Extract
Although we do not concur with their conclusions, we very much appreciate the stimulating comments by Erik Giltay et al.1 regarding our previous report2 on the association between baseline telomere length and subsequent telomere shortening. They argue that the correlation observed in our and in other studies2–4 is mainly due to mathematical coupling and suggest using the correlation due to mathematical coupling as the comparator rather than a correlation coefficient of zero. To enforce their view, Giltay and co-workers have also performed simulation studies with two random variables, X and Y, and then tested the correlation between X and Δ = X − Y.
However, this simulation is not appropriate because it ignores that X and Y are repeated measurements in the same individuals and highly correlated (rSpearman = 0.652, P = 4.7 × 10−63).2 Only for two series of independent random numbers X and Y with the same standard deviation, the correlation between X − Y and X expected based on mathematical coupling is indeed as formulated by Giltay et al. (please see Tu and Gilthorpe5 for a comprehensive review). However, as Giltay et al. correctly state, the null hypothesis β = 0 is not a correct null hypothesis any more. Tu and Gilthorpe5 proposed a method for testing the correlation between X and X – Y (
). Since this test is based on Pearson’s correlation coefficient, it cannot be seen as a correction for the Spearman’s correlation coefficient, which we presented in the paper, but it is comparable with the P value presented for the linear regression model.
