arXiv subjects

Yael Travis-Lumer

Publications and source records attributed to Yael Travis-Lumer.

3 recordsLinked to original sources

arXiv2025

Cox Regression on the Plane

The Cox proportional hazards model is the most widely used regression model in univariate survival analysis, yet extensions to bivariate survival data remain scarce. We propose two novel extensions based on a Lehmann-type representation of the survival function. The first, the simple Lehmann model, is a direct extension that retains a straightforward structure. The second, the generalized Lehmann model, allows greater flexibility by incorporating three distinct regression parameters and includes the simple Lehmann model as a special case. The models admit a direct interpretation in terms of survival probabilities, providing a transparent, fully semiparametric framework for assessing covariate effects on both marginal survival probabilities and their dependence, without requiring specification of a copula or frailty distribution. To estimate the regression parameters, we build on a pseudo-observation-based approach for bivariate survival data and extend it to the generalized model via a two-step procedure. We establish consistency and asymptotic normality of the resulting estimators. The proposed approach is illustrated through simulation studies and an application to data from the Global Retinoblastoma Outcome Study.

stat.ME↗

arXiv2024

Pseudo-Observations for Bivariate Survival Data

The pseudo-observations approach has been gaining popularity as a method to estimate covariate effects on censored survival data. It is used regularly to estimate covariate effects on quantities such as survival probabilities, restricted mean life, cumulative incidence, and others. In this work, we propose to generalize the pseudo-observations approach to situations where a bivariate failure-time variable is observed, subject to right censoring. The idea is to first estimate the joint survival function of both failure times and then use it to define the relevant pseudo-observations. Once the pseudo-observations are calculated, they are used as the response in a generalized linear model. We consider two common nonparametric estimators of the joint survival function: the estimator of Lin and Ying (1993) and the Dabrowska estimator (Dabrowska, 1988). For both estimators, we show that our bivariate pseudo-observations approach produces regression estimates that are consistent and asymptotically normal. Our proposed method enables estimation of covariate effects on quantities such as the joint survival probability at a fixed bivariate time point, or simultaneously at several time points, and consequentially can estimate covariate-adjusted conditional survival probabilities. We demonstrate the method using simulations and an analysis of two real-world datasets.

stat.ME↗

arXiv2019

Kernel Machines for Current Status Data

In survival analysis, estimating the failure time distribution is an important and difficult task, since usually the data is subject to censoring. Specifically, in this paper we consider current status data, a type of data where all of the observations are censored. The format of the data is such that the failure time is restricted to knowledge of whether or not the failure time exceeds a random monitoring time. We propose a flexible kernel machine approach for estimation of the failure time expectation as a function of the covariates, with current status data. In order to obtain the kernel machine decision function, we minimize a regularized version of the empirical risk with respect to a new loss function. Using finite sample bounds and novel oracle inequalities, we prove that the obtained estimator converges to the true conditional expectation for a large family of probability measures. Finally, we present a simulation study and an analysis of real-world data that compares the performance of the proposed approach to existing methods. We show empirically that our approach is comparable to current state of the art, and in some cases is even better.

math.ST↗