“…For example, in a study of the relationship between fibrinogen level and serum transferrin level among hemodialysis patients, Kaysen et al [15] analyzed the fibrinogen level and serum transferrin level by firstly normalizing them by BMI, which indicates that there may exist a multiplicative fashion relationship between the unobserved primary variables and the confounding variables. For the statistical modeling of the distortion measurement errors data, readers can refer to the parametric models [3,[27][28][29][32][33][34][35][36]46,47,51,53], the partial linear models [21], the partial linear single index models [52], the dimension reduction models [54]. However, these existing literature do not consider estimation proposals for the PLAMs under the distortion measurement errors setting.…”