Sieve Maximum Likelihood Estimator for Semiparametric Regression Models With Current Status Data

• Published in: Journal of the American Statistical Association Vol. 99; no. 466; pp. 346 - 356
• Main Authors: Xue, Hongqi, Lam, K. F, Li, Guoying
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.06.2004; American Statistical Association; Taylor & Francis Ltd
• Subjects: Applications; Asymptotically efficient estimator; Biology, psychology, social sciences; Calcification; Clinical research; Clinical trials; Convergence; Cost analysis; Data analysis; Data collection; Estimators; Exact sciences and technology; Fisher information; General topics; Linear inference, regression; Linear models; Linear regression; Mathematical functions; Mathematical independent variables; Mathematical methods; Mathematics; Maximum likelihood estimation; Maximum likelihood estimator; Maximum likelihood estimators; Medical sciences; Optimal convergence rate; Optimization algorithms; Partial linear model; Probability and statistics; Regression analysis; Research methods; Sample size; Sciences and techniques of general use; Simulation; Statistical methods; Statistics; Strongly consistent; Theory and Methods; Asymptotic property; Asymptotic behavior; Rate function; Nonparametric regression; Gaussian distribution; Non parametric estimation; Parametric model; Covariate; Semiparametric method; Statistical simulation; Semiparametric model; Convergence; Parametric method; Statistical method; Statistical regression; Response function; Randomized design; Regression model; Convergence rate; Clinical trial; Asymptotic approximation; Maximum likelihood; Application
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/016214504000000313

In a randomized controlled clinical trial study where the response variable of interest is the time to occurrence of a certain event, it is often too expensive or even impossible to observe the exact time. However, the current status of the subject at a random time of inspection is much more natural, feasible, and practical in terms of cost-effectiveness. This article considers a semiparametric regression model that consists of parametric and nonparametric regression components. A sieve maximum likelihood estimator (MLE) is proposed to estimate the regression parameter, allowing exploration of the nonlinear relationship between a certain covariate and the response function. Asymptotic properties of the proposed sieve MLEs are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. Moreover, the estimators of the unknown parameters are asymptotically efficient and normally distributed, and the estimator of the nonparametric function has an optimal convergence rate. Simulation studies were carried out to investigate the performance of the proposed method. For illustration purposes, the method is applied to a dataset from a study of the calcification of the hydrogel intraocular lenses, a complication of cataract treatment.