Reply to: “A note on normality”

Reply to: ‘‘A note on normality’’ To the Editor: The issue raised by Lott is appropriate. We need to assess whether the residuals, the differences between observed and predicted values, are normally distributed in order to perform the linear regression. We excluded three outliers, 1740, 4018, and 4296 and calculated the residuals of serum interleukin (IL)-33 levels or log-transformed serum IL-33 levels to assess the normality assumption, using the data in our study.1,2 The histograms of the outcomes and the residuals are shown (Fig 1). The residuals of serum IL-33 levels (Fig 1, C ) or log-transformed serum IL-33 levels (Fig 1, D) were almost normally distributed. The distribution of log-transformed serum IL-33 levels (Fig 1, B) approximated a normal distribution in contrast to that of serum IL-33 levels (Fig 1, A). We performed the multiple regression analysis to examine the robustness of results, using log-transformed serum IL-33 levels after excluding three outliers, 1740, 4018, and 4296. The multiple regression analysis showed that the EASI score (P \ .001) and history of rhinoconjunctivitis (P ¼ .042) accounted for elevation of serum IL-33 levels among these factors (Table I). In conclusion, we confirmed that it was appropriate to perform the linear regression of

Table I. Multiple regression analysis to evaluate which factors account for elevation of serum IL-33 levels after excluding 3 outliers Log-transformed IL-33 levels Regression coefficient (Standard error) P-value

Age Gender ( female = 0; male = 1) EASI score History of asthma (no = 0; yes = 1) History of rhinoconjunctivitis (no = 0; yes = 1)

0.003 (0.008) 0.058 (0.188)

.711 .760

0.027 (0.007) 0.246 (0.182)

\.001 .181

0.355 (0.170)

.042

log-transformed serum IL-33 levels in our study by assessing the distribution of residuals after omitting outliers. The results of reanalysis showed that serum levels of IL-33 were closely related to the EASI score in the patients with atopic dermatitis, as well as to the previous results.1,2 Risa Tamagawa-Mineoka, MD, PhD,a Satoshi Teramukai, PhD,b and Norito Katoh, MD, PhDa Departments of Dermatologya and Biostatisticsb, Graduate School of Medical Science, Kyoto Prefectural University of Medicine, Japan

Fig 1. Histograms of serum IL-33 levels (A), log-transformed serum IL-33 levels (B), and the residuals of serum IL-33 levels (C) or log-transformed serum IL-33 levels (D) in patients with atopic dermatitis (AD) (n ¼ 59). J AM ACAD DERMATOL

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Funding sources: None. Conflicts of interest: None declared. Correspondence to: Risa Tamagawa-Mineoka, MD, PhD, Department of Dermatology, Kyoto Prefectural University of Medicine Graduate School of Medical Science, 465 Kajii-cho, Kawaramachi-Hirokoji, Kamigyo-ku, Kyoto 602-8566, Japan E-mail: [email protected]

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REFERENCES 1. Tamagawa-Mineoka R, Okuzawa Y, Masuda K, Katoh N. Increased serum levels of interleukin 33 in patients with atopic dermatitis. J Am Acad Dermatol. 2014;70:882-888. 2. Tamagawa-Mineoka R, Teramukai S, Katoh N. Response to ‘‘Statistical comments on ‘Increased serum levels of interleukin 33 in patients with atopic dermatitis.’’’ J Am Acad Dermatol. 2015;72:200. http://dx.doi.org/10.1016/j.jaad.2015.02.1105