Adjusted adaptive Lasso for covariate model-building in nonlinear mixed-effect pharmacokinetic models.

One important aim in population pharmacokinetics (PK) and pharmacodynamics is identification and quantification of the relationships between the parameters and covariates. Lasso has been suggested as a technique for simultaneous estimation and covariate selection. In linear regression, it has been shown that Lasso possesses no oracle properties, which means it asymptotically performs as though the true underlying model was given in advance. Adaptive Lasso (ALasso) with appropriate initial weights is claimed to possess oracle properties; however, it can lead to poor predictive performance when there is multicollinearity between covariates. This simulation study implemented a new version of ALasso, called adjusted ALasso (AALasso), to take into account the ratio of the standard error of the maximum likelihood (ML) estimator to the ML coefficient as the initial weight in ALasso to deal with multicollinearity in non-linear mixed-effect models. The performance of AALasso was compared with that of ALasso and Lasso. PK data was simulated in four set-ups from a one-compartment bolus input model. Covariates were created by sampling from a multivariate standard normal distribution with no, low (0.2), moderate (0.5) or high (0.7) correlation. The true covariates influenced only clearance at different magnitudes. AALasso, ALasso and Lasso were compared in terms of mean absolute prediction error and error of the estimated covariate coefficient. The results show that AALasso performed better in small data sets, even in those in which a high correlation existed between covariates. This makes AALasso a promising method for covariate selection in nonlinear mixed-effect models.

Improving the estimation of parameter uncertainty distributions in nonlinear mixed effects models using sampling importance resampling.

Taking parameter uncertainty into account is key to make drug development decisions such as testing whether trial endpoints meet defined criteria. Currently used methods for assessing parameter uncertainty in NLMEM have limitations, and there is a lack of diagnostics for when these limitations occur. In this work, a method based on sampling importance resampling (SIR) is proposed, which has the advantage of being free of distributional assumptions and does not require repeated parameter estimation. To perform SIR, a high number of parameter vectors are simulated from a given proposal uncertainty distribution. Their likelihood given the true uncertainty is then approximated by the ratio between the likelihood of the data given each vector and the likelihood of each vector given the proposal distribution, called the importance ratio. Non-parametric uncertainty distributions are obtained by resampling parameter vectors according to probabilities proportional to their importance ratios. Two simulation examples and three real data examples were used to define how SIR should be performed with NLMEM and to investigate the performance of the method. The simulation examples showed that SIR was able to recover the true parameter uncertainty. The real data examples showed that parameter 95 % confidence intervals (CI) obtained with SIR, the covariance matrix, bootstrap and log-likelihood profiling were generally in agreement when 95 % CI were symmetric. For parameters showing asymmetric 95 % CI, SIR 95 % CI provided a close agreement with log-likelihood profiling but often differed from bootstrap 95 % CI which had been shown to be suboptimal for the chosen examples. This work also provides guidance towards the SIR workflow, i.e.,which proposal distribution to choose and how many parameter vectors to sample when performing SIR, using diagnostics developed for this purpose. SIR is a promising approach for assessing parameter uncertainty as it is applicable in many situations where other methods for assessing parameter uncertainty fail, such as in the presence of small datasets, highly nonlinear models or meta-analysis.

A fast method for testing covariates in population PK/PD Models.

The development of covariate models within the population modeling program like NONMEM is generally a time-consuming and non-trivial task. In this study, a fast procedure to approximate the change in objective function values of covariate-parameter models is presented and evaluated. The proposed method is a first-order conditional estimation (FOCE)-based linear approximation of the influence of covariates on the model predictions. Simulated and real datasets were used to compare this method with the conventional nonlinear mixed effect model using both first-order (FO) and FOCE approximations. The methods were mainly assessed in terms of difference in objective function values (ΔOFV) between base and covariate models. The FOCE linearization was superior to the FO linearization and showed a high degree of concordance with corresponding nonlinear models in ΔOFV. The linear and nonlinear FOCE models provided similar coefficient estimates and identified the same covariate-parameter relations as statistically significant or non-significant for the real and simulated datasets. The time required to fit tesaglitazar and docetaxel datasets with 4 and 15 parameter-covariate relations using the linearization method was 5.1 and 0.5 min compared with 152 and 34 h, respectively, with the nonlinear models. The FOCE linearization method allows for a fast estimation of covariate-parameter relations models with good concordance with the nonlinear models. This allows a more efficient model building and may allow the utilization of model building techniques that would otherwise be too time-consuming.