Exploratory biochemical data analysis: a comparison of two sample means and diagnostic displays

The occurrence of acne in women with hyperandrogenemia is well known; a question remains, however, as to whether a further positive relationship can be detected between the intensity of acne and the levels of testosterone, androgen precursors and sex hormone binding globulin (SHBG). A procedure of interactive data analysis extracting relevant information from original data was applied. Exploratory data analysis (EDA) identifies basic statistical features and patterns of data using a variety of diagnostic displays. The need for this step is particularly acute in biochemical and clinical data, the distribution of which is mostly non-Gaussian and often corrupted by the outliers. The omission of EDA can lead to incorrect results and false conclusions. In the EDA (i) several graphical tools for summarizing data are applied, (ii) the peculiarities of a sample distribution are investigated, (iii) a construction of distribution is carried out, (iv) a graphical comparison of the sample distribution with selected theoretical distributions is employed. The proposed procedure is illustrated by typical case study in the evaluation of differences between mean values of serum levels of testosterone, androgen precursors and SHBG in a group of patients with mild and severe forms of acne. A knowledge of the interval estimate of the mean value in both groups enables their comparison at the chosen probability level. As will be apparent from the evaluation of inter-group SHBG differences, an incorrect approach to the determination of group mean values could result in a complete misinterpretation of the data. The results indicate that androgens are not significantly related to the intensity of acne, and that SHBG is higher in patients with more severe forms of acne.