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We would like to thank Dr. Rosenthal for his comment on our research. Dr. Rosenthal highlights that a change in FEV will inevitably be negatively correlated with the initial value; otherwise known as regression to the mean. One important distinction with our work is that we calculated the conditional change score based on z-scores and thus demonstrate the changes that are greater than that predicted by regression to the mean. By calculating the conditional change using z-scores we change the scale which is used and account for this fallacy. Reporting the differences using Bland-Alman is an alternative approach but will be limited to analysis of fixed time-intervals and if the variability is constant across age and time.
I was surprised to see figure 2 in the paper by Stanojevic et al (1) on assessing paediatric FEV1 reproducibility as, on the face of it, the authors may have fallen into a notorious statistical trap. A change in any variable (FEV1, blood pressure etc) is ALWAYS negatively correlated with the initial value because if x is initial value then y-x is the change, so inevitably related. If as an example one uses two separate sets of 100 normally distributed random numbers, each set with mean 100 and standard deviation 12 to mimic percent FEV1 and plot the first set as X against the difference between the two sets (Y-X) it will show an entirely spurious negative correlation (r = -0.7) with typically around 50% of the ‘variance’ explained. Altman(2) instead has recommended plotting a change against their average as an improved way of assessing the true relationship and using identical values, the spurious correlation disappears.
1. Stanojevic S, Filipow N, Ratjen F. Paediatric reproducibility limits for the forced expiratory volume in 1 s. Thorax 2020;75:891-896.
2. Altman DG. From: Practical statistics for medical research. Chapman and Hall, Boca Raton, USA. 1999:282-285.