Lifetime Data AnalysisPub Date : 2023-04-01Epub Date: 2021-10-26DOI: 10.1007/s10985-021-09535-3
Nils Lid Hjort, Emil Aas Stoltenberg
{"title":"The partly parametric and partly nonparametric additive risk model.","authors":"Nils Lid Hjort, Emil Aas Stoltenberg","doi":"10.1007/s10985-021-09535-3","DOIUrl":"10.1007/s10985-021-09535-3","url":null,"abstract":"<p><p>Aalen's linear hazard rate regression model is a useful and increasingly popular alternative to Cox' multiplicative hazard rate model. It postulates that an individual has hazard rate function [Formula: see text] in terms of his covariate values [Formula: see text]. These are typically levels of various hazard factors, and may also be time-dependent. The hazard factor functions [Formula: see text] are the parameters of the model and are estimated from data. This is traditionally accomplished in a fully nonparametric way. This paper develops methodology for estimating the hazard factor functions when some of them are modelled parametrically while the others are left unspecified. Large-sample results are reached inside this partly parametric, partly nonparametric framework, which also enables us to assess the goodness of fit of the model's parametric components. In addition, these results are used to pinpoint how much precision is gained, using the parametric-nonparametric model, over the standard nonparametric method. A real-data application is included, along with a brief simulation study.</p>","PeriodicalId":49908,"journal":{"name":"Lifetime Data Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10006282/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9493084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Paul Frédéric Blanche, Anders Holt, Thomas Scheike
{"title":"On logistic regression with right censored data, with or without competing risks, and its use for estimating treatment effects.","authors":"Paul Frédéric Blanche, Anders Holt, Thomas Scheike","doi":"10.1007/s10985-022-09564-6","DOIUrl":"https://doi.org/10.1007/s10985-022-09564-6","url":null,"abstract":"<p><p>Simple logistic regression can be adapted to deal with right-censoring by inverse probability of censoring weighting (IPCW). We here compare two such IPCW approaches, one based on weighting the outcome, the other based on weighting the estimating equations. We study the large sample properties of the two approaches and show that which of the two weighting methods is the most efficient depends on the censoring distribution. We show by theoretical computations that the methods can be surprisingly different in realistic settings. We further show how to use the two weighting approaches for logistic regression to estimate causal treatment effects, for both observational studies and randomized clinical trials (RCT). Several estimators for observational studies are compared and we present an application to registry data. We also revisit interesting robustness properties of logistic regression in the context of RCTs, with a particular focus on the IPCW weighting. We find that these robustness properties still hold when the censoring weights are correctly specified, but not necessarily otherwise.</p>","PeriodicalId":49908,"journal":{"name":"Lifetime Data Analysis","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9134954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Analysis and asymptotic theory for nested case-control designs under highly stratified proportional hazards models.","authors":"Larry Goldstein, Bryan Langholz","doi":"10.1007/s10985-022-09582-4","DOIUrl":"https://doi.org/10.1007/s10985-022-09582-4","url":null,"abstract":"<p><p>Nested case-control sampled event time data under a highly stratified proportional hazards model, in which the number of strata increases proportional to sample size, is described and analyzed. The data can be characterized as stratified sampling from the event time risk sets and the analysis approach of Borgan et al. (Ann Stat 23:1749-1778, 1995) is adapted to accommodate both the stratification and case-control sampling from the stratified risk sets. Conditions for the consistency and asymptotic normality of the maximum partial likelihood estimator are provided and the results are used to compare the efficiency of the stratified analysis to an unstratified analysis when the baseline hazards can be semi-parametrically modeled in two special cases. Using the stratified sampling representation of the stratified analysis, methods for absolute risk estimation described by Borgan et al. (1995) for nested case-control data are used to develop methods for absolute risk estimation under the stratified model. The methods are illustrated by a year of birth stratified analysis of radon exposure and lung cancer mortality in a cohort of uranium miners from the Colorado Plateau.</p>","PeriodicalId":49908,"journal":{"name":"Lifetime Data Analysis","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9139939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Phase-type models for competing risks, with emphasis on identifiability issues.","authors":"Bo Henry Lindqvist","doi":"10.1007/s10985-022-09547-7","DOIUrl":"https://doi.org/10.1007/s10985-022-09547-7","url":null,"abstract":"<p><p>We first review some main results for phase-type distributions, including a discussion of Coxian distributions and their canonical representations. We then consider the extension of phase-type modeling to cover competing risks. This extension involves the consideration of finite state Markov chains with more than one absorbing state, letting each absorbing state correspond to a particular risk. The non-uniqueness of Markov chain representations of phase-type distributions is well known. In the paper we study corresponding issues for the competing risks case with the aim of obtaining identifiable parameterizations. Statistical inference for the Coxian competing risks model is briefly discussed and some real data are analyzed for illustration.</p>","PeriodicalId":49908,"journal":{"name":"Lifetime Data Analysis","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10006281/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9194640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Julie K Furberg, Per K Andersen, Sofie Korn, Morten Overgaard, Henrik Ravn
{"title":"Bivariate pseudo-observations for recurrent event analysis with terminal events.","authors":"Julie K Furberg, Per K Andersen, Sofie Korn, Morten Overgaard, Henrik Ravn","doi":"10.1007/s10985-021-09533-5","DOIUrl":"https://doi.org/10.1007/s10985-021-09533-5","url":null,"abstract":"<p><p>The analysis of recurrent events in the presence of terminal events requires special attention. Several approaches have been suggested for such analyses either using intensity models or marginal models. When analysing treatment effects on recurrent events in controlled trials, special attention should be paid to competing deaths and their impact on interpretation. This paper proposes a method that formulates a marginal model for recurrent events and terminal events simultaneously. Estimation is based on pseudo-observations for both the expected number of events and survival probabilities. Various relevant hypothesis tests in the framework are explored. Theoretical derivations and simulation studies are conducted to investigate the behaviour of the method. The method is applied to two real data examples. The bivariate marginal pseudo-observation model carries the strength of a two-dimensional modelling procedure and performs well in comparison with available models. Finally, an extension to a three-dimensional model, which decomposes the terminal event per death cause, is proposed and exemplified.</p>","PeriodicalId":49908,"journal":{"name":"Lifetime Data Analysis","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9140831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lifetime Data AnalysisPub Date : 2023-04-01Epub Date: 2023-02-08DOI: 10.1007/s10985-022-09586-0
Ruth H Keogh, Karla Diaz-Ordaz, Nicholas P Jewell, Malcolm G Semple, Liesbeth C de Wreede, Hein Putter
{"title":"Estimating distribution of length of stay in a multi-state model conditional on the pathway, with an application to patients hospitalised with Covid-19.","authors":"Ruth H Keogh, Karla Diaz-Ordaz, Nicholas P Jewell, Malcolm G Semple, Liesbeth C de Wreede, Hein Putter","doi":"10.1007/s10985-022-09586-0","DOIUrl":"10.1007/s10985-022-09586-0","url":null,"abstract":"<p><p>Multi-state models are used to describe how individuals transition through different states over time. The distribution of the time spent in different states, referred to as 'length of stay', is often of interest. Methods for estimating expected length of stay in a given state are well established. The focus of this paper is on the distribution of the time spent in different states conditional on the complete pathway taken through the states, which we call 'conditional length of stay'. This work is motivated by questions about length of stay in hospital wards and intensive care units among patients hospitalised due to Covid-19. Conditional length of stay estimates are useful as a way of summarising individuals' transitions through the multi-state model, and also as inputs to mathematical models used in planning hospital capacity requirements. We describe non-parametric methods for estimating conditional length of stay distributions in a multi-state model in the presence of censoring, including conditional expected length of stay (CELOS). Methods are described for an illness-death model and then for the more complex motivating example. The methods are assessed using a simulation study and shown to give unbiased estimates of CELOS, whereas naive estimates of CELOS based on empirical averages are biased in the presence of censoring. The methods are applied to estimate conditional length of stay distributions for individuals hospitalised due to Covid-19 in the UK, using data on 42,980 individuals hospitalised from March to July 2020 from the COVID19 Clinical Information Network.</p>","PeriodicalId":49908,"journal":{"name":"Lifetime Data Analysis","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9908509/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9507211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yolanda M Gómez, Diego I Gallardo, Marcelo Bourguignon, Eduardo Bertolli, Vinicius F Calsavara
{"title":"A general class of promotion time cure rate models with a new biological interpretation.","authors":"Yolanda M Gómez, Diego I Gallardo, Marcelo Bourguignon, Eduardo Bertolli, Vinicius F Calsavara","doi":"10.1007/s10985-022-09575-3","DOIUrl":"https://doi.org/10.1007/s10985-022-09575-3","url":null,"abstract":"<p><p>Over the last decades, the challenges in survival models have been changing considerably and full probabilistic modeling is crucial in many medical applications. Motivated from a new biological interpretation of cancer metastasis, we introduce a general method for obtaining more flexible cure rate models. The proposal model extended the promotion time cure rate model. Furthermore, it includes several well-known models as special cases and defines many new special models. We derive several properties of the hazard function for the proposed model and establish mathematical relationships with the promotion time cure rate model. We consider a frequentist approach to perform inferences, and the maximum likelihood method is employed to estimate the model parameters. Simulation studies are conducted to evaluate its performance with a discussion of the obtained results. A real dataset from population-based study of incident cases of melanoma diagnosed in the state of São Paulo, Brazil, is discussed in detail.</p>","PeriodicalId":49908,"journal":{"name":"Lifetime Data Analysis","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10645029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Bayesian Design of Clinical Trials Using Joint Cure Rate Models for Longitudinal and Time-to-Event Data.","authors":"Jiawei Xu, Matthew A Psioda, Joseph G Ibrahim","doi":"10.1007/s10985-022-09581-5","DOIUrl":"https://doi.org/10.1007/s10985-022-09581-5","url":null,"abstract":"<p><p>For clinical trial design and analysis, there has been extensive work related to using joint models for longitudinal and time-to-event data without a cure fraction (i.e., when all patients are at risk for the event of interest), but comparatively little treatment has been given to design and analysis of clinical trials using joint models that incorporate a cure fraction. In this paper, we develop a Bayesian clinical trial design methodology focused on evaluating the treatment's effect on a time-to-event endpoint using a promotion time cure rate model, where the longitudinal process is incorporated into the hazard model for the promotion times. A piecewise linear hazard model for the period after assessment of the longitudinal measure ends is proposed as an alternative to extrapolating the longitudinal trajectory. This may be advantageous in scenarios where the period of time from the end of longitudinal measurements until the end of observation is substantial. Inference for the time-to-event endpoint is based on a novel estimand which combines the treatment's effect on the probability of cure and its effect on the promotion time distribution, mediated by the longitudinal outcome. We propose an approach for sample size determination such that the design has a high power and a well-controlled type I error rate with both operating characteristics defined from a Bayesian perspective. We demonstrate the methodology by designing a breast cancer clinical trial with a primary time-to-event endpoint where longitudinal outcomes are measured periodically during follow up.</p>","PeriodicalId":49908,"journal":{"name":"Lifetime Data Analysis","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10698884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Double bias correction for high-dimensional sparse additive hazards regression with covariate measurement errors.","authors":"Xiaobo Wang, Jiayu Huang, Guosheng Yin, Jian Huang, Yuanshan Wu","doi":"10.1007/s10985-022-09568-2","DOIUrl":"https://doi.org/10.1007/s10985-022-09568-2","url":null,"abstract":"<p><p>We propose an inferential procedure for additive hazards regression with high-dimensional survival data, where the covariates are prone to measurement errors. We develop a double bias correction method by first correcting the bias arising from measurement errors in covariates through an estimating function for the regression parameter. By adopting the convex relaxation technique, a regularized estimator for the regression parameter is obtained by elaborately designing a feasible loss based on the estimating function, which is solved via linear programming. Using the Neyman orthogonality, we propose an asymptotically unbiased estimator which further corrects the bias caused by the convex relaxation and regularization. We derive the convergence rate of the proposed estimator and establish the asymptotic normality for the low-dimensional parameter estimator and the linear combination thereof, accompanied with a consistent estimator for the variance. Numerical experiments are carried out on both simulated and real datasets to demonstrate the promising performance of the proposed double bias correction method.</p>","PeriodicalId":49908,"journal":{"name":"Lifetime Data Analysis","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9196498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lifetime Data AnalysisPub Date : 2023-01-01Epub Date: 2022-10-08DOI: 10.1007/s10985-022-09579-z
Prabhashi W Withana Gamage, Christopher S McMahan, Lianming Wang
{"title":"A flexible parametric approach for analyzing arbitrarily censored data that are potentially subject to left truncation under the proportional hazards model.","authors":"Prabhashi W Withana Gamage, Christopher S McMahan, Lianming Wang","doi":"10.1007/s10985-022-09579-z","DOIUrl":"10.1007/s10985-022-09579-z","url":null,"abstract":"<p><p>The proportional hazards (PH) model is, arguably, the most popular model for the analysis of lifetime data arising from epidemiological studies, among many others. In such applications, analysts may be faced with censored outcomes and/or studies which institute enrollment criterion leading to left truncation. Censored outcomes arise when the event of interest is not observed but rather is known relevant to an observation time(s). Left truncated data occur in studies that exclude participants who have experienced the event prior to being enrolled in the study. If not accounted for, both of these features can lead to inaccurate inferences about the population under study. Thus, to overcome this challenge, herein we propose a novel unified PH model that can be used to accommodate both of these features. In particular, our approach can seamlessly analyze exactly observed failure times along with interval-censored observations, while aptly accounting for left truncation. To facilitate model fitting, an expectation-maximization algorithm is developed through the introduction of carefully structured latent random variables. To provide modeling flexibility, a monotone spline representation is used to approximate the cumulative baseline hazard function. The performance of our methodology is evaluated through a simulation study and is further illustrated through the analysis of two motivating data sets; one that involves child mortality in Nigeria and the other prostate cancer.</p>","PeriodicalId":49908,"journal":{"name":"Lifetime Data Analysis","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9852023/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10642053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}