Random-effects models for longitudinal data with errors-in-variables
Description
There is a vast literature on parameter estimation for linear models in which one or more variables is measurement with error. However little of this methodology has been applied to models for longitudinal analysis. Laird and Ware (1982) proposed a general family of random effects models which have been very popular for longitudinal analysis. The focus of this research is on parameter estimation for the family of random effects models when one or more of the covariate variables is measured with error. The research consists of three parts: development of estimation methodology, evaluation of this methodology and analysis of data The estimation methodology is developed as an extension of the usual EM algorithm for random effects models. Modifications necessary for some different models among the random effects family are considered. The methodology is flexible and allows for estimation when the measurement error covariance matrices are known and when only estimates are available To evaluate the new methodology, a simulation study was conducted. The results of the simulation study suggest that when the measurement error is additive and the measurement error variance is known, parameter estimation is improved by using the correction methodology. The correction methodology appears to be robust to both non-normal covariates and non-normal measurement errors. If the measurement error variance is unknown, but a good estimate is available, the correction methodology may still provide better estimates than the uncorrected methodology. If a good estimate of the measurement error variance is unavailable, an analysis might be improved by examining the sensitivity of the parameter estimates to potential levels of measurement error The new estimation methodology was used to analyze data from an occupational study which examined the relationship between pulmonary function and cotton dust exposure. Results of the analysis indicate that if a considerable proportion of the variability in the exposure measures is due to measurement error, the magnitude of the association between annual decline in lung function and average exposure may have been substantially underestimated. Since an estimate of the measurement error variability was unavailable the extent of this underestimation could not be precisely determined. In the future, greater emphasis should be placed on the characterization and correction of measurement error in longitudinal studies