arXiv subjects

Xijia Liu

Publications and source records attributed to Xijia Liu.

5 recordsLinked to original sources

arXiv2026

Rethinking Individual Risk and Aggregation in Survival Analysis: A Latent Mechanism Framework

Survival analysis provides a well-established framework for modeling time-to-event data, with hazard and survival functions formally defined as population-level quantities. In applied work, however, these quantities are often interpreted as representing individual-level risk, despite the absence of a clear generative account linking individual risk mechanisms to observed survival data. This paper develops a latent hazard framework that makes this relationship explicit by modeling event times as arising from unobserved, individual-specific hazard mechanisms and viewing population-level survival quantities as aggregates over heterogeneous mechanisms. Within this framework, we show that individual hazard trajectories are not identifiable from survival data under partial information. More generally, the conditional distribution of latent hazard mechanisms given covariates is structurally non-identifiable, even when population-level survival functions are fully known. This non-identifiability arises from the aggregation inherent in survival data and persists independently of model flexibility or estimation strategy. Finally, we show that classical survival models can be systematically reinterpreted according to how they handle this unresolved conditional mechanism distribution. This paper provides a unified framework for understanding heterogeneity, identifiability, and interpretation in survival analysis, and clarifies how population-level survival models should be interpreted when individual risk mechanisms are only partially observed, thereby establishing explicit information constraints for principled modeling and inference.

stat.ME↗

arXiv2026

Doubly robust estimation with functional outcomes missing at random

We present and study semi-parametric estimators for the mean of functional outcomes in situations where some of these outcomes are missing and covariate information is available on all units. Assuming that the missingness mechanism depends only on the covariates (missing at random assumption), we present two estimators for the functional mean parameter, using working models for the functional outcome given the covariates, and the probability of missingness given the covariates. We contribute by establishing that both these estimators have Gaussian processes as limiting distributions and explicitly give their covariance functions. One of the estimators is double robust in the sense that the limiting distribution holds whenever at least one of the nuisance models is correctly specified. These results allow us to present simultaneous confidence bands for the mean function with asymptotically guaranteed coverage. A Monte Carlo study shows the finite sample properties of the proposed functional estimators and their associated simultaneous inference. The use of the method is illustrated in an application where the mean of counterfactual outcomes is targeted.

math.ST↗

arXiv2020

Splinets -- efficient orthonormalization of the B-splines

A new efficient orthogonalization of the B-spline basis is proposed and contrasted with some previous orthogonalized methods. The resulting orthogonal basis of splines is best visualized as a net of functions rather than a sequence of them. For this reason, the basis is referred to as a splinet. The splinets feature clear advantages over other spline bases. They efficiently exploit 'near-orthogonalization' featured by the B-splines and gains are achieved at two levels: locality that is exhibited through small size of the total support of a splinet and computational efficiency that follows from a small number of orthogonalization procedures needed to be performed on the B-splines to achieve orthogonality. These efficiencies are formally proven by showing the asymptotic rates with respect to the number of elements in a splinet. The natural symmetry of the B-splines in the case of the equally spaced knots is preserved in the splinets, while quasi-symmetrical features are also seen for the case of arbitrarily spaced knots.

math.ST↗

arXiv2019

Statistical Methods in Computed Tomography Image Estimation

Purpose: There is increasing interest in computed tomography (CT) image estimations from magnetic resonance (MR) images. The estimated CT images can be utilised for attenuation correction, patient positioning, and dose planning in diagnostic and radiotherapy workflows. This study aims to introduce a novel statistical learning approach for improving CT estimation from MR images and to compare the performance of our method with the existing model based CT image estimation methods. Methods: The statistical learning approach proposed here consists of two stages. At the training stage, prior knowledges about tissue-types from CT images were used together with a Gaussian mixture model (GMM) to explore CT image estimations from MR images. Since the prior knowledges are not available at the prediction stage, a classifier based on RUSBoost algorithm was trained to estimate the tissue-types from MR images. For a new patient, the trained classifier and GMMs were used to predict CT image from MR images. The classifier and GMMs were validated by using voxel level 10-fold cross-validation and patient-level leave-one-out cross-validation, respectively. Results: The proposed approach has outperformance in CT estimation quality in comparison with the existing model based methods, especially on bone tissues. Our method improved CT image estimation by 5% and 23% on the whole brain and bone tissues, respectively. Conclusions: Evaluation of our method shows that it is a promising method to generate CT image substitutes for the implementation of fully MR-based radiotherapy and PET/MRI applications.

stat.ME↗

arXiv2017

Contrast Agent Quantification by Using Spatial Information in Dynamic Contrast Enhanced MRI

The purpose of this study is to investigate a method, using simulations, to improve contrast agent quantification in Dynamic Contrast Enhanced MRI. Bayesian hierarchical models (BHMs) are applied to smaller images ($10\times10\times10$) such that spatial information can be incorporated. Then exploratory analysis is done for larger images ($64\times64\times64$) by using maximum a posteriori (MAP). For smaller images: the estimators of proposed BHMs show improvements in terms of the root mean squared error compared to the estimators in existing method for a noise level equivalent of a 12-channel head coil at 3T. Moreover, Leroux model outperforms Besag models. For larger images: MAP estimators also show improvements by assigning Leroux prior.

stat.AP↗