In Reply We thank Ayubi and Safiri for their comments regarding our study1 that evaluated the risk of human leukocyte antigen (HLA) alleles on cold medicine–associated Stevens-Johnson syndrome. As highlighted, the 2 × 2 contingency table of HLA-A*66:01 (represented as [14, 2; 61, 0]) was sparse because of a rare observation of the high-risk HLA allele among the population. Considering this finding’s potential effects on clinical medicine, we separately calculated a P value and odds ratio (OR) by using different types of statistical approaches to estimate the risk of the allele (a Fisher exact test for a P value and a Woolf correction for OR), as clarified in the Methods section of our article. It is generally known that an asymptotic approximation of the test statistics, such as the χ2 test and a regression analysis, could be inaccurate for such a sparse contingency table, especially when including a zero value. Therefore, we applied a Fisher exact test to calculate a P value, which handles the exact probability from a hypergeometric distribution and does not rely on asymptotic approximation (PExact = .04). We admit that estimating ORs for sparse data is still controversial compared with P value estimation. We applied a Woolf correction for the OR that adds 0.5 to each contingency table cell (ie, 14.5, 2.5, 61.5, and 0.5 in the mentioned table). While a Woolf correction can provide conservative ORs, because this method slightly changes the contingency table cell values themselves, a discrepancy between the estimated P value and the 95% confidence intervals of the OR occurred, as pointed by the commenters. This strategy to calculate the Fisher exact test and OR by a Woolf correction in parallel is widely accepted in the field of HLA risk analysis and should not affect reliability of our study.
Okada Y, Ueta M. Data Sparsity in Study on Human Leukocyte Antigen Class I Genes Associated With Stevens-Johnson Syndrome and Severe Ocular Complications—Reply. JAMA Ophthalmol. Published online July 13, 2017. doi:10.1001/jamaophthalmol.2017.2289