Optimal Scheduling of Bevacizumab and Pemetrexed/Cisplatin Dosing in Non-Small Cell Lung Cancer

Abstract

Bevacizumab-pemetrexed/cisplatin (BEV-PEM/CIS) is a first-line therapeutic for advanced nonsquamous non-small cell lung cancer. Bevacizumab potentiates PEM/CIS cytotoxicity by inducing transient tumor vasculature normalization. BEV-PEM/CIS has a narrow therapeutic window. Therefore, it is an attractive target for administration schedule optimization. The present study leverages our previous work on BEV-PEM/CIS pharmacodynamic modeling in non-small cell lung cancer-bearing mice to estimate the optimal gap in the scheduling of sequential BEV-PEM/CIS. We predicted the optimal gap in BEV-PEM/CIS dosing to be 2.0 days in mice and 1.2 days in humans. Our simulations suggest that the efficacy loss in scheduling BEV-PEM/CIS at too great of a gap is much less than the efficacy loss in scheduling BEV-PEM/CIS at too short of a gap.

Figure 1

Structural model diagram. The scheme of the structural model is depicted to the right. Unperturbed cells grow at rate governed by α and β. When a cytotoxic is introduced into the system, the cytotoxic impairs the growth of the tumor by sending cells into a death succession. The parameter that determines the cytotoxic efficacy, γ, is scaled by both the concentration of cytotoxics, C(t), and the volume of the tumor, V(t). Bevacizumab improves vascular quality, Q(t), after time delay, τ, which scales the cytotoxic effect by parameter δ. When a cell is damaged by cytotoxics, it begins a progression from unperturbed growth—compartment V(t)—to damage compartments Z ₁ through Z ₁. Eventually the cell exits the tumor volume as it dies. The rate of transfer between damage compartments is governed by intercompartmental clearance parameter k.

Figure 2

Standard goodness‐of‐fit diagnostic plots. On the left is individual predictions vs. observations and on the right are the individualized weighted residuals (IWRES) vs. time. During model fitting, observations were natural log–transformed to stabilize predictions. Therefore, residuals, predictions, and observations are natural log–transformed in these figures. The predictions are approximately normally distributed. On the left, the one‐to‐one prediction line is the center solid black line, the spline (average agreement between individual prediction and observation) is solid orange, and the dashed black lines are the borders of the 90% prediction interval. On the right, the zero residual error line is the center dashed black line and the spline is solid orange. The dashed black lines are the borders of the 90% prediction interval.

Figure 3

Sample of individual fits. The blue dots represent individual observations, whereas the solid violet line represents individual fits. Some mice—e.g., mice in the control group—were not tracked for the full course of the study. These animals experienced complications as a result of the experiment and either spontaneously passed or were euthanized to prevent excessive suffering. PEM‐CIS, pemetrexed‐cisplatin; RFU, relative fluorescence unit.

Figure 4

Combined and stratified visual predictive checks. The blue lines are the 10th, 50th, and 90th empirical percentiles calculated for each unique value of time. Blue and pink areas represent 90% prediction intervals for the 10th (blue), 50th (pink), and 90th (blue) percentiles. Prediction intervals are calculated by Monte Carlo simulation. To create prediction intervals for each unique value of time, 500 simulations are performed using random individual parameters. The red areas and red‐circled points represent areas where empirical measurements fall outside of the bounds of the 90% prediction intervals. PEM‐CIS, pemetrexed‐cisplatin; RFU, relative fluorescence unit; VPC, visual predictive check.

Figure 5

Human pharmacodynamic and pharmacodynamic simulations summary. To produce these figures, bevacizumab was administered anywhere from 0–10 days (in steps of 0.1) before pemetrexed/cisplatin was administered. Tumor growth was simulated from 0–67 days with no interindividual variability and no relative standard error of the estimate. In the top figure, the AUC of tumor growth vs. gap (0–10 days) is depicted. In the middle figure, tumor dynamics over time, with gap indicated by color, are depicted. In the bottom panel, the pharmacokinetics of bevacizumab–pemetrexed/cisplatin is depicted with gap indicated by color. The top figure indicates that the optimal scheduling gap is 1.2 days and the middle figure depicts the difference in tumor volume between administration gaps. The patient with optimal scheduling had a final tumor volume ~30% the size of the concomitant scheduling.