Delta efficiency calculation in Tour de France champion is wrong

TO THE EDITOR: We previously raised concerns (6) about the methodology used to assess Lance Armstrong's muscle effi- ciency in the popular Journal of Applied Physiology paper entitled "Improved muscle efficiency displayed as Tour de France champion matures" (1). Subsequently, Coyle made available raw data from the January 1993 test that revealed several additional deviations from the published methodology. Coyle used a 20-min ergometer protocol (not 25 min), includ- ing 2- and 3-min stages where respiratory exchange ratios (RER) exceeded 1.00. An RER 1.00 invalidates use of the Lusk equations (5) to estimate energy expenditure. A review of the raw data established that the published delta efficiency (DE) values in the Armstrong paper were calculated using the wrong equation. Coyle's published methodology (1) and that used by his group on several previous occasions (2, 4, 7) stipulates that linear regression (y mx b) be used to calculate DE, as the reciprocal of the slope from the relation- ship between the energy equivalent of oxygen uptake and cycling power output. However, Coyle calculated DE using the general formula 100 ¥(X Y)/¥(X2). This calculation is equivalent to linear regression using y mx, which forces the regression line through the origin. Resting metabolic rate (RMR) as well as the cost of cycling without load (including the variable cost of ventilation and circulation) mandate that the regression line used to calculate DE cannot pass through the origin. In their benchmark paper, Gaesser and Brooks (3) argue that DE, as the first derivative of the increase in caloric cost of exercise with respect to ordered increases in work, is a "float- ing base-line" method. Hence it is essential that the regression is not forced through zero when calculating DE. By employing y mx for each of the four data sets used to calculate DE, Coyle has assumed that Armstrong's RMR and cost of cycling without a load was not influenced by orchiectomy and chemo- therapy, plus well-publicized weight fluctuations during the