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Longitudinal pharmacometric models offer many advantages in the analysis of clinical trial data, but potentially inflated type I error and biased drug effect estimates, as a consequence of model misspecifications and multiple testing, are main drawbacks. In this work, we used real data to compare these aspects for a standard approach (STD) and a new one using mixture models, called individual model averaging (IMA). Placebo arm data sets were obtained from three clinical studies assessing ADAS-Cog scores, Likert pain scores, and seizure frequency. By randomly (1:1) assigning patients in the above data sets to “treatment” or “placebo,” we created data sets where any significant drug effect was known to be a false positive. Repeating the process of random assignment and analysis for significant drug effect many times (N = 1000) for each of the 40 to 66 placebo-drug model combinations, statistics of the type I error and drug effect bias were obtained. Across all models and the three data types, the type I error was (5th, 25th, 50th, 75th, 95th percentiles) 4.1, 11.4, 40.6, 100.0, 100.0 for STD, and 1.6, 3.5, 4.3, 5.0, 6.0 for IMA. IMA showed no bias in the drug effect estimates, whereas in STD bias was frequently present. In conclusion, STD is associated with inflated type I error and risk of biased drug effect estimates. IMA demonstrated controlled type I error and no bias. Supplementary Information The online version contains supplementary material available at 10.1208/s12248-021-00596-8.

This study aimed to illustrate how a new methodology to assess clinical trial outcome measures using a longitudinal item response theory–based model (IRM) could serve as an alternative to mixed model repeated measures (MMRM). Data from the EXACT (Exacerbation of chronic pulmonary disease tool) which is used to capture frequency, severity, and duration of exacerbations in COPD were analyzed using an IRM. The IRM included a graded response model characterizing item parameters and functions describing symptom-time course. Total scores were simulated (month 12) using uncertainty in parameter estimates. The 50th (2.5th, 97.5th) percentiles of the resulting simulated differences in average total score (drug minus placebo) represented the estimated drug effect (95%CI), which was compared with published MMRM results. Furthermore, differences in sample size, sensitivity, specificity, and type I and II errors between approaches were explored. Patients received either oral danirixin 75 mg twice daily (n = 45) or placebo (n = 48) on top of standard of care over 52 weeks. A step function best described the COPD symptoms-time course in both trial arms. The IRM improved precision of the estimated drug effect compared to MMRM, resulting in a sample size of 2.5 times larger for the MMRM analysis to achieve the IRM precision. The IRM showed a higher probability of a positive predictive value (34%) than MMRM (22%). An item model–based analysis data gave more precise estimates of drug effect than MMRM analysis for the same endpoint in this one case study. Supplementary Information The online version contains supplementary material available at 10.1208/s12248-021-00600-1.

Parameter estimation of a nonlinear model based on maximizing the likelihood using gradient-based numerical optimization methods can often fail due to premature termination of the optimization algorithm. One reason for such failure is that these numerical optimization methods cannot distinguish between the minimum, maximum, and a saddle point; hence, the parameters found by these optimization algorithms can possibly be in any of these three stationary points on the likelihood surface. We have found that for maximization of the likelihood for nonlinear mixed effects models used in pharmaceutical development, the optimization algorithm Broyden-Fletcher-Goldfarb-Shanno (BFGS) often terminates in saddle points, and we propose an algorithm, saddle-reset, to avoid the termination at saddle points, based on the second partial derivative test. In this algorithm, we use the approximated Hessian matrix at the point where BFGS terminates, perturb the point in the direction of the eigenvector associated with the lowest eigenvalue, and restart the BFGS algorithm. We have implemented this algorithm in industry standard software for nonlinear mixed effects modeling (NONMEM, version 7.4 and up) and showed that it can be used to avoid termination of parameter estimation at saddle points, as well as unveil practical parameter non-identifiability. We demonstrate this using four published pharmacometric models and two models specifically designed to be practically non-identifiable.

In physiologically based pharmacokinetic (PBPK) modelling, the large number of input parameters, limited amount of available data and the structural model complexity generally hinder simultaneous estimation of uncertain and/or unknown parameters. These parameters are generally subject to estimation. However, the approaches taken for parameter estimation vary widely. Global sensitivity analyses are proposed as a method to systematically determine the most influential parameters that can be subject to estimation. Herein, a global sensitivity analysis was conducted to identify the key drug and physiological parameters influencing drug disposition in PBPK models and to potentially reduce the PBPK model dimensionality. The impact of these parameters was evaluated on the tissue-to-unbound plasma partition coefficients (Kpus) predicted by the Rodgers and Rowland model using Latin hypercube sampling combined to partial rank correlation coefficients (PRCC). For most drug classes, PRCC showed that LogP and fraction unbound in plasma (fup) were generally the most influential parameters for Kpu predictions. For strong bases, blood:plasma partitioning was one of the most influential parameter. Uncertainty in tissue composition parameters had a large impact on Kpu and Vss predictions for all classes. Among tissue composition parameters, changes in Kpu outputs were especially attributed to changes in tissue acidic phospholipid concentrations and extracellular protein tissue:plasma ratio values. In conclusion, this work demonstrates that for parameter estimation involving PBPK models and dimensionality reduction purposes, less influential parameters might be assigned fixed values depending on the parameter space, while influential parameters could be subject to parameters estimation. QC 20200205

Rating and composite scales are commonly used to assess treatment efficacy. The two main strategies for modelling such endpoints are to treat them as a continuous or an ordered categorical variable (CV or OC). Both strategies have disadvantages, including making assumptions that violate the integer nature of the data (CV) and requiring many parameters for scales with many response categories (OC). We present a method, called the bounded integer (BI) model, which utilises the probit function with fixed cut-offs to estimate the probability of a certain score through a latent variable. This method was successfully implemented to describe six data sets from four different therapeutic areas: Parkinson’s disease, Alzheimer’s disease, schizophrenia, and neuropathic pain. Five scales were investigated, ranging from 11 to 181 categories. The fit (likelihood) was better for the BI model than for corresponding OC or CV models (ΔAIC range 11–1555) in all cases but one (∆AIC − 63), while the number of parameters was the same or lower. Markovian elements were successfully implemented within the method. The performance in external validation, assessed through cross-validation, was also in favour of the new model (ΔOFV range 22–1694) except in one case (∆OFV − 70). A residual for diagnostic purposes is discussed. This study shows that the BI model respects the integer nature of data and is parsimonious in terms of number of estimated parameters. Electronic supplementary material The online version of this article (10.1208/s12248-019-0343-9) contains supplementary material, which is available to authorized users.

We investigated the possible advantages of using linearization to evaluate models of residual unexplained variability (RUV) for automated model building in a similar fashion to the recently developed method “residual modeling.” Residual modeling, although fast and easy to automate, cannot identify the impact of implementing the needed RUV model on the imprecision of the rest of model parameters. We used six RUV models to be tested with 12 real data examples. Each example was first linearized; then, we assessed the agreement in improvement of fit between the base model and its extended models for linearization and conventional analysis, in comparison to residual modeling performance. Afterward, we compared the estimates of parameters’ variabilities and their uncertainties obtained by linearization to conventional analysis. Linearization accurately identified and quantified the nature and magnitude of RUV model misspecification similar to residual modeling. In addition, linearization identified the direction of change and quantified the magnitude of this change in variability parameters and their uncertainties. This method is implemented in the software package PsN for automated model building/evaluation with continuous data. Electronic supplementary material The online version of this article (10.1208/s12248-019-0310-5) contains supplementary material, which is available to authorized users.

Accurate prediction of drug-drug interactions (DDI) is a challenging task in drug discovery and development. It requires determination of enzyme inhibition in vitro which is highly system-dependent for many compounds. The aim of this study was to investigate whether the determination of intracellular unbound concentrations in primary human hepatocytes can be used to bridge discrepancies between results obtained using human liver microsomes and hepatocytes. Specifically, we investigated if Kpuu could reconcile differences in CYP enzyme inhibition values (Ki or IC50). Firstly, our methodology for determination of Kpuu was optimized for human hepatocytes, using four well-studied reference compounds. Secondly, the methodology was applied to a series of structurally related CYP2C9 inhibitors from a Roche discovery project. Lastly, the Kpuu values of three commonly used CYP3A4 inhibitors—ketoconazole, itraconazole, and posaconazole—were determined and compared to compound-specific hepatic enrichment factors obtained from physiologically based modeling of clinical DDI studies with these three compounds. Kpuu obtained in suspended human hepatocytes gave good predictions of system-dependent differences in vitro. The Kpuu was also in fair agreement with the compound-specific hepatic enrichment factors in DDI models and can therefore be used to improve estimations of enrichment factors in physiologically based pharmacokinetic modeling. Electronic supplementary material The online version of this article (10.1208/s12248-019-0344-8) contains supplementary material, which is available to authorized users.

It is important to be able to simulate and predict formulation effects on the pharmacokinetics of a drug in order to optimize effectivity in clinical practice and drug development. Two formulations containing doxorubicin are used in the treatment of hepatocellular carcinoma (HCC): a Lipiodol-based emulsion (LIPDOX) and a loadable microbead system (DEBDOX). Although equally effective, the formulations are vastly different, and little is known about the parameters affecting doxorubicin release in vivo. However, mathematical modeling can be used to predict doxorubicin release properties from these formulations and its in vivo pharmacokinetic (PK) profiles. A porcine semi-physiologically based pharmacokinetic (PBPK) model was scaled to a human physiologically based biopharmaceutical (PBBP) model that was altered to include HCC. DOX in vitro and in vivo release data from LIPDOX or DEBDOX were collected from the literature and combined with these in silico models. The simulated pharmacokinetic profiles were then compared with observed porcine and human HCC patient data. DOX pharmacokinetic profiles of LIPDOX-treated HCC patients were best predicted from release data sets acquired by in vitro methods that did not use a diffusion barrier. For the DEBDOX group, the best predictions were from the in vitro release method with a low ion concentration and a reduced loading dose. The in silico modeling combined with historical release data was effective in predicting in vivo plasma exposure. This can give useful insights into the release method properties necessary for correct in vivo predictions of pharmacokinetic profiles of HCC patients dosed with LIPDOX or DEBDOX.

In this work, an alternative model to discrete-time Markov model (DTMM) or standard continuous-time Markov model (CTMM) for analyzing ordered categorical data with Markov properties is presented: the minimal CTMM (mCTMM). Through a CTMM reparameterization and under the assumption that the transition rate between two consecutive states is independent on the state, the Markov property is expressed through a single parameter, the mean equilibration time, and the steady-state probabilities are described by a proportional odds (PO) model. The mCTMM performance was evaluated and compared to the PO model (ignoring Markov features) and to published Markov models using three real data examples: the four-state fatigue and hand-foot syndrome data in cancer patients initially described by DTMM and the 11-state Likert pain score data in diabetic patients previously analyzed with a count model including Markovian transition probability inflation. The mCTMM better described the data than the PO model, and adequately predicted the average number of transitions per patient and the maximum achieved scores in all examples. As expected, mCTMM could not describe the data as well as more flexible DTMM but required fewer estimated parameters. The mCTMM better fitted Likert data than the count model. The mCTMM enables to explore the effect of potential predictive factors such as drug exposure and covariates, on ordered categorical data, while accounting for Markov features, in cases where DTMM and/or standard CTMM is not applicable or conveniently implemented, e.g., non-uniform time intervals between observations or large number of categories.