Nonlinear models for repeated measurement data: An overview and update

A framework for longitudinal latent factor modelling of treatment response in clinical trials with applications to Psoriatic Arthritis and Rheumatoid Arthritis

OBJECTIVE

Clinical trials involve the collection of a wealth of data, comprising multiple diverse measurements performed at baseline and follow-up visits over the course of a trial. The most common primary analysis is restricted to a single, potentially composite endpoint at one time point. While such an analytical focus promotes simple and replicable conclusions, it does not necessarily fully capture the multi-faceted effects of a drug in a complex disease setting. Therefore, to complement existing approaches, we set out here to design a longitudinal multivariate analytical framework that accepts as input an entire clinical trial database, comprising all measurements, patients, and time points across multiple trials.

METHODS

Our framework composes probabilistic principal component analysis with a longitudinal linear mixed effects model, thereby enabling clinical interpretation of multivariate results, while handling data missing at random, and incorporating covariates and covariance structure in a computationally efficient and principled way.

RESULTS

We illustrate our approach by applying it to four phase III clinical trials of secukinumab in Psoriatic Arthritis (PsA) and Rheumatoid Arthritis (RA). We identify three clinically plausible latent factors that collectively explain 74.5% of empirical variation in the longitudinal patient database. We estimate longitudinal trajectories of these factors, thereby enabling joint characterisation of disease progression and drug effect. We perform benchmarking experiments demonstrating our method's competitive performance at estimating average treatment effects compared to existing statistical and machine learning methods, and showing that our modular approach leads to relatively computationally efficient model fitting.

CONCLUSION

Our multivariate longitudinal framework has the potential to illuminate the properties of existing composite endpoint methods, and to enable the development of novel clinical endpoints that provide enhanced and complementary perspectives on treatment response.

A review of mechanistic learning in mathematical oncology

Mechanistic learning refers to the synergistic combination of mechanistic mathematical modeling and data-driven machine or deep learning. This emerging field finds increasing applications in (mathematical) oncology. This review aims to capture the current state of the field and provides a perspective on how mechanistic learning may progress in the oncology domain. We highlight the synergistic potential of mechanistic learning and point out similarities and differences between purely data-driven and mechanistic approaches concerning model complexity, data requirements, outputs generated, and interpretability of the algorithms and their results. Four categories of mechanistic learning (sequential, parallel, extrinsic, intrinsic) of mechanistic learning are presented with specific examples. We discuss a range of techniques including physics-informed neural networks, surrogate model learning, and digital twins. Example applications address complex problems predominantly from the domain of oncology research such as longitudinal tumor response predictions or time-to-event modeling. As the field of mechanistic learning advances, we aim for this review and proposed categorization framework to foster additional collaboration between the data- and knowledge-driven modeling fields. Further collaboration will help address difficult issues in oncology such as limited data availability, requirements of model transparency, and complex input data which are embraced in a mechanistic learning framework.

A global multicohort study to map subcortical brain development and cognition in infancy and early childhood

The human brain grows quickly during infancy and early childhood, but factors influencing brain maturation in this period remain poorly understood. To address this gap, we harmonized data from eight diverse cohorts, creating one of the largest pediatric neuroimaging datasets to date focused on birth to 6 years of age. We mapped the developmental trajectory of intracranial and subcortical volumes in ∼2,000 children and studied how sociodemographic factors and adverse birth outcomes influence brain structure and cognition. The amygdala was the first subcortical volume to mature, whereas the thalamus exhibited protracted development. Males had larger brain volumes than females, and children born preterm or with low birthweight showed catch-up growth with age. Socioeconomic factors exerted region- and time-specific effects. Regarding cognition, males scored lower than females; preterm birth affected all developmental areas tested, and socioeconomic factors affected visual reception and receptive language. Brain-cognition correlations revealed region-specific associations.

Computation of nonparametric, mixed effects, maximum likelihood, biosensor data based-estimators for the distributions of random parameters in an abstract parabolic model for the transdermal transport of alcohol

The existence and consistency of a maximum likelihood estimator for the joint probability distribution of random parameters in discrete-time abstract parabolic systems was established by taking a nonparametric approach in the context of a mixed effects statistical model using a Prohorov metric framework on a set of feasible measures. A theoretical convergence result for a finite dimensional approximation scheme for computing the maximum likelihood estimator was also established and the efficacy of the approach was demonstrated by applying the scheme to the transdermal transport of alcohol modeled by a random parabolic partial differential equation (PDE). Numerical studies included show that the maximum likelihood estimator is statistically consistent, demonstrated by the convergence of the estimated distribution to the "true" distribution in an example involving simulated data. The algorithm developed was then applied to two datasets collected using two different transdermal alcohol biosensors. Using the leave-one-out cross-validation (LOOCV) method, we found an estimate for the distribution of the random parameters based on a training set. The input from a test drinking episode was then used to quantify the uncertainty propagated from the random parameters to the output of the model in the form of a 95 error band surrounding the estimated output signal.

Smoothed simulated pseudo-maximum likelihood estimation for nonlinear mixed effects models with censored responses

Nonlinear mixed effects models have been widely applied to analyses of data that arise from biological, agricultural, and environmental sciences. Estimation of and inference on parameters in nonlinear mixed effects models are often based on the specification of a likelihood function. Maximizing this likelihood function can be complicated by the specification of the random effects distribution, especially in the presence of multiple random effects. The implementation of nonlinear mixed effects models can be further complicated by left-censored responses, representing measurements from bioassays where the exact quantification below a certain threshold is not possible. Motivated by the need to characterize the nonlinear human immunodeficiency virus RNA viral load trajectories after the interruption of antiretroviral therapy, we propose a smoothed simulated pseudo-maximum likelihood estimation approach to fit nonlinear mixed effects models in the presence of left-censored observations. We establish the consistency and asymptotic normality of the resulting estimators. We develop testing procedures for the correlation among random effects and for testing the distributional assumptions on random effects against a specific alternative. In contrast to the existing variants of expectation-maximization approaches, the proposed methods offer flexibility in the specification of the random effects distribution and convenience in making inference about higher-order correlation parameters. We evaluate the finite-sample performance of the proposed methods through extensive simulation studies and illustrate them on a combined dataset from six AIDS Clinical Trials Group treatment interruption studies.

Modeling stand biomass for Moso bamboo forests in Eastern China

Stand biomass models can be used as basic decision-making tools in forest management planning. The Moso bamboo (Phyllostachys pubescens) forest, a major forest system in tropical and subtropical regions, represents a substantial carbon sink, slowing down the rise of greenhouse gas concentrations in the earth's atmosphere. Bamboo stand biomass models are important for the assessment of the contribution of carbon to the terrestrial ecosystem. We constructed a stand biomass model for Moso bamboo using destructively sampled data from 45 sample plots that were located across the Yixing state-owned farm in Jiangsu Province, China. Among several bamboo stand variables used as predictors in the stand biomass models, mean diameter at breast height (MDBH), mean height (MH), and canopy density (CD) of bamboo contributed significantly to the model. To increase the model's accuracy, we introduced the effects of bamboo forest block as a random effect into the model through mixed-effects modeling. The mixed-effects model described a large part of stand biomass variation (R2 = 0.6987), significantly higher than that of the ordinary least squares regression model (R2 = 0.5748). Our results show an increased bamboo stand biomass with increasing MH and CD, confirming our model's biological logic. The proposed stand biomass model may have important management implications; for example, it can be combined with other bamboo models to estimate bamboo canopy biomass, carbon sequestration, and bamboo biomass at different growth stages.

The Impact of Functional Form Complexity on Model Overfitting for Nonlinear Mixed-Effects Models

Nonlinear mixed-effects models (NLMEMs) allow researchers to model curvilinear patterns of growth, but there is ambiguity as to what functional form the data follow. Often, researchers fit multiple nonlinear functions to data and use model selection criteria to decide which functional form fits the data "best." Frequently used model selection criteria only account for the number of parameters in a model but overlook the complexity of intrinsically nonlinear functional forms. This can lead to overfitting and hinder the generalizability and reproducibility of results. The primary goal of this study was to evaluate the performance of eight model selection criteria via a Monte Carlo simulation study and assess under what conditions these criteria are sensitive to model overfitting as it relates to functional form complexity. Results highlighted criteria with the potential to capture overfitting for intrinsically nonlinear functional forms for NLMEMs. Information criteria and the stochastic information complexity criterion recovered the true model more often than the average or conditional concordance correlation. Results also suggest that the amount of residual variance and sample size have an impact on model selection for NLMEMs. Implications for future research and recommendations for application are also provided.

How quickly does a wound heal? Bayesian calibration of a mathematical model of venous leg ulcer healing

Chronic wounds, such as venous leg ulcers, are difficult to treat and can reduce the quality of life for patients. Clinical trials have been conducted to identify the most effective venous leg ulcer treatments and the clinical factors that may indicate whether a wound will successfully heal. More recently, mathematical modelling has been used to gain insight into biological factors that may affect treatment success but are difficult to measure clinically, such as the rate of oxygen flow into wounded tissue. In this work, we calibrate an existing mathematical model using a Bayesian approach with clinical data for individual patients to explore which clinical factors may impact the rate of wound healing for individuals. Although the model describes group-level behaviour well, it is not able to capture individual-level responses in all cases. From the individual-level analysis, we propose distributions for coefficients of clinical factors in a linear regression model, but ultimately find that it is difficult to draw conclusions about which factors lead to faster wound healing based on the existing model and data. This work highlights the challenges of using Bayesian methods to calibrate partial differential equation models to individual patient clinical data. However, the methods used in this work may be modified and extended to calibrate spatiotemporal mathematical models to multiple data sets, such as clinical trials with several patients, to extract additional information from the model and answer outstanding biological questions.

Wine Closure Performance of Three Common Closure Types: Chemical and Sensory Impact on a Sauvignon Blanc Wine

A Napa Valley Sauvignon blanc wine was bottled with 200 each of a natural cork, a screw cap, and a synthetic cork. As browning is an index for wine oxidation, we assessed the brown color of each bottle with a spectrophotometer over 30 months. A random-effects regression model for longitudinal data on all bottles and closure groups found a browning growth trajectory for each closure group. Changes in the wine’s browning behavior at 18 months and 30 months showed that the browning of the wine bottles appeared to slow down later in the storage period, especially for natural corks. The between-bottle variation was the highest for the natural cork. At 30 months, we separated the bottles by the extent of browning and samples were pulled from the high, mid, and low levels of browning levels for each closure. The degree of browning is inversely correlated with free SO₂ levels ranging from 5 to 12 mg/L. However, a Quantitative Descriptive Analysis (QDA™) sensory panel could not detect any difference in their aroma and flavor profile between closure types regardless of browning level. Even low levels of free SO₂ retain protection against strong oxidation aromas, and visual browning detected by spectrophotometer seemed to precede oxidative aroma and flavor changes of the aging Sauvignon blanc.

The midpoint of cortical thinning between late childhood and early adulthood differs between individuals and brain regions: Evidence from longitudinal modelling in a 12-wave neuroimaging sample

Charting human brain maturation between childhood and adulthood is a fundamental prerequisite for understanding the rapid biological and psychological changes during human development. Two barriers have precluded the quantification of maturational trajectories: demands on data and demands on estimation. Using high-temporal resolution neuroimaging data of up to 12-waves in the HUBU cohort (N = 90, aged 7-21 years) we investigate changes in apparent cortical thickness across childhood and adolescence. Fitting a four-parameter logistic nonlinear random effects mixed model, we quantified the characteristic, s-shaped, trajectory of cortical thinning in adolescence. This approach yields biologically meaningful parameters, including the midpoint of cortical thinning (MCT), which corresponds to the age at which the cortex shows most rapid thinning - in our sample occurring, on average, at 14 years of age. These results show that, given suitable data and models, cortical maturation can be quantified with precision for each individual and brain region.

The Oxidative Potential of Fine Particulate Matter and Biological Perturbations in Human Plasma and Saliva Metabolome

Particulate oxidative potential may comprise a key health-relevant parameter of particulate matter (PM) toxicity. To identify biological perturbations associated with particulate oxidative potential and examine the underlying molecular mechanisms, we recruited 54 participants from two dormitories near and far from a congested highway in Atlanta, GA. Fine particulate matter oxidative potential ("FPMOP") levels at the dormitories were measured using dithiothreitol assay. Plasma and saliva samples were collected from participants four times for longitudinal high-resolution metabolic profiling. We conducted metabolome-wide association studies to identify metabolic signals with FPMOP. Leukotriene metabolism and galactose metabolism were top pathways associated with ≥5 FPMOP-related indicators in plasma, while vitamin E metabolism and leukotriene metabolism were found associated with most FPMOP indicators in saliva. We observed different patterns of perturbed pathways significantly associated with water-soluble and -insoluble FPMOPs, respectively. We confirmed five metabolites directly associated with FPMOP, including hypoxanthine, histidine, pyruvate, lactate/glyceraldehyde, and azelaic acid, which were implications of perturbations in acute inflammation, nucleic acid damage and repair, and energy perturbation. The unique metabolic signals were specific to FPMOP, but not PM mass, providing initial indication that FPMOP might constitute a more sensitive, health-relevant measure for elucidating etiologies related to PM_2.5 exposures.

Luminal androgen receptor breast cancer subtype and investigation of the microenvironment and neoadjuvant chemotherapy response

Triple-negative breast cancer (TNBC) is the most aggressive breast cancer subtype with low overall survival rates and high molecular heterogeneity; therefore, few targeted therapies are available. The luminal androgen receptor (LAR) is the most consistently identified TNBC subtype, but the clinical utility has yet to be established. Here, we constructed a novel genomic classifier, LAR-Sig, that distinguishes the LAR subtype from other TNBC subtypes and provide evidence that it is a clinically distinct disease. A meta-analysis of seven TNBC datasets (n = 1086 samples) from neoadjuvant clinical trials demonstrated that LAR patients have significantly reduced response (pCR) rates than non-LAR TNBC patients (odds ratio = 2.11, 95% CI: 1.33, 2.89). Moreover, deconvolution of the tumor microenvironment confirmed an enrichment of luminal epithelium corresponding with a decrease in basal and myoepithelium in LAR TNBC tumors. Increased immunosuppression in LAR patients may lead to a decreased presence of cycling T-cells and plasma cells. While, an increased presence of myofibroblast-like cancer-associated cells may impede drug delivery and treatment. In summary, the lower levels of tumor infiltrating lymphocytes (TILs), reduced immune activity in the micro-environment, and lower pCR rates after NAC, suggest that new therapeutic strategies for the LAR TNBC subtype need to be developed.

An Approach to Estimate Individual Tree Ages Based on Time Series Diameter Data—A Test Case for Three Subtropical Tree Species in China

Accurate knowledge of individual tree ages is critical for forestry and ecological research. However, previous methods suffer from flaws such as tree damage, low efficiency, or ignoring autocorrelation among residuals. In this paper, an approach for estimating the ages of individual trees is proposed based on the diameter series of Cinnamomum camphora (Cinnamomum camphora (L.) Presl), Schima superba (Schima superba Gardn. et Champ.), and Liquidambar formosana (Liquidambar formosana Hance). Diameter series were obtained by stem analysis. Panel data contains more information, more variability, and more efficiency than pure time series data or cross-sectional data, which is why diameter series at stump and breast heights were chosen to form the panel data. After choosing a base growth equation, a constraint was added to the equation to improve stability. The difference method was used to reduce autocorrelation and the parameter classification method was used to improve model suitability. Finally, the diameter increment equation of parameter a-classification was developed. The mean errors of estimated ages based on the panel data at breast height for C. camphora, S. superba, and L. formosana were 0.47, 2.46, and −0.56 years and the root mean square errors were 2.04, 3.15 and 2.47 years, respectively. For C. camphora and L. formosana, the estimated accuracy based on the panel data was higher at breast height than at stump height. This approach to estimating individual tree ages is highly accurate and reliable, and provides a feasible way to obtain tree ages by field measurement.

Bayesian Nonlinear Models for Repeated Measurement Data: An Overview, Implementation, and Applications

Nonlinear mixed effects models have become a standard platform for analysis when data is in the form of continuous and repeated measurements of subjects from a population of interest, while temporal profiles of subjects commonly follow a nonlinear tendency. While frequentist analysis of nonlinear mixed effects models has a long history, Bayesian analysis of the models has received comparatively little attention until the late 1980s, primarily due to the time-consuming nature of Bayesian computation. Since the early 1990s, Bayesian approaches for the models began to emerge to leverage rapid developments in computing power, and have recently received significant attention due to (1) superiority to quantify the uncertainty of parameter estimation; (2) utility to incorporate prior knowledge into the models; and (3) flexibility to match exactly the increasing complexity of scientific research arising from diverse industrial and academic fields. This review article presents an overview of modeling strategies to implement Bayesian approaches for the nonlinear mixed effects models, ranging from designing a scientific question out of real-life problems to practical computations.

A Bayesian approach to model individual differences and to partition individuals: case studies in growth and learning curves

The first objective of the paper is to implement a two stage Bayesian hierarchical nonlinear model for growth and learning curves, particular cases of longitudinal data with an underlying nonlinear time dependence. The aim is to model simultaneously individual trajectories over time, each with specific and potentially different characteristics, and a time-dependent behavior shared among individuals, including eventual effect of covariates. At the first stage inter-individual differences are taken into account, while, at the second stage, we search for an average model. The second objective is to partition individuals into homogeneous groups, when inter individual parameters present high level of heterogeneity. A new multivariate partitioning approach is proposed to cluster individuals according to the posterior distributions of the parameters describing the individual time-dependent behaviour. To assess the proposed methods, we present simulated data and two applications to real data, one related to growth curve modeling in agriculture and one related to learning curves for motor skills. Furthermore a comparison with finite mixture analysis is shown.

Comparison of alternative arterial anastomosis site during liver transplantation when the recipient's hepatic artery is unusable

BACKGROUND

Few studies have analyzed outcomes of liver transplantation (LT) when the recipient hepatic artery (HA) was not usable.

METHODS

We retrospectively evaluated the outcomes of LT performed using the different alternative sites to HA.

RESULTS

Between 2002 and 2017, 1,677 LT were performed in our institution among which 141 (8.4%) with unusable recipient HA were analyzed. Four groups were defined according to the site of anastomosis: the splenic artery (SA group, n=26), coeliac trunk (CT group, n=12), aorta using or not the donor's vessel (Ao group, n=91) and aorta using a vascular prosthesis (Ao-P group, n=12) as conduit. The median number of intraoperative red blood cell transfusions was significantly increased in the Ao and Ao-P groups (5, 5, 8.5 and 16 for SA, CT, Ao and Ao-P group respectively, P=0.002), as well as fresh frozen plasma (4.5, 2.5, 10, 17 for the SA, CT, Ao and Ao-P groups respectively, P=0.001). Hospitalization duration was also significantly increased in the Ao and Ao-P groups (15, 16, 24, 26.5 days for the SA, CT, Ao and Ao-P groups respectively, P<0.001). The occurrence of early allograft dysfunction (EAD) (P=0.07) or arterial complications (P=0.26) was not statistically different. Level of factor V, INR, bilirubin and creatinine during the 7th postoperative days (POD) was significantly improved in the SA group. No difference was observed regarding graft (P=0.18) and patient (P=0.16) survival.

CONCLUSIONS

In case of unusable HA, intraoperative and postoperative outcomes are improved when using the SA or CT compared to aorta.

Winter weight loss of different subspecies of honey bee Apis mellifera colonies (Linnaeus, 1758) in southwestern Sweden

Honey bees are currently facing mounting pressures that have resulted in population declines in many parts of the world. In northern climates winter is a bottleneck for honey bees and a thorough understanding of the colonies’ ability to withstand the winter is needed in order to protect the bees from further decline. In this study the influence of weather variables on colony weight loss was studied over one winter (2019–2020) in two apiaries (32 colonies in total) in southwestern Sweden with weather stations recording wind and temperature at 5-min intervals. Three subspecies of honey bees and one hybrid were studied: the native Apis mellifera mellifera, the Italian A. m. ligustica, the Carniolan A. m. carnica and the hybrid Buckfast. Additionally, we recorded Varroa mite infestation. To analyze factors involved in resource consumption, three modelling approaches using weather and weight data were developed: the first links daily consumption rates with environmental variables, the second modelled the cumulative weight change over time, and the third estimated weight change over time taking light intensity and temperature into account. Weight losses were in general low (0.039 ± 0.013kg/day and colony) and comparable to southern locations, likely due to an exceptionally warm winter (average temperature 3.5°C). Weight losses differed only marginally between subspecies with indications that A. m. mellifera was having a more conservative resource consumption, but more studies are needed to confirm this. We did not find any effect of Varroa mite numbers on weight loss. Increased light intensity and temperature both triggered the resource consumption in honey bees. The temperature effect on resource consumption is in accordance with the metabolic theory of ecology. The consequences of these findings on honey bee survival under predicted climate changes, is still an open question that needs further analysis.

Additive quantile mixed effects modelling with application to longitudinal CD4 count data

Quantile regression offers an invaluable tool to discern effects that would be missed by other conventional regression models, which are solely based on modeling conditional mean. Quantile regression for mixed-effects models has become practical for longitudinal data analysis due to the recent computational advances and the ready availability of efficient linear programming algorithms. Recently, quantile regression has also been extended to additive mixed-effects models, providing an efficient and flexible framework for nonparametric as well as parametric longitudinal forms of data analysis focused on features of the outcome beyond its central tendency. This study applies the additive quantile mixed model to analyze the longitudinal CD4 count of HIV-infected patients enrolled in a follow-up study at the Centre of the AIDS Programme of Research in South Africa. The objective of the study is to justify how the procedure developed can obtain robust nonlinear and linear effects at different conditional distribution locations. With respect to time and baseline BMI effect, the study shows a significant nonlinear effect on CD4 count across all fitted quantiles. Furthermore, across all fitted quantiles, the effect of the parametric covariates of baseline viral load, place of residence, and the number of sexual partners was found to be major significant factors on the progression of patients' CD4 count who had been initiated on the Highly Active Antiretroviral Therapy study.

An effective processing pipeline for harmonizing DNA methylation data from Illumina's 450K and EPIC platforms for epidemiological studies

OBJECTIVE

Illumina BeadChip arrays are commonly used to generate DNA methylation data for large epidemiological studies. Updates in technology over time create challenges for data harmonization within and between studies, many of which obtained data from the older 450K and newer EPIC platforms. The pre-processing pipeline for DNA methylation is not trivial, and influences the downstream analyses. Incorporating different platforms adds a new level of technical variability that has not yet been taken into account by recommended pipelines. Our study evaluated the performance of various tools on different versions of platform data harmonization at each step of pre-processing pipeline, including quality control (QC), normalization, batch effect adjustment, and genomic inflation. We illustrate our novel approach using 450K and EPIC data from the Diabetes Autoimmunity Study in the Young (DAISY) prospective cohort.

RESULTS

We found normalization and probe filtering had the biggest effect on data harmonization. Employing a meta-analysis was an effective and easily executable method for accounting for platform variability. Correcting for genomic inflation also helped with harmonization. We present guidelines for studies seeking to harmonize data from the 450K and EPIC platforms, which includes the use of technical replicates for evaluating numerous pre-processing steps, and employing a meta-analysis.

Hierarchical Bayesian estimation of covariate effects on airway and alveolar nitric oxide

Exhaled breath biomarkers are an important emerging field. The fractional concentration of exhaled nitric oxide (FeNO) is a marker of airway inflammation with clinical and epidemiological applications (e.g., air pollution health effects studies). Systems of differential equations describe FeNO—measured non-invasively at the mouth—as a function of exhalation flow rate and parameters representing airway and alveolar sources of NO in the airway. Traditionally, NO parameters have been estimated separately for each study participant (Stage I) and then related to covariates (Stage II). Statistical properties of these two-step approaches have not been investigated. In simulation studies, we evaluated finite sample properties of existing two-step methods as well as a novel Unified Hierarchical Bayesian (U-HB) model. The U-HB is a one-step estimation method developed with the goal of properly propagating uncertainty as well as increasing power and reducing type I error for estimating associations of covariates with NO parameters. We demonstrated the U-HB method in an analysis of data from the southern California Children’s Health Study relating traffic-related air pollution exposure to airway and alveolar airway inflammation.

Collective Variational Inference for Personalized and Generative Physiological Modeling: A Case Study on Hemorrhage Resuscitation

OBJECTIVE

Individual physiological experiments typically provide useful but incomplete information about a studied physiological process. As a result, inferring the unknown parameters of a physiological model from experimental data is often challenging. The objective of this paper is to propose and illustrate the efficacy of a collective variational inference (C-VI) method, intended to reconcile low-information and heterogeneous data from a collection of experiments to produce robust personalized and generative physiological models.

METHODS

To derive the C-VI method, we utilize a probabilistic graphical model to impose structure on the available physiological data, and algorithmically characterize the graphical model using variational Bayesian inference techniques. To illustrate the efficacy of the C-VI method, we apply it to a case study on the mathematical modeling of hemorrhage resuscitation.

RESULTS

In the context of hemorrhage resuscitation modeling, the C-VI method could reconcile heterogeneous combinations of hematocrit, cardiac output, and blood pressure data across multiple experiments to obtain (i) robust personalized models along with associated measures of uncertainty and signal quality, and (ii) a generative model capable of reproducing the physiological behavior of the population.

CONCLUSION

The C-VI method facilitates the personalized and generative modeling of physiological processes in the presence of low-information and heterogeneous data.

SIGNIFICANCE

The resulting models provide a solid basis for the development and testing of interpretable physiological monitoring, decision-support, and closed-loop control algorithms.

Taking Kinetic Evaluations of Degradation Data to the Next Level with Nonlinear Mixed-Effects Models

When data on the degradation of a chemical substance have been collected in a number of environmental media (e.g., in different soils), two strategies can be followed for data evaluation. Currently, each individual dataset is evaluated separately, and representative degradation parameters are obtained by calculating averages of the kinetic parameters. However, such averages often take on unrealistic values if certain degradation parameters are ill-defined in some of the datasets. Moreover, the most appropriate degradation model is selected for each individual dataset, which is time consuming and then requires workarounds for averaging parameters from different models. Therefore, a simultaneous evaluation of all available data is desirable. If the environmental media are viewed as random samples from a population, an advanced strategy based on assumptions about the statistical distribution of the kinetic parameters across the population can be used. Here, we show the advantages of such simultaneous evaluations based on nonlinear mixed-effects models that incorporate such assumptions in the evaluation process. The advantages of this approach are demonstrated using synthetically generated data with known statistical properties and using publicly available experimental degradation data on two pesticidal active substances.

Is Brief Exposure to Green Space in School the Best Option to Improve Attention in Children?

The positive effects of Green Spaces on health are thought to be achieved through the mechanisms of mitigation, instoration and restoration. One of the benefits of Green Spaces may be the restoration of attention and so the objective of this research is testing empirically whether exposure to a green environment improves attention in school children. For so doing, we first used a split-unit statistical design in each of four schools, then combined the primary results via meta-analysis. The Attention Network Test (ANT) was used to measure attention before and after exposure and a total of 167 seven-year-old students participated in the experiments. Overall, our experimental results do not support the hypothesis that students’ exposure to activities in green vs. grey spaces affected their performance in ANT. This was so despite the fact that neither age nor gender biases have been detected and despite that our experiments have been proved to be sufficiently statistically powerful. It would be advisable to consider air pollution and noise. We also recommend that participants attend the experiment with mental exhaustion to maximize the ability to detect significant changes.

Timing HIV infection with a simple and accurate population viral dynamics model

Clinical trials for HIV prevention can require knowledge of infection times to subsequently determine protective drug levels. Yet, infection timing is difficult when study visits are sparse. Using population nonlinear mixed-effects (pNLME) statistical inference and viral loads from 46 RV217 study participants, we developed a relatively simple HIV primary infection model that achieved an excellent fit to all data. We also discovered that Aptima assay values from the study strongly correlated with viral loads, enabling imputation of very early viral loads for 28/46 participants. Estimated times between infecting exposures and first positives were generally longer than prior estimates (average of two weeks) and were robust to missing viral upslope data. On simulated data, we found that tighter sampling before diagnosis improved estimation more than tighter sampling after diagnosis. Sampling weekly before and monthly after diagnosis was a pragmatic design for good timing accuracy. Our pNLME timing approach is widely applicable to other infections with existing mathematical models. The present model could be used to simulate future HIV trials and may help estimate protective thresholds from the recently completed antibody-mediated prevention trials.

Stability analysis of clustering of Norris' visual analogue scale: Applying the consensus clustering approach

ABSTRACT

Visual analogue scales are widely used to measure subjective responses. Norris' 16 visual analogue scales (N_VAS) measure subjective feelings of alertness and mood. Up to now, different scientists have clustered items of N_VAS into different ways and Bond and Lader's way has been the most frequently used in clinical research. However, there are concerns about the stability of this clustering over different subject samples and different drug classes. The aim of this study was to test whether Bond and Lader's clustering was stable in terms of subject samples and drug effects. Alternative clustering of N_VAS was tested.Data from studies with 3 types of drugs: cannabinoid receptor agonist (delta-9-tetrahydrocannabinol [THC]), muscarinic antagonist (scopolamine), and benzodiazepines (midazolam and lorazepam), collected between 2005 and 2012, were used for this analysis. Exploratory factor analysis (EFA) was used to test the clustering algorithm of Bond and Lader. Consensus clustering was performed to test the stability of clustering results over samples and over different drug types. Stability analysis was performed using a three-cluster assumption, and then on other alternative assumptions.Heat maps of the consensus matrix (CM) and density plots showed instability of the three-cluster hypothesis and suggested instability over the 3 drug classes. Two- and four-cluster hypothesis were also tested. Heat maps of the CM and density plots suggested that the two-cluster assumption was superior.In summary, the two-cluster assumption leads to a provably stable outcome over samples and the 3 drug types based on the data used.

Machine learning in pharmacometrics: Opportunities and challenges

The explosive growth in medical devices, imaging and diagnostics, computing, and communication and information technologies in drug development and healthcare has created an ever-expanding data landscape that the pharmacometrics (PMX) research community must now traverse. The tools of machine learning (ML) have emerged as a powerful computational approach in other data-rich disciplines but its effective utilization in the pharmaceutical sciences and PMX modelling is in its infancy. ML-based methods can complement PMX modelling by enabling the information in diverse sources of big data, e.g. population-based public databases and disease-specific clinical registries, to be harnessed because they are capable of efficiently identifying salient variables associated with outcomes and delineating their interdependencies. ML algorithms are computationally efficient, have strong predictive capabilities and can enable learning in the big data setting. ML algorithms can be viewed as providing a computational bridge from big data to complement PMX modelling. This review provides an overview of the strengths and weaknesses of ML approaches vis-à-vis population methods, assesses current research into ML applications in the pharmaceutical sciences and provides perspective for potential opportunities and strategies for the successful integration and utilization of ML in PMX.

Learning latent heterogeneity for type 2 diabetes patients using longitudinal health markers in electronic health records

Electronic health records (EHRs) from type 2 diabetes (T2D) patients consist of longitudinally and sparsely measured health markers at clinical encounters. Our goal is to use such data to learn latent patterns that can inform patient's health status related to T2D while accounting for challenges in retrospectively collected EHRs. To handle challenges such as correlated longitudinal measurements, irregular and informative encounter times, and mixed marker types, we propose multivariate generalized linear models to learn latent patient subgroups. In our model, covariate effects were time-dependent and latent Gaussian processes were introduced to model between-marker correlations over time. Using inferred latent processes, we integrated the irregularly measured health markers of mixed types into composite scores and applied hierarchical clustering to learn latent subgroup structures among T2D patients. Application to an EHR dataset of T2D patients showed different trends of age, sex, and race effects on hypertension/high blood pressure, total cholesterol, glycated hemoglobin, high-density lipoprotein, and medications. The associations among these markers varied over time during the study window. Clustering results revealed four subgroups, each with distinct health status. The same patterns were further confirmed using new EHR records of the same cohort. We developed a novel latent model to integrate longitudinal health markers in EHRs and characterize patient latent heterogeneities. Analysis indicated that there were distinct subgroups of T2D patients, suggesting that effective healthcare managements for these patients should be performed separately for each subgroup.

Modeling and characterization of inter-individual variability in CD8 T cell responses in mice

To develop vaccines it is mandatory yet challenging to account for inter-individual variability during immune responses. Even in laboratory mice, T cell responses of single individuals exhibit a high heterogeneity that may come from genetic backgrounds, intra-specific processes (e.g. antigen-processing and presentation) and immunization protocols.

To account for inter-individual variability in CD8 T cell responses in mice, we propose a dynamical model coupled to a statistical, nonlinear mixed effects model. Average and individual dynamics during a CD8 T cell response are characterized in different immunization contexts (vaccinia virus and tumor). On one hand, we identify biological processes that generate inter-individual variability (activation rate of naive cells, the mortality rate of effector cells, and dynamics of the immunogen). On the other hand, introducing categorical covariates to analyze two different immunization regimens, we highlight the steps of the response impacted by immunogens (priming, differentiation of naive cells, expansion of effector cells and generation of memory cells). The robustness of the model is assessed by confrontation to new experimental data.

Our approach allows to investigate immune responses in various immunization contexts, when measurements are scarce or missing, and contributes to a better understanding of inter-individual variability in CD8 T cell immune responses.

Improving convergence in growth mixture models without covariance structure constraints

Growth mixture models are a popular method to uncover heterogeneity in growth trajectories. Harnessing the power of growth mixture models in applications is difficult given the prevalence of nonconvergence when fitting growth mixture models to empirical data. Growth mixture models are rooted in the random effect tradition, and nonconvergence often leads researchers to modify their intended model with constraints in the random effect covariance structure to facilitate estimation. While practical, doing so has been shown to adversely affect parameter estimates, class assignment, and class enumeration. Instead, we advocate specifying the models with a marginal approach to prevent the widespread practice of sacrificing class-specific covariance structures to appease nonconvergence. A simulation is provided to show the importance of modeling class-specific covariance structures and builds off existing literature showing that applying constraints to the covariance leads to poor performance. These results suggest that retaining class-specific covariance structures should be a top priority and that marginal models like covariance pattern growth mixture models that model the covariance structure without random effects are well-suited for such a purpose, particularly with modest sample sizes and attrition commonly found in applications. An application to PTSD data with such characteristics is provided to demonstrate (a) convergence difficulties with random effect models, (b) how covariance structure constraints improve convergence but to the detriment of performance, and (c) how covariance pattern growth mixture models may provide a path forward that improves convergence without forfeiting class-specific covariance structures.

Predicting the Future Course of Opioid Overdose Mortality: An Example From Two US States

BACKGROUND

The rapid growth of opioid abuse and the related mortality across the United States has spurred the development of predictive models for the allocation of public health resources. These models should characterize heterogeneous growth across states using a drug epidemic framework that enables assessments of epidemic onset, rates of growth, and limited capacities for epidemic growth.

METHODS

We used opioid overdose mortality data for 146 North and South Carolina counties from 2001 through 2014 to compare the retrodictive and predictive performance of a logistic growth model that parameterizes onsets, growth, and carrying capacity within a traditional Bayesian Poisson space-time model.

RESULTS

In fitting the models to past data, the performance of the logistic growth model was superior to the standard Bayesian Poisson space-time model (deviance information criterion: 8,088 vs. 8,256), with reduced spatial and independent errors. Predictively, the logistic model more accurately estimated fatality rates 1, 2, and 3 years in the future (root mean squared error medians were lower for 95.7% of counties from 2012 to 2014). Capacity limits were higher in counties with greater population size, percent population age 45-64, and percent white population. Epidemic onset was associated with greater same-year and past-year incidence of overdose hospitalizations.

CONCLUSION

Growth in annual rates of opioid fatalities was capacity limited, heterogeneous across counties, and spatially correlated, requiring spatial epidemic models for the accurate and reliable prediction of future outcomes related to opioid abuse. Indicators of risk are identifiable and can be used to predict future mortality outcomes.

An Algorithm for Nonparametric Estimation of a Multivariate Mixing Distribution with Applications to Population Pharmacokinetics

Population pharmacokinetic (PK) modeling has become a cornerstone of drug development and optimal patient dosing. This approach offers great benefits for datasets with sparse sampling, such as in pediatric patients, and can describe between-patient variability. While most current algorithms assume normal or log-normal distributions for PK parameters, we present a mathematically consistent nonparametric maximum likelihood (NPML) method for estimating multivariate mixing distributions without any assumption about the shape of the distribution. This approach can handle distributions with any shape for all PK parameters. It is shown in convexity theory that the NPML estimator is discrete, meaning that it has finite number of points with nonzero probability. In fact, there are at most N points where N is the number of observed subjects. The original infinite NPML problem then becomes the finite dimensional problem of finding the location and probability of the support points. In the simplest case, each point essentially represents the set of PK parameters for one patient. The probability of the points is found by a primal-dual interior-point method; the location of the support points is found by an adaptive grid method. Our method is able to handle high-dimensional and complex multivariate mixture models. An important application is discussed for the problem of population pharmacokinetics and a nontrivial example is treated. Our algorithm has been successfully applied in hundreds of published pharmacometric studies. In addition to population pharmacokinetics, this research also applies to empirical Bayes estimation and many other areas of applied mathematics. Thereby, this approach presents an important addition to the pharmacometric toolbox for drug development and optimal patient dosing.

Efficient algorithms for covariate analysis with dynamic data using nonlinear mixed-effects model

Nonlinear mixed-effects modeling is one of the most popular tools for analyzing repeated measurement data, particularly for applications in the biomedical fields. Multiple integration and nonlinear optimization are the two major challenges for likelihood-based methods in nonlinear mixed-effects modeling. To solve these problems, approaches based on empirical Bayesian estimates have been proposed by breaking the problem into a nonlinear mixed-effects model with no covariates and a linear regression model without random effect. This approach is time-efficient as it involves no covariates in the nonlinear optimization. However, covariate effects based on empirical Bayesian estimates are underestimated and the bias depends on the extent of shrinkage. Marginal correction method has been proposed to correct the bias caused by shrinkage to some extent. However, the marginal approach appears to be suboptimal when testing covariate effects on multiple model parameters, a situation that is often encountered in real-world data analysis. In addition, the marginal approach cannot correct the inaccuracy in the associated p-values. In this paper, we proposed a simultaneous correction method (nSCEBE), which can handle the situation where covariate analysis is performed on multiple model parameters. Simulation studies and real data analysis showed that nSCEBE is accurate and efficient for both effect-size estimation and p-value calculation compared with the existing methods. Importantly, nSCEBE can be >2000 times faster than the standard mixed-effects models, potentially allowing utilization for high-dimension covariate analysis for longitudinal or repeated measured outcomes.

Fine-Tuning of Energy Levels Regulates SUC2 via a SNF1-Dependent Feedback Loop

Nutrient sensing pathways are playing an important role in cellular response to different energy levels. In budding yeast, Saccharomyces cerevisiae, the sucrose non-fermenting protein kinase complex SNF1 is a master regulator of energy homeostasis. It is affected by multiple inputs, among which energy levels is the most prominent. Cells which are exposed to a switch in carbon source availability display a change in the gene expression machinery. It has been shown that the magnitude of the change varies from cell to cell. In a glucose rich environment Snf1/Mig1 pathway represses the expression of its downstream target, such as SUC2. However, upon glucose depletion SNF1 is activated which leads to an increase in SUC2 expression. Our single cell experiments indicate that upon starvation, gene expression pattern of SUC2 shows rapid increase followed by a decrease to initial state with high cell-to-cell variability. The mechanism behind this behavior is currently unknown. In this work we study the long-term behavior of the Snf1/Mig1 pathway upon glucose starvation with a microfluidics and non-linear mixed effect modeling approach. We show a negative feedback mechanism, involving Snf1 and Reg1, which reduces SUC2 expression after the initial strong activation. Snf1 kinase activity plays a key role in this feedback mechanism. Our systems biology approach proposes a negative feedback mechanism that works through the SNF1 complex and is controlled by energy levels. We further show that Reg1 likely is involved in the negative feedback mechanism.

Piecewise latent growth models: beyond modeling linear-linear processes

Piecewise latent growth models (LGMs) for linear-linear processes have been well-documented and studied in recent years. However, in the latent growth modeling literature, advancements to other functional forms as well as to multiple changepoints or knots have been nearly non-existent. This manuscript deals with three extensions. The first is to a piecewise latent growth model incorporating higher-order polynomials. The second is to extend the basic framework to three phases. The last extension is to inherently nonlinear functions. In these extensions, the changepoint(s) is a parameter to be estimated and may be fixed or allowed to vary across subjects as an application warrants. The approaches are developed and two illustrative empirical examples from psychology are used to highlight the methodological nuances. Annotated statistical software is provided to make these elaborations accessible to practitioners and methodologists.

Quantitative Analysis of Effects of a Single 60Co Gamma Ray Point Exposure on Time-Dependent Change in Locomotor Activity in Rats

Investigating initial behavioral changes caused by irradiation of animals might provide important information to aid understanding of early health effects of radiation exposure and clinical features of radiation injury. Although previous studies in rodents suggested that radiation exposure leads to reduced activity, detailed properties of the effects were unrevealed due to a lack of proper statistical analysis, which is needed to better elucidate details of changes in locomotor activity. Ten-week-old male Wistar rats were subjected to single point external whole-body irradiation with ⁶⁰Co gamma rays at 0, 2.0, 3.5, and 5.0 Gy (four rats per group). Infrared sensors were used to continuously record the locomotor activity of each rat. The cumulative number of movements during the night was defined as "activity" for each day. A non-linear mixed effects model accounting for individual differences and daily fluctuation of activity was applied to analyze the rats' longitudinal locomotor data. Our statistical method revealed characteristics of the changes in locomotor activity after radiation exposure, showing that (1) reduction in activity occurred immediately-and in a dose-dependent manner-after irradiation and (2) recovery to pre-irradiation levels required almost one week, with the same recovery rate in each dose group.

SCEBE: an efficient and scalable algorithm for genome-wide association studies on longitudinal outcomes with mixed-effects modeling

Genome-wide association studies (GWAS) using longitudinal phenotypes collected over time is appealing due to the improvement of power. However, computation burden has been a challenge because of the complex algorithms for modeling the longitudinal data. Approximation methods based on empirical Bayesian estimates (EBEs) from mixed-effects modeling have been developed to expedite the analysis. However, our analysis demonstrated that bias in both association test and estimation for the existing EBE-based methods remains an issue. We propose an incredibly fast and unbiased method (simultaneous correction for EBE, SCEBE) that can correct the bias in the naive EBE approach and provide unbiased P-values and estimates of effect size. Through application to Alzheimer's Disease Neuroimaging Initiative data with 6 414 695 single nucleotide polymorphisms, we demonstrated that SCEBE can efficiently perform large-scale GWAS with longitudinal outcomes, providing nearly 10 000 times improvement of computational efficiency and shortening the computation time from months to minutes. The SCEBE package and the example datasets are available at https://github.com/Myuan2019/SCEBE.

Practical Use of Regularization in Individualizing a Mathematical Model of Cardiovascular Hemodynamics Using Scarce Data

Individualizing physiological models to a patient can enable patient-specific monitoring and treatment in critical care environments. However, this task often presents a unique "practical identifiability" challenge due to the conflict between model complexity and data scarcity. Regularization provides an established framework to cope with this conflict by compensating for data scarcity with prior knowledge. However, regularization has not been widely pursued in individualizing physiological models to facilitate patient-specific critical care. Thus, the goal of this work is to garner potentially generalizable insight into the practical use of regularization in individualizing a complex physiological model using scarce data by investigating its effect in a clinically significant critical care case study of blood volume kinetics and cardiovascular hemodynamics in hemorrhage and circulatory resuscitation. We construct a population-average model as prior knowledge and individualize the physiological model via regularization to illustrate that regularization can be effective in individualizing a physiological model to learn salient individual-specific characteristics (resulting in the goodness of fit to individual-specific data) while restricting unnecessary deviations from the population-average model (achieving practical identifiability). We also illustrate that regularization yields parsimonious individualization of only sensitive parameters as well as adequate physiological plausibility and relevance in predicting internal physiological states.

Ensemble Learning to Improve the Prediction of Fetal Macrosomia and Large-for-Gestational Age

Background: The objective of this study was to investigate the use of ensemble methods to improve the prediction of fetal macrosomia and large for gestational age from prenatal ultrasound imaging measurements. Methods: We evaluated and compared the prediction accuracies of nonlinear and quadratic mixed-effects models coupled with 26 different empirical formulas for estimating fetal weights in predicting large fetuses at birth. The data for the investigation were taken from the Successive Small-for-Gestational-Age-Births study. Ensemble methods, a class of machine learning techniques, were used to improve the prediction accuracies by combining the individual models and empirical formulas. Results: The prediction accuracy of individual statistical models and empirical formulas varied considerably in predicting macrosomia but varied less in predicting large for gestational age. Two ensemble methods, voting and stacking, with model selection, can combine the strengths of individual models and formulas and can improve the prediction accuracy. Conclusions: Ensemble learning can improve the prediction of fetal macrosomia and large for gestational age and have the potential to assist obstetricians in clinical decisions.

A novel quantification of information for longitudinal data analyzed by mixed-effects modeling

Nonlinear mixed-effects (NLME) modeling is one of the most powerful tools for analyzing longitudinal data especially under the sparse sampling design. The determinant of the Fisher information matrix is a commonly used global metric of the information that can be provided by the data under a given model. However, in clinical studies, it is also important to measure how much information the data provide for a certain parameter of interest under the assumed model, for example, the clearance in population pharmacokinetic models. This paper proposes a new, easy-to-interpret information metric, the "relative information" (RI), which is designed for specific parameters of a model and takes a value between 0% and 100%. We establish the relationship between interindividual variability for a specific parameter and the variance of the associated parameter estimator, demonstrating that, under a "perfect" experiment (eg, infinite samples or/and minimum experimental error), the RI and the variance of the model parameter estimator converge, respectively, to 100% and the ratio of the interindividual variability for that parameter and the number of subjects. Extensive simulation experiments and analyses of three real datasets show that our proposed RI metric can accurately characterize the information for parameters of interest for NLME models. The new information metric can be readily used to facilitate study designs and model diagnosis.

Latent process model of the 6-minute walk test in Duchenne muscular dystrophy : A Bayesian approach to quantifying rare disease progression

Duchenne muscular dystrophy (DMD) is a rare X-linked genetic pediatric disease characterized by a lack of functional dystrophin production in the body, resulting in muscle deterioration. Lower body muscle weakness progresses to non-ambulation typically by early teenage years, followed by upper body muscle deterioration and ultimately death by the late twenties. The objective of this study was to enhance the quantitative understanding of DMD disease progression through nonlinear mixed effects modeling of the population mean and variability of the 6-min walk test (6MWT) clinical endpoint. An indirect response model with a latent process was fit to digitized literature data using full Bayesian estimation. The modeling data set consisted of 22 healthy controls and 218 DMD patients from one interventional and four observational trials. The model reasonably described the central tendency and population variability of the 6MWT in healthy subjects and DMD patients. An exploratory categorical covariate analysis indicated that there was no apparent effect of corticosteroid administration on DMD disease progression. The population predicted 6MWT began to rise at 1.32 years of age, plateauing at 654 meters (m) at 17.2 years of age for the healthy population. The DMD trajectory reached a maximum of 411 m at 8.90 years before declining and falling below 1 m at age 18.0. The model has potential to be used as a Bayesian estimation and posterior simulation tool to make informed model-based drug development decisions that incorporate prior knowledge with new data.