Survival analysis encompasses a broad range of methods for analyzing time-to-event data, with one key objective being the comparison of survival curves across groups. Traditional approaches for identifying clusters of survival curves often rely on computationally intensive bootstrap techniques to approximate the null hypothesis distribution. While effective, these methods impose significant computational burdens. In this work, we propose a novel approach that leverages the k-means and log-rank test to efficiently identify and cluster survival curves. Our method eliminates the need for computationally expensive resampling, significantly reducing processing time while maintaining statistical reliability. By systematically evaluating survival curves and determining optimal clusters, the proposed method ensures a practical and scalable alternative for large-scale survival data analysis. Through simulation studies, we demonstrate that our approach achieves results comparable to existing bootstrap-based clustering methods while dramatically improving computational efficiency. These findings suggest that the log-rank-based clustering procedure offers a viable and time-efficient solution for researchers working with multiple survival curves in medical and epidemiological studies.

To evaluate the translational capabilities of foundation models, we develop a pathological concept learning approach focused on kidney cancer. By leveraging TNM staging guidelines and pathology reports, we build comprehensive pathological concepts for kidney cancer. Then, we extract deep features from whole slide images using foundation models, construct pathological graphs to capture spatial correlations, and trained graph neural networks to identify these concepts. Finally, we demonstrate the effectiveness of this approach in kidney cancer survival analysis, highlighting its explainability and fairness in identifying low- and high-risk patients. The source code has been released by https://github.com/shangqigao/RadioPath.

We investigate how to calculate Kaplan-Meier survival curves across multiple health-care jurisdictions while protecting patient privacy with node-level differential privacy. Each site discloses its curve only once, adding Laplace noise whose scale is determined by the length of the common time grid; the server then averages the noisy curves, so the overall privacy budget remains unchanged. We benchmark four one-shot smoothing techniques: Discrete Cosine Transform, Haar Wavelet shrinkage, adaptive Total-Variation denoising, and a parametric Weibull fit on the NCCTG lung-cancer cohort under five privacy levels and three partition scenarios (uniform, moderately skewed, highly imbalanced). Total-Variation gives the best mean accuracy, whereas the frequency-domain smoothers offer stronger worst-case robustness and the Weibull model shows the most stable behaviour at the strictest privacy setting. Across all methods the released curves keep the empirical log-rank type-I error below fifteen percent for privacy budgets of 0.5 and higher, demonstrating that clinically useful survival information can be shared without iterative training or heavy cryptography.

Appendix A: Preliminary results Appendix B: Proofs of sections 2 and 3 Appendix C: Proof of Theorem 4.1 (null distribution) Appendix D: Proof of Theorem 4.2 (consistency under alternatives) Appendix E: Efficient wild bootstrap implementation Appendix F: Review of related quasi-independence tests Appendix G: Additional experiments and discussion The following Proposition is an intermediate result, which is need to prove Lemmas C.3 and D.1. Let us consider the statement i). B.1 Proof of Proposition 2.1 Proof: From Equation (4), we have Ψ Before proving Theorem 4.1 we give some essential definitions which will be used by our proofs. Assume that K is bounded. The previous result, together with Lemma C.1, allow us to deduce Ψ C.2 Proof of Lemma C.1 In order to prove Lemma of C.1, we require some intermediate results.

We consider settings in which the data of interest correspond to pairs of ordered times, e.g, the birth times of the first and second child, the times at which a new user creates an account and makes the first purchase on a website, and the entry and survival times of patients in a clinical trial.

Interpreting critical variables involved in complex biological processes related to survival time can help understand prediction from survival models, evaluate treatment efficacy, and develop new therapies for patients. Currently, the predictive results of deep learning (DL)-based models are better than or as good as standard survival methods, they are often disregarded because of their lack of transparency and little interpretability, which is crucial to their adoption in clinical applications. In this paper, we introduce a novel, easily deployable approach, called EXplainable CEnsored Learning (EXCEL), to iteratively exploit critical variables and simultaneously implement (DL) model training based on these variables. First, on a toy dataset, we illustrate the principle of EXCEL; then, we mathematically analyze our proposed method, and we derive and prove tight generalization error bounds; next, on two semi-synthetic datasets, we show that EXCEL has good anti-noise ability and stability; finally, we apply EXCEL to a variety of real-world survival datasets including clinical data and genetic data, demonstrating that EXCEL can effectively identify critical features and achieve performance on par with or better than the original models. It is worth pointing out that EXCEL is flexibly deployed in existing or emerging models for explainable survival data in the presence of right censoring.

We consider settings in which the data of interest correspond to pairs of ordered times, e.g, the birth times of the first and second child, the times at which a new user creates an account and makes the first purchase on a website, and the entry and survival times of patients in a clinical trial. In these settings, the two times are not independent (the second occurs after the first), yet it is still of interest to determine whether there exists significant dependence {\em beyond} their ordering in time. We refer to this notion as "quasi-(in)dependence". For instance, in a clinical trial, to avoid biased selection, we might wish to verify that recruitment times are quasi-independent of survival times, where dependencies might arise due to seasonal effects. In this paper, we propose a nonparametric statistical test of quasi-independence. Our test considers a potentially infinite space of alternatives, making it suitable for complex data where the nature of the possible quasi-dependence is not known in advance. Standard parametric approaches are recovered as special cases, such as the classical conditional Kendall's tau, and log-rank tests. The tests apply in the right-censored setting: an essential feature in clinical trials, where patients can withdraw from the study. We provide an asymptotic analysis of our test-statistic, and demonstrate in experiments that our test obtains better power than existing approaches, while being more computationally efficient.

With the incorporation of new data gathering methods in clinical research, it becomes fundamental for survival analysis techniques to deal with high-dimensional or/and non-standard covariates. In this paper we introduce a general non-parametric independence test between right-censored survival times and covariates taking values on a general (not necessarily Euclidean) space $\mathcal{X}$. We show that 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, finding sufficient conditions to ensure that our test is omnibus. The test statistic can be computed straightforwardly, and the rejection threshold is obtained via an asymptotically consistent Wild-Bootstrap procedure. We perform extensive simulations demonstrating that our testing procedure generally performs better than competing approaches in detecting complex nonlinear dependence.

Weighted log-rank tests are arguably the most widely used tests by practitioners for the two-sample problem in the context of right-censored data. Many approaches have been considered to make weighted log-rank tests more robust against a broader family of alternatives, among them: considering linear combinations of weighted log-rank tests or taking the maximum between a finite collection of them. In this paper, we propose as test-statistic the supremum of a collection of (potentially infinite) weight-indexed log-rank tests where the index space is the unit ball of a reproducing kernel Hilbert space (RKHS). By using the good properties of the RKHS's we provide an exact and simple evaluation of the test-statistic and establish relationships between previous tests in the literature. Additionally, we show that for a special family of RKHS's, the proposed test is omnibus. We finalise by performing an empirical evaluation of the proposed methodology and show an application to a real data scenario.