Approximate maximum likelihood estimation for logistic regression with covariate measurement error

Optimal model averaging for partially linear models with missing response variables and error-prone covariates

We consider the problem of optimal model averaging for partially linear models when the responses are missing at random and some covariates are measured with error. A novel weight choice criterion based on the Mallows-type criterion is proposed for the weight vector to be used in the model averaging. The resulting model averaging estimator for the partially linear models is shown to be asymptotically optimal under some regularity conditions in terms of achieving the smallest possible squared loss. In addition, the existence of a local minimizing weight vector and its convergence rate to the risk-based optimal weight vector are established. Simulation studies suggest that the proposed model averaging method generally outperforms existing methods. As an illustration, the proposed method is applied to analyze an HIV-CD4 dataset.

Logistic regression with correlated measurement error and misclassification in covariates

Many areas of research, such as nutritional epidemiology, may encounter measurement errors of continuous covariates and misclassification of categorical variables when modeling. It is well known that ignoring measurement errors or misclassification can lead to biased results. But most research has focused on solving these two problems separately. Addressing both measurement error and misclassification simultaneously in a single analysis is less actively studied. In this article, we propose a new correction method for a logistic regression to handle correlated error variables involved in multivariate continuous covariates and misclassification in a categorical variable simultaneously. It is not computationally intensive since a closed-form of the approximate likelihood function conditional on observed covariates is derived. The asymptotic normality of this proposed estimator is established under regularity conditions and its finite-sample performance is empirically examined by simulation studies. We apply this new estimation method to handle measurement error in some nutrients of interest and misclassification of a categorical variable named physical activity in the European Prospective Investigation into Cancer and Nutrition-InterAct Study data. Analyses show that fruit is negatively associated with type 2 diabetes for a group of women doing active physical activity, protein has positive association with type 2 diabetes for the group of less active physical activity, and actual physical activity has a greater effect on reducing the risk of type 2 diabetes than observed physical activity.

Approximate profile likelihood estimation for Cox regression with covariate measurement error

In nutritional epidemiology, measurement error in covariates is a well-known problem since dietary intakes are usually assessed through self-reporting. In this article, we consider an additive error model in which error variables are highly correlated, and propose a new method called approximate profile likelihood estimation (APLE) for covariates measured with error in the Cox regression. Asymptotic normality of this estimator is established under regularity conditions, and simulation studies are conducted to examine the finite sample performance of the proposed estimator empirically. Moreover, the popular correction method called regression calibration is shown to be a special case of APLE. We then apply APLE to deal with measurement error in some nutrients of interest in the EPIC-InterAct Study under a sensitivity analysis framework.