标题：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
期刊名称：International Journal of Statistics and Probability
印刷版ISSN：1927-7032
电子版ISSN：1927-7040
出版年度：2014
卷号：3
期号：4
页码：25
DOI：10.5539/ijsp.v3n4p25
出版社：Canadian Center of Science and Education
摘要：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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