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In this article we extend the factor copula model to deal with right-censored event time data grouped in clusters. The new methodology allows for clusters to have variable sizes ranging from small to large and intracluster dependence to be flexibly modeled by any parametric family of bivariate copulas, thus encompassing a wide range of dependence structures. Incorporation of covariates (possibly time dependent) in the margins is also supported. Three estimation procedures are proposed: both one- and two-stage parametric and a two-stage semiparametric method where marginal survival functions are estimated by using a Cox proportional hazards model. We prove that the estimators are consistent and asymptotically normally distributed, and assess their finite sample behavior with simulation studies. Furthermore, we illustrate the proposed methods on a data set containing the time to first insemination after calving in dairy cattle clustered in herds of different sizes.

In biomedical research, weighted logrank tests are frequently applied to compare two samples of randomly right censored survival times. We address the question how to combine a number of weighted logrank statistics to achieve good power of the corresponding survival test for a whole linear space or cone of alternatives, which are given by hazard rates. This leads to a new class of semiparametric projection tests that are motivated by likelihood ratio tests for an asymptotic model. We show that these tests can be carried out as permutation tests and discuss their asymptotic properties. A simulation study together with the analysis of a classical data set illustrates the advantages.

The paper extends the latent promotion time cure rate marker model of Kim, Xi and Chen for right-censored survival data. Instead of modelling the cure rate parameter as a deterministic function of risk factors, they assumed that the cure rate parameter of a targeted population is distributed over a number of ordinal levels according to the probabilities governed by the risk factors. We propose to use a mixture of linear dependent tail-free processes as the prior for the distribution of the cure rate parameter, resulting in a latent promotion time cure rate model. This approach provides an immediate answer to perhaps one of the most pressing questions 'what is the probability that a targeted population has high proportions (e.g. greater than 70%) of being cured?'. The approach proposed can accommodate a rich class of distributions for the cure rate parameter, while centred at gamma densities. The algorithms that are developed in this work allow the fitting of latent promotion time cure rate models with several survival models for metastatic tumour cells.

In this paper, we establish both naive and formal Bayesian justifications of Cox's (1975) partial likelihood and its various modifications. We extend the original work of Kalbfieisch (1978), who showed that the partial likelihood is a limiting marginal posterior under noninformative priors for baseline hazards. We extend the result to scenarios with time‐dependent covariates and time‐varying regression parameters. We establish results for continuous time as well as grouped survival data. In addition, we present a Bayesian justification of a modified partial likelihood for handling ties. We also present tools for simplification of the Gibbs sampling algorithm for implementing partial likelihood based Bayesian inference in various practical applications.

This article proposes an approach to estimate and make inference on the parameters of copula link-based survival models. The methodology allows for the margins to be specified using flexible parametric formulations for time-to-event data, the baseline survival functions to be modeled using monotonic splines, and each parameter of the assumed joint survival distribution to depend on an additive predictor incorporating several types of covariate effects. All the model's coefficients as well as the smoothing parameters associated with the relevant components in the additive predictors are estimated using a carefully structured efficient and stable penalized likelihood algorithm. Some theoretical properties are also discussed. The proposed modeling framework is evaluated in a simulation study and illustrated using a real dataset. The relevant numerical computations can be easily carried out using the freely available GJRM R package. Supplementary materials for this article are available online.

This paper presents the exponentiated alpha-power log-logistic (EAPLL) distribution, which extends the log-logistic distribution. The EAPLL distribution emphasizes its suitability for survival data modeling by providing analytical simplicity and accommodating both monotone and non-monotone failure rates. We derive some of its mathematical properties and test eight estimation methods using an extensive simulation study. To determine the best estimation approach, we rank mean estimates, mean square errors, and average absolute biases on a partial and overall ranking. Furthermore, we use the EAPLL distribution to examine three real-life survival data sets, demonstrating its superior performance over competing log-logistic distributions. This study adds vital insights to survival analysis methodology and provides a solid framework for modeling various survival data scenarios.

Background Time to benefit (TTB) has emerged as a clinically interpretable estimand for characterizing when treatment effects become meaningful over time. Unlike conventional survival summaries, TTB is implicitly defined through marginal differences in survival probabilities and is therefore highly sensitive to modeling assumptions. In multicenter studies involving clustered time-to-event data, unobserved heterogeneity and misspecification of the baseline hazard present additional challenges for coherent TTB estimation. Methods We propose a unified framework for estimating TTB in clustered survival settings using marginal survival modeling with shared frailty. Specifically, TTB is defined on the marginal population scale by integrating over the frailty distribution, ensuring coherence between the estimand and its clinical interpretation. Both parametric and flexible spline-based baseline hazard models are evaluated. Uncertainty is quantified using the Delta method and Monte Carlo (MC)-based inference procedures. Extensive simulation studies are conducted to characterize estimator behavior under varying degrees of heterogeneity, censoring, and hazard misspecification. Furthermore, the framework is illustrated using data from the Systolic Blood Pressure Intervention Trial (SPRINT), a large multicenter randomized clinical trial. Results Simulation results indicate that ignoring latent heterogeneity or misspecifying the baseline hazard can bias TTB estimation and produce miscalibrated confidence intervals, particularly under small absolute risk reduction thresholds. Flexible hazard models combined with MC-based inference yield more stable estimates and improved coverage in the presence of model misspecification. In the SPRINT application, TTB point estimates remained relatively consistent across modeling approaches, while statistically significant frailty effects revealed meaningful between-site heterogeneity, highlighting its importance for accurate uncertainty quantification. Conclusions TTB is a model-sensitive implicit estimand; reliable estimation in clustered survival settings requires explicit alignment among the estimand definition, the survival model, and the inference strategy. The proposed framework provides a principled and practical approach to TTB estimation in multicenter studies, facilitating transparent and interpretable reporting of TTB in both clinical and real-world research contexts.

Statistical methods for survival analysis play a central role in the assessment of treatment effects in randomized clinical trials in cardiovascular disease, cancer, and many other fields. The most common approach to analysis involves fitting a Cox regression model including a treatment indicator, and basing inference on the large sample properties of the regression coefficient estimator. Despite the fact that treatment assignment is randomized, the hazard ratio is not a quantity which admits a causal interpretation in the case of unmodelled heterogeneity. This problem arises because the risk sets beyond the first event time are comprised of the subset of individuals who have not previously failed. The balance in the distribution of potential confounders between treatment arms is lost by this implicit conditioning, whether or not censoring is present. Thus while the Cox model may be used as a basis for valid tests of the null hypotheses of no treatment effect if robust variance estimates are used, modeling frameworks more compatible with causal reasoning may be preferrable in general for estimation.

Statistical inference for cluster randomized trials often involves complex derived endpoints, such as biomarker ratios or cumulative products, which significantly complicate the application of standard asymptotic theory. When the number of clusters is limited or intra-cluster dependence is pronounced, conventional nonparametric procedures relying on large-sample chi-squared approximations frequently break down, leading to inflated Type I error rates and inadequate confidence interval coverage. This paper develops a rigorous, unified framework to circumvent these inferential failures by constructing a rank-based k -sample test statistic specifically tailored for clustered, right-censored survival data. We derive a multivariate saddlepoint approximation for the exact permutation distribution under an urn randomization scheme, providing a solution that yields higher-order precision. This analytical strategy recovers the accuracy of computationally exhaustive Monte Carlo resampling at a fraction of the numerical cost. Furthermore, the efficiency of the saddlepoint approach enables the practical construction of nonparametric confidence intervals for relative treatment effects via test inversion. Extensive simulations demonstrate that our proposed method preserves nominal significance levels in the small-cluster regimes where standard techniques prove unreliable. The practical utility of the methodology is further evidenced through the analysis of three multi-center clinical trials-concerning leukemia, vision loss, and periodontitis-where the saddlepoint approximation provides robust and trustworthy inferential conclusions in borderline cases that would otherwise yield conflicting results.

With the advancement of information technology, large-scale data have become increasingly common. Subsampling methods for the statistical analysis of such data require computing the sampling probability for each observation, a process that can be computationally intensive. In this paper, we extend the perturbed subsampling approach to the Cox proportional hazards model, a widely used method in survival analysis to address the statistical analysis of large-scale survival data. Specifically, we propose a perturbed subsampling algorithm for this model. The effectiveness of the proposed method is evaluated through simulation studies and real-data analysis.