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LETTER |
The authors are with the Department of Public Health Sciences, University of Toronto, Toronto, Ontario.
Correspondence: Requests for reprints should be sent to Peizhong Peter Wang, MD, Department of Public Health Sciences, Faculty of Medicine, McMurrich Bldg, University of Toronto, Toronto, Ontario M5S 1A8, Canada (e-mail: wang{at}uhnres.utoronto.ca).
Because our research interest is in disability, we read Freedman and Martin's article on chronic conditions and disability1 with special interest. Several aspects of their work concerned us.
The authors introduced the concept "total contribution of a given factor," which can be expressed as a summation of (X95 - X84) • (ß95 + ß84)/2 and (ß95-ß84) • (X95 + X84)/2. According to Freedman and Martin's notations, ß84 and ß95 are the regression coefficients for the contribution of condition X to the risk of activity limitation and X84 and X95 are the prevalence of condition X in the general population derived from the 1984 and 1995 data, respectively. However, the authors failed to elaborate the meaning of this concept and left readers wondering what "total contribution" meant.
With some algebraic operation, the above summation can be greatly simplified to X95 • ß95 - X84 • ß84, because ßyear and Xyear are the individual average risk for activity limitation and the prevalence in the population for a given chronic condition, respectively. The product of the 2 (ß • X) is simply the population attributable risk2 for condition X. Therefore, "total contribution of a given factor" as reported by the authors should be accurately interpreted as the difference of 2 adjusted population attributable risks for a given condition in 2 different years. A better understanding of this concept would help the data presentation greatly; the numbers in Table 5 would be better reported as percentages rather than the confusing decimal numbers.
We feel that the results from this study have been overinterpreted. The 2 sets of coefficients for comparison were derived from 2 cross-sectional surveys. Therefore, the association between activity limitation and a given chronic condition, which was reflected in the difference in coefficients for the same chronic condition at 2 time points, could also be influenced by other changes, rather than changes in activity limitation and the chronic condition of interest, between the 2 surveys. When 2 coefficients from 2 surveys are compared, it is unrealistic to assume that all other factors are equal. However, this fundamental limitation was not adequately addressed.
Furthermore, the overall goodness of fit for the upper-body models is poor. Chroniccondition variables plus all other covariates can explain only 7% of all variation in upper-body limitation. How the model's predictability affects the interpretation and generalization of results should also be discussed.
We believe that the impact of chronic conditions on activity limitation should be explored in terms of both individual and population effects, as the 2 may not be necessarily in agreement. For osteoporosis, for instance, the individual effects on activity limitation differed significantly (ß84 = 0.081, ß95 = 0.005), but the population attributable risks did not change much (X95 • ß95 - X84 • ß84 = 0.3%). Therefore, it is clear that at the individual level, the effect of osteoporosis on activity limitation became less severe, which is reflected in the significant change in ßs between 1984 and 1994. However, owing to the increased prevalence of osteoporosis during the 10 years, the effect of osteoporosis on activity limitation at the population level remained constant.
Finally, we have concerns about some of the statistical tests reported in this article. The authors used a very liberal P value of .1. Consequently, some of the 95% confidence intervals included 0 but were still treated as statistically significant (Table 4). For example, the differences for cancer (0.027 ± 0.029), arthritis (-0.018 ± 0.020) in the upper body, and osteoporosis (–0.222 ± 0.257) were treated as if they were statistically significant. The study was based on large samples, and therefore type I error is more likely to be a concern. In situations like this, a more demanding P value, such as .01, should be used. Also, the P values for differences reported in Table 2 cannot be correct. Using the information provided in that table, we verified these P values and found that at least the differences for broken hip, diabetes, and hypertension were not statistically significant (P > .1). The incorrect statistical tests pose no small threat to the succeeding Results and Discussion.
References
1.
Freedman VA, Martin LG. Contribution of chronic conditions to aggregate changes in old-age functioning. Am J Public Health.2000;90:1755–1760.
2. Rothman KJ, Greenland S. Modern Epidemiology. Philadelphia, Pa: Lippincott-Raven; 1998.
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