Abstract

The linear transformation model is one of the most commonly used classes of

models for regression analysis of failure time data.

In this paper, we consider its

estimation based on interval-censored data in the presence of both functional and

missing covariates with the focus on simultaneous estimation and variable selection, a

problem for which it does not seem to exist an established approach. For the problem, we first consider estimation and develop a sieve maximum likelihood estimation

procedure based on functional principal component analysis and the use of the inverse

probability weighting technique to handle the infinite-dimensional nature of functional

predictors and missing-at-random covariates, respectively. Then we consider variable

selection and propose a penalized estimation approach by employing the minimum

approximated information criterion, which eliminates the need for tuning parameter

selection that is required for most of the existing methods. The proposed estimators

are shown to be consistent and possess the oracle property, and a simulation study

is conducted and suggests that the proposed methods work well in practice. Finally,

they are applied to an Alzheimer’s Disease study that motivated this investigation and

the analysis provides some new insights about the roles of high-dimensional imaging

and clinical factors.

Key words and phrases: Functional data analysis; Interval-censored data; Penalized likelihood; Transfor- mation model; Variable selection

Information

Preprint No.SS-2026-0046
Manuscript IDSS-2026-0046
Complete AuthorsYichen Lou, Mingyue Du, Jianguo Sun
Corresponding AuthorsMingyue Du
Emailsmingydu@jlu.edu.cn

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Acknowledgments

The authors wish to thank the Co-Editor, Dr. John Stufken, the Associate Editor and a reviewer

for their many insightful and valuable comments and suggestions that greatly improved the paper.

The research was partly supported by Scientific Research Foundation of the Education Department

of Jilin Province (Grant No. JJKH20261483KJ) to the second author.

Supplementary Materials

contains the required regularity conditions and the proofs of Theorems 1

and 2 as well as some extra numerical results.

Supplementary materials are available for download.