Evaluation of bias, precision, robustness and runtime for estimation methods in NONMEM 7.

NONMEM is the most widely used software for population pharmacokinetic (PK)-pharmacodynamic (PD) analyses. The latest version, NONMEM 7 (NM7), includes several sampling-based estimation methods in addition to the classical methods. In this study, performance of the estimation methods available in NM7 was investigated with respect to bias, precision, robustness and runtime for a diverse set of PD models. Simulations of 500 data sets from each PD model were reanalyzed with the available estimation methods to investigate bias and precision. Simulations of 100 data sets were used to investigate robustness by comparing final estimates obtained after estimations starting from the true parameter values and initial estimates randomly generated using the CHAIN feature in NM7. Average estimation time for each algorithm and each model was calculated from the runtimes reported by NM7. The method giving the lowest bias and highest precision across models was importance sampling, closely followed by FOCE/LAPLACE and stochastic approximation expectation-maximization. The methods relative robustness differed between models and no method showed clear superior performance. FOCE/LAPLACE was the method with the shortest runtime for all models, followed by iterative two-stage. The Bayesian Markov Chain Monte Carlo method, used in this study for point estimation, performed worst in all tested metrics.

Comparison of methods for handling missing covariate data.

Missing covariate data is a common problem in nonlinear mixed effects modelling of clinical data. The aim of this study was to implement and compare methods for handling missing covariate data in nonlinear mixed effects modelling under different missing data mechanisms. Simulations generated data for 200 individuals with a 50% difference in clearance between males and females. Three different types of missing data mechanisms were simulated and information about sex was missing for 50% of the individuals. Six methods for handling the missing covariate were compared in a stochastic simulations and estimations study where 200 data sets were simulated. The methods were compared according to bias and precision of parameter estimates. Multiple imputation based on weight and response, full maximum likelihood modelling using information on weight and full maximum likelihood modelling where the proportion of males among the individuals lacking information about sex was estimated (EST) gave precise and unbiased estimates in the presence of missing data when data were missing completely at random or missing at random. When data were missing not at random, the only method resulting in low bias and high parameter precision was EST.

Multiple imputation of missing covariates in NONMEM and evaluation of the method's sensitivity to η-shrinkage.

Multiple imputation (MI) is an approach widely used in statistical analysis of incomplete data. However, its application to missing data problems in nonlinear mixed-effects modelling is limited. The objective was to implement a four-step MI method for handling missing covariate data in NONMEM and to evaluate the method's sensitivity to η-shrinkage. Four steps were needed; (1) estimation of empirical Bayes estimates (EBEs) using a base model without the partly missing covariate, (2) a regression model for the covariate values given the EBEs from subjects with covariate information, (3) imputation of covariates using the regression model and (4) estimation of the population model. Steps (3) and (4) were repeated several times. The procedure was automated in PsN and is now available as the mimp functionality ( http://psn.sourceforge.net/ ). The method's sensitivity to shrinkage in EBEs was evaluated in a simulation study where the covariate was missing according to a missing at random type of missing data mechanism. The η-shrinkage was increased in steps from 4.5 to 54%. Two hundred datasets were simulated and analysed for each scenario. When shrinkage was low the MI method gave unbiased and precise estimates of all population parameters. With increased shrinkage the estimates became less precise but remained unbiased.

A population pharmacokinetic/pharmacodynamic model of methotrexate and mucositis scores in osteosarcoma.

Methotrexate, when used in high doses (12 g/m²) in the treatment of osteosarcoma, shows wide between-subject variability (BSV) in its pharmacokinetics. High-dose methotrexate is associated with severe toxicity; therefore, therapeutic drug monitoring (TDM) is carried out to guide rescue therapy and monitor for nephrotoxicity. Mucositis is a commonly encountered dose-limiting toxicity that often leads to delays in subsequent courses of chemotherapy. This, in turn, results in a reduction in the dosing intensity, which is essential in the treatment of osteosarcoma. The aims of this study were to develop a population pharmacokinetic (PK) model from TDM using physiologically relevant covariates and to investigate the correlation between mucositis scores and methotrexate pharmacokinetics. In total, 46 osteosarcoma patients (30 men and 16 women; age, 4-51 years) were recruited, and blood samples were collected for routine TDM once every 24 hours. Mucositis scores, graded according to the National Cancer Institute Common Toxicity Criteria, were recorded for 28 of the patients (18 men and 10 women; age, 8-51 years) predose and postdose. A population PK model was developed in NONMEM VI. A 2-compartment PK model was chosen, and clearance (CL) was divided into filtration and secretion/metabolism components. All parameters were scaled with body weight, and, in addition, total CL was scaled with age- and sex-adjusted serum creatinine. Between-subject variability was modeled for all parameters, and between-occasion variability was included in CL. For a typical 70 kg man of 18 years or older, the parameter estimates for the final model were CL(filt) = 2.69 L/h/70 kg, CL(sec) = 10.9 L/h/70 kg, V1 = 74.3 L/70 kg, Q = 0.110 L/h/70 kg, and V2 = 4.10 L/70 kg. Sequential pharmacodynamic modeling consisted of mucositis scores as 5-point ordered categorical data. A significant linear relationship between individual area under the curve (AUC) and mucositis score probability was found, and the probability of having mucositis score ≥ 1 increased with increasing AUC and was almost 50% at the average cumulative AUC after 2 consecutive methotrexate doses.