scholarly journals Smooth confidence intervals for the survival function under random right censoring

2012 ◽  
Vol 6 (0) ◽  
pp. 843-860 ◽  
Author(s):  
Dimitrios Bagkavos ◽  
Dimitrios Ioannides
Keyword(s):  
Confidence Intervals ◽  
Survival Function ◽  
Right Censoring

scholarly journals Nonparametric generalized fiducial inference for survival functions under censoring

Biometrika ◽  
2019 ◽  
Vol 106 (3) ◽  
pp. 501-518 ◽  
Author(s):  
Y Cui ◽  
J Hannig
Keyword(s):  
Confidence Intervals ◽  
Average Length ◽  
Asymptotic Methods ◽  
Survival Function ◽  
Right Censoring ◽  
Rank Tests ◽  
Fiducial Inference ◽  
Fiducial Distribution ◽  
Von Mises ◽  
Log Rank Tests

Summary Since the introduction of fiducial inference by Fisher in the 1930s, its application has been largely confined to relatively simple, parametric problems. In this paper, we present what might be the first time fiducial inference is systematically applied to estimation of a nonparametric survival function under right censoring. We find that the resulting fiducial distribution gives rise to surprisingly good statistical procedures applicable to both one-sample and two-sample problems. In particular, we use the fiducial distribution of a survival function to construct pointwise and curvewise confidence intervals for the survival function, and propose tests based on the curvewise confidence interval. We establish a functional Bernstein–von Mises theorem, and perform thorough simulation studies in scenarios with different levels of censoring. The proposed fiducial-based confidence intervals maintain coverage in situations where asymptotic methods often have substantial coverage problems. Furthermore, the average length of the proposed confidence intervals is often shorter than the length of confidence intervals for competing methods that maintain coverage. Finally, the proposed fiducial test is more powerful than various types of log-rank tests and sup log-rank tests in some scenarios. We illustrate the proposed fiducial test by comparing chemotherapy against chemotherapy combined with radiotherapy, using data from the treatment of locally unresectable gastric cancer.

Survival forests for data with dependent censoring

2017 ◽  
Vol 28 (2) ◽  
pp. 445-461 ◽  
Author(s):  
Hoora Moradian ◽  
Denis Larocque ◽  
François Bellavance
Keyword(s):  
Survival Data ◽  
Survival Function ◽  
Real Data ◽  
Dependent Censoring ◽  
Right Censoring ◽  
True Time ◽  
Splitting Rule ◽  
The Individual ◽  
Individual Trees ◽  
Survival Forests

Tree-based methods are very powerful and popular tools for analysing survival data with right-censoring. The existing methods assume that the true time-to-event and the censoring times are independent given the covariates. We propose different ways to build survival forests when dependent censoring is suspected, by using an appropriate estimator of the survival function when aggregating the individual trees and/or by modifying the splitting rule. The appropriate estimator used in this paper is the copula-graphic estimator. We also propose a new method for building survival forests, called p-forest, that may be used not only when dependent censoring is suspected, but also as a new survival forest method in general. The results from a simulation study indicate that these modifications improve greatly the estimation of the survival function in situations of dependent censoring. A real data example illustrates how the proposed methods can be used to perform a sensitivity analysis.

scholarly journals 464Basics of survival analysis: age is not appropriate as time scale in Cox regression model

2021 ◽  
Vol 50 (Supplement_1) ◽  
Author(s):  
Yangyang Liu ◽  
Jingjing Zhang ◽  
Toshiharu Mitsuhashi ◽  
Toshihiko Matsuo ◽  
Takashi Yorifuji ◽  
...  
Keyword(s):  
Regression Model ◽  
Time Scale ◽  
Cox Regression ◽  
Cox Model ◽  
Survival Function ◽  
Likelihood Estimation ◽  
Continuous Variable ◽  
Study Time ◽  
Right Censoring ◽  
Cox Regression Model

Abstract Background Many previous methodological studies suggested to use age as time scale in Cox regression model, and some statistical analyses directly applied this conclusion. In the present study, we explain why age is not a more appropriate time scale compared to the time-on-study time scale. Methods We address this argument based on five aspects: Cox regression model, conditional likelihood estimation, dataset of left-truncation or right-censoring, algorithms and software for Cox model, and inferring survival function. Furthermore, logical and algorithmic errors arise in the procedure of parameter inference with age time scale, and that certain evaluation indicators proposed by previous studies are inappropriate. Results The function of time scale is mainly a sampling method for maximum likelihood estimation to infer coefficient of Cox regression model, and the method defined by the age time scale is incorrect in logics and algorithms. Furthermore, age as time scale creates new problems, such as the omission of covariates, loss of information as a continuous variable, increase in dropout, and inability to obtain the survival function. Conclusions For the Cox regression model, the classic time-on-study time scale is more appropriate compared to age as time scale. Key messages It is an important discussion because using age as time scale was first proposed decades ago, meaning that lots of turnovers in researchers, newbies tend to accept the assumptions of their predecessors, but the suitability has never been rigorously verified.

scholarly journals Stacked survival models for residual lifetime data

2022 ◽  
Vol 22 (1) ◽  
Author(s):  
James H. McVittie ◽  
David B. Wolfson ◽  
Vittorio Addona ◽  
Zhaoheng Li
Keyword(s):  
Maximum Likelihood ◽  
Confidence Intervals ◽  
Model Misspecification ◽  
Survival Function ◽  
Disease Onset ◽  
Survival Models ◽  
Brier Score ◽  
Residual Lifetime ◽  
Lifetime Data ◽  
Residual Lifetimes

AbstractWhen modelling the survival distribution of a disease for which the symptomatic progression of the associated condition is insidious, it is not always clear how to measure the failure/censoring times from some true date of disease onset. In a prevalent cohort study with follow-up, one approach for removing any potential influence from the uncertainty in the measurement of the true onset dates is through the utilization of only the residual lifetimes. As the residual lifetimes are measured from a well-defined screening date (prevalence day) to failure/censoring, these observed time durations are essentially error free. Using residual lifetime data, the nonparametric maximum likelihood estimator (NPMLE) may be used to estimate the underlying survival function. However, the resulting estimator can yield exceptionally wide confidence intervals. Alternatively, while parametric maximum likelihood estimation can yield narrower confidence intervals, it may not be robust to model misspecification. Using only right-censored residual lifetime data, we propose a stacking procedure to overcome the non-robustness of model misspecification; our proposed estimator comprises a linear combination of individual nonparametric/parametric survival function estimators, with optimal stacking weights obtained by minimizing a Brier Score loss function.

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