Kaplan-Meier survival analysis represents the most objective measure of treatment efficacy in oncology, though subjected to potential bias, which is worrisome in an era of precision medicine. Independent of the bias inherent to the design and execution of clinical trials, bias may be the result of patient censoring, or incomplete observation. Unlike disease/progression free survival, overall survival is based on a well defined time point and thus avoids interval censoring, but right-censoring, due to incomplete follow-up, may still be a source of bias. We study three mechanisms of right-censoring and find that one of them, surrogate of patient lost to follow-up, is able to impact Kaplan-Meier survival, improving significantly the estimation of survival in comparison with complete follow-up datasets, as measured by the hazard ratio. We also present two bias indexes able to signal datasets with right-censoring associated overestimation of survival. These bias indexes can detect bias in public available datasets
Factorial analyses offer a powerful nonparametric means to detect main or interaction effects among multiple treatments. For survival outcomes, e.g. from clinical trials, such techniques can be adopted for comparing reasonable quantifications of treatment effects. The key difficulty to solve in survival analysis concerns the proper handling of censoring. So far, all existing factorial analyses for survival data were developed under the independent censoring assumption, which is too strong for many applications. As a solution, the central aim of this article is to develop new methods in factori…
The analysis of randomized trials with time-to-event endpoints is nearly always plagued by the problem of censoring. As the censoring mechanism is usually unknown, analyses typically employ the assumption of non-informative censoring. While this assumption usually becomes more plausible as more baseline covariates are being adjusted for, such adjustment also raises concerns. Pre-specification of which covariates will be adjusted for (and how) is difficult, thus prompting the use of data-driven variable selection procedures, which may impede valid inferences to be drawn. The adjustment for cova…
One goal in survival analysis of right-censored data is to estimate the marginal survival function in the presence of dependent censoring. When many auxiliary covariates are sufficient to explain the dependent censoring, estimation based on either a semiparametric model or a nonparametric model of the conditional survival function can be problematic due to the high dimensionality of the auxiliary information. In this paper, we use two working models to condense these high-dimensional covariates in dimension reduction; then an estimate of the marginal survival function can be derived nonparamet…
Dependent Censoring Based on Geometric Optimization
Université Lumière Lyon 2（里昂第二大学）；Université Lyon 1（里昂第一大学）；ERIC（教育、社会与文化研究中心）；Université de Technologie de Compiègne（贡比涅技术大学）；LMAC（数学与计算力学实验室）；École d’Ingénieur Généraliste ESME（ESME工程师学院）
We present a new estimator of the restricted mean survival time in randomized trials where there is right censoring that may depend on treatment and baseline variables. The proposed estimator leverages prognostic baseline variables to obtain equal or better asymptotic precision compared to traditional estimators. Under regularity conditions and random censoring within strata of treatment and baseline variables, the proposed estimator has the following features: (i) it is interpretable under violations of the proportional hazards assumption; (ii) it is consistent and at least as precise as the …
In heterogeneous cohorts and those where censoring by non-primary risks is informative many conventional survival analysis methods are not applicable; the proportional hazards assumption is usually violated at population level and the observed crude hazard rates are no longer estimators of what they would have been in the absence of other risks. In this paper, we develop a fully Bayesian survival analysis to determine the probabilistically optimal description of a heterogeneous cohort and we propose a novel means of recovering hazard rates and survival functions `decontaminated' of the effects…
Methods for the evaluation of the predictive accuracy of biomarkers with respect to survival outcomes subject to right censoring have been discussed extensively in the literature. In cancer and other diseases, survival outcomes are commonly subject to interval censoring by design or due to the follow up schema. In this paper, we present an estimator for the area under the time-dependent receiver operating characteristic ROC curve for interval censored data based on a nonparametric sieve maximum likelihood approach. We establish the asymptotic properties of the proposed estimator, and illustrat…
In this paper, we consider a novel framework of positive-unlabeled data in which as positive data survival times are observed for subjects who have events during the observation time as positive data and as unlabeled data censoring times are observed but whether the event occurs or not are unknown for some subjects. We consider two cases: (1) when censoring time is observed in positive data, and (2) when it is not observed. For both cases, we developed parametric models, nonparametric models, and machine learning models and the estimation strategies for these models. Simulation studies show th…
Doubly Robust Conformalized Survival Analysis with Right-Censored Data
Department of Data Sciences and Operations（数据科学与运营系）；Department of Computer Science, University of Southern California（计算机科学系，南加州大学）；Merck & Co., Inc.（默克公司）
University of Maryland, Baltimore County（马里兰大学巴尔的摩县分校）
Multi-state survival analysis (MSA) uses multi-state models for the analysis of time-to-event data. In medical applications, MSA can provide insights about the complex disease progression in patients. A key challenge in MSA is the accurate subject-specific prediction of multi-state model quantities such as transition probability and state occupation probability in the presence of censoring. Traditional multi-state methods such as Aalen-Johansen (AJ) estimators and Cox-based methods are respectively limited by Markov and proportional hazards assumptions and are infeasible for making subject-spe…
Learning Survival Models with Right-Censored Reporting Delays
The Graduate University for Advanced Studies（高级研究大学）；Tokio Marine Holdings, Inc.（东京海上日赤保险株式会社）；The Institute of Statistical Mathematics（统计数学研究所）；RIKEN（理化学研究所）
We describe a new approach to estimating relative risks in time-to-event prediction problems with censored data in a fully parametric manner. Our approach does not require making strong assumptions of constant proportional hazard of the underlying survival distribution, as required by the Cox-proportional hazard model. By jointly learning deep nonlinear representations of the input covariates, we demonstrate the benefits of our approach when used to estimate survival risks through extensive experimentation on multiple real world datasets with different levels of censoring. We further demonstra…
In this paper, we expand the methodology presented in Mertens et. al (2020, Biometrical Journal) to the study of life-time (survival) outcome which is subject to censoring and when imputation is used to account for missing values. We consider the problem where missing values can occur in both the calibration data as well as newly - to-be-predicted - observations (validation). We focus on the Cox model. Methods are described to combine imputation with predictive calibration in survival modeling subject to censoring. Application to cross-validation is discussed. We demonstrate how conclusions br…
In many time-to-event studies, the event of interest is recurrent. Here, the data for each sample unit corresponds to a series of gap times between the subsequent events. Given a limited follow-up period, the last gap time might be right-censored. In contrast to classical analysis, gap times and censoring times cannot be assumed independent, i.e. the sequential nature of the data induces dependent censoring. Also, the recurrences typically vary between sample units leading to unbalanced data. To model the association pattern between gap times, so far only parametric margins combined with the r…
Pitfalls of Administrative Censoring in Survival Models with Time-Indexed Inputs
Center for Data Science, New York University（纽约大学数据科学中心）；University of Chicago（芝加哥大学）；NYU Grossman School of Medicine（纽约大学格罗斯曼医学院）；Ataraxis AI（Ataraxis人工智能公司）
When are time-to-event models a waste of time? Bridging mixture cure models and positive-unlabeled learning for binary classification under right-censoring
Deep models trained through maximum likelihood have achieved state-of-the-art results for survival analysis. Despite this training scheme, practitioners evaluate models under other criteria, such as binary classification losses at a chosen set of time horizons, e.g. Brier score (BS) and Bernoulli log likelihood (BLL). Models trained with maximum likelihood may have poor BS or BLL since maximum likelihood does not directly optimize these criteria. Directly optimizing criteria like BS requires inverse-weighting by the censoring distribution. However, estimating the censoring model under these me…
We study the comparison problem of distribution equality between two random samples under a right censoring scheme. To address this problem, we design a series of tests based on energy distance and kernel mean embeddings. We calibrate our tests using permutation methods and prove that they are consistent against all fixed continuous alternatives. To evaluate our proposed tests, we simulate survival curves from previous clinical trials. Additionally, we provide practitioners with a set of recommendations on how to select parameters/distances for the delay effect problem. Based on the method for…
The Brier score is commonly used for evaluating probability predictions. In survival analysis, with right-censored observations of the event times, this score can be weighted by the inverse probability of censoring (IPCW) to retain its original interpretation. It is common practice to estimate the censoring distribution with the Kaplan-Meier estimator, even though it assumes that the censoring distribution is independent of the covariates. This paper discusses the general impact of the censoring estimates on the Brier score and shows that the estimation of the censoring distribution can be pro…
In survival analysis the random censorship model refers to censoring and survival times being independent of each other. It is one of the fundamental assumptions in the theory of survival analysis. We explain the reason for it being so ubiquitous, and we investigate its presence in medical studies. We differentiate two types of censoring in medical studies (dropout and administrative), and we explain their importance in examining the existence of the random censorship model. We show that in order to presume the random censorship model it is not enough to have a design study which conforms to i…
