A regularization corrected score method for nonlinear regression models with covariate error

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 maximum likelihood estimation for logistic regression with covariate measurement error

In nutritional epidemiology, dietary intake assessed with a food frequency questionnaire is prone to measurement error. Ignoring the measurement error in covariates causes estimates to be biased and leads to a loss of power. In this paper, we consider an additive error model according to the characteristics of the European Prospective Investigation into Cancer and Nutrition (EPIC)-InterAct Study data, and derive an approximate maximum likelihood estimation (AMLE) for covariates with measurement error under logistic regression. This method can be regarded as an adjusted version of regression calibration and can provide an approximate consistent estimator. Asymptotic normality of this estimator is established under regularity conditions, and simulation studies are conducted to empirically examine the finite sample performance of the proposed method. We apply AMLE to deal with measurement errors in some interested nutrients of the EPIC-InterAct Study under a sensitivity analysis framework.

The role of matching when adjusting for baseline differences in the outcome variable of comparative effectiveness studies

AIM

Evaluate performance of analytical strategies commonly used to adjust for baseline differences in continuous outcome variables for comparative effectiveness studies.

PATIENTS & METHODS

Data simulations resembling a comparison of HbA1c values after initiation of antidiabetic treatments adjusting for baseline HbA1c. We evaluated change scores, analyses of covariance including linear, nonlinear with/without robust variance estimations, before and after optimal matching. We also evaluated the impact of measurement error.

RESULTS

With increasing HbA1c baseline differences between groups, bias in effect estimates and suboptimal CI coverage probabilities increased in all approaches. These issues were further compounded by measurement error. Matching on baseline HbA1c, substantially mitigated these issues.

CONCLUSION

In comparative studies with continuous outcomes, matching on baseline values of the outcome variable improves analytical performance.