We introduce a novel procedure to perform Bayesian non-parametric inference with right-censored data, the \emph{beta-Stacy bootstrap}. This approximates the posterior law of summaries of the survival distribution (e.g. the mean survival time). More precisely, our procedure approximates the joint posterior law of functionals of the beta-Stacy process, a non-parametric process prior that generalizes the Dirichlet process and that is widely used in survival analysis. The beta-Stacy bootstrap generalizes and unifies other common Bayesian bootstraps for complete or censored data based on non-parametric priors. It is defined by an exact sampling algorithm that does not require tuning of Markov Chain Monte Carlo steps. We illustrate the beta-Stacy bootstrap by analyzing survival data from a real clinical trial.
In this paper we introduce the subdistribution beta-Stacy process, a novel Bayesian nonparametric process prior for subdistribution functions useful for the analysis of competing risks data. In particular, we i) characterize this process from a predictive perspective by means of an urn model with reinforcement, ii) show that it is conjugate with respect to right-censored data, and iii) highlight its relations with other prior processes for competing risks data. Additionally, we consider the subdistribution beta-Stacy process prior in a nonparametric regression model for competing risks data wh…
We introduce a general non-parametric independence test between right-censored survival times and covariates, which may be multivariate. Our test statistic has a dual interpretation, first in terms of the supremum of a potentially infinite collection of weight-indexed log-rank tests, with weight functions belonging to a reproducing kernel Hilbert space (RKHS) of functions; and second, as the norm of the difference of embeddings of certain finite measures into the RKHS, similar to the Hilbert-Schmidt Independence Criterion (HSIC) test-statistic. We study the asymptotic properties of the test, f…
In a unified framework, we provide estimators and confidence bands for a variety of treatment effects when the outcome of interest, typically a duration, is subjected to right censoring. Our methodology accommodates average, distributional, and quantile treatment effects under different identifying assumptions including unconfoundedness, local treatment effects, and nonlinear differences-in-differences. The proposed estimators are easy to implement, have close-form representation, are fully data-driven upon estimation of nuisance parameters, and do not rely on parametric distributional assumpt…
Censored data are seldom taken into account in Species Sensitivity Distribution (SSD) analysis. However, they are found in virtually every dataset and sometimes represent the better part of the data. Stringent recommendations on data quality often lead to discard a lot of this meaningful data, often resulting in datasets of reduced size, which lack representativeness of any realistic community. However, it is reasonably simple to include censored data into SSD by using an extension of the standard maximum likelihood method. In this paper, we detail this approach based on the use of the R-packa…
We investigate the performance of model based bootstrap methods for constructing point-wise confidence intervals around the survival function with interval censored data. We show that bootstrapping from the nonparametric maximum likelihood estimator of the survival function is inconsistent for both the current status and case 2 interval censoring models. A model based smoothed bootstrap procedure is proposed and shown to be consistent. In addition, simulation studies are conducted to illustrate the (in)-consistency of the bootstrap methods. Our conclusions in the interval censoring model would…
The statistical regression technique is an extraordinarily essential data fitting tool to explore the potential possible generation mechanism of the random phenomenon. Therefore, the model selection or the variable selection is becoming extremely important so as to identify the most appropriate model with the most optimal explanation effect on the interesting response. In this paper, we discuss and compare the bootstrap-based model selection criteria on the standard censored regression model (Tobit regression model) under the circumstance of limited observation information. The Monte Carlo num…
We present a Bayesian nonparametric system reliability model which scales well and provides a great deal of flexibility in modeling. The Bayesian approach naturally handles the disparate amounts of component and subsystem data that may exist. However, traditional Bayesian reliability models are quite computationally complex, relying on MCMC techniques. Our approach utilizes the conjugate properties of the beta-Stacy process, which is the fundamental building block of our model. These individual models are linked together using a method of moments estimation approach. This model is computationa…
This paper investigates the (in)-consistency of various bootstrap methods for making inference on a change-point in time in the Cox model with right censored survival data. A criterion is established for the consistency of any bootstrap method. It is shown that the usual nonparametric bootstrap is inconsistent for the maximum partial likelihood estimation of the change-point. A new model-based bootstrap approach is proposed and its consistency established. Simulation studies are carried out to assess the performance of various bootstrap schemes.
The subject of tail estimation for randomly censored data from a heavy tailed distribution receives growing attention, motivated by applications for instance in actuarial statistics. The bias of the available estimators of the extreme value index can be substantial and depends strongly on the amount of censoring. We review the available estimators, propose a new bias reduced estimator, and show how shrinkage estimation can help to keep the MSE under control. A bootstrap algorithm is proposed to construct confidence intervals. We compare these new proposals with the existing estimators through …
This paper proposes a modelling strategy to infer the impact of a covariate on the dependence structure of right-censored clustered event time data. The joint survival function of the event times is modelled using a parametric conditional copula whose parameter depends on a cluster-level covariate in a functional way. We use a local likelihood approach to estimate the form of the copula parameter and outline a generalized likelihood ratio-type test strategy to formally test its constancy. A bootstrap procedure is employed to obtain an approximate $p$-value for the test. The performance of the …
This paper proposes a new test for the comparison of conditional quantile curves when the outcome of interest, typically a duration, is subject to right censoring. The test can be applied both in the case of two independent samples and for paired data, and can be used for the comparison of quantiles at a fixed quantile level, a finite set of levels or a range of quantile levels. The asymptotic distribution of the proposed test statistics is obtained both under the null hypothesis and under local alternatives. We describe a bootstrap procedure in order to approximate the critical values, and pr…
Under adaptive progressive Type-II censoring schemes, order restricted inference based on competing risks data is discussed in this article. The latent failure lifetimes for the competing causes are assumed to follow Weibull distributions, with an order restriction on the scale parameters of the distributions. The practical implication of this order restriction is that one of the risk factors is dominant, as often observed in competing risks scenarios. In this setting, likelihood estimation for the model parameters, along with bootstrap based techniques for constructing asymptotic confidence i…
In this article, the analysis of left truncated and right censored competing risks data is carried out, under the assumption of the latent failure times model. It is assumed that there are two competing causes of failures, although most of the results can be extended for more than two causes of failures. The lifetimes corresponding to the competing causes of failures are assumed to follow Weibull distributions with the same shape parameter but different scale parameters. The maximum likelihood estimation procedure of the model parameters is discussed, and confidence intervals are provided usin…
Randomized clinical trials are considered the gold standard for estimating causal effects. Nevertheless, in studies that are aimed at examining adverse effects of interventions, such trials are often impractical because of ethical and financial considerations. In observational studies, matching on the generalized propensity scores was proposed as a possible solution to estimate the treatment effects of multiple interventions. However, the derivation of point and interval estimates for these matching procedures can become complex with non-continuous or censored outcomes. We propose a novel Appr…
This paper introduces new effect parameters for factorial survival designs with possibly right-censored time-to-event data. In the special case of a two-sample design it coincides with the concordance or Wilcoxon parameter in survival analysis. More generally, the new parameters describe treatment or interaction effects and we develop estimates and tests to infer their presence. We rigorously study the asymptotic properties by means of empirical process techniques and additionally suggest wild bootstrapping for a consistent and distribution-free application of the inference procedures. The sma…
A novel approach for dealing with censored competing risks regression data is proposed. This is implemented by a mixture of accelerated failure time (AFT) models for a competing risks scenario within a cluster-weighted modelling (CWM) framework. Specifically, we make use of the log-normal AFT model here but any commonly used AFT model can be utilized. The alternating expectation conditional maximization algorithm (AECM) is used for parameter estimation and bootstrapping for standard error estimation. Finally, we present our results on some simulated and real competing risks data.
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 for a broad class of treatment effect estimands defined as functionals of treatment-specific survival functions, taking into account of missing data due to censoring. Mul…
Bayesian hierarchical bootstrap framework for causal subgroup estimation with a time-to-event outcome
Dalla Lana School of Public Health, University of Toronto（多伦多大学达拉·兰纳公共卫生学院）；Division of Gastroenterology, Hepatology Nutrition, The Hospital for Sick Children（多伦多加急儿童医院胃肠病、肝病与营养科）；University of Utah and Intermountain Healthcare Primary Children’s Hospital（犹他大学和盐湖城初级儿童医院）；Institute of Health Policy, Management and Evaluation, University of Toronto（多伦多大学卫生政策、管理与评估研究所）
In this paper, we investigate the classical and Bayesian estimation of unknown parameters of the Gumbel type-II distribution based on adaptive type-II progressive hybrid censored sample (AT-II PHCS). The maximum likelihood estimates (MLEs) and maximum product spacing estimates (MPSEs) are developed and computed numerically using Newton-Raphson method. Bayesian approaches are employed to estimate parameters under symmetric and asymmetric loss functions. Bayesian estimates are not in explicit forms. Thus, Bayesian estimates are obtained by using Markov chain Monte Carlo (MCMC) method along with …
In this work, we present a statistical treatment of stress-life (S-N) data drawn from a collection of records of fatigue experiments that were performed on 75S-T6 aluminum alloys. Our main objective is to predict the fatigue life of materials by providing a systematic approach to model calibration, model selection and model ranking with reference to S-N data. To this purpose, we consider fatigue-limit models and random fatigue-limit models that are specially designed to allow the treatment of the run-outs (right-censored data). We first fit the models to the data by maximum likelihood methods …
The Aalen-Johansen estimator generalizes the Kaplan-Meier estimator for independently left-truncated and right-censored survival data to estimating the transition probability matrix of a time-inhomogeneous Markov model with finite state space. Such multi-state models have a wide range of applications for modelling complex courses of a disease over the course of time, but the Markov assumption may often be in doubt. If censoring is entirely unrelated to the multi-state data, it has been noted that the Aalen-Johansen estimator, standardized by the initial empirical distribution of the multi-stat…
A new method for clustered survival data]{A new method for clustered survival data: Estimation of treatment effect heterogeneity and variable selection
