Abstract
Current status data arise commonly in applications when there is only one feasible observation time to check if the failure time has occurred, but the exact failure time remains unknown. To accommodate the covariate effect on failure time, the accelerated failure time (AFT) model has been widely used to analyze current status data with the distribution of the failure time assumed to be specified or unspecified. In this paper, we consider a logistic regression with a misclassfied covariate from the current status observation scheme. A semiparametric AFT model was built to model current status data to eliminate the bias caused by this misclassification. This model is also robust to the misspecification of the failure time compared to the parametric AFT model, as we assume an unknown distribution of the failure time in the proposed model. Furthermore, incorporating the covariate effect on the failure time increases the flexibility of the model. Finally, we adapt the Expectation-Maximization algorithm for estimation, which guarantees the convergence of the estimate. Both theory and empirical studies show the consistency of the estimator.
Highlights
In many applications, it is challenging to obtain an accurate measurement of a covariate
Lam and Xue [21] and Cook et al [9] developed semiparametric cure rate models to allow for the fact that not all individuals in the population are susceptible to such an event
We assess the performance of the proposed method by comparing the following methods: (i) the naıve method by using a logistic regression model and including the current status indicator Di as a covariate (Naive), i.e., we fit the model (3.4); (ii) the proposed method by fitting a semiparametric accelerated failure time (AFT) model for the seroconversion time (Proposed); (iii) the method by fitting a correctly specified parametric AFT model for the seroconversion time, which serves as a benchmark for comparisons (Parametric); and (iv) the method developed by [43] using a nonparametric estimate of the seroconversion time distribution (ZCW)
Summary
It is challenging to obtain an accurate measurement of a covariate. In practice, it is desirable to accommodate some covariates when modeling the distribution of the failure time To overcome this problem, in this paper we consider a logistic regression analysis with a misclassified covariate from a current status observation scheme, in which a semiparametric AFT model for the failure time was built. Both in theory and in simulation studies, all estimators are consistent under some regularity conditions This method is appealing in that it corrects the bias from covariate misclassification in the current status scheme. It accommodates the dependence of the failure time on covariates, leading to a more accurate and flexible model.
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