
In the analysis of survival outcome supplemented with both clinical information and high-dimensional gene expression data, use of the traditional Cox proportional hazards model (1972) fails to meet some emerging needs in biomedical research. First, the number of covariates is generally much larger the sample size. Secondly, predicting an outcome based on individual gene expression is inadequate because multiple biological processes and functional pathways regulate the expression associated with a gene. Another challenge is that the Cox model assumes that populations are homogenous, implying th…
University Medical Center Göttingen（哥廷根大学医学中心）；University of Regensburg（雷根斯堡大学）；Kiel University（基尔大学）；University Medical Center Schleswig-Holstein（石勒苏益格-荷尔斯泰因大学医学中心）
Estimating the effects of interventions on patient outcome is one of the key aspects of personalized medicine. Their inference is often challenged by the fact that the training data comprises only the outcome for the administered treatment, and not for alternative treatments (the so-called counterfactual outcomes). Several methods were suggested for this scenario based on observational data, i.e.~data where the intervention was not applied randomly, for both continuous and binary outcome variables. However, patient outcome is often recorded in terms of time-to-event data, comprising right-cens…
