Improving efficiency using the Rao-Blackwell theorem in corrected and conditional score estimation methods for joint models.

Longitudinal covariates in survival models are generally analyzed using random effects models. By framing the estimation of these survival models as a functional measurement error problem, semiparametric approaches such as the conditional score or the corrected score can be applied to find consistent estimators for survival model parameters without distributional assumptions on the random effects. However, in order to satisfy the standard assumptions of a survival model, the semiparametric methods in the literature only use covariate data before each event time. This suggests that these methods may make inefficient use of the longitudinal data. We propose an extension of these approaches that follows a generalization of Rao-Blackwell theorem. A Monte Carlo error augmentation procedure is developed to utilize the entirety of longitudinal information available. The efficiency improvement of the proposed semiparametric approach is confirmed theoretically and demonstrated in a simulation study. A real data set is analyzed as an illustration of a practical application.

A functional inference for multivariate current status data with mismeasured covariate.

Covariate measurement error problems have been recently studied for current status failure time data but not yet for multivariate current status data. Motivated by the three-hypers dataset from a health survey study, where the failure times for three-hypers (hyperglycemia, hypertension, hyperlipidemia) are subject to current status censoring and the covariate self-reported body mass index may be subject to measurement error, we propose a functional inference method under the proportional odds model for multivariate current status data with mismeasured covariates. The new proposal utilizes the working independence strategy to handle correlated current status observations from the same subject, as well as the conditional score approach to handle mismeasured covariate without specifying the covariate distribution. The asymptotic theory, together with a stable computation procedure combining the Newton-Raphson and self-consistency algorithms, is established for the proposed estimation method. We evaluate the method through simulation studies and illustrate it with three-hypers data.

Differential measurement errors in zero-truncated regression models for count data.

Measurement errors in covariates may result in biased estimates in regression analysis. Most methods to correct this bias assume nondifferential measurement errors-i.e., that measurement errors are independent of the response variable. However, in regression models for zero-truncated count data, the number of error-prone covariate measurements for a given observational unit can equal its response count, implying a situation of differential measurement errors. To address this challenge, we develop a modified conditional score approach to achieve consistent estimation. The proposed method represents a novel technique, with efficiency gains achieved by augmenting random errors, and performs well in a simulation study. The method is demonstrated in an ecology application.