A population pharmacodynamic model for lactate dehydrogenase and neuron specific enolase to predict tumor progression in small cell lung cancer patients

Abstract

The development of individualized therapies poses a major challenge in oncology. Significant hurdles to overcome include better disease monitoring and early prediction of clinical outcome. Current clinical practice consists of using Response Evaluation Criteria in Solid Tumors (RECIST) to categorize response to treatment. However, the utility of RECIST is restricted due to limitations on the frequency of measurement and its categorical rather than continuous nature. We propose a population modeling framework that relates circulating biomarkers in plasma, easily obtained from patients, to tumor progression levels assessed by imaging scans (i.e., RECIST categories). We successfully applied this framework to data regarding lactate dehydrogenase (LDH) and neuron specific enolase (NSE) concentrations in patients diagnosed with small cell lung cancer (SCLC). LDH and NSE have been proposed as independent prognostic factors for SCLC. However, their prognostic and predictive value has not been demonstrated in the context of standard clinical practice. Our model incorporates an underlying latent variable ("disease level") representing (unobserved) tumor size dynamics, which is assumed to drive biomarker production and to be influenced by exposure to treatment; these assumptions are in agreement with the known physiology of SCLC and these biomarkers. Our model predictions of unobserved disease level are strongly correlated with disease progression measured by RECIST criteria. In conclusion, the proposed framework enables prediction of treatment outcome based on circulating biomarkers and therefore can be a powerful tool to help clinicians monitor disease in SCLC.

Fig. 1

Example of an individual LDH time profile. Treatment (etoposide + platinum compound) consisted of six chemotherapy cycles administered every 3 weeks (i.e., from week 1 (diagnosis) to week 16). The three features identified in most patients are disease progression (weeks 1–4 and weeks 16–25), drug effect (weeks 4–10), and resistance effect (weeks 10–16). Vertical dashed lines represent time points at which tumor size was assessed through CT scans. Horizontal dotted lines correspond to the normal range of values of LDH

Fig. 2

Schematic view of the final model and differential equations used to describe the model. DISEASE is a latent variable that represents disease progression and drives LDH and NSE production. Radiotherapy (RT) and chemotherapy (CT) each affect disease level, where CT decreases its value and RT slows its linear growth. Resistance (REST) is modeled by linking cumulative exposure with a decrease in the drug effect. Granulocyte colony-stimulating factor (G-CSF) increases the physiological LDH synthesis

Fig. 3

a LDH observations (green circles) with individual predictions (green lines) on the left y axis and NSE observations (orange squares) with the individual predictions (orange lines) on the right y axis for nine selected patients. Observations and predictions for both biomarkers are log-transformed. b pvc-VPC of LDH (left) and NSE (right) for the final model against chemotherapy cycles. Cycle 7 corresponds to follow-up measurement. Solid black lines represent the 5th, 50th, and 95th percentiles of the observed data. Shaded areas are the 95% confidence intervals based on simulated data (n = 1,000) for the corresponding percentiles

Fig. 4

Typical simulated profiles (thick black solid lines) and individual simulated profiles (thin gray lines) from a population of 100 virtual individuals, using the model structure depicted in Fig. 2 and the estimates of model parameters shown in Table I. a Effect of chemotherapy exposure (1), the level of resistance corresponding to AUC_CT (2), and drug effects in the presence of resistance (3). b Predicted disease dynamics in different scenarios: (1) disease level in the absence of any treatment, (2) disease level in presence of chemotherapy, (3) disease level under radiotherapy and chemotherapy, and (4) disease progression as it is described in our model (in the presence of radiotherapy, chemotherapy, and resistance)

Fig. 5

ROC curves (i.e., true positive rate (sensitivity) vs. false positive rate (100-specificity)) for discriminating observed disease progression with simulated biomarker changes. Solid lines correspond to ROC curves, and the shaded area represents the confidence intervals obtained with bootstrapping

Fig. 6

Kaplan-Meier plot of progression-free survival (black line) and 95% prediction intervals (gray shaded area) based on 1,000 simulations. The hazard rate is described by a log-logistic distribution. The baseline hazard is increased by predicted changes in the latent disease variable between CT scan times (approximately 8 weeks)