Univariate Biomarker Distribution Simulations
As a first step, we sought proof-of-concept evidence to motivate the use of GAN for pharmacometrics. We focused on modeling the univariate distributions of 16 biomarkers that are clinically relevant for diabetes.
Table 1 summarizes demographic characteristics and the biomarker levels in the data set.
Figure 2 compares the distribution of the biomarkers in the training set to the generated distribution from the GANs for eight biomarkers; the remaining eight biomarkers are summarized in Supplementary Figure 1. Despite the log transformation, the set of scaled distributions for the biomarkers had diversity of patterns and evidence for non-normality: e.g., some of the biomarkers were left skewed (e.g., urine creatinine, Figure 2B), some were right skewed (e.g., fasting glucose, Figure 2C) and some had broad distributions (e.g., body mass index, Figure 2E and high sensitivity C-reactive protein, Supplementary Figure 1M).
The dark gray regions of the histograms show the overlap of the generated density histograms (salmon) and the test data density histograms (teal). The extensive regions of overlap in Figure 2 and Supplementary Figure 1 indicate the satisfactory concordance of GAN-generated distributions to the test data distribution for the 16 biomarkers.
The concordance was further assessed using quantile-quantile plots and Kolmogorov-Smirnov tests (Supplementary Figure 2). The quantile-quantile plots showed extensive clustering around the line of identity. Thep -values from the Kolmogorov-Smirnov test were not significant (p > 0.05) for the majority of GAN-generated biomarkers distributions. However, GAN-generated distributions for glucose, aspartate aminotransferase, gamma glutamyl transferase and high sensitivity C-reactive protein had p ≤ 0.05 despite the overall visual similarity with the test histogram probability distribution function.
These promising proof-of-concept results motivated further, more rigorous investigation of GAN applications for scenarios relevant to drug development and pharmacometrics.