Analyzing the Spatial Randomness in the Distribution of Acquired Melanocytic Neoplasms

Abstract

On the basis of the clinical impression and current knowledge, acquired melanocytic nevi and melanomas may not occur in random localizations. The goal of this study was to identify whether their distribution on the back is random and whether the location of melanoma correlates with its adjacent lesions. Therefore, patient-level and lesion-level spatial analyses were performed using the Clark‒Evans test for complete spatial randomness. A total of 311 patients with three-dimensional total body photography (average age of 40.08 [30‒49] years; male/female ratio: 128/183) with 5,108 eligible lesions in total were included in the study (mean sum of eligible lesions per patient of 16.42 [3‒199]). The patient-level analysis revealed that the distributions of acquired melanocytic neoplasms were more likely to deviate toward clustering than dispersion (average z-score of ‒0.55 [95% confidence interval = ‒0.69 to ‒0.41; P < 0.001]). The lesion-level analysis indicated a higher portion of melanomas (n = 57 of 72, 79.2% [95% confidence interval = 69.4‒88.9%]) appearing in proximity to neighboring melanocytic neoplasms than to nevi (n = 2,281 of 5,036, 45.3% [95% confidence interval = 43.9‒46.7%]). In conclusion, the nevi and melanomas' distribution on the back tends toward clustering as opposed to dispersion. Furthermore, melanomas are more likely to appear proximally to their neighboring neoplasms than to nevi. These findings may justify various oncogenic theories and improve diagnostic methodology.

Figure 1.. Allocation of the distributions of melanocytic lesions according to their classification for spatial randomness, categorized in various patient subgroups.

Y axis refers to the patient-sample subgroups, based on their eligible lesion counts (A) or history of melanoma on the back and presence of AMS (B). X axis refers to the z-scores calculated with the Clark-Evan test. 0 represents complete spatial randomness (CSR), while negative and positive z-scores represent clustering and dispersion, respectively. The orange lines correspond to the critical z-scores +/−1.96, based on the standard normal distribution levels of significance: (95% confidence level). The boundaries of each boxplot represent the interquartile range Q25 to Q75 and the blue circles represent the average values. The figure demonstrates that the Clark-Evans z-values of the various patient-sample subgroups follow a gaussian distribution.

Figure 2.. Visual examples of distributions for patients with high and low counts of eligible lesions.

The images demonstrate models of backs of patients included in the study, which were created after 3D TBP. The skin layer was removed and a green circle was placed in the center of each eligible lesion included in the study. Each eligible lesion is tagged with the letter ‘l’ followed by an ascending number. The top row contains patients with high counts of eligible lesions whereas the bottom row contains patients with low ones. Based on the Clark-Evans test, the first column contains patients with distributions classified as significantly clustered (Z < −1.96), the second column contains patients with random distributions (Z close to 0) and the third one includes patients with significantly dispersed distributions (Z > 1.96).