Regression Analysis with a Misclassified Covariate from a Current Status Observation Scheme

Abstract

Naive use of misclassified covariates leads to inconsistent estimators of covariate effects in regression models. A variety of methods have been proposed to address this problem including likelihood, pseudo-likelihood, estimating equation methods, and Bayesian methods, with all of these methods typically requiring either internal or external validation samples or replication studies. We consider a problem arising from a series of orthopedic studies in which interest lies in examining the effect of a short-term serological response and other covariates on the risk of developing a longer term thrombotic condition called deep vein thrombosis. The serological response is an indicator of whether the patient developed antibodies following exposure to an antithrombotic drug, but the seroconversion status of patients is only available at the time of a blood sample taken upon the discharge from hospital. The seroconversion time is therefore subject to a current status observation scheme, or Case I interval censoring, and subjects tested before seroconversion are misclassified as nonseroconverters. We develop a likelihood-based approach for fitting regression models that accounts for misclassification of the seroconversion status due to early testing using parametric and nonparametric estimates of the seroconversion time distribution. The method is shown to reduce the bias resulting from naive analyses in simulation studies and an application to the data from the orthopedic studies provides further illustration.

Using the accelerated failure time model to analyze current status data with misclassified covariates

“…However, patients were only tested at the time of hospital discharge, which in general is less than 10 days. According to Zeng, Cook and Warkentin [43], the median time from surgery to blood test is 5.9 days, and most seroconversions occur between 5 and 8 days. Therefore, negative test results may represent false negative classifications of the true seroconversion status since these patients may have been tested before they developed the antibody response.…”

“…where in the last step we used the fact that Y is independent of C, and that given (X, Z), D has no predictive value on Y ( [43]), so that P (Y | X, D, Z, C) = P (Y | X, Z), and that X is independent of C, so P (X | Z, C) = P (X | Z). Note that P (Z, C) contains no parameter of interest, so for inference of parameters of interest, we only need to consider the conditional density-mass function…”

“…). Maximizing Q 1 (β;θ (t) ,F (t) ) with respect to β can be easily achieved using standard statistical software by creating a pseudo-data set similar to [43].…”

“…We show the convergence of the estimators based on the following theorems: → 0, Condition (C0) is commonly assumed for this type of problem, such as in [43].…”

“…Zeng, Cook and Warkentin [43] considered a logistic regression analysis with a misclassified covariate from a current status observation scheme, from which they developed a likelihood-based approach for fitting regression models. Parametric and nonparametric estimates for the distribution of failure (seroconversion) time were developed.…”