Patients with advanced cancer who were treated with nivolumab between 20th April 2016 and 30th October 2018 at the Erasmus MC Cancer Institute (Rotterdam, The Netherlands) and the Amphia Hospital (Breda, The Netherlands) were included prospectively in this study (Dutch Trial Register number NTR7015/ NL6828), allowing for serial blood sampling during standard of care nivolumab treatment. The study was approved by the independent ethics committee (MEC 16–011) and all patients provided written informed consent. Blood samples were drawn prior to every 2-weekly nivolumab to measure trough concentrations. For those patients who gave extensive informed consent, intensive sampling was performed between the first and second administration of nivolumab. Patient characteristics and clinical data were prospectively collected.

For all patients (n = 221), nivolumab trough concentrations were determined for a selection of serum samples until end of treatment. Nivolumab serum concentrations were determined by an in-house developed and validated enzyme-linked immune sorbent assay (ELISA, as described previously [14]. Serum samples were selected to determine trough concentrations prior to each administration for the first 12 weeks, thereafter at evenly 12-weekly intervals until the end of treatment. For some patients (n = 3), intensive sampling allowed to determine nivolumab concentrations at 2 h, 2 days, and 1 week after the first administration in order to estimate a best-fit compartmental model.

The following baseline patient parameters were collected: gender, race, tumor type, performance status, age, body weight, body surface area (BSA), total volumetric tumor burden, serum creatinine, renal function, total serum protein, serum albumin, lactate dehydrogenase (LD) and leucocyte count. Performance status was determined according to Eastern Cooperative Oncology Group [15]. For NSCLC patients, weight loss was recorded and defined as a percentage of 2.5 or higher [16] during a period of 3 months prior to the first administration of nivolumab. BSA was calculated by the Mosteller equation [17]. Renal function was estimated using the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) formula [18].

For a subgroup of NSCLC patients (n = 30), total volumetric tumor burden at baseline was assessed by a thoracic radiologist (A.O.) in a blinded manner using IntelliSpace Portal version 8 (Philips Medical Systems Nederland B.V., The Netherlands). Only primary tumor lesions with a long axis > 10 mm, lymph nodes with a short axis > 15 mm and metastatic lesions with a long axis > 10 mm were included. Total volumetric tumor burden was not assessed if the primary tumor was not identifiable or its boundaries could not be defined, e.g. due to surrounding atelectasis or radiation effects.

Best overall response (BOR) was assessed according to Response Evaluation Criteria in Solid Tumors version 1.1 (RECIST v1.1, [19]). A minimum duration of 90 days for stable disease (SD) was required. Confirmation of PR or complete response (CR) was not required. PFS was defined as the time from the first administration of nivolumab until PD or death due to any cause, whichever occurred first. OS was defined as the time from the first administration of nivolumab until death due to any cause. IrAEs were registered from start of treatment until end of follow-up according to National Cancer Institute Common Terminology Criteria for Adverse Events version 4.03 (NCI-CTCAE v4.03). Data cut-off for these analyses was set at 1st of January 2019.

To determine patient parameters influencing nivolumab PK (primary objective 1), nonlinear mixed effect modeling software, NONMEM (version 7.4; ICON, Development Solutions, MD) was used to analyze the PK data. The first-order conditional estimation method with interaction was used for parameter estimation. Pirana software version 2.9.7 (Pirana, www.pirana-software.com) was used as a modeling environment, and data were further handled in the latest R desktop version 1.1.453 (R-project, www.rproject.org).

A two-compartment PPK model was developed to best fit the nivolumab pharmacokinetics with individual estimates of systemic drug clearance (schematically shown in Additional file 1: Figure S1). Two-compartment PPK models have previously been described to best fit pharmacokinetics of monoclonal antibodies in blood [20]. Since we had only trough PK levels available, modelling of nivolumab distribution was challenging. Hence, we assumed that the central volume (V1) equals the peripheral volume of distribution (V2) as previously described for nivolumab [21].

Between-subject variability (BSV) was tested for clearance and distribution volume. The inclusion of BSV was evaluated according to the change of objective function value (OFV, P < 0.05) and shrinkage. A shrinkage value below 25% was considered acceptable [22].

BSV was modelled according to Eq. 1: 1 Pi=P∙expηi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {P}_i=P\bullet \mathit{\exp}\left({\eta}_i\right) $$\end{document} where P_i represents the parameter estimate for each individual patient (i), P represents the typical population parameter estimate and η_i represents BSV distributed according to N (0, ω²).

Residual errors were described by a proportional error model (Eq. 2): 2 Cobs,ij=Cpred,ij×1+εp,ij\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {C}_{obs, ij}={C}_{pred, ij}\times \left(1+{\varepsilon}_{p, ij}\right) $$\end{document} where C_obs,ij and C_pred,ij represent the observed and predicted concentration for the (i) th subject and the (j) th measurement, respectively. ε_p,ij represents the proportional error distributed according to N (0,σ²).

Covariates were added to the PPK model (initial model M_i) to obtain a final model (final model M_f). Potential covariates were selected based on clinical plausibility and tested by a stepwise approach with forward inclusion (threshold p < 0.01) and backward elimination (threshold p < 0.005, [23–25]). The covariates were tested on clearance (CL) by multiplying a typical clearance value (CL_TV) with a factor for categorical (Factor_cat) and continuous (Factor_con) covariates (Eq. 3). 3 CL=CLTV×Factorcat×Factorcon\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ CL={CL}_{TV}\times {Factor}_{cat}\times {Factor}_{con} $$\end{document}

Categorical covariates were scored as ‘0’ or ‘1’. Equation 4 was applied for patients who scored ‘1’ in which θ _x represents the covariate effect size estimate. Continuous variables were tested with the PK model using Eq. 5 where cov represents the covariate measure, cov _median the population median of the covariate, and θ _y the covariate effect measure. 4 Factorcat=1+θx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {Factor}_{cat}=1+{\theta}_x $$\end{document} 5 Factorcon=covcovmedianθy\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {Factor}_{con}={\left(\frac{\mathit{\operatorname{cov}}}{{\mathit{\operatorname{cov}}}_{median}}\right)}^{\theta_y} $$\end{document}

Descriptive statistics included frequency and the median with range and inter-quartile range (IQR) of covariates. To analyze the relationship of systemic nivolumab clearance, which is inversely proportional to drug exposure, with treatment outcome (primary objective 2), patients were stratified by tumor type (NSCLC, melanoma, and RCC) and ranked according to BOR. To avoid potential confounding from covariates that may correlate with response, the initial model M_i was used to compare individual drug clearance estimates between different BOR groups (PD, SD, PR/CR). Equal variances among groups were assessed with Levene’s test, normal distribution was assessed using the skewness and kurtosis. Comparison of individual drug clearance was assessed for the three BOR groups by ANOVA and post-hoc independent samples t-tests.

To investigate the relationship of systemic nivolumab clearance with toxicity, patients were stratified by tumor type, grouped based on the occurrence of grade 0–2 or grade > 3 irAEs, and analyzed by independent samples t-test. To relate systemic nivolumab clearance to PFS and OS, NSCLC patients were grouped into quartiles: patients with low clearance (Q1) were compared with patients with high clearance (Q4) by the Kaplan-Meier approach. The relative risk of death or death/progression was assessed by the Cox proportional hazards model. Additional patient characteristics were included grouped by clearance quartile (Q1-Q4). A two-sided p-value < 0.05 was considered significant.

Post-processing of NONMEM generated data and statistical analysis was conducted with R and IBM SPSS Statistics version 24.0.0.1 (Chicago, IL).

Continuous and categorical clinical covariates were incorporated in the final two-compartment model by forward inclusion and backward elimination (Additional file 1: Table S1), resulting in four covariates reaching the significance threshold, namely: gender, BSA, albumin, and body weight. BSA had a higher impact on nivolumab pharmacokinetics than weight; the latter being rejected by the backward elimination step. The parameter estimates according to the M_f are shown in Table 2 including the results of internal validation. The NONMEM model can be found Additional file 1: Appendix 1. Inter-individual variance was reduced from 37% (as indicated by M_i) to 30.7% by incorporating these three covariates. Women had 22% lower clearance than men, as evidenced by a mean clearance of 0.185 and 0.237 L/day, respectively. The thresholds of BSA and baseline serum albumin that led to an estimated > 20% increase of systemic nivolumab clearance were > 2.2 m² (BSA) and < 37.5 g/L (albumin), respectively (Fig. 2).Tab2

Parameter estimates

Clinical outcome and occurrence of toxicity are shown in Additional file 1: Table S2. The initial model (M_i) was used to investigate the relationship between individual clearance of nivolumab and clinical response or toxicity in NSCLC, melanoma, and RCC (Fig. 3b-d). A negative clearance-response relationship was found in patients with NSCLC (p < 0.001), as a significantly higher clearance of 41.8% was observed in patients with PD (mean: 0.244; 95% CI: 0.223–0.265 L/day) compared to patients with PR/CR (0.172; 0.152–0.192). Patients with SD were identified as an intermediate group (0.211; 0.193–0.228). A non-significant trend similarly to NSCLC was observed in RCC (p = 0.054). Of note, no clearance-response relationship was observed in melanoma (p = 0.987). A clearance-irAE relationship was not found for NSCLC, melanoma, or RCC (respectively p = 0.28, p = 0.84 and p = 0.92; Additional file 1: Figure S2B-D), nor for all three tumor types pooled together (p = 0.31; Additional file 1: Figure S2A).Fig3Fig. 3

Clearance-response analysis: a Nivolumab clearance (L/day) of a all patients receiving nivolumab monotherapy grouped by best overall response (BOR), and stratified by b NSCLC, c melanoma, and d RCC. Single measurements are represented by open circles. Bars indicate the 95% confidence interval of the mean. Abbreviations: progressive disease (PD), stable disease (SD) and partial response/ complete response (PR/CR). P-values indicated by *** < 0.001 (post-hoc independent samples t-test)