Application of a Systems Pharmacology-Based Placebo Population Model to Analyze Long-Term Data of Postmenopausal Osteoporosis

Abstract

Osteoporosis is a progressive bone disease characterized by decreased bone mass resulting in increased fracture risk. The objective of this investigation was to test whether a recently developed disease systems analysis model for osteoporosis could describe disease progression in a placebo-treated population from the Early Postmenopausal Intervention Cohort (EPIC) study. First, we qualified the model using a subset from the placebo arm of the EPIC study of 222 women who had similar demographic characteristics as the 149 women from the placebo arm of the original population. Second, we applied the model to all 470 women. Bone mineral density (BMD) dynamics were changed to an indirect response model to describe lumbar spine and total hip BMD in this second population. This updated disease systems analysis placebo model describes the dynamics of all biomarkers in the corresponding datasets to a very good approximation; a good description of an individual placebo response will be valuable for evaluating treatments for osteoporosis.

Figure 1

Schematic representation of the mechanism-based disease systems analysis model. Active osteoblast and osteoclast cells and the indicated interactions form the mechanism-based core (shown in gray) of this model, which are linked to the biomarkers, NTX, BSAP, LS-BMD, and TH-BMD as shown in the dotted area. PTH stands for parathyroid hormone, TGF-β for transforming growth factor-β, OPG for osteoprotegerin, RANK for receptor activator of NF-κB, and RANKL for receptor activator of NF-κB ligand. RANKL binds to RANK and promotes osteoclast differentiation, while OPG inhibits this differentiation by binding RANKL. Figure and legend were adapted from Ref. 15.

Figure 2

Normalization of individual timescales based on years since menopause (YSM). (a) Typical imaginary disease progression curve for osteoporosis (black solid line). Disease progression is plotted as relative fraction of healthy status (=1) vs. years since menopause. Five subjects (no real data) are shown that have different YSM at the start of the study. For these subjects we assume that they complete the study duration of 4 years as indicated by the colored lines. At the start of the study, these five subjects are thus at different locations on the disease progression curve. The shaded gray area represents the exclusion criteria for YSM. The range of YSM for EPIC 1 (1≤YSM≤5) and for EPIC 2 (all YSM) is indicated by the black arrows. (b) Normalization based on study time for the five subjects (same colors as in a). This normalization harmonizes the individual subjects disease trajectory to an identical study starting point.

Figure 3

Visual predictive check plots of the degradation marker NTX, the bone formation marker BSAP, LS-BMD, and TH-BMD on the study timescale for the model applied to all women in the placebo arm (EPIC 2). The blue dots represent the percentage change from baseline of the available observations. The 5th, 50th, and 95th percentiles of the real data in the bins are presented by the red dashed, red solid, and red dashed line, respectively. The 5th, 50th, and 95th percentiles of the simulated data (n = 500) in the bins are presented by the black dashed, black solid, and black dashed line, respectively. The confidence interval for the simulated data 5th, 50th, and 95th percentiles for each of the bins is presented by the blue, red, and blue area, respectively. Note that BSAP was measured in a random sample of 205 women and not in the entire population.

Figure 4

Comparison of zeroth-order and indirect response model for BMD dynamics. (a) Changes in the net bone cell activity (S = z/y) vs. time for the zeroth-order process (ZO, solid line) and the indirect response model (IR, dashed line). The arrows indicate the start and end of the placebo treatment in the two studies. (b). Changes in LS-BMD (gray lines) and TH-BMD (black lines) for the zeroth-order process (solid line) and the indirect response model (dashed line). Scatterplot showing the change between baseline and the latest observation available for LS-BMD (c) and TH-BMD (d) vs. years since menopause.