Estimation of copolymerization reactivity ratios in the Berkson error regression model

Рассматривается проблема оценки относительной активности мономеров на основе дифференциального уравнения сополимеризации. Обосновано включение в модель погрешности измерения входного признака в виде ошибки Берксона. Предложен алгоритм одновременного оценивания констант сополимеризации и дисперсий ошибок с помощью метода максимального правдоподобия. На примере сополимеризации виниловых эфиров произведено сравнение разных методов оценивания констант сополимеризации. Показано, что метод на основе симметричных уравнений дает некорректные результаты. Результаты оценивания с помощью предложенного алгоритма наиболее близки к оценкам, полученным по нелинейному методу наименьших квадратов Purpose. The purpose of this paper is to study methods for estimating copolymerization reactivity ratios based on the differential composition equation. Methodology. Most estimation methods reduce the differential composition equation to a linear form. They are based on the least squares method and do not take into account the measurement error in the input variable. Therefore they lead to statistically incorrect results. When analyzing the problem on the basis of the error-in-variables model in the classical case, additional information is required to determine the magnitude of the errors in measuring the concentration of monomers in the mixture and in the copolymer. Inclusion of the measurement error in the input variable into the model as the Berkson error is more consistent with the actual conditions of the experiments. It allows simultaneous estimating both the reactivity ratios and the variances of measurement errors using the maximum likelihood method. Results. The algorithm have been developed for estimating reactivity ratios with no additional information. The empirical study of estimation methods has been carried out using the example of copolymerization of vinyl esters. Findings. It is shown that the method based on symmetric equations gives incorrect results. Estimation results using the proposed algorithm are closest to the estimates obtained by the nonlinear least squares method

Bias due to Berkson error: issues when using predicted values in place of observed covariates

Summary Studies often want to test for the association between an unmeasured covariate and an outcome. In the absence of a measurement, the study may substitute values generated from a prediction model. Justification for such methods can be found by noting that, with standard assumptions, this is equivalent to fitting a regression model for an outcome variable when at least one covariate is measured with Berkson error. Under this setting, it is known that consistent or nearly consistent inference can be obtained under many linear and nonlinear outcome models. In this article, we focus on the linear regression outcome model and show that this consistency property does not hold when there is unmeasured confounding in the outcome model, in which case the marginal inference based on a covariate measured with Berkson error differs from the same inference based on observed covariates. Since unmeasured confounding is ubiquitous in applications, this severely limits the practical use of such measurements, and, in particular, the substitution of predicted values for observed covariates. These issues are illustrated using data from the National Health and Nutrition Examination Survey to study the joint association of total percent body fat and body mass index with HbA1c. It is shown that using predicted total percent body fat in place of observed percent body fat yields inferences which often differ significantly, in some cases suggesting opposite relationships among covariates.