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.