The Application Of Statistical Methods In Evaluating Limit Of Detection

With the development of analytical methods, the R&D of sophisticated instruments and the requirement for the accuracy of measurement, trace analysis has become an important topic in modern analytical chemistry. As the development of trace analysis methodology, there are a series of problems related to the analytical methods for the analyte under very lower concentration. The evaluation of limit of detection (LOD) is one of critical issues in trace analysis. This paper mainly focus on how to determine the limit of detection based on the calibration curve.In the experiment to determine the limit of detection, the spiked concentration X was fixed before the experiment. However, the true value x of the concentration is often unknown because of the possible errors. Thus, the true value x may be expressed as the spiked concentration X plus i random error. Taking this into consideration, the calibration curve can be considered as a regression model with errors in variable (EV). It is clear that the Berkson measurement error model is more suitable for the above discussion than classical EV model. In addition, the calibration curve may be linear or nonlinear (such as the quadratic polynomial model, the exponential model and so on). Many studies have already been done when the calibration curve is linear. As far as we know, there is little discussion for the nonlinear model.Firstly, the methods to determine the LOD under the quadratic calibration model are discussed. Based on the estimators of parameters with least square error (LSE) criterion and its properties, two different methods are provided. As the explicit expression can’t be given, numerical analysis methods (for example, method of bisection) to get the approximation solutions can be considered.Secondly, we consider the case that the true value of the concentration can’t be observed directly. For the linear calibration model, we discuss the related linear Berkson model. The parameters are estimated by using LSE. With the unbiasedness and normality of estimators, LOD are derived under certain assumption. Then, for the calibration curve with quadratic form, the quadratic polynomial Berkson model is applied. The estimators are obtained by the minimum distance estimation (MDE). It was proved that consistency and asymptotic normality hold for the estimators. By the definitions of critical value and LOD, method to determine the LOD under the concept of prediction interval is given. In order to gain the numerical results, concrete algorithm is given, where BFGS algorithm as i variant of quasi-Newton method is used.Finally, simulation results are given to show the importance of taking the error in concentration into consideration. As a matter of fact, there is much difference between whether we consider the error or not. The result suggests that there is significant difference between them in some cases.For ease of practical use, the dissertation provides the procedures to determine the LOD based on cali-bration curve, where some important issues (such as testing for normality, testing for homogeneity of variance, selecting suitable calibration model and so on) are included. A real example is provided to show the whole process.