A simulation study for a linear measurement error model when error variances vary between measurements

When predicting scores in the Draize eye irritation test based on measurements of in vitro alternative tests, we are often faced with estimating parameters in a linear measurement error model with heterogeneous error variances. This article proposes a new statistical method for parameter estimation to address this issue. The proposed method is an extension of an earlier proposal that applied a linear measurement error model with homogeneous error variances, to cases with heterogeneous error variances. A simulation study to examine the performance of the proposed method was conducted in a framework that was adaptable to the data, which was obtained in a validation study of alternative methods to animal experiments conducted in Japan. The proposed method reduced the biases of estimates in comparison with an ordinary regression analysis method and three other methods under the assumption of homogeneous error variances. Although the proposed method did not fit the real data well, the resulting prediction formula was far better than those obtained by other methods.