Response

Dear Editor-in-Chief: “Constants that vary” (1) elegantly summarizes the fact that parameters in any fixed-effects model are constants only in the sense of representing values of population means, because values of the parameters for individuals always vary from the mean. We ourselves pointed out how the mean value for a factor converting changes in time to exhaustion into changes in time-trial time provides only an approximation for individuals, and we explained how to use several times to exhaustion for more precise conversion (2). The approximation is not as bad as Atkinson and Nevill think. Consider a study in which a single time to exhaustion is used pre and post a treatment, and assume that the underlying mean change in power output is typical for interventions aimed at athletic performance, say 2.0%. The apparently large between-subject variation of 28% in the conversion factor produces an error of typically only 0.5% in an individual's 2.0% change. This error is small compared with the standard error of measurement of power output in time trials, which is approximately 2–3% (4); it may also be negligible compared with the variation arising from individual responses to the treatment. This insight helps explain why interventions producing small changes in power output have been studied successfully with times to exhaustion. Atkinson and Nevill requested analysis of reliability of time-trial times predicted from times to exhaustion “using estimates of model parameters specific to a particular subject at a specific time.” We reported such predictions and analyses in Figure 1 and Table 3 of our paper. The outcome—low within-runner variability—was our empirical evidence that times to exhaustion are inherently reliable. Atkinson and Nevill's concerns about pacing are addressed partly in our reply (3) to Jeukendrup and Currell (5). Their suggestion that boredom contributes to the large within-subject variability in time to exhaustion echoes that in a paper coauthored by one of us in 1998 (6). We now know that the variability is due mainly to the shape of the power–duration curve, but the extent to which boredom contributes for anyone making near-maximal effort in any kind of long endurance test is unclear. For this and other reasons, the best endurance test for elite athletes is still not known. Atkinson and Nevill's suggestion that measurement of physiological variables at set times could give clues to subjects about elapsed time in time-to-exhaustion tests is insightful, and measurement protocols need to be devised to avoid this potential problem. As with Jeukendrup and Currell, we are disappointed with Atkinson and Nevill's failure to recognize our achievements. The casual reader of these two letters and of our paper—like the authors of the letters themselves—may not appreciate that, among much else, we have derived factors that allow a quick and reasonably accurate conversion of a percent change in a time to exhaustion into a practical percent change in time-trial time. These factors, and those for longer tests (4), are particularly useful for interpreting outcomes in published studies where time to exhaustion is the outcome measure. Will G. Hopkins, Ph.D. Erica A. Hinckson, Ph.D. Division of Sport and Recreation Auckland University of Technology Auckland, New Zealand