The Application Of EIV Model Based On Orthogonal Least-squares Method In Medical Research

Objective: In medical research, observed variables often contain errors. Using thetraditional analysis method could result to bias, so variables with error model(error-in-variables, EIV) is gradually being concerned in statistical circles, andresponding parameter estimation has been a hot spot in the field in recent years. Thispaper used a variable containing error model based on orthogonal least squaresestimation of the regression analysis (methods of orthogonal least-squares, orthogonalregression, OR), and explored the application in linear evaluation and the averagetreatment effect estimation.Methods: For the existence of measurement error regression models, whether linearfitting or curve fitting, the assumption is the error variance is known, or the ratio of thecredibility is known. And there are already moment estimation , maximum likelihoodestimation and tool variable method. But in the actual study, unknown error variance ismore prevalent, so in this paper, variables containing error based on orthogonal leastsquares estimation method was used to estimate the parameters of the model under theassumption that the error variance ratio is known, and expand the corresponding intervalestimation and hypothesis testing in order to facilitate further statistical inference. Thispaper also try to extend the model in multivariate linear models and nonlinear datafitting, while exploring OR method's best application conditions, then illustrate themodel results of the practical application comparing with the classical method.Result: This paper conducted linear and nonlinear data fitting considering randomerrors in the independent variable s and dependent variable at the same time. Data simulation us ed Matlab programming software . First, the model generated pre-simulation data, and then use d OR estimation, ordinary least squares (OLS) method and the moment estimation method (MM), fitting the data respectively, and compare dthe three method s with intuitive icons showing the effect of fitting the model parameters . In the example of the seven conventional biochemical test methods for linear program evaluation, fit seven sets of data in linear and polynomial ; examine the res ults of their experiments to detect the linear level . At last, we classified the results as linear 1, linear 2, nonlinear and non-precision four categories. The results showed that when the best fit is linear 1, the regression coefficient s of OR were relatively large r than OLS coefficients, which is regarded as correction for attenuation. When the best fit number is greater than 1, OR fitting's coefficients of variationgenerally smaller than the corresponding OLS method results, indicating that OR method has better precision ; and nonlinear level indicator ADL values calculated by the method OR were relatively sensitive to distinguish the nonlinear data under the premise of clinical significant , to guide the further calibration of the linear range ofpilot projects. In the average treatment effect estimation part, the estimated standard error of ATE by OR method is smaller than the other two traditional methods, which indicates that this method is effective to ensure the ATE estimationaccuracy in the presence of measurement error.Conclusionsonclusions: For linear fitting results , us e variance explained by model (VEM) toevaluate the effect, while for the non-linear data, use residual standarddeviation and area of curve fitting . The result shows that the classical fittingmethods are of course simple and practical advantages , but when the variable s'error could not be ignored , the result of OR fitting maintains the most reasonable fromthe geometric sense. When Errors of the independent variables are small enough tobe ignored, the OR method degenerates to OLS method.