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Letters to the Editor |
Department of Radiology, Montefiore Medical Center, 111 East 210th Street, Bronx, NY 10467. e-mail: mlaks2000@yahoo.com
Editor:
In their article (1) about the association of age with the size of the extrahepatic bile duct, Dr Horrow and colleagues claim evidence against the opinions of Wu et al (2), asserting that a 10-mm diameter can be normal in the elderly, as well as the textbook opinion of Laing that "[a] simple rule of thumb is to consider as normal a 4 mm mean duct diameter at age 40, a 5 mm mean duct diameter at age 50, a 6 mm mean duct diameter at age 60, and so on" (3). They based their claim on a regression analysis of measurements in 258 asymptomatic patients. They found that the slope of their regression line differed significantly from 0.1 mm per year.
Unfortunately, Drs Horrow and colleagues are mistaken. Their regression analysis addresses only the average value for the common duct diameter as a function of age, while the other authors are discussing something else—the upper limit of normal value. To project from the average value predicted by a regression line to an upper limit of normal value would require further statistical analysis of the regression assumptions, which the authors do not document. Just as the mean value of a physiologic variable can vary as a function of time, so commonly will also the SD (and thus the variance). Even if the regression line were to have a slope of zero, if the SD of the duct diameter increases as a function of time, then the upper limit of normal value would increase with age.
To predict values of the upper limit of normal, the authors should have used their data to construct what are called percentile curves or reference ranges as a function of time. There is an extensive statistical literature on the subject of the construction of these curves. I refer the authors to a couple of articles (4,5). A polynomial regression model might have also provided a significantly better fit of the data set than the linear model the authors used. The authors need to evaluate the residuals for normality, as well as check other assumptions, as they build reference ranges to predict values of the upper limit of normal.
I am also puzzled about the following: According to figure 1, 20–30 patients were older than 80 years, and yet I see only 10 corresponding data points displayed in figure 2. I estimate, roughly, that only about half of the data points claimed in figure 1 are displayed in figure 2.
There are apparently significant differences between the authors’ results and those of Kaim et al (6), notwithstanding the differences in the precise location of the measurements. The number of patients in either study who were without stone disease and older than 75 years were comparable (45 in the article by Kaim et al while between 59 and 77 in the article by Dr Horrow and colleagues). Perhaps some unrecognized selection biases have crept into these studies and account for the discordance of results. Accordingly, this issue certainly deserves further review and data collection at other institutions for corroboration and assessment, given its obvious importance to the radiologic community.
Perhaps Radiology should consider creating a policy of asking authors to submit full data sets (suitably masked with regard to patient identity) for inclusion in the Web-based published version of the Journal. This might be done in standard format such as Excel or comma- or space-delineated format. This would facilitate independent statistical reanalysis; evaluation of the results; and the comparison, correlation, and integration of the results of different studies.
REFERENCES
Department of Anesthesiology, Drexel University College of Medicine, Philadelphia, Pa*
Mindy M. Horrow, MD
Department of Radiology, Albert Einstein Medical Center, 5501 Old York Road, Philadelphia, PA 19141-3098
We thank Dr Laks for his thoughtful comments and appreciate the attention that our work has received (1). Of course, Dr Laks correctly asserts that even though the expected value (mean) of the extrahepatic bile duct diameter may not vary with age, its reference range, that is its CI, may do so in such a manner as to include the 1.0 mm per decade value in its upper limit.
We respectfully disagree, however, that either Wu et al (2) or Laing (3) "are discussing something else" about which we "are mistaken." Their analyses and discussions do not examine the upper limits of normal, CIs, or prediction intervals. Rather, Wu et al use values in pediatric patients that exert inordinate influence on the regression performed, and Laing merely reports their work.
Nevertheless, Dr Laks’ issue remains. To address this, we organized the data according to decade of life and calculated percentile values for extrahepatic bile duct diameter from the raw data (4). As displayed in the Table, neither the 90th percentile values nor even the maximum values (>99th percentile values) calculated in this nonparametric manner support the use of 1.0 mm per decade as the upper limit of normal, as inferred by Dr Laks from the work of Wu et al. A more extensive analysis in which fitted distributions are used (5) would not only encumber interpretation by adding assumptions about the data but appears unwarranted on the basis of the results in the Table.
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Perret et al (7) reported a series of 1,018 patients aged 60–96 years while our work was in press. They demonstrated minimal increase in the common bile duct diameter: 3.6 mm ± 0.26 at age 60 years and 4.0 mm ± 0.25 at age 85 years or older. Not only did their regression results (r = 0.1377, slope = 0.156 mm/decade) demonstrate a weak and clinically insignificant association, in agreement with our results (1), but their scatterplot does not support an increase of variance with age, as postulated by Dr Laks, which is sufficient to justify inclusion of a 1.0 mm per decade of life upper limit in reasonably constructed reference ranges. In fact, 1,000 of their 1,018 patients, all aged at least 60 years, had duct diameters less than 6.0 mm, which directly refutes 1.0 mm per decade as an upper limit of normal.
We encourage others to publish their prospective series of these data untainted by the inclusion of pediatric subjects in whom the extrahepatic bile duct will grow. Regarding publication of raw data on Web sites in a downloadable format, although there are benefits as stated by Dr Laks, the authors invite journal editors to ponder the issues of intellectual property and possible facilitation of plagiarism or possible data theft raised by such a practice.
REFERENCES
Dr Laks indicates that the use of the "average value" for common duct diameter by Dr Horrow and colleagues prohibits comparison with the study by Wu et al, who he says used the "upper limit of normal" value. Dr Laks says that "[t]o project from the average value predicted by a regression line to an upper limit of normal value would require further statistical analysis of the regression assumptions, which the authors do not document." This is true; however, it is not clear that Dr Horrow and colleagues are interested in the upper limit of normal. Dr Laks says "[e]ven were the regression line to have a slope of zero, if the SD of the duct diameter increases as a function of time, then the upper limit of normal value would increase with age." There is no indication that the variance increases with age. The regression analysis reported by Dr Horrow and colleagues assumes a constant variance. They report in the Results section that the residual analysis indicates the appropriateness of this assumption, that is, "[a]nalysis of regression residuals does not suggest an alternative model."
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