A workflow for the joint modeling of longitudinal and event data in the development of therapeutics: Tools, statistical methods, and diagnostics.

Clinical trials investigate treatment endpoints that usually include measurements of pharmacodynamic and efficacy biomarkers in early-phase studies and patient-reported outcomes as well as event risks or rates in late-phase studies. In recent years, a systematic trend in clinical trial data analytics and modeling has been observed, where retrospective data are integrated into a quantitative framework to prospectively support analyses of interim data and design of ongoing and future studies of novel therapeutics. Joint modeling is an advanced statistical methodology that allows for the investigation of clinical trial outcomes by quantifying the association between baseline and/or longitudinal biomarkers and event risk. Using an exemplar data set from non-small cell lung cancer studies, we propose and test a workflow for joint modeling. It allows a modeling scientist to comprehensively explore the data, build survival models, investigate goodness-of-fit, and subsequently perform outcome predictions using interim biomarker data from an ongoing study. The workflow illustrates a full process, from data exploration to predictive simulations, for selected multivariate linear and nonlinear mixed-effects models and software tools in an integrative and exhaustive manner.

Longitudinal FEV1 and Exacerbation Risk in COPD: Quantifying the Association Using Joint Modelling.

BACKGROUND: Lung function, measured as forced expiratory volume in one second (FEV1), and exacerbations are two endpoints evaluated in chronic obstructive pulmonary disease (COPD) clinical trials. Joint analysis of these endpoints could potentially increase statistical power and enable assessment of efficacy in shorter and smaller clinical trials. OBJECTIVE: To evaluate joint modelling as a tool for analyzing treatment effects in COPD clinical trials by quantifying the association between longitudinal improvements in FEV1 and exacerbation risk reduction. METHODS: A joint model of longitudinal FEV1 and exacerbation risk was developed based on patient-level data from a Phase III clinical study in moderate-to-severe COPD (1740 patients), evaluating efficacy of fixed-dose combinations of a long-acting bronchodilator, formoterol, and an inhaled corticosteroid, budesonide. Two additional studies (1604 and 1042 patients) were used for external model validation and parameter re-estimation. RESULTS: A significant (p<0.0001) association between FEV1 and exacerbation risk was estimated, with an approximate 10% reduction in exacerbation risk per 100 mL improvement in FEV1, consistent across trials and treatment arms. The risk reduction associated with improvements in FEV1 was relatively small compared to the overall exacerbation risk reduction for treatment arms including budesonide (10-15% per 160 µg budesonide). High baseline breathlessness score and previous history of exacerbations also influenced the risk of exacerbation. CONCLUSION: Joint modelling can be used to co-analyze longitudinal FEV1 and exacerbation data in COPD clinical trials. The association between the endpoints was consistent and appeared unrelated to treatment mechanism, suggesting that improved lung function is indicative of an exacerbation risk reduction. The risk reduction associated with improved FEV1 was, however, generally small and no major impact on exacerbation trial design can be expected based on FEV1 alone. Further exploration with other longitudinal endpoints should be considered to further evaluate the use of joint modelling in analyzing COPD clinical trials.

Longitudinal Tumor Size and Neutrophil-to-Lymphocyte Ratio Are Prognostic Biomarkers for Overall Survival in Patients With Advanced Non-Small Cell Lung Cancer Treated With Durvalumab.

Therapy optimization remains an important challenge in the treatment of advanced non-small cell lung cancer (NSCLC). We investigated tumor size (sum of the longest diameters (SLD) of target lesions) and neutrophil-to-lymphocyte ratio (NLR) as longitudinal biomarkers for survival prediction. Data sets from 335 patients with NSCLC from study NCT02087423 and 202 patients with NSCLC from study NCT01693562 of durvalumab were used for model qualification and validation, respectively. Nonlinear Bayesian joint models were designed to assess the impact of longitudinal measurements of SLD and NLR on patient subgrouping (by Response Evaluation Criteria in Solid Tumors 1.1 criteria at 3 months after therapy start), long-term survival, and precision of survival predictions. Various validation scenarios were investigated. We determined a more distinct patient subgrouping and a substantial increase in the precision of survival estimates after the incorporation of longitudinal measurements. The highest performance was achieved using a multivariate SLD and NLR model, which enabled predictions of NSCLC clinical outcomes.

Comparative quantitative systems pharmacology modeling of anti-PCSK9 therapeutic modalities in hypercholesterolemia.

Since the discovery of proprotein convertase subtilisin/kexin type 9 (PCSK9) as an attractive target in the treatment of hypercholesterolemia, multiple anti-PCSK9 therapeutic modalities have been pursued in drug development. The objective of this research is to set the stage for the quantitative benchmarking of two anti-PCSK9 pharmacological modality classes, monoclonal antibodies (mAbs) and small interfering RNA (siRNA). To this end, we developed an integrative mathematical model of lipoprotein homeostasis describing the dynamic interplay between PCSK9, LDL-cholesterol (LDL-C), VLDL-cholesterol, HDL-cholesterol (HDL-C), apoB, lipoprotein a [Lp(a)], and triglycerides (TGs). We demonstrate that LDL-C decreased proportionally to PCSK9 reduction for both mAb and siRNA modalities. At marketed doses, however, treatment with mAbs resulted in an additional ∼20% LDL-C reduction compared with siRNA. We further used the model as an evaluation tool and determined that no quantitative differences were observed in HDL-C, Lp(a), TG, or apoB responses, suggesting that the disruption of PCSK9 synthesis would provide no additional effects on lipoprotein-related biomarkers in the patient segment investigated. Predictive model simulations further indicate that siRNA therapies may reach reductions in LDL-C levels comparable to those achieved with mAbs if the current threshold of 80% PCSK9 inhibition via siRNA could be overcome.

Exenatide effects on gastric emptying rate and the glucose rate of appearance in plasma: A quantitative assessment using an integrative systems pharmacology model.

This study aimed to quantify the effect of the immediate release (IR) of exenatide, a short-acting glucagon-like peptide-1 (GLP-1) receptor agonist (GLP-1RA), on gastric emptying rate (GER) and the glucose rate of appearance (GluRA), and evaluate the influence of drug characteristics and food-related factors on postprandial plasma glucose (PPG) stabilization under GLP-1RA treatment. A quantitative systems pharmacology (QSP) approach was used, and the proposed model was based on data from published sources including: (1) GLP-1 and exenatide plasma concentration-time profiles; (2) GER estimates under placebo, GLP-1 or exenatide IR dosing; and (3) GluRA measurements upon food intake. According to the model's predictions, the recommended twice-daily 5- and 10-µg exenatide IR treatment is associated with GluRA flattening after morning and evening meals (48%-49%), whereas the midday GluRA peak is affected to a lesser degree (5%-30%) due to lower plasma drug concentrations. This effect was dose-dependent and influenced by food carbohydrate content, but not by the lag time between exenatide injection and meal ingestion. Hence, GER inhibition by exenatide IR represents an important additional mechanism of its effect on PPG.

Interpretation of metabolic memory phenomenon using a physiological systems model: What drives oxidative stress following glucose normalization?

Hyperglycemia is generally associated with oxidative stress, which plays a key role in diabetes-related complications. A complex, quantitative relationship has been established between glucose levels and oxidative stress, both in vitro and in vivo. For example, oxidative stress is known to persist after glucose normalization, a phenomenon described as metabolic memory. Also, uncontrolled glucose levels appear to be more detrimental to patients with diabetes (non-constant glucose levels) vs. patients with high, constant glucose levels. The objective of the current study was to delineate the mechanisms underlying such behaviors, using a mechanistic physiological systems modeling approach that captures and integrates essential underlying pathophysiological processes. The proposed model was based on a system of ordinary differential equations. It describes the interplay between reactive oxygen species production potential (ROS), ROS-induced cell alterations, and subsequent adaptation mechanisms. Model parameters were calibrated using different sources of experimental information, including ROS production in cell cultures exposed to various concentration profiles of constant and oscillating glucose levels. The model adequately reproduced the ROS excess generation after glucose normalization. Such behavior appeared to be driven by positive feedback regulations between ROS and ROS-induced cell alterations. The further oxidative stress-related detrimental effect as induced by unstable glucose levels can be explained by inability of cells to adapt to dynamic environment. Cell adaptation to instable high glucose declines during glucose normalization phases, and further glucose increase promotes similar or higher oxidative stress. In contrast, gradual ROS production potential decrease, driven by adaptation, is observed in cells exposed to constant high glucose.

Prediction of long-term treatment outcome in HCV following 24 day PEG-IFN alpha-2b therapy using population pharmacokinetic-pharmacodynamic mixture modeling and classification analysis.

Mathematical models have been widely used for understanding the dynamics of the hepatitis C virus (HCV). We propose a method to predict final clinical outcome for 24 HIV-HCV - coinfected patients with the help of a mathematical model based on the first two weeks of PEG-IFN therapy. Applying a pharmacokinetic-pharmacodynamic (PKPD) approach, together with mixture models, to the adapted model of viral dynamics developed by Neumann et al., we have analyzed the influence of PEG-IFN on the kinetics and interaction of target cells, infected cells and virus mRNA. It was found that PEG-IFN pharmacokinetic parameters were similar in sustained virological responders and nonresponders, while the plasma PEG-IFN concentration that decreases HCV production by 50% (EC50) and the rate of infected cell death were different. The treatment outcome depended mainly on the initial viral mRNA concentration and the rate of infected cell death. The population PKPD approach with a mixture model enabled the determination of individual PKPD parameters and showed high sensitivity (93.5%) and specificity (97.4%) for the prediction of the treatment outcome.

Conserved and divergent features of kinetochores and spindle microtubule ends from five species.

Interfaces between spindle microtubules and kinetochores were examined in diverse species by electron tomography and image analysis. Overall structures were conserved in a mammal, an alga, a nematode, and two kinds of yeasts; all lacked dense outer plates, and most kinetochore microtubule ends flared into curved protofilaments that were connected to chromatin by slender fibrils. Analyses of curvature on >8,500 protofilaments showed that all classes of spindle microtubules displayed some flaring protofilaments, including those growing in the anaphase interzone. Curved protofilaments on anaphase kinetochore microtubules were no more flared than their metaphase counterparts, but they were longer. Flaring protofilaments in budding yeasts were linked by fibrils to densities that resembled nucleosomes; these are probably the yeast kinetochores. Analogous densities in fission yeast were larger and less well-defined, but both yeasts showed ring- or partial ring-shaped structures girding their kinetochore microtubules. Flaring protofilaments linked to chromatin are well placed to exert force on chromosomes, assuring stable attachment and reliable anaphase segregation.

Regulation of leukotriene and 5oxoETE synthesis and the effect of 5-lipoxygenase inhibitors: a mathematical modeling approach.

BACKGROUND: 5-lipoxygenase (5-LO) is a key enzyme in the synthesis of leukotrienes and 5-Oxo-6E,8Z,11Z,14Z-eicosatetraenoic acid (oxoETE). These inflammatory signaling molecules play a role in the pathology of asthma and so 5-LO inhibition is a promising target for asthma therapy. The 5-LO redox inhibitor zileuton (Zyflo IR/CR(®)) is currently marketed for the treatment of asthma in adults and children, but widespread use of zileuton is limited by its efficacy/safety profile, potentially related to its redox characteristics. Thus, a quantitative, mechanistic description of its functioning may be useful for development of improved anti-inflammatory targeting this mechanism. RESULTS: A mathematical model describing the operation of 5-LO, phospholipase A2, glutathione peroxidase and 5-hydroxyeicosanoid dehydrogenase was developed. The catalytic cycles of the enzymes were reconstructed and kinetic parameters estimated on the basis of available experimental data. The final model describes each stage of cys-leukotriene biosynthesis and the reactions involved in oxoETE production. Regulation of these processes by substrates (phospholipid concentration) and intracellular redox state (concentrations of reduced glutathione, glutathione (GSH), and lipid peroxide) were taken into account. The model enabled us to reveal differences between redox and non-redox 5-LO inhibitors under conditions of oxidative stress. Despite both redox and non-redox inhibitors suppressing leukotriene A4 (LTA4) synthesis, redox inhibitors are predicted to increase oxoETE production, thus compromising efficacy. This phenomena can be explained in terms of the pseudo-peroxidase activity of 5-LO and the ability of lipid peroxides to transform 5-LO into its active form even in the presence of redox inhibitors. CONCLUSIONS: The mathematical model developed described quantitatively different mechanisms of 5-LO inhibition and simulations revealed differences between the potential therapeutic outcomes for these mechanisms.

Fibrils connect microtubule tips with kinetochores: a mechanism to couple tubulin dynamics to chromosome motion.

Kinetochores of mitotic chromosomes are coupled to spindle microtubules in ways that allow the energy from tubulin dynamics to drive chromosome motion. Most kinetochore-associated microtubule ends display curving "protofilaments," strands of tubulin dimers that bend away from the microtubule axis. Both a kinetochore "plate" and an encircling, ring-shaped protein complex have been proposed to link protofilament bending to poleward chromosome motion. Here we show by electron tomography that slender fibrils connect curved protofilaments directly to the inner kinetochore. Fibril-protofilament associations correlate with a local straightening of the flared protofilaments. Theoretical analysis reveals that protofilament-fibril connections would be efficient couplers for chromosome motion, and experimental work on two very different kinetochore components suggests that filamentous proteins can couple shortening microtubules to cargo movements. These analyses define a ring-independent mechanism for harnessing microtubule dynamics directly to chromosome movement.