Serum pentraxin-3 follows a logarithmic distribution particularly at low expected levels

L E T T E R T O T H E E D I T O R

Serum pentraxin-3 follows a logarithmic distribution particularly

at low expected levels

Dear Editors,

We read the article by Ozer Balin et al

with interest and would

like to comment on the results, focusing on data expression and

statistical evaluation regarding serum pentraxin-3 (PTX3) levels.

PTX3, a soluble pattern recognition receptor, is an acute-phase

protein, and its level in systemic circulation was proposed as a

marker for the prediction and/or prognostication of

cardiovascu-lar, metabolic, infectious, and inflammatory disorders as in the

present study.

As in the case of C-reactive protein (CRP),

dis-tribution of serum PTX3 is skewed to the right (positive

skew-ness) in healthy population,

but unlike CRP, it may increase

by up to 1000 to 10 000 times in case of disease, and its range

F I G U R E 1 Histograms (A,B) and Q–Q plots (C,D) showing distribution of serum pentraxin-3 (PTX3) and deviation from normal before (A,C) and after (B,D) logarithmic transformation. Frequencies of measurements in 0 to 5000 pg/mL band were provided as an inner histogram (A). Note that the histogram appeared normal, and skewness and kurtosis were around zero with a Shapiro-Wilk statistic of 0.968 (P = .11) after transformation. Modified with permission.4International League of Associations for Rheumatology (ILAR): Springer Nature ©2016

Received: 16 July 2019 Accepted: 28 July 2019

DOI: 10.1111/iwj.13184

© 2019 Medicalhelplines.com Inc and John Wiley & Sons Ltd

is quite wide in healthy population.

Based on our previous

findings in a healthy control group,

we tested the hypothesis

if logarithmic transformation could yield a normal distribution

in these wide-ranging and skewed data. After transformation,

the histogram appeared to be normal and skewness and

kurtosis were around zero with a Shapiro

–Wilk statistic of

0.968 (P = .11) (Figure 1). Similarly, logarithmic

transforma-tion resulted in near-normal distributransforma-tions in disease groups

too (Figure 2). In studies with higher numbers of

parti-cipants, healthy or with disease, it is the logarithmic

distribu-tion of serum PTX3 that made the researchers use

logarithmic/exponential scales when reporting their data.

In

the case of a small sample size and high expected serum

PTX3 levels, it is depicted in Figure 3 how the data

distribu-tion may appear normal, particularly after excluding the

extreme values (ie, the outliers), which is a common statistical

practice. This was possibly the case in many previous

stud-ies.

However, extreme values in a linear scale are an

integral feature of a logarithmic/exponential distribution

and should not be missed.

In conclusion, logarithmic transformation of serum

PTX3 levels may yield normal distribution, particularly at

low expected levels, and makes parametric analysis of

vari-ance possible. Beside an easier data expression and more

powerful statistical analysis, this may enable logarithmic/

exponential, instead of linear cut-offs to be used in

discrim-inating between potential diagnostic and/or prognostic

groups in future studies.

C O N F L I C T O F I N T E R E S T

The authors declare no potential conflict of interest.

O R C I D

Ufuk _llgen

https://orcid.org/0000-0001-6443-6426

Ufuk _llgen

Müçteba Enes Yayla

Cenk Gökalp

Hakan Emmungil

Nurs¸en Düzgün

_{Department of Rheumatology, Trakya University Medical}

School, Edirne, Turkey

Department of Rheumatology, Ankara University Medical

School, Ankara, Turkey

_{Department of Nephrology, Trakya University Medical}

School, Edirne, Turkey

_{Department of Rheumatology, Ufuk University Medical}

School, Ankara, Turkey

Correspondence

Ufuk _Ilgen, MD, Department of Rheumatology, Trakya

University Hospital, 22100 Edirne, Turkey.

Email: ufukilgen@gmail.com

(PTX3) in disease groups (ie, systemic sclerosis and systemic lupus erythematosus) yielded near-normal distributions as in the case of healthy population. Modified with permission.4International League of Associations for Rheumatology (ILAR): Springer Nature ©2016

0 100 200 300 400 500 600 1 2 3 4 5 6 7 8 9 10 Fr equency

Serum pentraxin-3 quantiles

Low-expected High-expected High-expected with a small sample size

F I G U R E 3 Distribution of serum pentraxin-3 at low and high expected levels. Note that the decrease in skewness at high expected levels may result in a normal-like distribution, particularly if the quantiles 8 to 10 with a low number of cases were considered outliers. At high expected levels with a small sample size, the tail of the histogram may automatically disappear, again leaving a normal-like distribution

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