Correcting for Measurement Error in Segmented Cox Model
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Measurement error in the covariate of main interest (e.g. the exposure variable, or the risk factor) is common in epidemiologic and health studies. It can effect the relative risk estimator or other types of coefficients derived from the fitted regression model. In order to perform a measurement error analysis, one needs information about the error structure. Two sources of validation data are an internal subset of the main data, and external or independent study. For the both sources, the true covariate is measured (that is, without error), or alternatively, its surrogate, which is error-prone covariate, is measured several times (repeated measures). This paper compares the precision in estimation via the different validation sources in the Cox model with a changepoint in the main covariate, using the bias correction methods RC and RR. The theoretical properties under each validation source is presented. In a simulation study it is found that the best validation source in terms of smaller mean square error and narrower confidence interval is the internal validation with measure of the true covariate in a common disease case, and the external validation with repeated measures of the surrogate for a rare disease case. In addition, it is found that addressing the correlation between the true covariate and its surrogate, and the value of the changepoint, is needed, especially in the rare disease case.
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