Exceptional case studies.

CASE STUDIES ARE RARE in our journals and for good reason: without a sample, it is hard to assess the representativeness or uniqueness of an individual. The case studies that do get published are therefore so obviously exceptional that we cannot help but be interested in where nature or nurture has taken one of our species. The individual is usually an athlete, and the science amounts to identifying a likely physiological basis for the exceptional ability. The case study of a world champion sprinter in this issue of the Journal of Applied Physiology (2) includes impressive data on the physiology of single fibers and the transcriptome of the response of the fibers to exercise. Some data on mean values from normal healthy individuals are provided for comparison. For example, the power in the athlete’s superfast (IIx) fibers is reported as 35.1 1.4 W/l (mean SD), which the authors note is approximately twice that in three cited studies of healthy untrained males (1, 3, 4). Is this difference enough to account for this athlete’s talent? That depends, not just on the mean of normal individuals but on the spread of the values, the standard deviation. In all three studies the authors had committed the usual bad practice of reporting standard errors of the mean, but after conversion, the values were 11.4 5.7, 15.5 4.7, and 15.4 0.9 W/l (mean SD). These estimates are based on only 3-15 fibers, so they are not particularly precise. The athlete’s mean is also based on only 10 fibers, but given the athlete’s small SD, his mean is precise relative to the gap between it and that of normal men. Assuming an overall mean and SD in normal men of 15 5 W/l, the gap is about four SDs, which is sometimes referred to as a z-score, or more properly a t-score. Such scores are easier to understand when converted to percentiles using the function for the cumulative t distribution (T.DIST in Excel). The conversion is based on the assumption that the normal population is indeed normal in the statistical sense. In reality the distribution is probably skewed by a long tail, and the athlete is out on that tail. Log transformation of all the values would therefore be advisable before generating the t-score, but let us assume normality without transformation. If the population standard deviation had been defined by a large number of degrees of freedom, the t distribution would be effectively the normal distribution, and this sprinter’s IIx fibers would be on the 99.997th percentile or 1 in 30,000. Here the standard deviation has only 18 degrees of freedom (based on 23 fibers from 21 men in 3 samples), so the athlete’s percentile score drops to 99.96, or about 1 in 2,500. That is still impressive, but his sprinting performance is probably one in a million or more, so the other exceptional aspects of the physiology of his fibers probably contribute and need to be documented in this manner. There might still be a need to invoke an exceptional central nervous system as well as exceptional muscles to help explain his ability. In summary, authors reporting physiological measures of an exceptionally talented individual should provide standard deviations as well as means of the measures in an appropriate normal population group. With reasonable assumptions, the individual’s values can be converted to percentile scores, which allow some quantitative assessment of the extent to which the physiology accounts for the exceptional talent.