The risk of febrile neutropenia in breast cancer patients following adjuvant chemotherapy is predicted by the time course of interleukin‐6 and C‐reactive protein by modelling

Abstract

Aims

Early identification of patients with febrile neutropenia (FN) is desirable for initiation of preventive treatment, such as with antibiotics. In this study, the time courses of two inflammation biomarkers, interleukin (IL)‐6 and C‐reactive protein (CRP), following adjuvant chemotherapy of breast cancer, were characterized. The potential to predict development of FN by IL‐6 and CRP, and other model‐derived and clinical variables, was explored.

Methods

The IL‐6 and CRP time courses in cycles 1 and 4 of breast cancer treatment were described by turnover models where the probability for an elevated production following initiation of chemotherapy was estimated. Parametric time‐to‐event models were developed to describe FN occurrence to assess: (i) predictors available before chemotherapy is initiated; (ii) predictors available before FN occurs; and (iii) predictors available when FN occurs.

Results

The IL‐6 and CRP time courses were successfully characterized with peak IL‐6 typically occurring 2 days prior to CRP peak. Of all evaluated variables the CRP time course was most closely associated with the occurrence of FN. Since the CRP peak typically occurred at the time of FN diagnosis it will, however, have limited value for identifying the need for preventive treatment. The time course of IL‐6 was the predictor that could best forecast FN events. Of the variables available at baseline, age was the best, although in comparison a relatively weak, predictor.

Conclusions

The developed models add quantitative knowledge about IL‐6 and CRP and their relationship to the development of FN. The study suggests that IL‐6 may have potential as a clinical predictor of FN if monitored during myelosuppressive chemotherapy.

What is Already Known about this Subject

• Patients receiving chemotherapy may experience febrile neutropenia (FN). It is desirable to identify these patients before such an event.

• Interleukin (IL)‐6 and C‐reactive protein (CRP) have previously been related to FN but not quantitatively.

What this Study Adds

• The IL‐6 and CRP time courses were characterized and quantitatively associated with the risk of developing FN. IL‐6 is suggested to be a more valuable predictor than CRP since IL‐6 elevations occur earlier.

• Monitoring of IL‐6 during myelosuppressive chemotherapy has potential to indicate the need for prophylactic treatment to prevent FN.

Introduction

Febrile neutropenia (FN) is a severe and life‐threatening complication among patients treated with chemotherapeutic agents, and is characterized by a low absolute neutrophil count (ANC; generally < 0.5 × 10⁹ cells l^–1 or expected to fall below 0.5 × 10⁹ cells l^–1) together with fever (oral temperature >38.3°C or two consecutive oral temperatures >38°C during 2 h) 1. The incidence of FN is mainly dependent on the chemotherapy regimen 2, 3, 4. For early breast cancer patients treated with adjuvant 5‐fluorouracil–epirubicin–cyclophosphamide and docetaxel (FEC‐Doc) without primary granulocyte‐colony stimulating factor (G‐CSF) prophylaxis, approximately 25% develop FN in routine clinical practice 5. An overall mortality in inpatients with FN of 9.5% has been reported, but the rate depends on the cancer type, demographic factors, type of infection and comorbidities 6. Additional consequences of FN include substantial increases in costs 6 as well as reduced relative dose intensity (i.e. the ratio delivered to planned chemotherapy dose), which has been related to worse survival 7.

G‐CSF regulates the proliferation of neutrophils 8 and several guidelines recommend primary prophylaxis with G‐CSF for patients who have ≥20% risk for developing FN 9, 10, 11. The risk for FN in cancer patients treated with FEC‐Doc is ≥10% 12. It would, however, be of value to improve the possibility to predict FN before clinical signs of FN, since prophylactic treatment with G‐CSF and antibiotics is associated with side‐effects and should therefore be avoided for patients with limited benefit from such therapy. Most of the factors that have been identified as predictors of FN are static. Therefore, the dynamics of circulating immune‐related biomarkers may provide additional predictive or diagnostic value. A pronounced increase in the biomarker concentration could signal that the patient is at high risk to develop FN. In a previous study, the frequently used semimechanistic myelosuppression model 13, was used to describe the time course of chemotherapy‐induced myelosuppression and it was found that a rapid decline in the ANC was related to the probability of developing FN 14. Other important immune‐mediating biomarkers include interleukin 6 (IL‐6) and C‐reactive protein (CRP). IL‐6 is a pleiotropic cytokine that mediates multiple processes in response to inflammation, such as induction of antibody production and the acute‐phase response. CRP is an acute‐phase protein that is produced by hepatocytes after stimulation by IL‐6 for example 15. IL‐6 and CRP are regarded as early markers of inflammation and have been related to infections in FN 16, 17 but not quantitatively to FN in a model‐based analysis.

The aim of this study was to characterize the time courses of IL‐6 and CRP in breast cancer patients, treated with adjuvant chemotherapy, by using nonlinear mixed‐effects models. Subsequently, baseline‐available and model‐derived variables were assessed as potential predictors of FN in a parametric time‐to‐event (TTE) model characterizing the hazard for development of FN.

Material and methods

Patients, treatment and data

Longitudinal IL‐6 and CRP data, together with information on the time of FN, were collected in a study of 49 breast cancer patients treated with adjuvant chemotherapy 18. For the purpose of this analysis, FN was defined as grade 3 or 4 neutropenia with concurrent fever, regardless of cause. Most patients (n = 39) received three cycles of FEC (starting doses; 1‐h, 2‐min and 15‐min infusions of 75 mg m^–2 epirubicin, 600 mg m^–2 5‐fluorouracil and 600 mg m^–2 cyclophosphamide, respectively) followed by three cycles of docetaxel (starting dose; 1‐hour infusion of 80 mg m^–2). Six patients received the treatment in the reverse order. Two patients received six cycles FEC, one patient received three cycles FEC followed by two cycles docetaxel and an additional cycle FEC and one patient received three cycles docetaxel and three cycles cyclophosphamide, epirubicin and capecitabine (3500 mg day^–1, days 1–14 in each cycle). Trastuzumab was added to the therapy if applicable according to the local routine care. IL‐6 and CRP data were primarily collected in cycles 1 and 4 and therefore this analysis only included those two cycles. IL‐6 and CRP were measured on five occasions in each of the two cycles, except for the first 10 enrolled patients, where IL‐6 and CRP were measured on seven different days in cycle 1. Additional measurements of CRP were available from patients that developed FN, as part of the routine care. The days of sampling varied slightly depending on whether docetaxel or FEC was administered. For the first 10 patients in cycle 1, samples were collected predose, days 7–9, 9–11, 11–13, 13–15, 15–18 and 20–22, and predose, days 4–6, 6–8, 8–10, 10–13, 13–15 and 20–22 following FEC and docetaxel cycles, respectively. For all other patients and cycles, samples were collected predose, days 7–12, 12–14, 14–16 and 18–22, and predose, days 5–8, 8–10, 10–15 and 18–22 for FEC‐ and docetaxel‐related cycles, respectively. The exact time of the sample collection was recorded and used in the analysis. No drug concentrations were measured. The study was approved by the local ethics committee in Uppsala, Sweden (Dnr 2006/353). Written informed consent was provided by all patients before being enrolled into the study.

Analytical methods

IL‐6 was analysed using an enzyme‐linked immunosorbent assay (Quantikine Human Immunoassay ELISA Kit, HS included, R&D systems, Inc., Minneapolis, MN, USA). The IL‐6 assay range was 0.2–300 pg ml^–1. CRP was analysed according to routine clinical practice 19 and the lower limit of quantification was 0.16 mg l^–1. The inter‐ and intra‐assay coefficients of variation were <10% for both IL‐6 and CRP.

Characterization of the IL‐6 and CRP time courses

Patients could have elevated biomarker concentrations in cycle 1 and/or in cycle 4. These elevations were described with a surge function for elevated biomarker production, g(t) (Equation (1)), together with a turnover model (Equation 2), for the description of biomarker time courses.

$$\mathrm{g}\left(\mathrm{t}\right)=\frac{{\mathrm{SA}}_{\text{BioM}}}{{\left(\frac{\mathrm{t}-{\mathrm{PT}}_{\text{BioM}}}{{\mathrm{SW}}_{\text{BioM}}}\right)}^4+1}$$ (1)

$$\frac{\text{dBioM}}{\mathrm{dt}}={\mathrm{R}}_{\text{in},\text{BioM}}·\left(1+\mathrm{g}\left(\mathrm{t}\right)\right)-{\mathrm{k}}_{\text{out},\text{BioM}}·\text{BioM}$$ (2a)

$$\mathrm{Bio}{\mathrm{M}}_0=\frac{{\mathrm{R}}_{\text{in},\text{BioM}}}{{\mathrm{k}}_{\text{out},\text{BioM}}}$$ (2b)

SA_BioM is the surge amplitude, PT_BioM is the surge peak time and SW_BioM is the surge width. Note that SA_BioM is the relative increase in R_in,BioM (the zero‐order biomarker production rate) and does not have a (concentration) unit. BioM is the circulating biomarker concentration (i.e. either CRP or IL‐6), k_out,BioM is the first‐order fractional biomarker turnover rate constant and BioM₀ is the biomarker concentration at baseline. The exponent in the surge function was fixed to 4 20, 21. The MTIME‐functionality in NONMEM (software for nonlinear mixed‐effects modelling) 22 was also explored during the initial model development, where a different biomarker production from the baseline production was estimated during a limited period.

Since not all patients had elevated biomarker concentrations, the mixture functionality implemented in NONMEM 22 was used to identify subpopulations that had or did not have elevated concentrations in cycles 1 and 4. The probability for elevated production was assessed as separate probability‐related parameters or by assuming the same probabilities for elevation in cycles 1 and 4. A description of the mixture model is given in the Table S1. Interindividual variability was explored for all model parameters, and interoccasion (intercycle) variability 23 on the surge‐related parameters. Identification of the subpopulations was used by setting Equation (1) to 0 for the subpopulations that had no elevated biomarker production. The correlation between IL‐6 and CRP was investigated by including covariance between the random effects and/or by letting IL‐6 induce the CRP production either through a linear function (IL‐6‐EFF, described by the SLOPE parameter) or through an E_max model. The differential equation system for a linear regulation of CRP by IL‐6 is given in Supplementary Material 1.

TTE model for development of FN

Parametric TTE models were developed for the occurrence of FN in cycles 1 and/or 4. Time‐constant (exponential distribution) and time‐dependent hazards (Weibull distribution) for development of FN were investigated in the initial step. Only one event per cycle was allowed for each patient. The hazard was set to 0 until 3.5 days after dose since no patient experienced grade 3 neutropenia before that time. In the subsequent step, a search for predictors of the hazard for FN was performed. These analyses were based on three types of potential predictors and were performed in parallel: (i) available prior to chemotherapy; (ii) available prior to FN; and (iii) available when FN occurs. A summary of these variables is given in Table 1. The partial area under the curve variables pAUC_IL‐6(t) and pAUC_CRP(t) (Table 1) were generated by integrating the change from IL‐6 and CRP baselines, respectively, over time from initiation of the cycle until the time of FN. Note that the time course of ANC was not evaluated as a predictor in the current analysis since the ANC itself is part of the definition of FN and a majority of patients had grade 3 or 4 neutropenia.

Table 1.

Description of the evaluated potential predictors

			Availability of the potential predictor
Potential predictor	Description (unit)	Median value (range)	Prior to chemotherapy	Prior to FN	When FN occurs
Age	(years)	54 (31–73)	X	X	X
Body weight	(kg)	70 (54–111)	X	X	X
Treatment	FEC or docetaxel		X	X	X
Observed ANC 0,1	cycle 1 ANC baseline (109 cells l–1)	3.6 (1.8–8.9)	X	X	X
Observed ANC 0	cycle‐specific ANC baseline (109 cells l–1)	3.6 (2.1–8.9)	X	X	X
Observed G‐CSF 0,1	cycle 1 G‐CSF baseline (ng l–1)	40.0 (1.4–831.2)	X	X	X
Observed G‐CSF 0	cycle‐specific G‐CSF baseline (ng l–1)	40.0 (1.4–359.2)	X	X	X
Observed IL‐6 0,1	cycle 1 G‐CSF baseline (pg ml–1)	2.9 (0.2–37.3)	X	X	X
Observed IL‐6 0	cycle‐specific G‐CSF baseline (pg ml–1)	2.9 (0.2–37.3)	X	X	X
Observed CRP 0,1	cycle 1 G‐CSF baseline (mg l–1)	1.9 (0.3–24.0)	X	X	X
Observed CRP 0	cycle‐specific G‐CSF baseline (mg l–1)	1.9 (0.3–24.0)	X	X	X
ANC 0,i	estimated individual ANC baseline 18 (109 cells l–1)	3.7 (2.3–5.5)		X	X
G‐CSF 0,i	estimated individual G‐CSF baseline 18 (ng l–1)	25.1 (5.7–103.7)		X	X
IL‐6 0,i	estimated individual IL‐6 baseline (pg ml–1)	2.2 (0.8–24.9)		X	X
IL‐6(t)	predicted absolute IL‐6 time course (pg ml–1)	time‐varying		X	X
LN_IL‐6(t)	log of IL‐6(t)/IL‐60	time‐varying		X	X
RCFB IL‐6(t)	predicted relative change from baseline IL‐6 time course	time‐varying		X	X
pAUC IL‐6(t)	partial IL‐6 area under the curve (pg h ml–1)	time‐varying		X	X
k out,IL‐6,i	Individual first‐order fractional IL‐6 turnover rate constant (h−1)	0.014 (0.002–0.068)			X
SA CRP,i	Individual CRP surge amplitude	0 (0–0.65)			X
CRP 0,i	estimated individual CRP baseline (mg l–1)	1.8 (0.2–13.0)			X
CRP(t)	predicted absolute CRP time course (mg l–1)	time‐varying			X
LN_CRP(t)	log of CRP (t)/CRP0	time‐varying			X
RCFB CRP(t)	predicted relative change from baseline CRP time course	time‐varying			X
pAUC CRP	partial IL‐6 area under the curve (mg h l–1)	time‐varying			X

ANC, Absolute neutrophil count; CRP, C‐reactive protein; FEC, 5‐fluorouracil, epirubicin, cyclophosphamide; G‐CSF, Granulocyte colony stimulating factor; IL‐6, Interleukin 6

The individual pharmacokinetic parameter approach 24 was used for assessing the IL‐6 and CRP related variables in the TTE model. Other modelling approaches 24, 25 were explored but resulted in model instability.

The predictors were added one at a time. Variables that improved the model fit significantly (P < 0.05) were defined as predictors. If more than one predictor was identified, the predictor that resulted in the largest drop in the objective function value (OFV) was included in the model. This process was repeated until no additional predictor could be identified.

Data analysis

The models were developed using nonlinear mixed‐effects modelling in NONMEM 7.3 22. The first‐order conditional estimation method with interaction (FOCEI) was applied for the biomarker modelling and the exact likelihood was used for parameter estimation in the TTE models. Perl‐speaks‐NONMEM (PsN) version 4 was used to execute model runs, process model output and produce visual predictive checks (VPCs) of the models 26. Pirana version 2 was used for generating run records 26. Data management and additional processing of the NONMEM output were performed in the R software version 3.2 (www.R-project.org). Graphical evaluation of the output was done in the R‐based programs Xpose4 26 and ggplot2 27.

Model discrimination was performed based on changes in the OFV (i.e. –2 log likelihood), provided by NONMEM, and on inspection of graphical diagnostics. For models that are nested, the ΔOFVs are nominally χ² distributed where the degrees of freedom (df) are the difference in number of parameters (larger to smaller model). A P‐value of <0.05 was used for significance testing. An actual significance level in terms of an OFV, corresponding to a P‐value of 0.05, was acquired from the randomization test, implemented in PsN 26, for the TTE models. Prediction‐corrected VPCs were used to assess the predictive properties of the biomarker models and to guide model development 28. The predictive properties of the TTE model was assessed with Kaplan–Meier (KM) plots where the observed FN data were compared to 1000 simulated KM datasets, given the TTE model. Uncertainty of the parameter estimates were computed by using the sampling importance resampling approach 29.

No transformation of the IL‐6 concentrations was done, while for CRP log‐transformed concentrations were used in the analysis. Proportional (or additive on the log‐scale) and combined (proportional and additive) residual error models were investigated.

Results

The overall modelling framework is presented in Figure 1.

Figure 1.

Schematic representation of the modelling framework. The interleukin (IL)‐6 and C‐reactive protein (CRP) model consists of turnover models for both IL‐6 and CRP, where the CRP production is regulated by IL‐6. The time‐to‐event (TTE) models for febrile neutropenia (FN), were based on model‐derived and baseline‐available predictors. Solid lines represent mass movements and dotted lines correspond to effects. R_in,IL‐6, zero‐order IL‐6 production rate; R_in,CRP, zero‐order CRP production rate; k_out,IL‐6, first‐order IL‐6 turnover rate constant; k_out,CRP, first‐order CRP turnover rate constant; g(t)_IL‐6, empirical IL‐6 surge function (equation 3); g(t)_CRP empirical CRP surge functions (equation 3); Slope, parameter relating the relative change from IL‐6 baseline time course (RCFB_IL‐6) to the CRP production; CE_IL‐6 is the effect concentration of the log of IL‐6(t)/IL‐6_0,population time course; k_e0 is the effect compartment rate constant (k_e0 = k_e1); β₁, parameter relating age to FN; β₂, parameter relating the time course of CE_IL‐6(t) to FN; β₃, parameter relating the model‐derived ANC₀ (baseline absolute neutrophil count) to FN and β₄, parameter relating the log of CRP (t)/CRP_0,population time course to FN

Data

At least one IL‐6/CRP observation was observed in 49 and 45 patients in cycles 1 and 4, respectively. There were 445 and 482 IL‐6 and CRP measurements in total, respectively. No CRP sample was below the limit of quantification; 14 IL‐6 samples were, but their reported values were used in the analysis. One patient had a very high baseline value of IL‐6 in cycle 1 (28 times higher than the median observed IL‐6 baseline) and the subsequent measurements did not follow the same pattern as the other patient profiles. Therefore, both IL‐6 and CRP data in cycle 1 from this patient were omitted during all parts of the analysis (this patient did not develop FN). Another patient had a high IL‐6 baseline in cycle 1 (17 times higher than the median observed IL‐6 baseline), this observation was also omitted from the analysis.

Eleven patients developed FN and one of these patients developed FN in both cycles 1 and 4. In total, there were 12 FN episodes (six each in cycles 1 and 4). Six episodes were related to Grade 3 and six to Grade 4 neutropenia. Six episodes were related to clinically‐defined infections and six to fever of unknown origin. All patients who developed FN in cycle 1 received FEC and those who developed FN in cycle 4 received docetaxel. Three patients with FN in cycle 4 received trastuzumab in addition to docetaxel.

IL‐6 and CRP model

The final biomarker model included 16 different possible subpopulations, although only a single probability parameter for each of IL‐6 and CRP needed to be estimated. The model improved when the CRP production was stimulated by a change in IL‐6 [RCFB_IL‐6(t)] using a linear function (OFV dropped 61 units). Interoccasion variability was related to all CRP surge parameters (SA_CRP, SW_CRP and PT_CRP) and to the IL‐6 peak time (PT_IL‐6) and interindividual variability to IL‐6₀, CRP₀ and k_out,IL‐6. No parameter correlations could be identified.

The probability for elevated CRP production mediated by the surge function (44%), was lower than for IL‐6 (63%). However, since CRP elevations also were a consequence of elevated IL‐6 concentrations (through the IL‐6 regulation function), the actual number of CRP elevations were higher than for IL‐6. The subpopulation‐related probability therefore did not directly reflect the frequency of elevated CRP production.

The CRP peak time was constrained to be the IL‐6 peak time plus an estimated additional time. The PT_IL‐6 (137 h) was consequently forced to be shorter than the PT_CRP (187 h) for all patients. For all patients with FN, except one (no IL‐6 elevation), both the IL‐6 and CRP concentrations were estimated to be elevated in the cycle wherein the patient developed FN. The peak concentrations for IL‐6 were typically predicted to occur 1.3 days prior to the FN diagnosis, while the peak CRP concentrations were predicted to occur just before the FN diagnosis (i.e. 0.4 days prior to FN). For all patients with FN, both the IL‐6 and CRP concentration were predicted to start increasing before the FN diagnosis. Note that the biomarker predictions were based on the biomarker model without influence of the FN data.

The prediction‐corrected VPCs of the final biomarker model showed in general a good fit for both IL‐6 and CRP (Figure 2). Some under‐prediction of the lower percentile, mainly for CRP in cycle 4, can, however, be observed. The observed peak biomarker concentrations appeared slightly higher in cycle 4 (Figure 2), but no statistically significant difference was identified. The uncertainties in the parameter estimates were generally low, as reflected by small RSEs (generally <30%). All final parameter estimates for the IL‐6 and CRP model are given in Table 2. The biomarker model code together with a small example dataset are provided in Supplementary Material 2 and 3, respectively.

Figure 2.

Prediction‐corrected visual predictive check for the final biomarker model. The plot is stratified by biomarker (interleukin‐6 in the top panel and C‐reactive protein in the bottom panel) and cycle. The solid and the upper and lower dashed red lines are the median, 90^th and the 10^th percentiles of the observed data, respectively. The shaded red, upper and lower green areas are the 95% confidence intervals around the median, 90^th and 10^th percentiles of the simulated data (n = 500), respectively. Open circles represent observations

Table 2.

Parameter estimates for the final biomarker model and the different febrile neutropenia models

Parameter (biomarker model)	Units	Value (RSE)	IIV (RSE)
IL‐6 0	pg ml–1	2.50 (9.2)	68.0 (11)
CRP 0	mg l–1	1.88 (12)	80.5 (11)
k out,IL‐6	h−1	0.0141 (25)	130 (22)
k out,CRP	h−1	0.0224 (13)
P elevation,IL‐6	%	63.4 (10)
P elevation,CRP	%	44.3 (20)
Slope	RCFBIL‐6(t) −1	1.05 (18)
Proportional error (IL‐6)	%	54.7 (4.7)
Proportional error (CRP)	%	53.0 (4.1)

Surge parameters (biomarker model)	Units	Value (RSE)	IOV (RSE)
SA IL‐6	‐	7.99 (16)
SA CRP	‐	4.40 (21)	61.4 (38)
SW IL‐6	h	32.4 (11)
SW CRP	h	53.8 (17)	83.8 (32)
PT IL‐6	h	137.0 (9.7)	59.7 (14)
PT CRP+	h	50.3 (32)	81.3 (27)

Prior‐to‐chemotherapy‐model	Units	Value (RSE)
h 0	h−1	5.70·10−3 (31)
β 1	years−1	0.0754 (40)

Prior‐to‐FN‐model	Units	Value (RSE)
h 0	h−1	3.30·10−4 (110)
k e0	h−1	0.491 (40)
β 2	LN_IL‐6(t)−1	3.13 (15)
β 3	l (109 cells)–1	−1.07 (33)

When‐FN‐occurs‐model	Units	Value (RSE)
h 0	h−1	7.61·10−5 (120)
β 4	LN_CRP(t)−1	2.33 (12)

RSE, relative standard error, generated from the sampling importance resampling procedure; IIV, interindividual variability (given as a % coefficient of variation); IOV, interoccasion variability (given as a % coefficient of variation); IL‐6₀, baseline IL‐6 concentration; CRP₀, baseline CRP concentration; k_out,IL‐6, first‐order fractional IL‐6 turnover rate constant; k_out,IL‐6, first‐order fractional CRP turnover rate constant; P_{elevation,IL‐6}, the probability for IL‐6 elevated concentration (regulated by the IL‐6 surge function) in either cycle 1 or 4; P_{elevation,CRP}, the probability for CRP elevated concentration (regulated by the CRP surge function) in either cycle 1 or 4; Slope, parameter relating the relative change from IL‐6 baseline time course [RCFB_IL‐6(t)] to the CRP production; SA_IL‐6, IL‐6 surge amplitude, SA_CRP, CRP surge amplitude; SW_IL‐6, IL‐6 surge width; SW_CRP, CRP surge width; PT_IL‐6, IL‐6 surge peak time; PT_CRP+, time added to PT_IL‐6 to get the CRP surge peak time; h₀, the baseline hazard for FN; β₁, parameter relating age to FN; β₂, parameter relating the log of the normalized IL‐6 time course [LN_IL‐6(t)] to FN; β₃, parameter relating the model‐derived ANC₀ (baseline absolute neutrophil count) to FN and β₄, parameter relating the log of the normalized CRP time course [LN_CRP(t)] to FN; k_e0, effect compartment rate constant

TTE model for development of FN

A TTE model with time‐constant hazard was sufficient to describe the distribution of FN in the base model. The final prior‐to‐chemotherapy, prior‐to‐FN and when‐FN‐occurs models were parameterized as in Equations 3a–c, respectively. Parameter estimates are reported in Table 2.

The RSEs related to h₀ were relatively large in all three models, especially in the prior‐to‐FN (110%) and when‐FN‐occurs models (120%). This was, however, not considered problematic since it is logical that the baseline hazard is very low and uncertain when an increase in the hazard is well described by the predictors.

KM plots for the base and the three different alternative final models are presented in Figure 3. The observed distribution of FN is within the 95% confidence interval for all models, while the tighter 50% confidence interval demonstrates a slight misspecification of all models. Models including time‐varying predictors could better describe the reduction in the hazard during the last days of the cycle. External validation of the models would be valuable but would require a new study to be performed.

Figure 3.

Kaplan–Meier visual predictive checks for the base, prior‐to‐chemotherapy, prior‐to‐febrile neutropenia (FN) and when‐FN‐occurs models. The solid black line represents the observed time‐to‐FN data in both cycle 1 and 4. The shaded light and dark purple areas are the 95% and 50% confidence intervals, respectively, based on the simulated data (n = 1000)

Variables available prior to chemotherapy

Age as a predictor of FN improved the fit of most variables available before chemotherapy was initiated (ΔOFV = 6.06). The cycle‐specific and cycle 1 observed CRP baseline also provided statistically significant improvements in the univariate step (ΔOFV = 4.28 and 4.89, respectively). However, none of the variables improved the model fit when added on top of age.

Variables available prior to FN

The predicted IL‐6 time course was a good predictor and described the FN data considerably better than age. Significant drops in the OFV in the univariate analysis with variables available prior to FN were, in addition to age, observed for LN_IL‐6(t) (ΔOFV = 37.04), IL‐6(t) (ΔOFV = 25.50), pAUC_IL‐6(t) (ΔOFV = 13.27), RCFB_IL‐6(t) (ΔOFV = 13.18), IL‐6_0,i (ΔOFV = 9.58) and CRP_0,i (ΔOFV = 6.28). LN_IL‐6(t) was hence chosen and included in the model in subsequent steps, while IL‐6(t) and RCFB_IL‐6(t) were omitted from further evaluation since they were correlated with LN_IL‐6(t). An effect compartment was included to describe the effect delay between the IL‐6 elevation and FN diagnosis (ΔOFV = 9.47). ANC_0,i added additional descriptive value (ΔOFV = 10.26). No other variable was significant on top of LN_IL‐6(t) and ANC₀ in this subanalysis.

Variables available when FN occurs

In the univariate analysis the significant predictors were LN_CRP(t) (ΔOFV = 68.87), CRP(t) (ΔOFV = 52.00), RCFB_CRP(t) (ΔOFV = 38.81) and pAUC_CRP(t) (ΔOFV = 13.05), in addition to significant available prior to FN predictors. When LN_CRP(t) was included in the model, it was not significant to add more variables.

$$\mathrm{h}\left(\mathrm{t}\right)={\mathrm{h}}_0·{\mathrm{e}}^{\left({\mathrm{\beta }}_1·\left(\mathrm{AGE}-54\right)\right)}$$ (3a)

$$\mathrm{h}\left(\mathrm{t}\right)={\mathrm{h}}_0·{\mathrm{e}}^{\left[{\mathrm{\beta }}_2·\mathrm{LN}\_\mathrm{IL}-6\left(\mathrm{t}\right)+{\mathrm{\beta }}_3·\left(\text{AN}{\mathrm{C}}_0-3.53\right)\right]}$$ (3b)

$$\mathrm{h}\left(\mathrm{t}\right)={\mathrm{h}}_0·{\mathrm{e}}^{\left[{\mathrm{\beta }}_4·\mathrm{LN}\_\mathrm{CRP}\left(\mathrm{t}\right)\right]}$$ (3c)

h(t) is the hazard at time t, h₀ is the baseline hazard and β₁, β₂, β₃ and β₄ are parameters relating age, LN_IL‐6(t), ANC₀ and LN_CRP(t) to the risk of developing FN, respectively. Age was not a statistically significant covariate when CRP and IL‐6 was included.

Discussion

In the current analysis, the time courses of IL‐6 and CRP were first quantified and subsequently assessed as predictors of FN. The estimated typical IL‐6 and CRP baselines were 2.50 pg ml^–1 and 1.88 mg l^–1, respectively. This is similar to previous reports in similar patient populations (i.e. breast cancer patients who underwent breast surgery) 30, 31, 32, 33, 34, 35. The median IL‐6 and CRP peak concentrations (10.4 pg ml^–1 and 15.5 mg l^–1, respectively) were typically observed around 8 and 8.5 days after dose, respectively, among patients who were estimated to have a peak in the current study. This was earlier than the median time of the observed ANC nadir (i.e. 9 and 14 days following treatment with docetaxel and FEC, respectively, data not shown) and median time of FN diagnosis (i.e. 10 and 13 days, respectively).

The developed IL‐6 and CRP model successfully describe their temporal increases. The values of k_out for IL‐6 and CRP corresponded to half‐lives of 49 and 31 h, respectively. CRP half‐lives of 4–62 h 36, 37, 38, 39 have been reported, which agree with the estimated CRP half‐life in the current study. The literature reports a wide distribution of the IL‐6 half‐life, from a few minutes to a couple of hours and closer to 1 day. The reports of shorter half‐lives have been acquired in studies where endogenous IL‐6 was measured in severely sick patients (with meningococcal disease) 40 and in healthy male subjects who had only minor changes in IL‐6 concentration during exercise 41. Longer half‐lives were reported in patients who had knee and arthroplasties (15 h) 39 and based on model‐predicted IL‐6 concentration in response to cyclosporine infusion in bone marrow transplanted patients (21 h) 42. The different half‐life values may be due to the differences in study designs, study population, bioanalytical assay or method to determine the half‐life.

It is not unusual that patients with FN show no clinical signs of infection other than fever and it is therefore desirable to identify predictive variables of FN to initiate treatment with rescue‐medication before the patient is diagnosed with FN. For example, the inflammatory response in patients with neutropenia may be reduced in comparison to individuals without neutropenia. In this study, we performed three subanalyses based on the availability of the variable assessed as potential predictor of FN (i.e. prior‐to‐chemotherapy, prior‐to‐FN and when‐FN‐occurs). CRP resulted overall in the largest drop in OFV, but was found to have low value as a predictor since the CRP peak occurred close in time to FN diagnosis. Age has been acknowledged as a predictor of FN in multiple guidelines 1, 10, 43 and has the advantage of being a covariate available before treatment is initiated. Its association to FN was, however, only statistically significant in the prior‐to‐chemotherapy model, where IL‐6 and CRP measurements after initiation of treatment was ignored, and then with a modest improvement in the model fit (ΔOFV = 6.06). Despite the limited drop in OFV the model predicted that a 70‐year‐old patient had a 3.3 times higher risk for FN than a 54‐year‐old patient.

Model‐based metrics relying on IL‐6 or CRP elevations were found to relate to the FN data much better (ΔOFV = 37.04 and 68.87, respectively) than age. Such metrics may also add a mechanistic and quantitative understanding of the development of FN and corresponding clinical variables could potentially be measured and used clinically. CRP provided a better model improvement than IL‐6, probably because the CRP peak concentration occurred closer to the time of FN than the IL‐6 peak concentration (which had, in most patients, already decreased when FN occurred). CRP may be a good variable to confirm FN, but have limited value as a marker for initiating treatment to prevent FN. The hazard ratio was 5.0 for a value of LN_CRP(t) corresponding to an absolute CRP concentration of 10 mg l^–1, compared to a concentration of 5 mg l^–1.

When only variables available prior to FN were considered (i.e. omitting CRP variables, except CRP₀), the IL‐6 time course was the best predictor. An effect‐compartment model was allowed for describing a time‐delay from IL‐6 elevation to the increased hazard to develop FN (estimated to have a half‐life of 1.4 days). For an absolute IL‐6 concentration of 10 pg ml^–1, compared to a concentration of 5 pg ml^–1, the hazard ratio was 8.8. An ANC baseline value of 2.5 × 10⁹ cells l^–1, compared to the population typical ANC baseline (3.53 × 10⁹ cells l^–1), was related to a 5.1 times higher risk for FN. Consequently, IL‐6 is probably closely correlated with the development of FN and it could be valuable to measure IL‐6 routinely in the clinics to identify patients at risk for developing FN.

In the current analysis, it was not possible to separate different types of origins of FN due to the low number of events of each type. However, the work presented in this study could be extended to a larger patient population to separate predictors for the different types of origins of FN. It could then be possible to identify patients that need treatment with antibiotics and/or G‐CSF. To limit the increasing resistance to antibiotics 44 it is desired to avoid unnecessary use. In a recent meta‐analysis where biomarkers were measured after the onset of fever 16, both IL‐6 and CRP were identified to be related to bacterial infections in patients with FN, although procalcitonin (produced in response to endotoxins) was preferred over IL‐6 (second best) and CRP. The studies included in the meta‐analysis used cut‐off values as risk‐factors of bacterial FN and did not consider the levels of inflammatory biomarkers in the absence of fever. In the current analysis, the relationships of IL‐6 to CRP and between IL‐6, CRP and FN were quantified, thereby not relying on the time when samples were drawn or static cut‐off values. Our results indicate that the degree of response in IL‐6 and CRP, beyond what is covered by a cut‐off value, may be of importance. Moreover, this analysis also included patients without fever to determine the biomarker response as a predictor of FN. Additional studies, primarily with a more frequent sampling schedule and more patients, would also be helpful to validate the findings in the current analysis externally.

In conclusion, the time courses of IL‐6 and CRP were successfully characterized using turnover models in combinations with functions describing elevated biomarker concentrations. Three alternative time‐to‐FN models were developed, based on the type of predictors that could be available in a clinical situation. The time course of CRP during adjuvant chemotherapy quantitatively associates the instantaneous risk for FN, and the relationship was here quantified, while an increase in IL‐6 potentially can play an important role to forecast development of FN.

Competing Interests

There are no competing interests to declare.

The clinical study and analysis was supported financially by the Swedish Cancer Society. The clinical study was also supported by Stiftelsen Onkologiska klinikens i Uppsala Forskningsfond.

Contributors

A.L.Q., M.O.K., H.L. and L.E.F. contributed to the study design. A.L.Q. and H.L. acquired and managed the data. I.N., L.E.F., M.O.K. and E.I.N. performed the analysis and drafted the manuscript. All authors interpreted the results, contributed to critical review of the manuscript and approved the final version of the paper.

Supporting information

Supplementary material 1 Differential equation system describing the linear IL‐6 regulation of CRP

Supplementary material 2 NONMEM code for the IL‐6 and CRP model

Supplementary material 3 Example data set for the IL‐6 and CRP model

Table S1 Description of the 16‐subpopulation mixture model. Plus and minus signs indicate an elevated biomarker concentration and no elevated biomarker concentration, respectively

Netterberg, I. , Karlsson, M. O. , Nielsen, E. I. , Quartino, A. L. , Lindman, H. , and Friberg, L. E. (2018) The risk of febrile neutropenia in breast cancer patients following adjuvant chemotherapy is predicted by the time course of interleukin‐6 and C‐reactive protein by modelling. Br J Clin Pharmacol, 84: 490–500. doi: 10.1111/bcp.13477.