Population pharmacokinetics of platinum after nedaplatin administration and model validation in adult patients

Abstract

Aims

The pharmacokinetics of unbound platinum after administration of an anticancer drug nedaplatin, cis-diammineglycolateplatinum were examined using population analysis. The relevant covariates and the extent of inter- and intra-individual variability were evaluated.

Methods

In order to clarify the pharmacokinetic profile of nedaplatin, unbound platinum concentrations (789 points) in plasma after intravenous infusion of nedaplatin were obtained from 183 courses for 141 patients. Plasma concentration data were analysed by nonlinear mixed effect modelling using NONMEM to evaluate the population mean parameters and variances for inter- and intra-individual random effects. The final population model was validated by parameter sensitivity analysis using objective function mapping, the bootstrap resampling and a data-splitting technique, i.e. the Jackknife method, and the predictive performance of the final model was evaluated.

Results

A two-compartment pharmacokinetic model with zero-order input and first order elimination described the current data well. The significant covariates were creatinine clearance (CLcr) for clearance of platinum (CL) {population mean [95% confidence interval (CI)] CL (l h⁻¹) = 4.47 (3.27, 5.67) + 0.0738 (0.0581, 0.0896) × CLcr (CLcr: ml min⁻¹)} and body weight (BW: kg) for volume of distribution of platinum (Vc) [Vc (l) = 12.0 (7.5, 16.5) + 0.163 (0.081, 0.246) × BW]. Inter-individual variations (CV%, 95% CI) for CL and Vc were 25.5% (20.7, 29.6) and 21.4% (17.0, 24.1), respectively, and intra-individual variation (CV%, 95% CI) was 12.6% (10.5, 14.4). The effects of pretreatment with nedaplatin or other platinum agents on clearance and volume of distribution were also tested, but no significant effect was found. The relationship between the observed and predicted unbound platinum concentration by empirical Bayesian prediction showed good correlation with no bias, suggesting that the final model explains well the observed data in the patients. The mean prediction error and root mean square prediction error (95% CI) were − 0.0164 µg ml⁻¹ (− 0.4379, 0.4051) and 0.2155 µg ml⁻¹ (not calculable, 0.6523), respectively. The values of mean, standard error and 95% CI for objective function mapping, the bootstrap resampling, the Jackknife estimates and the final model coincided well.

Conclusions

A population pharmacokinetic model was developed for unbound platinum after intravenous infusion of nedaplatin. Only creatinine clearance was found to be a significant covariate of clearance, and BW was found to be a significant covariate of volume of distribution. These population pharmacokinetic estimates are useful for setting initial dosing of nedaplatin using its population mean and can also be used for setting appropriate dosage regimens using empirical Bayesian forecasting.

Introduction

Nedaplatin, cis-diammineglycolatoplatinum, is an anticancer agent, which is a platinum derivative like cisplatin (CDDP) and carboplatin (CBDCA) [1, 2]. In phase II clinical studies, high activities against head and neck cancer, nonsmall cell lung carcinoma, oesophageal cancer, testicular tumour, and cervical cancer have been reported [3–9]. Nedaplatin has also been reported to have higher antitumour activity than CDDP in preclinical and in vitro studies [10, 11]. The protein binding of nedaplatin is lower than that of CDDP [12] and the plasma concentration profile of unbound platinum in humans after nedaplatin infusion is similar to that of total platinum. Nedaplatin has a short elimination half-life (1.1–4.4 h) and a pharmacokinetic profile similar to that of CBDCA [12, 13]. The clinical use of CDDP is limited by nephrotoxicity, but nedaplatin causes less nephrotoxicity [14–17]. The limiting factor may be its haematological toxicity, which has also been found with CBDCA [15].

In anticancer chemotherapy, it is usual to use the maximum tolerance dose (MTD) with respect to side-effects [18–20], and therefore serious side-effects often occur, especially in patients exposed to a high platinum concentration. To control the plasma concentration of platinum, the optimum dosage regimen should be individualized by taking the pharmacokinetic variability into consideration. For this purpose it is useful to predict platinum clearance, and we have already developed a simple formula for predicting platinum clearance based on individual renal function, i.e. creatinine clearance, after nedaplatin dosing [21]. An alternative approach, a population pharmacokinetics based on nonlinear mixed effect modelling, is also useful and can evaluate covariates affecting the pharmacokinetics of a drug and also unknown inter- and intra-individual pharmacokinetic variability. The results of population analysis (i.e. population pharmacokinetic parameters) can then be used to construct nomograms to set up appropriate dosing regimens based on patients’ characteristics (covariates) and to assess the individual pharmacokinetic profile with further optimization by empirical Bayesian forecasting when some plasma concentrations were measured. For these purposes, the developed population model should be validated to confirm the stability, robustness and predictive performance.

In this study, we developed and validated a population pharmacokinetic model for unbound platinum after nedaplatin dosing for the purpose of evaluating pharmacokinetic variability and possible covariates, and also to use the model for empirical Bayesian forecasting. The robustness of the final model was evaluated using various conventional techniques.

Methods

Patients and data collection

Plasma unbound platinum concentration data (789 points) were retrospectively obtained from 183 courses for 141 Japanese adult patients with lung, oesophageal, cervical or ovarian cancer in 14 institutions. All data were collected as part of a multicentre post-marketing surveillance of nedaplatin, and informed consent and ethics approval were obtained in each institution. Demographic data including gender, age, body weight (BW), serum creatinine level (Scr), and creatinine clearance (CLcr) were also collected. Scr and CLcr were determined in each institution. Observed CLcr values estimated by 24-h urine collection and also the CLcr calculated according to the Cockcroft–Gault formula [22] were used for model construction. The dose and infusion period varied among the patients over ranges of 20–107 mg m⁻² and 1–3 h, respectively. The number of data points per patient for measurable plasma unbound platinum concentration were 3–7. Plasma samples were taken at the end of infusion and during the postinfusion phase at appropriate intervals. All plasma platinum concentrations before the start of nedaplatin infusion were under the detection limit. Although both total (bound and unbound) and unbound platinum concentrations were measured, we used only the data for unbound platinum in the present study because this form has been related to cytotoxic effects [23, 24].

Assay methods

Plasma unbound fraction was separated by an ultrafiltration method. Total and unbound platinum concentrations in plasma were measured by an atomic absorption spectrometry assay method in Shionogi Biomedical Laboratories (Osaka, Japan) [25]. The lower detection limit for this method is 0.2 µg ml⁻¹. Demographic data and measured values in clinical laboratory tests were obtained from each hospital.

Population model building

Plasma concentration data were analysed by nonlinear mixed effect modelling using a package software NONMEM system (Version V) to estimate the population mean parameters and the variances for inter- and intra-individual variability. The NONMEM option of the first-order conditional estimation (FOCE) method with η–e interaction was used. The statistical significance of a parameter was evaluated based on the likelihood ratio test using the minimum values of the objective function produced by NONMEM. A difference of objective function values of 10.83 which indicates a P-value of < 0.001 corresponding to a difference of 1 degree of freedom was considered as statistically significant.

In order to determine the basic pharmacokinetic structural model, the one- and the two-compartment pharmacokinetic models with zero-order input and first-order elimination with no covariates were first tested.

For the interindividual random error for each parameter, both an exponential error model and an additive error model were tested with no covariates, and an exponential error model was found better as given by Equation 1.

where P_ij is the j-th basic pharmacokinetic parameters in the i-th individual, is the typical value of the j-th parameter (i.e. population mean), and η_ij is a random variable for i-th individual in j-th parameters with mean zero and variance ω_j². The nondiagonal elements of the covariance matrix for η were ignored for reducing the number of parameters in NONMEM estimation. For intra-individual (residual) variability, both an exponential error model and an additive error model were tested and an exponential model given by Equation 2 was found better.

$$\text{Y}=\text{F}.\text{exp}\left(\varepsilon \right)$$

In Equation 2, Y and F are the observed and predicted plasma platinum concentrations, respectively, and e is a normal random variable with mean zero and variance of σ².

Selected structural model (actually the two-compartment model as explained later) with no covariates (i.e. the primitive model) was fitted to the plasma platinum concentration data, and all possible covariates for CL and Vc were tested stepwise based on the log-likelihood ratio test. The demographic factors of age and BW, and some clinical factors, Scr and CLcr were tested as possible covariates for CL and Vc. The observed CLcr values as well as the CLcr calculated according to the Cockcroft–Gault formula [22] were tested. The effects of pretreatments with nedaplatin or other platinum agents on CL and Vc were also tested.

Validation of the final population model

Several methods for model validation have been reported [26–30]. In this study, we applied the objective function mapping method to analyse parameter sensitivity [31], as well as bootstrap resampling [29] and data splitting to examine the validity of the parameter estimates.

The objective function mapping method was applied to confirm the parameter stability, sensitivity, and to determine the shape of the parameter space. By fixing the parameter value of interest to ± 5, 10, 15, 20, 30, 40, and 60% of its population estimate, other parameters were re-estimated by NONMEM [31]. Changes in the objective function (ΔOBJ) for each re-estimation were plotted. The plots of ΔOBJ for each parameter were then fitted by a polynomial equation (three orders). Assuming the χ² distribution for ΔOBJ, the values for a parameter which corresponds to ΔOBJ = ± 3.84 represent 95% confidence limits for the parameter [32]. The 95% confidence intervals obtained for each population mean and variance parameters were compared with those obtained based on the standard error (SE) of the NONMEM estimates in the final model.

The bootstrap resampling was applied to assess the stability of the final parameter estimates and to confirm the robustness of the final model [29]. The 1000 bootstrap samples were generated and the parameter estimates for each of the 1000 samples were re-estimated using NONMEM in the final model. The mean, SE and 95% confidence intervals (CI) obtained for each of the mean and variance parameters estimated for bootstrap samples were also compared with those of the NONMEM estimates in the final model. The 95% CIs were obtained by point estimate ± 1.96 × SE of estimate.

The data-splitting method was applied to assess the contribution of data from individuals on the modelling results, and to confirm the robustness of the final model [33]. Patients in the full data set were randomly divided into 10 subsets, each of which contained data from approximately 90% of the patients. Each subset of data was analysed by NONMEM using the final model and the parameter estimates for each of the 10 runs were obtained. Next, the parameter estimates determined from the data sets containing 90% of the patients were compared with those resulting from the complete data sets. The objective function was calculated by another NONMEM run for the full data set with the parameter estimates fixed at the estimates from the subset data analysis, and they were compared with the objective function obtained in full data set with the final model. The 95% CI for parameter estimates were obtained by Jackknife estimates and were compared with those using the mean and SE of the NONMEM estimation for the final model [34].

In order to examine the predictive performance of the final model, the NONMEM estimates for platinum concentration from each of the 10 subsets were used to predict the plasma profiles in the remaining 10% of patients’ data. Then the predicted values based on both population mean parameter estimates (referred to as PRED) and empirical Bayesian method (referred to as IPRED) were compared with the observed values at the corresponding sampling time. To evaluate predictive performance, the mean prediction error (ME) and root mean square prediction error (RMSE) were used, respectively [35].

Results

Model building

Table 1 summarizes the patients’ characteristics and backgrounds of anticancer treatment. Plasma samples were taken at the end of infusion in all courses, and the distribution of sampling time after the end of infusion was as follows: 0.5–1 h (22 courses), 1–2 h (171), 2–3 h (85), 3–4 h (111), 4–6 h (123), 6–12 h (42), 12–24 h (5). The number of courses with pretreatment of platinum derivatives was as follows: nedaplatin (36 courses), cisplatin (34), carboplatin (3), combination of nedaplatin and cisplatin (15), and none (95). The number of courses with concomitant drugs was as follows: cyclophosphamide (15 courses), ifosfamide (5), combination of ifosfamide and bleomycin (20), combination of ifosfamide and peplomycin (1), combination of ifosfamide and vindesine (2), vindesine (46), gemcitabine (2), etoposide (7), vinorelbine (18), cisplatin 1 week later (25), and none (42). For 36 patients, the second or third dose of nedaplatin was administered after a dosing interval of about a month. We used the platinum concentration data as if they had been obtained from different individuals even though the data were taken at the first and second or later courses in the same individual. This is based on the assumption that the time course profile of platinum concentration was not affected by the pretreatment of nedaplatin, because the dosing interval was sufficiently longer than the elimination half-life of platinum. To confirm this assumption, we compared the platinum clearance (CL) estimated by dose/AUC. Plasma platinum concentrations were measure at both the first and second dosing in 30 patients. Mean values (and CI) for CL in these patients were 11.1 l h⁻¹ (5.9, 20.7) and 10.7 l h⁻¹ (4.4, 26.2), for the first and second dosing, respectively, and they were not significantly different (P-value by paired t-test = 0.746). Plasma platinum concentrations were measured at both of the first and the third dosing in six patients, and CL in these patients were 9.3 l h⁻¹ (4.8, 17.9) and 8.5 l h⁻¹ (5.0, 14.6), respectively, and were not significantly different (P = 0.62). Plasma platinum concentrations were measured at both of the second and the third dosing in 11 patients and CL were 9.5 l h⁻¹ (5.7, 15.9) and 9.0 l h⁻¹ (5.2, 15.4), respectively, and were not significantly different (P = 0.64). From these results and based on the fact that about two-thirds of the patients had the plasma concentration data in only one course, we decided not to incorporate an interoccasional variability term into the NONMEM analysis. Figure 1 shows the unbound platinum concentration profiles for all patients. The preliminary analysis without covariates showed that a two-compartment model described the profile better than a one-compartment model, leading to its use for the following model-building procedures. Clearance of platinum (CL), transfer rate constants between the two compartments, k₁₂, k₂₁, and the volume of distribution of the central compartment (Vc) were identified as the basic pharmacokinetic parameters to be estimated.

Table 1. Backgrounds of patient data used in population analysis.

Total number of patients (courses)	141 (183)
Male	57 (63)
Female	84 (120)
Number of plasma samples	789
Samples/patient	4.3 ± 1.1	[2–7]
Infusion duration time (min)	91.3 ± 43.1	[60–210]
Dose (mg)	108.9 ± 37.0	[13–180]
Dose (mg m−2)	72.0 ± 22.4	[9–110]
Age (years)	58.0 ± 10.7	[29–81]
Body weight (kg)	54.2 ± 10.0	[34–84]
Scr (mg dl−1)	0.73 ± 0.20	[0.40–1.36]
Observed CLcr (ml min−1)	82.2 ± 25.9	[19.1–165.6]
Calculated CLcr (ml min−1)	80.5 ± 26.7	[19.7–178.8]

Mean ± SD [minimum–maximum].

Figure 1.

Observed plasma unbound platinum concentration profiles after termination of intravenous infusion of nedaplatin. Data were not normalized by dose or infusion duration.

The final model was found to consist of CL, which depended on the calculated CLcr and Vc, which depended on BW. The effect of pretreatments with nedaplatin or other platinum agents on CL and Vc was also tested, but no significant effect was found. Table 2 shows the final estimates of the population pharmacokinetic parameters of unbound platinum after intravenous infusion of nedaplatin. Figure 2a shows the relationship between the observed and the predicted unbound platinum concentration based on the final parameter estimates (PRED). Figure 2b shows the relationship between the observed and the predicted unbound platinum concentration by empirical Bayesian prediction (individual post hoc prediction, IPRED). Both plots show good correlation with no bias, suggesting that the final model explains well the observed data in the patients. ME (CI) and RMSE (CI) were − 0.0187 µg ml⁻¹ (−1.0330, 0.9955) and 0.5175 µg ml⁻¹[not calculable (NC), 1.3580] for PRED, and − 0.0164 µg ml⁻¹ (−0.4379, 0.4051) and 0.2155 µg ml⁻¹ (NC, 0.6523) for IPRED, respectively, where lower limits of RMSE were NC.

Table 2. Final estimates of population pharmacokinetics parameters.

	Population mean	Inter-individual variation (CV%)
CL (l h−1)	4.47 + 0.0738 × CLcr*	25.5 (20.7–29.6)
	(3.27–5.67) (0.0581–0.0896)
Vc (l)	12.0 + 0.163 × BW†	21.4 (17.0–24.10)
	(7.5–16.5) (0.081–0.246)
K12 (h−1)	0.304 (0.069–0.540)	–‡
k21 (h−1)	0.925 (0.470–1.381)	39.7 (20.3–52.5)
Intra-individual variation (CV%)		12.6 (10.5–14.4)

^*CLcr (ml min⁻¹): calculated CLcr by Cockcroft–Gault formula.

^†BW (kg), Body weight.

^‡Not estimated. Values in parentheses are 95% confidence intervals calculated using the standard error estimates by NONMEM.

Figure 2.

(a) Relationship between observed and predicted concentrations by population mean parameters of the final model. (b) Relationship between observed and predicted concentrations by post hoc estimation.

Validation of the final model

Figure 3 shows an example of the objective function mapping, for slope for CL. No local minimum was found in any of the parameters in the ranges tested, and it was confirmed the true estimate gives the minimum values of objective function. The shapes of the curves confirmed the precision, sensitivity and robustness of the final estimates. The 95% CI of objective function mapping and those of the final model coincided well (Table 3).

Figure 3.

An example of objective function mapping (for slope on CL). Plots are objective functions obtained by fixing one of the pharmacokinetic parameters to ± 5, 10, 15, 20, 30, 40, 50 and 60% of the population estimate and allowing NONMEM to re-estimate all other parameters. The ordinate indicates the difference of the objective function. The curves show the fitting results using a polynomial regression. The vertical lines indicate the range of the parameter corresponding to the change in the objective function of 3.84.

Table 3. Comparison of 95% confidence intervals estimated by SE of the NONMEM final estimates, objective function mapping and bootstrapping and Jackknife estimate.

	NONMEM final estimate			Objective function mapping
Parameters 95% CI	Mean	SE	95% CI			95% CI
Intercept for CL	4.47	0.61	(3.27–5.67)			(3.24–5.71)
Slope for CL	0.0738	0.0080	(0.0581–0.0895)			(0.0578–0.0904)
Intercept for Vc	12.0	2.3	(7.5–16.5)			(7.7–16.5)
Slope for Vc	0.163	0.042	(0.081–0.245)			(0.082–0.246)
k12	0.304	0.120	(0.069–0.539)			(0.195–0.476)
k21	0.925	0.232	(0.470–1.380)			(0.628–1.230)
ω2 for CL	0.0649	0.0112	(0.0429–0.0869)			(0.052–0.079)
ω2 for Vc	0.0456	0.0084	(0.0291–0.0621)			(0.034–0.061)
ω2 for k21	0.158	0.060	(0.041–0.275)			(0.051–0.280)
σ2	0.0158	0.0024	(0.0110–0.0206)			(0.012–0.022)
	Bootstrap resampling			Jackknife estimation
Parameters	Mean	SE	95% CI	Mean	SE	95% CI
Intercept for CL	4.57	0.64	(3.31–5.82)	4.28	0.77	(2.54–6.02)
Slope for CL	0.0740	0.0084	(0.0575–0.0905)	0.0769	0.0098	(0.0546–0.0991)
Intercept for Vc	12.2	2.1	(8.0–16.3)	11.6	2.4	(6.2–17.1)
Slope for Vc	0.162	0.040	(0.084–0.241)	0.168	0.044	(0.068–0.267)
k12	0.287	0.041	(0.206–0.368)	0.289	0.120	(0.018–0.559)
k21	0.891	0.082	(0.730–1.052)	0.934	0.225	(0.425–1.443)
ω2 for CL	0.0629	0.0074	(0.0484–0.0774)	0.0657	0.0117	(0.0394–0.0921)
ω2 for Vc	0.0444	0.0071	(0.0305–0.0583)	0.0461	0.0067	(0.0311–0.0612)
ω2 for k21	0.146	0.050	(0.049–0.243)	0.145	0.070	(− 0.013 to 0.304)
σ2	0.0152	0.0012	(0.0129–0.0175)	0.0164	0.0022	(0.0114–0.0215)

95% CI, 95% Confidence intervals.

The mean, SE and 95% CI for each parameter estimated by the bootstrap resampling are shown in Table 3. Those values for the bootstrapping and the final model coincided well except SE for k₁₂ and k₂₁. The values of SE for k₁₂ and k₂₁ estimated by the bootstrapping were lower than those for the NONMEM estimates.

Figure 4 shows the parameter estimates of slope for CL for the full data set (i.e. the final estimates) and also for the 10 different subsets. Results for other parameters showed similar patterns and are not shown here. The values for the subsets were in the range of ± 1 SE of the final estimates. Moreover, the objective functions obtained by another NONMEM run for a full data set fixing the parameter estimates for 10 subsets were from − 1322.6 to − 1320.4, and the absolute difference of these values from that of the final model (− 1324.1) was < 3.84.

Figure 4.

Parameter estimates for slope of CL for full data set and 10 subsets. Plots are the parameter values obtained by the NONMEM estimate based on the complete data set (○) and each of the 10 partial data sets (•). The solid, dashed and long dashed lines indicate the parameter value, ± SE and ± 2 SE range which was calculated based on the complete data set.

The mean and SE of the Jackknife estimates and the 95% CI and those of the final model also coincided well, as shown in Table 3.

The predictive performance in each subset of the remaining patients was also evaluated and the values of ME and RMSE are shown in Table 4.

Table 4. Predictive performance for subsets.

	PRED*		IPRED†
Subsets	ME (µg ml−1)	RMSE (µg ml−1)	ME (µg ml−1)	RMSE (µg ml−1)
1	0.1266	0.7065	− 0.0146	0.2756
2	− 0.0785	0.4265	− 0.0095	0.1510
3	0.0166	0.3995	− 0.0085	0.1256
4	− 0.0610	0.4814	− 0.0305	0.1664
5	− 0.0183	0.5405	− 0.0257	0.2181
6	− 0.0855	0.4122	0.0091	0.2012
7	− 0.0214	0.5262	− 0.0055	0.2461
8	− 0.0035	0.4889	− 0.0007	0.3044
9	0.0713	0.6064	− 0.0071	0.2498
10	− 0.1025	0.5597	− 0.0355	0.1903
Mean	− 0.0156	0.5148	− 0.0128	0.2129
SD	0.0726	0.0951	0.0139	0.0568
95% CI‡	− 1.0106	–	− 0.4245	–
	0.9794	1.2818	0.3988	0.5673

^*PRED, Prediction using population mean parameters.

^†IPRED, Prediction obtained by empirical Bayesian.

^‡95% CI, 95% Confidence intervals. Lower (top) and upper (bottom).

In the final model, the CLcr calculated by the Cockcroft–Gault formula was found to show better correlation than the observed CLcr.

Discussion

The measurement errors in the observed CLcr seemed to vary to a greater extent than in the calculated CLcr from the relationship between CL and each CLcr (data not shown). Considering the clinical situation that Scr can be easily and frequently measured, it seems more convenient to use the calculated CLcr. The estimated values for slope of the calculated and observed CLcr were 0.073 (CI 0.057, 0.088) and 0.066 (CI 0.048, 0.085), respectively, which are very similar.

While the effect of pretreatment of nedaplatin or other platinum agents on platinum CL after nedaplatin dosing was significant (P = 0.05, log likelihood difference − 4.609), the extent of the decrease in CL was only 10.1%. In order to clarify the change in platinum clearance during nedaplatin treatments, the difference of platinum clearance in identical patients was tested by the paired t-test. The differences of mean CL between the first cycle and the second or later cycle in the same patients were tested. The mean (SD) values of each CL were 11.3 (3.2) and 11.5 (4.3) l h⁻¹ in the first and the second or later cycles, respectively, which were not significantly different (P = 0.507). Therefore, we concluded that the effect of pretreatment on CL can be ignored. A decrease in platinum CL decrease after repeated dosing of CDDP has been reported [36]. Some patients had received CDDP but nedaplatin was administered after a long enough interval to allow recovery of renal function. Considering that nedaplatin pretreatments do not alter the CL with monthly administration, it is thought that nedaplatin causes low nephrotoxicity. However, if the renal function in a patient varies during nedaplatin treatment, an index for renal function (CLcr or Scr) should be measured just prior to nedaplatin dosing to adjust the dosage by way of, for example, empirical Bayesian forecasting.

The results of model validation confirmed that the estimates of the values of the parameters were consistent and stable because the 95% CI calculated by four methods, i.e. the method based on the SE of the NONMEM estimate, the objective function mapping method, the bootstrapping and the Jackknife method, were almost the same as shown (Table 3). Further, the results of the data-splitting method indicated that no subset of the patient population affected the estimates of the pharmacokinetic parameters, and predictive performance was found to be similar to the estimated performance.

In conclusion, we constructed a population pharmacokinetic model for unbound platinum after intravenous infusion of nedaplatin. Only CLcr was found to be a significant covariate of CL, and BW was found to be a significant covariate of Vc. The population pharmacokinetic estimates are useful for the multiple dosing of nedaplatin as well as for initial treatment, and can also be employed for setting optimum dosage regimens using empirical Bayesian forecasting.