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 for $Y$.  A perfect proxy measure would be unbiased (i.e., result in a regression line with a $y$-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 paired $t$ test 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 paired $t$ test 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.

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