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National Institute of Diabetes and Digestive and Kidney Diseases 1550 East Indian School Road Phoenix, AZ 85014 E-mail: rlindsay{at}mail.nih.gov
Dear Sir:
In their article in the October 2000 issue of the Journal, Wang et al (1) examined the tracking of body mass index (BMI; in kg/m2) of children in China. They concluded that the BMIs of thin and fat children (defined as those in the lowest and highest quartiles of BMI, respectively) were more likely to track (ie, remain in the same quartile of BMI at follow-up).
We agree with Wang et al that this is an important area of study but are concerned that their analysis of tracking may be misleading. They stratified the children by quartile of BMI at the first examination (see Table 2 of their article) and then calculated the percentage of those who tracked or alternatively moved up or down the quartile ranking. Where variables are correlated, we suspected that the likelihood of the quartile changing might not be the same for all quartiles, being less in the extreme quartiles. We suggest that this statistical property, rather than any underlying biologic factor, may have been the reason for the increase in tracking that Wang et al reported in the extreme quartiles of initial BMI.
We demonstrated this effect by simulation. We generated 1000 observations (x) to represent a first measurement of BMI that was generated randomly from a normal distribution by using the RANNOR function of SAS (SAS Institute Inc, Cary, NC). A second correlated (r = 0.7) observation (y), to simulate a later measurement of BMI, was generated by the formula y = x + z, where z is a further random number generated by RANNOR. Observations x and y were then ranked and examined for evidence of tracking in a manner similar to that used by Wang et al. An increase in tracking was apparent in the extreme quartiles. Thus, in this first simulation, 62% of those in the lowest and highest quartiles of x tracked (ie, were also in the lowest and highest quartile of y, respectively) and only 34% in quartiles 2 and 3 tracked. A repeat of this simulation (1000 times) showed that with this degree of correlation, tracking occurred in 60.7% of observations on average (95% CI: 56.8, 64.4) in the extreme quartiles (1 and 4) and in 36.0% of observations (31.6, 39.6) in the central quartiles (2 and 3). These values changed depending on the degree of correlation between the 2 variables (data not shown), approaching 25% for all quartiles as the degree of correlation decreased to 0.
Simulation also showed that the extent of tracking in individual quartiles was potentially affected by the underlying distribution of the data (data not shown). Use of correlation coefficients within quartiles (rather than the percentage of tracking) is subject to similar problems. In the simulated set described above, which had a normal distribution and a Pearson's correlation coefficient of 0.7, correlation coefficients of x and y were highly dependent on the quartile; the Spearman correlation coefficient was 0.40 (95% CI: 0.30, 0.49) within quartiles 1 and 4 and was 0.19 (0.09, 0.3) within quartiles 2 and 3.
Given these simulations, we believe that the conclusion of Wang et al regarding tracking of BMI in the extreme quartiles may be misleading. In their Table 4, Wang et al reported that tracking of overweight increases if at least one parent is overweight and that, conversely, tracking of underweight increases if at least one parent is underweight. This appears to be an important observation; however, we are concerned that their data may be confounded by the same problem. If children of overweight and underweight parents lie in extreme quartiles of the first observation of BMI, they may artifactually appear to track more strongly.
Wang et al asked an important biological question: do the biological variables of individuals identified by place in the population distribution or by other factors such as family history differ in stability over time? The above simulations suggest that increased tracking in extreme quartiles, as they define tracking, is an expected property of correlated variables and may have no bearing on the biology underlying BMI.
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