Regression to the Mean

Autor: R. Stephens Crockett, Gary D. Novack
Rok vydání: 2009
Předmět:
Zdroj: The Ocular Surface. 7:163-165
ISSN: 1542-0124
Popis: ©2009 Ethis Communications, Inc. The Ocular Surface ISSN: 1542-0124. Novack GD, Crockett RS. Regression to the mean. 2009;7(3):163-165. W e are frequently involved in evaluating studies of new ophthalmology agents. The efficacy of some treatments can be measured in mm Hg with a tonometer or by letters on an eye chart. In ocular surface disease, it can be demonstrated by mm of wetting of a Schirmer strip. However, frequently, efficacy is measured with use of categorical scales for signs or symptoms rated by clinical investigators or patients. The variability of the disease and the variability of these categorical scales can produce variability in results.1 In vehicle-controlled studies, where one seeks to find a difference in favor of the new agent, variability is the enemy. However, another frequently heard enemy is “regression to the mean.” In group meetings when this term is used, heads nod in apparent agreement — but what does this really mean, and how do you minimize such a confounding effect? Regression toward the mean, in statistics, is the phenomenon whereby members of a population with extreme values on a given measure for one observation will, for purely statistical reasons, probably give less extreme measurements on other occasions when they are observed. To illustrate this point, we provide data gathered from a nonophthalmic source. One of the authors (GDN) is a bicycle rider, and among his routes is a 22.5-mile road ride with approximately 1100 feet of climbing. It is a circle course, so the net effect of wind is assumed to be zero. Shown in Figure 1 is the distribution of elapsed time for 78 rides in 2007 and 2008. The mean time was 86 minutes, with a standard deviation of 3 minutes. You can see there were some really fast rides (80 minutes is the best [Figure 2]) and some slow ones (95 minutes is the worst). At 84 minutes, the mode, the most frequent time, was slightly faster than the mean, with the median 86 minutes. In statistical terms, this distribution is relatively “normal” — ie, a bell-shaped curve. Now imagine you are designing a study of the impact of new bicycle wheels on cyclists’ performance. You would want to have a rider who was slow enough that there was a potential for improvement. So, assume you select a ride time of 90 minutes or slower for entry. Assuming that the experience of one rider is descriptive of the “patient” population, that would be met 9% of the time. You could give the riders the new wheels and then observe their ride times. If the ride time decreased, you could conclude that the wheels resulted in improved performance. However, another interpretation is that the rider just “regressed to the mean” — ie, irrespective of the new wheels, the rider just performed closer to the average time of 86 minutes. What other tools are available to the trial designer to minimize confounding interpretations of this experiment? You could select a ride time of 87 minutes or less. This would be met 40% of the time, and since it is near the mean, “regression to the mean” is less likely. However, it challenges an initial assumption — a fast rider may not have as much potential for improvement (ie, a floor effect). You could require that riders qualify not on 20
Databáze: OpenAIRE
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