Simulation extrapolation method for measurement error: A review

Abstract

Measurement error is pervasive in statistics due to the non-availability of authentic data. The reasons for measurement error mainly relate to cost, convenience, and human error. Measurement error can result in non-negligible bias due to attenuated estimates, reduced power of statistical tests, and lower coverage probabilities of the coefficient estimators in a regression model. Several methods have been proposed to correct for measurement error, all of which can be grouped into two broad categories based on the underlying model—functional and structural. Functional models provide flexibility and robustness to estimators by placing minimal or no assumptions on the distribution of the mismeasured covariate or by treating them as a fixed entity, as opposed to a structural model which treats the underlying mismeasured covariates as random with a specified structure. The simulation extrapolation method is one method that is used for the partial correction of measurement error in both structural and functional models. Reviews of measurement error correction techniques are available in the literature. However, none of the previously conducted reviews has exclusively focused on simulation extrapolation and its application in continuous measurement error models, despite its widespread use and ease of application. We attempt to close this gap in the literature by highlighting its development over the past two and a half decades.

The mean residual life model for the right‐censored data in the presence of covariate measurement errors

“…Under the Cox's proportional hazards (PH) model, there exists an abundant literature dealing with covariate measurement error. Both the regression calibration 1 and simulation extrapolation 2,3 methods can reduce the biases resulting from the naive approaches but may still lead to inconsistent estimators. Assuming normal errors, Tsiatis and Davidian 4 and Nakamura 5 proposed conditional score and corrected score approaches, respectively, to obtain consistent estimators of the regression parameters.…”

The analysis and forecast of Chinese population using ARIMA model

“…Extrapolation can be a valuable tool for making forecasts and projections, but it should be employed with care and in conjunction with a critical evaluation of the data and context to ensure the reliability of the predictions [8]. The method of using the logistic growth model is also a common approach in demography.…”