Statistical issues in survival analysis (Weibull measurement error)
October 22, 2025 The authors studied the approximate maximum likelihood estimation (AMLE), which has been proved to be an effective method to correct both measurement error and misclassification simultaneously in a logistic regression model, to correct biases caused by both measurement error and misclassification in covariates from a Weibull accelerated failure time model. Measurement error correction has come out of epidemiological literature and was applied more in simple models and even logistic regression, but it has made its way to survival analysis. Several different methods were developed from Frequentist to Bayesian. Although the Weibull regression model is often modeled through the accelerated failure time (AFT) format, none of the correction methods proposed that they had cited can handle the problem when a Weibull regression model has both measurement error in continuous covariates and misclassification in categorical variables. Addressing both measurement error and misclassification simultaneously in a single survival analysis becomes challenging since one has to consider considering errors caused by different types of covariates. The authors then lay out additive measurement error and misclassification models. First they assume that the errors are non-differential. The true values of the X’s are related through surrogates through W’s via an additive error model: Wj = aj + bjXj + Uj where j=1…p and X is assumed to follow a multivariate normal distribution. Regression calibration (RC) is a widely accepted method to use for correcting measurement error. RC is the MLE of a likelihood function on the conditional expectation of true covariate on observed covariate. They show obtaining a regression calibration estimator (RCE) and native estimator using maximum likelihood approach with Newton-Raphson algorithm in the survreg function in the