Luke Fostvedt

Fully Bayesian approaches are not commonly implemented for population pharmacokinetic (PK) modeling. In this paper, we evaluate the use of Stan with R and Torsten for population PK modeling of somatrogon, a recombinant long‐acting growth hormone approved for the treatment of growth hormone deficiency. As a software for Bayesian inference, Stan provides an easy way to conduct MCMC sampling for a wide range of models with efficient sampling algorithms, and there are several diagnostic tools to evaluate the MCMC convergence and other potential issues. Three different sets of priors were evaluated for estimation and prediction: a weakly informative uniform set, a moderately informative set, and a very informative set of priors. All three prior sets showed good performance and all chains mixed well. There were some minor differences in the final parameter posterior distributions while implementing different prior sets, but the posterior predictions covered the observations nicely, not only for the individuals included in posterior sampling but also for new individuals. The impact of a centered versus non‐centered parameterization were evaluated, with the non‐centered approach improving the estimation time, but it was still computationally intensive. Computational resources had the biggest impact on sampling time. Stan took approximately 2.5 h total for the MCMC sampling on a high‐performance computing platform (6 cores) and may be reduced further with additional computational resources. The model and comparisons presented show that with adequate computational resources, the Bayesian approaches using Stan and Torsten are useful for population PK analysis, especially for the analysis of special populations, small sample datasets, and when complex model structures are needed.

Abrocitinib is a selective Janus kinase 1 inhibitor approved for the treatment of atopic dermatitis. It is metabolized primarily by cytochrome P450 (CYP) 2C19 (approximately 53%) and CYP2C9 (approximately 30%), which form 2 active metabolites. The pharmacologic activity of abrocitinib is attributable to the unbound exposures of abrocitinib and those metabolites with active moiety area under the plasma concentration–time curve (AUC) considered the best measure of the total pharmacological effect. The effect of CYP2C19 and/or CYP2C9 genotypes on abrocitinib and active moiety exposures were evaluated using a meta‐analysis of the noncompartmental estimates of exposure pooled from 10 clinical studies. A linear mixed‐effects model was developed on the basis of the power model to evaluate the effect of CYP2C19 and/or CYP2C9 genotypes on exposure (i.e., abrocitinib AUC and peak plasma concentration, active moiety AUC and peak plasma concentration). The genotypes were evaluated individually and as a combined phenotype effect. When evaluating the poor metabolizers of CYP2C19 or CYP2C9 individually, the estimated increases were 44.9% and 42.0% in active moiety AUC, respectively. The combined phenotype models showed a 0.6% decrease, and 25.1% and 10.5% increases in the active moiety AUC for “elevated,” “mixed,” and “reduced” metabolizers, respectively. Overall, the active moiety exposures did not appear to be affected to a clinically meaningful extent by different genotypes of CYP2C19 and/or CYP2C9.

PoissonERM is an R package used to conduct exposure–response (ER) analysis on binary outcomes for establishing the relationship between exposure and the occurrence of adverse events (AE). While Poisson regression could be implemented with glm(), PoissonERM provides a simple way to semi‐automate the entire analysis and generate an abbreviated report as an R markdown (Rmd) file that includes the essential analysis details with brief conclusions. PoissonERM processes the provided data set using the information from the user's control script and generates summary tables/figures for the exposure metrics, covariates, and event counts of each endpoint (each type of AE). After checking the incidence rate of each AE, the correlation, and missing values in each covariate, an exposure–response model is developed for each endpoint based on the provided specifications. PoissonERM has the flexibility to incorporate and compare multiple scale transformations in its modeling. The best exposure metric is selected based on a univariate model's p‐value or deviance () as specified. If a covariate search is specified in the control script, the final model is developed using backward elimination. PoissonERM identifies and avoids highly correlated covariates in the final model development of each endpoint. Predicting event incidence rates using external (simulated) exposure metric data is an additional functionality in PoissonERM, which is useful to understand the event occurrence associated with certain dose regimens. The summary outputs of the cleaned data, model developments, and predictions are saved in the working folder and can be compiled into a HTML report using Rmd.

Dacomitinib is a second‐generation, irreversible EGFR tyrosine kinase inhibitor for first‐line treatment of patients with metastatic non‐small cell lung cancer and EGFR‐activating mutations. A high rate of dose reductions in the pivotal trial led to an observed inverse exposure‐response (ER) relationship with the primary end points. Three ER models were developed to determine if the starting dose from the pivotal trial, 45 mg once daily (q.d.) dose, is appropriate: a longitudinal logistic regression model for adverse event‐related dose changes, a Claret tumor growth inhibition (TGI) model, and a Cox model for progression‐free survival (PFS) based on the TGI model predictions. This analysis included 266 patients taking dacomitinib with a starting dose of 45 mg (N = 250) or 30 mg (N = 16) q.d. The ER relationships with the time‐varying exposure metrics, most recent maximum plasma concentration (C_max) and average concentration (C_avg) from the first dose, were established for the dose reduction and TGI models, respectively. The TGI model characterized the tumor inhibition over time with constant growth rate (k_L = 0.0012 years⁻¹) and highly variable kill rate (k_D = 1.002 years⁻¹/[μg/L]^θcavg, coefficient of variation [CV] = 89%) and drug resistance (λ = 14.47 years⁻¹, CV = 96%) leading to prolonged tumor shrinkage. The ER relationship was characterized using an exposure parameter with a power parameterization (θcavg = 0.454, p < 0.0001). The Cox model found that baseline tumor size (p = 0.0166) and week 8 tumor shrinkage rate (p = 0.0726) were the best predictors of PFS. Simulations of dose reductions and drug interruptions on tumor shrinkage over time showed greater and more prolonged tumor shrinkage with a starting dose of 45 mg q.d.

Background and Objective Abrocitinib is a Janus kinase 1 inhibitor in development for the treatment of atopic dermatitis (AD). This work characterized orally administered abrocitinib population pharmacokinetics in healthy individuals, patients with psoriasis, and patients with AD and the effects of covariates on abrocitinib exposure. Methods Abrocitinib concentration measurements (n = 6206) from 995 individuals from 11 clinical trials (seven phase I, two phase II, and two phase III) were analyzed, and a non-linear mixed-effects model was developed. Simulations of abrocitinib dose proportionality and steady-state accumulation of maximal plasma drug concentration (C_max) and area under the curve (AUC) were conducted using the final model. Results A two-compartment model with parallel zero- and first-order absorption, time-dependent bioavailability, and time- and dose-dependent clearance best described abrocitinib pharmacokinetics. Abrocitinib coadministration with rifampin resulted in lower exposure, whereas Asian/other race coadministration with fluconazole and fluvoxamine, inflammatory skin conditions (psoriasis/AD), and hepatic impairment resulted in higher exposure. After differences in body weight are accounted for, Asian participants demonstrated a 1.43- and 1.48-fold increase in C_max and AUC, respectively. The overall distribution of exposures (C_max and AUC) was similar in adolescents and adults after accounting for differences in total body weight. Conclusions A population pharmacokinetics model was developed for abrocitinib that can be used to predict abrocitinib steady-state exposure in the presence of drug–drug interaction effects or intrinsic patient factors. Key covariates in the study population accounting for variability in abrocitinib exposures are Asian race and adolescent age, although these factors are not clinically meaningful. Clinical Trial Numbers NCT01835197, NCT02163161, NCT02201524, NCT02780167, NCT03349060, NCT03575871, NCT03634345, NCT03637790, NCT03626415, NCT03386279, NCT03937258.

While an initial clinical absorption, distribution, metabolism, and excretion (ADME) study (Study 1; N = 6) with 100 mg/100 µCi [¹⁴C]lorlatinib, radiolabeled on the carbonyl carbon, confirmed that the primary metabolic pathways for lorlatinib are oxidation (N‐demethylation, N‐oxidation) and N‐glucuronidation, it also revealed an unanticipated, intramolecular cleavage metabolic pathway of lorlatinib, yielding a major circulating benzoic acid metabolite (M8), and an unlabeled pyrido‐pyrazole substructure. Concerns regarding the fate of unknown metabolites associated with this intramolecular cleavage pathway led to conduct of a second ADME study (Study 2; N = 6) of identical design but with the radiolabel positioned on the pyrazole ring. Results were similar with respect to the overall mass balance, lorlatinib plasma exposures, and metabolic profiles in excreta for the metabolites that retained the radiolabel in both studies. Differences were observed in plasma total radioactivity exposures (2‐fold area under the plasma concentration–time curve from time 0 to infinity difference) and relative ratios of the percentage of dose recovered in urine vs feces (48% vs 41% in Study 1; 28% vs 64% in Study 2). In addition, an approximately 3‐fold difference in the mean molar exposure ratio of M8 to lorlatinib was observed for values derived from metabolic profiling data relative to those derived from specific bioanalytical methods (0.5 vs 1.4 for Studies 1 and 2, respectively). These interstudy differences were attributed to a combination of factors, including alteration of radiolabel position, orthogonal analytical methodologies, and intersubject variability, and illustrate that results from clinical ADME studies are not unambiguous and should be interpreted within the context of the specific study design considerations.

Gemtuzumab ozogamicin (Mylotarg; Pfizer, New York, NY) was the first antibody–drug conjugate to be approved for CD33‐positive acute myeloid leukemia (AML). However, it was voluntarily withdrawn from the US market due to lack of clinical benefit in the confirmatory phase III trial. In 2012, several investigator cooperative studies using a different dosing regimen showed efficacy, but pharmacokinetic (PK) data were not collected in these trials. Through simulation of expected concentrations for new dosing regimens, PK/pharmacodynamic modeling was able to support the safety and efficacy of these regimens. Significant exposure–response relationships were found for the attainment of complete remission with and without platelet recovery, attainment of blast‐free status, the time course of myelosuppression, several grade ≥ 3 hepatic adverse events, and veno‐occlusive disease. Gemtuzumab ozogamicin received full approval by the US Food and Drug Administration (FDA) in September 2017 for newly diagnosed and relapsed AML in adult patients and relapsed AML in pediatric patients aged 2–17 years.

This thesis focuses on many different modeling approaches that can be used to evaluate large education data sets. In education research, it is common to have multiple sources of variation designed into the study. If these are ignored, substantial bias can be introduced into the statistical model. We address this issue for three different classes of models: classical linear mixed effects models, quantile regression, and quantile regression of structural equation models. With the classical mixed effects model, we consider a joint modeling approach to estimation and evaluate the affect of correlation on the estimation of both fixed and random effects. For the structural equations models, we have evaluated the performance of a quantile regression imputation model. The other quantile regression model uses the Asymmetric Laplace Distribution to incorporate random effects with estimation performed using a bayesian approach. Multivariate mixed effects models can be used to simultaneously model several outcomes. We look at the effect of different correlations on the model estimation. In our simulations, all of the off-diagonal correlations were the same. However, the estimation allowed the correlation matrix to be unstructured. We looked at both a longitudinal and hierarchical situation where predicted and parameters are selected to mimic situations seen in education research. The simulation results show that the joint modeling approach does not outperform a univariate modeling approach. The estimation of the covariances and correlations are unbiased when only random intercepts are included in the model. When random slopes are also included, the random effect variances tend to be underestimated using the joint modeling approach. Estimate of the correlations between similar random effects are good, but estimates of non-similar random effects exhibit severe bias. Missing response and covariate values are common issues in large scale studies. We evaluate an imputation approach for quantile regression with recursive structural equations. In these models, the estimation of a structural effect is the primary concern. We apply an imputation approach that uses quantile regression to impute missing values. We provide simulations evaluating the estimation and 95\% coverage from this approach both single-level and hierarchical data. Using this imputation approach for a recursive structural equation model, we provide an application studying the effect of selected quantiles of economic, social, and cultural status (ESCS) on selected quantiles for student test scores in mathematics, reading, and science from the PISA 2012 survey. Our findings show that when the rate of missingness is low ($\sim$10\%), the