Bayesian Inference for Multivariate Survival Data with a Cure Fraction

AbstractWe develop Bayesian methods for right censored multivariate failure time data for populations with a cure fraction. We propose a new model, called the multivariate cure rate model, and provide a natural motivation and interpretation of it. To create the correlation structure between the failure times, we introduce a frailty term, which is assumed to have a positive stable distribution. The resulting correlation structure induced by the frailty term is quite appealing and leads to a nice characterization of the association between the failure times. Several novel properties of the model are derived. First, conditional on the frailty term, it is shown that the model has a proportional hazards structure with the covariates depending naturally on the cure rate. Second, we establish mathematical relationships between the marginal survivor functions of the multivariate cure rate model and the more standard mixture model for modelling cure rates. With the introduction of latent variables, we show that the new model is computationally appealing, and novel computational Markov chain Monte Carlo (MCMC) methods are developed to sample from the posterior distribution of the parameters. Specifically, we propose a modified version of the collapsed Gibbs technique (J. S. Liu, 1994, J. Amer. Statist. Assoc.89, 958–966) to sample from the posterior distribution. This development will lead to an efficient Gibbs sampling procedure, which would otherwise be extremely difficult. We characterize the propriety of the joint posterior distribution of the parameters using a class of noninformative improper priors. A real dataset from a melanoma clinical trial is presented to illustrate the methodology

Maximum likelihood estimation in a partially observed stratified regression model with censored data

The stratified proportional intensity model generalizes Cox's proportional intensity model by allowing different groups of the population under study to have distinct baseline intensity functions. In this article, we consider the problem of estimation in this model when the variable indicating the stratum is unobserved for some individuals in the studied sample. In this setting, we construct nonparametric maximum likelihood estimators for the parameters of the stratified model and we establish their consistency and asymptotic normality. Consistent estimators for the limiting variances are also obtained

On the Reliability of Machine Learning Models for Survival Analysis When Cure Is a Possibility

[Abstract]: In classical survival analysis, it is assumed that all the individuals will experience the event of interest. However, if there is a proportion of subjects who will never experience the event, then a standard survival approach is not appropriate, and cure models should be considered instead. This paper deals with the problem of adapting a machine learning approach for classical survival analysis to a situation when cure (i.e., not suffering the event) is a possibility. Specifically, a brief review of cure models and recent machine learning methodologies is presented, and an adaptation of machine learning approaches to account for cured individuals is introduced. In order to validate the proposed methods, we present an extensive simulation study in which we compare the performance of the adapted machine learning algorithms with existing cure models. The results show the good behavior of the semiparametric or the nonparametric approaches, depending on the simulated scenario. The practical utility of the methodology is showcased through two real-world dataset illustrations. In the first one, the results show the gain of using the nonparametric mixture cure model approach. In the second example, the results show the poor performance of some machine learning methods for small sample sizes.This project was funded by the Xunta de Galicia (Axencia Galega de Innovación) Research projects COVID-19 presented in ISCIII IN845D 2020/26, Operational Program FEDER Galicia 2014–2020; by the Centro de Investigación de Galicia “CITIC”, funded by Xunta de Galicia and the European Union European Regional Development Fund (ERDF)-Galicia 2014–2020 Program, by grant ED431G 2019/01; and by the Spanish Ministerio de Economía y Competitividad (research projects PID2019-109238GB-C22 and PID2021-128045OA-I00). ALC was sponsored by the BEATRIZ GALINDO JUNIOR Spanish Grant from MICINN (Ministerio de Ciencia e Innovación) with code BGP18/00154. ALC was partially supported by the MICINN Grant PID2020-113578RB-I00 and partial support of Xunta de Galicia (Grupos de Referencia Competitiva ED431C-2020-14). We gratefully acknowledge the support of NVIDIA Corporation with the donation of the Titan Xp GPU used for this research.Xunta de Galicia; ED431G 2019/01Xunta de Galicia; ED431C-2020-14Xunta de Galicia; IN845D 2020/2

Deep Learning for Survival Analysis: A Review

The influx of deep learning (DL) techniques into the field of survival analysis in recent years, coupled with the increasing availability of high-dimensional omics data and unstructured data like images or text, has led to substantial methodological progress; for instance, learning from such high-dimensional or unstructured data. Numerous modern DL-based survival methods have been developed since the mid-2010s; however, they often address only a small subset of scenarios in the time-to-event data setting - e.g., single-risk right-censored survival tasks - and neglect to incorporate more complex (and common) settings. Partially, this is due to a lack of exchange between experts in the respective fields. In this work, we provide a comprehensive systematic review of DL-based methods for time-to-event analysis, characterizing them according to both survival- and DL-related attributes. In doing so, we hope to provide a helpful overview to practitioners who are interested in DL techniques applicable to their specific use case as well as to enable researchers from both fields to identify directions for future investigation. We provide a detailed characterization of the methods included in this review as an open-source, interactive table: https://survival-org.github.io/DL4Survival. As this research area is advancing rapidly, we encourage the research community to contribute to keeping the information up to date.Comment: 24 pages, 6 figures, 2 tables, 1 interactive tabl

Methods for non-proportional hazards in clinical trials: A systematic review

For the analysis of time-to-event data, frequently used methods such as the log-rank test or the Cox proportional hazards model are based on the proportional hazards assumption, which is often debatable. Although a wide range of parametric and non-parametric methods for non-proportional hazards (NPH) has been proposed, there is no consensus on the best approaches. To close this gap, we conducted a systematic literature search to identify statistical methods and software appropriate under NPH. Our literature search identified 907 abstracts, out of which we included 211 articles, mostly methodological ones. Review articles and applications were less frequently identified. The articles discuss effect measures, effect estimation and regression approaches, hypothesis tests, and sample size calculation approaches, which are often tailored to specific NPH situations. Using a unified notation, we provide an overview of methods available. Furthermore, we derive some guidance from the identified articles. We summarized the contents from the literature review in a concise way in the main text and provide more detailed explanations in the supplement (page 29)