skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Nonparametric generalized fiducial inference for survival functions under censoring
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.  more » « less
Award ID(s):
1633074 1916115
PAR ID:
10197791
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Biometrika
Volume:
106
Issue:
3
ISSN:
0006-3444
Page Range / eLocation ID:
501 to 518
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; (, Proceedings of Machine Learning Research)
    We propose a method to quantify uncertainty around individual survival distribution estimates using right-censored data, compatible with any survival model. Unlike classical confidence intervals, the survival bands produced by this method offer predictive rather than population-level inference, making them useful for personalized risk screening. For example, in a low-risk screening scenario, they can be applied to flag patients whose survival band at 12 months lies entirely above 50\%, while ensuring that at least half of flagged individuals will survive past that time on average. Our approach builds on recent advances in conformal inference and integrates ideas from inverse probability of censoring weighting and multiple testing with false discovery rate control. We provide asymptotic guarantees and show promising performance in finite samples with both simulated and real data. 
    more » « less
  2. ; ; (, Journal of Statistical Distributions and Applications)
    null (Ed.)
    Abstract Zero-inflated and hurdle models are widely applied to count data possessing excess zeros, where they can simultaneously model the process from how the zeros were generated and potentially help mitigate the effects of overdispersion relative to the assumed count distribution. Which model to use depends on how the zeros are generated: zero-inflated models add an additional probability mass on zero, while hurdle models are two-part models comprised of a degenerate distribution for the zeros and a zero-truncated distribution. Developing confidence intervals for such models is challenging since no closed-form function is available to calculate the mean. In this study, generalized fiducial inference is used to construct confidence intervals for the means of zero-inflated Poisson and Poisson hurdle models. The proposed methods are assessed by an intensive simulation study. An illustrative example demonstrates the inference methods. 
    more » « less
  3. ; ; (, Biometrics)
    Abstract With advances in biomedical research, biomarkers are becoming increasingly important prognostic factors for predicting overall survival, while the measurement of biomarkers is often censored due to instruments' lower limits of detection. This leads to two types of censoring: random censoring in overall survival outcomes and fixed censoring in biomarker covariates, posing new challenges in statistical modeling and inference. Existing methods for analyzing such data focus primarily on linear regression ignoring censored responses or semiparametric accelerated failure time models with covariates under detection limits (DL). In this paper, we propose a quantile regression for survival data with covariates subject to DL. Comparing to existing methods, the proposed approach provides a more versatile tool for modeling the distribution of survival outcomes by allowing covariate effects to vary across conditional quantiles of the survival time and requiring no parametric distribution assumptions for outcome data. To estimate the quantile process of regression coefficients, we develop a novel multiple imputation approach based on another quantile regression for covariates under DL, avoiding stringent parametric restrictions on censored covariates as often assumed in the literature. Under regularity conditions, we show that the estimation procedure yields uniformly consistent and asymptotically normal estimators. Simulation results demonstrate the satisfactory finite‐sample performance of the method. We also apply our method to the motivating data from a study of genetic and inflammatory markers of Sepsis. 
    more » « less
  4. ; ; ; (, Biometrika)
    Summary This paper introduces an assumption-lean method that constructs valid and efficient lower predictive bounds for survival times with censored data. We build on recent work by Candès et al. (2023), whose approach first subsets the data to discard any data points with early censoring times and then uses a reweighting technique, namely, weighted conformal inference (Tibshirani et al., 2019), to correct for the distribution shift introduced by this subsetting procedure. For our new method, instead of constraining to a fixed threshold for the censoring time when subsetting the data, we allow for a covariate-dependent and data-adaptive subsetting step, which is better able to capture the heterogeneity of the censoring mechanism. As a result, our method can lead to lower predictive bounds that are less conservative and give more accurate information. We show that in the Type-I right-censoring setting, if either the censoring mechanism or the conditional quantile of the survival time is well estimated, our proposed procedure achieves nearly exact marginal coverage, where in the latter case we additionally have approximate conditional coverage. We evaluate the validity and efficiency of our proposed algorithm in numerical experiments, illustrating its advantage when compared with other competing methods. Finally, our method is applied to a real dataset to generate lower predictive bounds for users’ active times on a mobile app. 
    more » « less
  5. ; ; ; (, Biometrics)
    Abstract Censored survival data are common in clinical trial studies. We propose a unified framework for sensitivity analysis to censoring at random in survival data using multiple imputation and martingale, called SMIM. The proposed framework adopts the δ‐adjusted and control‐based models, indexed by the sensitivity parameter, entailing censoring at random and a wide collection of censoring not at random assumptions. Also, it targets a broad class of treatment effect estimands defined as functionals of treatment‐specific survival functions, taking into account missing data due to censoring. Multiple imputation facilitates the use of simple full‐sample estimation; however, the standard Rubin's combining rule may overestimate the variance for inference in the sensitivity analysis framework. We decompose the multiple imputation estimator into a martingale series based on the sequential construction of the estimator and propose the wild bootstrap inference by resampling the martingale series. The new bootstrap inference has a theoretical guarantee for consistency and is computationally efficient compared to the nonparametric bootstrap counterpart. We evaluate the finite‐sample performance of the proposed SMIM through simulation and an application on an HIV clinical trial. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email