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Current status data are commonly encountered in medical and epidemiologicalstudies in which the failure time for study units is the outcome variable ofinterest. Data of this form are characterized by the fact that the failure timeis 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 itsstructure, the analysis of such data can be challenging. To circumvent thesechallenges and to provide for a flexible modeling construct which can be usedto analyze current status data, herein, a partially linear additivetransformation model is proposed. In the formulation of this model, constrained$B$-splines are employed to model the monotone transformation function andnonlinear covariate effects. To provide for more efficient estimates, apenalization technique is used to regularize the estimation of all unknownfunctions. An easy to implement hybrid algorithm is developed for model fittingand a simple estimator of the large-sample variance-covariance matrix isproposed. It is shown theoretically that the proposed estimators of thefinite-dimensional regression coefficients are root-$n$ consistent,asymptotically normal, and achieve the semi-parametric information bound whilethe estimators of the nonparametric components attain the optimal rate ofconvergence. The finite-sample performance of the proposed methodology isevaluated through extensive numerical studies and is further demonstratedthrough the analysis of uterine leiomyomata data.

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