title: Transformations to additivity in measurement error models.
abstract: In many problems, one wants to model the relationship between a response Y and a covariate X. Sometimes it is difficult, expensive, or even impossible to observe X directly, but one can instead observe a substitute variable W that is easier to obtain. By far, the most common model for the relationship between the actual covariate of interest X and the substitute W is W = X + U, where the variable U represents measurement error. This assumption of additive measurement error may be unreasonable for certain data sets. We propose a new model, namely h(W) = h(X) + U, where h(.) is a monotone transformation function selected from some family H of monotone functions. The idea of the new model is that, in the correct scale, measurement error is additive. We propose two possible transformation families H. One is based on selecting a transformation that makes the within-sample mean and standard deviation of replicated W's uncorrelated. The second is based on selecting the transformation so that the errors (U's) fit a prespecified distribution. Transformation families used are the parametric power transformations and a cubic spline family. Several data examples are presented to illustrate the methods.
authors.affiliation: Lilly Research Laboratories, Eli Lilly and Company, Indianapolis, Indiana 46285, USA.
authors.forename: R S
authors.initials: RS
authors.lastname: Eckert
authors.forename: R J
authors.initials: RJ
authors.lastname: Carroll
authors.forename: N
authors.initials: N
authors.lastname: Wang
mesh_terms: D000328:Adult; D000368:Aged; D001699:Biometry; D003327:Coronary Disease / Q000209:etiology; D004435:Eating; D005260:Female; D006801:Humans; D008297:Male; D008875:Middle Aged; D015233:Models, Statistical; D012965:Sodium Chloride / Q000652:urine
chemical_list: D012965:Sodium Chloride