# A penalized likelihood approach for efficiently estimating a partially linear additive transformation model with current status data

## TL;DR

This paper introduces a penalized likelihood method for efficiently estimating a flexible partially linear additive transformation model tailored for current status data, addressing challenges in medical and epidemiological research.

## Contribution

It proposes a novel penalized likelihood approach with constrained B-splines for modeling monotone transformations and nonlinear effects, along with an efficient hybrid algorithm for estimation.

## Key findings

- Estimators of regression coefficients are root-n consistent and asymptotically normal.
- Nonparametric estimators achieve optimal convergence rates.
- Method performs well in simulations and real data analysis.

## Abstract

Current status data are commonly encountered in medical and epidemiological studies in which the failure time for study units is the outcome variable of interest. Data of this form are characterized by the fact that the failure time is not directly observed but rather is known relative to an observation time; i.e., the failure times are either left- or right-censored. Due to its structure, the analysis of such data can be challenging. To circumvent these challenges and to provide for a flexible modeling construct which can be used to analyze current status data, herein, a partially linear additive transformation model is proposed. In the formulation of this model, constrained $B$-splines are employed to model the monotone transformation function and nonlinear covariate effects. To provide for more efficient estimates, a penalization technique is used to regularize the estimation of all unknown functions. An easy to implement hybrid algorithm is developed for model fitting and a simple estimator of the large-sample variance-covariance matrix is proposed. It is shown theoretically that the proposed estimators of the finite-dimensional regression coefficients are root-$n$ consistent, asymptotically normal, and achieve the semi-parametric information bound while the estimators of the nonparametric components attain the optimal rate of convergence. The finite-sample performance of the proposed methodology is evaluated through extensive numerical studies and is further demonstrated through the analysis of uterine leiomyomata data.