title: Evaluating Variables as Unbiased Proxies for Other Measures: Assessing the Step Test Exercise Prescription as a Proxy for the Maximal, High-intensity Peak Oxygen Consumption in Older Adults.
abstract: To assess validity of a low-intensity measure of fitness (X) in a population of older adults as a proxy measure for the original, high-intensity measure (Y), we used ordinary least square regression with the new, potential proxy measure (X) as the sole explanatory variable forY. A perfect proxy measure would be unbiased (i.e., result in a regression line with ay-intercept of zero and a slope of one) with no error (variance equal to zero). We evaluated the properties of potential biases of proxy measures. A two degree-of-freedom approach using a contrast matrix in the setting of simple linear ordinary least squares regression was compared to a one degree-of-freedom pairedttest alternative approach. We found that substantial improvements in power could be gained through use of the two degree-of-freedom approach in many settings, while scenarios where no linear bias was present there could be modest gains from the pairedttest approach. In general, the advantages of the two degree-of-freedom approach outweighed the benefits of the one degree-of-freedom approach. Using the two degree-of-freedom approach, we assessed the data from our motivating example and found that the low-intensity fitness measure was biased, and thus was not a good proxy for the original, high-intensity measure of fitness in older adults.
authors.affiliation: Department of Biostatistics, The University of Kansas Medical Center, Kansas City, KS, U.S.A ; The University of Kansas Alzheimer's Disease Center, Kansas City, KS, U.S.A.
authors.forename: Jonathan D
authors.initials: JD
authors.lastname: Mahnken
authors.affiliation: Department of Biostatistics, The University of Kansas Medical Center, Kansas City, KS, U.S.A.
authors.forename: Xueyi
authors.initials: X
authors.lastname: Chen
authors.affiliation: Department of Biostatistics, The University of Kansas Medical Center, Kansas City, KS, U.S.A.
authors.forename: Alexandra R
authors.initials: AR
authors.lastname: Brown
authors.affiliation: The University of Kansas Alzheimer's Disease Center, Kansas City, KS, U.S.A ; Department of Neurology, The University of Kansas Medical Center, Kansas City, KS, U.S.A.
authors.forename: Eric D
authors.initials: ED
authors.lastname: Vidoni
authors.affiliation: Department of Physical Therapy and Rehabilitation Science, The University of Kansas Medical Center, Kansas City, KS, U.S.A.
authors.forename: Sandra A
authors.initials: SA
authors.lastname: Billinger
authors.affiliation: Department of Biostatistics, The University of Kansas Medical Center, Kansas City, KS, U.S.A.
authors.forename: Byron J
authors.initials: BJ
authors.lastname: Gajewski
keywords: bias; linear contrast; ordinary least squares regression; paired t test