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Carolina Population Center Department of Nutrition University of North Carolina at Chapel Hill Chapel Hill, NC 27516-3997
Department of Biostatistics University of North Carolina at Chapel Hill Chapel Hill, NC 27516-3997
Dear Sir:
The response of Lindsay et al to our article (1) is a thoughtful one that brings up an important point relevant to most studies of tracking, particularly regarding the interpretation of research findings when tracking is defined based on relative positions in a population (eg, quartiles or percentiles). Lindsay et al are correct in stating that when variables are positively correlated the probability of maintaining the quartile (tracking) is higher in the top or bottom quartile than in the middle quartiles. Their point raises an interesting question about the widely used approach of tracking research of nutritional status. Because of the biological consequences of being in a high or low BMI category, most scholars have studied tracking based on a person's ranking in a population (eg, BMI quartile or percentile).
Our original study focused mainly on understanding tracking patterns and not on determining whether the tracking patterns we observed were mainly due to biological factors or to a statistical property. Also, from a public health point of view, if children with extreme BMI values are likely to maintain such a status over time, efforts should be made to help them modify their body weight given the evidence of the correlation between overweight and health risks and the adverse effects of malnutrition (2, 3).
We suspect that both statistical and biological factors may have contributed to the tracking patterns we and many others observed. To test this hypothesis, we conducted further analyses. Many tracking studies found a lower correlation than that found by Lindsay et al, and the strength of the correlations varied by samples and follow-up intervals (4, 5). Lindsay et al cited a correlation of 0.7 for their simulation analysis; we found a correlation of 0.4. Other frequently cited tracking studies found correlations of 0.4–0.6 (6), 0.5 (7), and 0.6 (8) between childhood and adolescence.
Using the correlation we observed (0.4) and the same approach used by Lindsay et al (Y2 = Y1 + Z), we generated 2 sets of normal, random variables: Y1 (measures at time 1) and Y2 (measures at time 2). We repeated this simulation 500 times and our results were quite different from Lindsay et al's, who reported that the proportion of tracking in the top and bottom quartiles was 60.7% using a correlation of 0.7. Our simulations showed that 42.8% (95% CI: 37.4%, 48.4%) of those in the top and bottom quartiles of BMI at time 1 would remain in the same quartile in time 2. Our theoretic calculation of the conditional probability of Y2 in quartile 1, given Y1 in quartile 1 while treating the cutoffs as known, also showed that the proportion was 42.9%; this was the same for quartile 4. In contrast, our results with the real Chinese data found that 50.8% of the children remained in the bottom quartile of BMI and 46.3% remained in the top quartile of BMI. Thus, the following statistical question arises: are the differences between the randomly generated proportion in the bottom and top quartiles and our findings significant? We found that the percentage of children in quartile 1 who tracked (50.8%; 95% CI: 44.5%, 57.1%) was significantly greater than 42.9% (P < 0.05), although the percentage of children in quartile 4 who tracked (46.3%; 95% CI: 40.0%, 52.6%) was not significantly different from 42.9%. This finding indicates that even if the statistical model used by Lindsay et al is assumed to be appropriate, it still did not completely explain all of the tracking we observed.
In tracking research it is crucial for scholars to show whether the tracking is nonrandom. In the real world, changes in children's BMIs over time are more complex; therefore, these changes are what should be studied. Lindsay et al help to make this point. Children have different baseline lifestyles, growth patterns, social-environmental factors, and genetic predispositions and changes in their lifestyles and environment during follow-up can influence changes in their BMIs. For example, obese adolescents may be more likely to modify their eating behavior and reduce body weight; thin children's parents may be more likely to try to provide their children with better care and nutrition to improve their growth. We suspect that more complex models (eg, Y2 = + ßY1 + 1Q1 + 2Q4 + Z, where Q1 and Q4 indicate the top and bottom quartiles, respectively) than the one proposed (Y2 = Y1 + Z) may be needed to better test the statistical property of tracking.
In addition, running counter to tracking is another phenomenon, regression toward the mean, that we cannot fully study but also must understand. We are not sure how to both simulate randomly the results based on a correlation, such as Lindsay et al used or we found, and to simulate the compounding regression-to-the-mean effect. Nevertheless, the question Lindsay et al raised may further suggest the importance of studying who is more likely to track their status (eg, high BMI) if they initially have such a status. Our study attempted to study the predictors of tracking.
In summary, we think that Lindsay et al raised an important point. To better understand when tracking results are significant also requires consideration of other phenomena such as regression to the mean, otherwise it is premature to conclude that tracking in extreme BMI quartiles is an expected property of correlated variables and may bear no biological meaning. Moreover, it is not clear whether testing the difference between a randomly generated tracking result and our real-world results would allow us to test in a meaningful way whether the tracking is significant.
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