Imputation and likelihood methods for matrix-variate logistic regression with response misclassification

Matrix-variate logistic regression is useful in facilitating the relationship between the binary response and matrix-variates, which arise commonly from medical imaging research. However, such a model is impaired by the presence of response misclassification. It is imperative to account for the misclassification effects when employing matrix-variate logistic regression to handle such data. In this article, we develop two inferential methods that account for the misclassification effects. The first method, called an imputation method, has roots in the score function derived from the misclassification-free context, and replaces the involved response variable with an unbiased pseudo-response variable, i.e., expressed in terms of the observed surrogate measurement. The second method is to directly derive the likelihood function for the observed response surrogate and then conduct estimation accordingly. Our development is carried out for two settings where misclassification rates are either known or estimated from validation data. The proposed methods are justified both theoretically and empirically. We analyze the Breast Cancer Wisconsin (Prognostic) data with the proposed methods.

Automated summary

This article introduces two inferential methods for matrix-variate logistic regression that account for response misclassification effects, including an imputation method and a method directly deriving the likelihood function for observed response surrogates. Both methods are theoretically and empirically validated, and demonstrated to be effective in analyzing the Breast Cancer Wisconsin (Prognostic) data.