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Cross Cancer Institute Edmonton AB T6G 1Z2, Canada
I have been trying to apply the educational articles about proper use of statistics that have appeared recently in AJR. The recent article by Crystal et al. [1] has raised a question. Their abstract states that sonography has a significantly higher cancer detection rate in a subgroup of high-risk women (p < 0.04) than in a baseline-risk group. Their data were four cancers in 318 high-risk women versus three cancers in 1,199 baseline-risk women.
Without applying statistics, my initial impression was that such small numbers of cancers would not be sufficient to prove a difference. Then I tried a few statistics, first using a simple chi-square comparison of proportions. The null hypothesis seems to be that the women in both groups are basically from the same population, with the same risk and expected cancer rates. The chi-square test gave a p value of 0.0184. Then, realizing that data values smaller than five were being used, I computed a Fisher's exact test that returned a p value of 0.0331.
I noticed that Crystal et al. [1] used a two-tailed Fisher's exact probability test that, according to an online statistics calculator [2], gives a p value of 0.0382. Can the authors or perhaps the AJR statistical consultants explain what is the most appropriate statistic in this case?
On further reflection, the subgroup of "high-risk" patients appears to be mixing different risk levels together. Women with a first-degree family history of breast cancer in one family member have a relative risk of 2.56–2.8, depending on their age at their first live childbirth, according to the Gail model [3]. This subgroup is combined with the subgroup with mammographically dense breasts, estimated to have a relative risk of 1.12–1.76 [4]. But women with a personal history of breast cancer have a relative risk that is an order of magnitude higher, which could potentially bias the high-risk group considerably. Perhaps the authors could clarify whether any of the four cancers they detected were from women with a personal history of breast cancer.
These questions do not detract from the important finding of the article by Crystal et al. [1]—that the overall cancer detection rate is 0.46%—which I believe would have a 95% confidence interval from 0.18% to 0.94% and the reassuringly low biopsy rate of 2.5%.
References
Ben-Gurion University of the Negev Beer-Sheva 84101,
Israel
The Rachel Nash Jerusalem Comprehensive Breast Clinic Jerusalem
95484, Israel
Elisheva Kaplan Eshkol Comprehensive Breast Health Center Soroka
University Medical Center Beer-Sheva 84101, Israel
We thank Dr. Halls for his thoughtful letter about our article [1].
Various tests might be used for statistical comparison of proportions. The parametric Z test [2] is used for large sample sizes when the data have an underlying normal distribution. Alternative hypothesis testing methods are available if the sample sizes are not sufficiently large.
The chi-square test is a nonparametric test of statistical significance for proportions. It does have some requirements: the sample must be randomly drawn from the population, data must be reported in raw frequencies (not percentages), measured variables must be independent, and expected frequencies cannot be too small.
In our study [1], the expected frequency of cancers detected on screening sonography in high-risk women is 1.46. According to Dawson and Trapp [2], if any expected frequency is less than 2, or if more than 20% of the expected frequencies are less than 5, then Fisher's exact test should be used.
Proper use of one-tailed versus two-tailed tests depends on the investigator's question. Thus, a one-tailed test establishes the direction of association between predictor and outcome and can be used when the investigator knows that this association does exist. In our case, we could not claim axiomatically that a positive association exists between high risk of breast cancer and cancer detection rates on screening sonography. The two-tailed test we used establishes only whether an association exists and does not specify direction.
The determination of the breast cancer risk is another important issue raised in Halls' letter. We believe that future breast cancer screening recommendations will be tailored according to the individualized risk. In our study, we defined "high risk" as having a first-degree family history or personal history of breast cancer. Halls claims that women with a personal history of breast cancer have a relative risk that is "an order of magnitude higher" than women with first-degree family history. This assertion intuitively seems to be true, and indeed two of four cancers diagnosed in our high-risk group were women with a personal history of contralateral breast cancer.
However, published data do not support this claim. Dawson et al. [3], in their review of contralateral breast cancer, appraise the relative risk of contralateral tumor as 1.5–5.5 times higher than the risk of primary breast cancer in the general population.
On the other hand, Armstrong et al. [4], in their review assessing the risk of breast cancer, report a 1.4–13.6 relative risk for women with a first-degree relative family history of breast cancer.
We point out that Kolb et al. [5] used similar criteria in their definition of high risk. They performed screening sonography in 13,547 women with dense breasts and also found a significant increase in the cancer detection rate in women who were at high risk versus women at normal risk (p = 0.012, Fisher's exact test).
Single-center studies have various limitations. We believe that the ongoing multicenter trial of breast screening sonography [6] will have sufficient statistical power to justify the use of screening sonography in the routine screening guidelines for high-risk women with dense breast tissue.
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