A Cautionary Note on Using Propensity Score Calibration to Control for Unmeasured Confounding Bias When the Surrogacy Assumption Is Absent

Conventional propensity score methods encounter challenges when unmeasured confounding is present, as it becomes impossible to accurately estimate the gold-standard propensity score when data on certain confounders are unavailable. Propensity score calibration (PSC) addresses this issue by constructing a surrogate for the gold-standard propensity score under the surrogacy assumption. This assumption posits that the error-prone propensity score, based on observed confounders, is independent of the outcome when conditioned on the gold-standard propensity score and the exposure. However, this assumption implies that confounders cannot directly impact the outcome and that their effects on the outcome are solely mediated through the propensity score. This raises concerns regarding the applicability of PSC in practical settings where confounders can directly affect the outcome. While PSC aims to target a conditional treatment effect by conditioning on a subject's unobservable propensity score, the causal interest in the latter case lies in a conditional treatment effect conditioned on a subject's baseline characteristics. Our analysis reveals that PSC is generally biased unless the effects of confounders on the outcome and treatment are proportional to each other. Furthermore, we identify 2 sources of bias: 1) the noncollapsibility of effect measures, such as the odds ratio or hazard ratio and 2) residual confounding, as the calibrated propensity score may not possess the properties of a valid propensity score.

In Vitro Digestibility and Models of Cumulative Gas Production of Forage-Free Diet

Our objectives were to evaluate the use of cottonseed cake in replacing corn silage in a diet without forage and to identify the model with higher precision and accuracy of adjustment of parameters of ruminal degradation kinetics. A diet containing corn silage and another with cottonseed cake as a fiber source were formulated. Gompertz, Dual-pool Logistic, Brody, and Ørskov models were evaluated for goodness of fit to gas production. There were significant differences in dry matter (DM), organic matter (OM), and neutral detergent fiber (NDF) in the in vitro digestibility for diets and fiber sources. The estimated values of the Gompertz (6.77), Brody (6.72), and Ørskov (6.73) models were similar to the observed mean of gas production in the corn silage diet (6.73 mL/100 mg DM). Similarly, the estimated values of the Brody (5.87) and Ørskov (5.89) models were similar to the observed mean of gas production in the cottonseed cake diet (5.87 mL/100 mg DM). The roughage-free diet containing cottonseed cake as a fiber source stimulated higher gas production. Brody and Ørskov models presented higher precision and accuracy in the fitting of kinetics of degradation independent of the fiber source in the diet.

Comparison of Nonlinear Growth Models to Estimate Growth Curves in Kivircik Sheep under a Semi-Intensive Production System

The Kivircik is an indigenous sheep breed from Turkey, and it has superior meat quality compared to other indigenous breeds. Therefore, farmers prioritize Kivircik lamb fattening instead of milk production. Here, we aimed to determine the best nonlinear growth model, i.e., Gompertz, Logistic, Von Bertalanffy, and Brody, to describe the growth curve of Kivircik lambs. The body weight data from birth until 150 days of age belonging to 612 lambs were used as the material of this study. The best fitting model was selected by considering the adjusted coefficient of determination (R²_adj), residual mean square, and Akaike's (AIC) and Bayesian information criteria (BIC). Even though the Brody model had a better statistical fit, considering its biological interpretation, the Gompertz model was identified as an appropriate model for describing Kivircik lamb growth. Male lambs, twin lambs, and lambs born in winter had higher mature live weights (44.2 kg, 71.2 kg, and 38.5 kg, respectively) and rate of weight gain (2.1, 2.6, and 2.0, respectively). However, our subgroups revealed a similar rate of maturity (0.01). Growth models are important tools for deciding the optimal slaughter age and they provide valuable information on the management practices of both sexes, birth types, and birth seasons. These results can be applied to breeding programs for early selection, enabling intervention strategies when needed.

Pharmacokinetic Model of Tenofovir and Emtricitabine and Their Intracellular Metabolites in Patients in the ANRS 134-COPHAR 3 Trial Using Dose Records

Tenofovir (TFV) and emtricitabine (FTC) are part of the recommended highly active antiretroviral therapy (ART). Both molecules show a large interindividual pharmacokinetic (PK) variability. Here, we modeled the concentrations of plasma TFV and FTC and their intracellular metabolites (TFV diphosphate [TFV-DP] and FTC triphosphate [FTC-TP]) collected after 4 and 24 weeks of treatment in 34 patients from the ANRS 134-COPHAR 3 trial. These patients received daily (QD) atazanavir (300 mg), ritonavir (100 mg), and a fixed-dose combination of coformulated TFV disoproxil fumarate (300 mg) and FTC (200 mg). Dosing history was collected using a medication event monitoring system. A three-compartment model with absorption delay (Tlag) was selected to describe the PK of, respectively, TFV/TFV-DP and FTC/FTC-TP. TFV and FTC apparent clearances, 114 L/h (relative standard error [RSE] = 8%) and 18.1 L/h (RSE = 5%), respectively, were found to decrease with age. However, no significant association was found with the polymorphisms ABCC2 rs717620, ABCC4 rs1751034, and ABCB1 rs1045642. The model allows prediction of TFV-DP and FTC-TP concentrations at steady state with alternative regimens.

Causality Analysis with Information Geometry: A Comparison

The quantification of causality is vital for understanding various important phenomena in nature and laboratories, such as brain networks, environmental dynamics, and pathologies. The two most widely used methods for measuring causality are Granger Causality (GC) and Transfer Entropy (TE), which rely on measuring the improvement in the prediction of one process based on the knowledge of another process at an earlier time. However, they have their own limitations, e.g., in applications to nonlinear, non-stationary data, or non-parametric models. In this study, we propose an alternative approach to quantify causality through information geometry that overcomes such limitations. Specifically, based on the information rate that measures the rate of change of the time-dependent distribution, we develop a model-free approach called information rate causality that captures the occurrence of the causality based on the change in the distribution of one process caused by another. This measurement is suitable for analyzing numerically generated non-stationary, nonlinear data. The latter are generated by simulating different types of discrete autoregressive models which contain linear and nonlinear interactions in unidirectional and bidirectional time-series signals. Our results show that information rate causalitycan capture the coupling of both linear and nonlinear data better than GC and TE in the several examples explored in the paper.

Review of linear and nonlinear models in breath analysis by Cyranose 320

BACKGROUND

Analysis of volatile organic compounds (VOC) in breath specimens has potential for point of care (POC) screening due to ease of sample collection. While the electronic nose (e-nose) is a standard VOC measure across a wide range of industries, it has not been adopted for POC screening in healthcare. One limitation of the e-nose is the absence of mathematical models of data analysis that yield easily interpreted findings at POC. The purposes of this review were to (1) examine the sensitivity/specificity results from studies that analyzed breath smellprints using the Cyranose 320, a widely used commercial e-nose, and (2) determine whether linear or nonlinear mathematical models are superior for analyzing Cyranose 320 breath smellprints.
Methods: This systematic review was conducted according to the guidelines of the Preferred Reporting Items for Systematic Review and Meta-Analyses using keywords related to e-nose and breath. 
Results: Twenty-two articles met the eligibility criteria. Two studies used a linear model while the rest used nonlinear models. The two studies that used a linear model had a smaller range for median of sensitivity and higher median (71% - 96%; Mdn = 83.5%) compared to the studies that used nonlinear models (46% - 100%; Mdn = 74%). Additionally, studies that used linear models had a smaller range for median of specificity but lower median (70% - 92%; Mdn = 81%) compared to studies that used nonlinear models (57% - 97%; Mdn = 83%).
Conclusions: Linear models achieved smaller ranges for medians of sensitivity and specificity compared to nonlinear models supporting additional investigations of their use for POC testing. Because our findings were derived from studies of heterogenous medical conditions, it is not known if they generalize to specific diagnoses.

Estimating Shelf Life Through Tolerance Intervals Extended to Nonlinear Response Trends

Methods for estimating pharmaceutical shelf life based on tolerance intervals are proposed by Schwenke, et al. AAPS PharmSciTech. 2020;21:290, [1] where a critical quality attribute that follows a simple linear (straight line) response trend across storage time is presented as the traditional example. A random coefficient mixed linear regression model is used to characterize the between batch and within batch variation. These methods are further discussed for various stability study scenarios, number of stability batches, and levels of assumed risk in Schwenke, et al. AAPS PharmSciTech. 2021;22:273, [4] through a simulation study, again based on a critical quality attribute assuming a simple linear response. However, in practice, not all stability response profiles conveniently follow straight line or linear trends. The purpose of this paper is to extend the proposed tolerance interval and random coefficient mixed regression methods for estimating pharmaceutical shelf life to critical quality attributes that follow more complex stability response profiles. As an example, a nonlinear response is typically characterized by either an increasing or decreasing response, starting from an initial concentration, trending with storage time towards some limiting response or asymptote. Nonlinear responses cannot be statistically analyzed with linear model methods. Practical information supported by simulation results based on a pharmaceutical stability study are discussed to allow for appropriate statistical analyses and shelf life estimates through random coefficient mixed nonlinear regression and tolerance interval methods.

Population total and unbound pharmacokinetics and pharmacodynamics of ciprofol and M4 in subjects with various renal functions

AIMS

The aim of this study was to develop a population pharmacokinetic (PK) model to simultaneously describe both total and unbound concentrations of ciprofol and its major glucuronide metabolite, M4, and to link it to the population pharmacodynamics (PD) model in subjects with various renal functions.

METHODS

A total of 401 and 459 pairs of total and unbound plasma concentrations of ciprofol and M4, respectively, as well as 2190 bispectral index (BIS) data from 24 Chinese subjects with various renal functions were available. Covariates that may potentially contribute to the PK and PD variability of ciprofol were screened using a stepwise procedure. The optimal ciprofol induction dosing regimen was determined by model-based simulations.

RESULTS

The PK of unbound ciprofol could best be described by a three-compartment model, while a two-compartment model could adequately describe unbound M4 PK. The concentrations of total and unbound ciprofol and M4 were linked using a linear protein binding model. The relationship between plasma concentrations of ciprofol and BIS data was best described by an inhibitory sigmoidal E_max model with a two-compartment biophase distribution compartment. Hemoglobin was the identified covariate determining the central compartment clearance of ciprofol; uric acid was a covariate affecting the central compartment clearance of M4 and protein binding rate, k_B . The included covariates had no effect on the PD of ciprofol. Simulation results indicated that the label-recommended dose regimen was adequate for anaesthesia induction.

CONCLUSIONS

The developed model fully characterized the population PK and PD profiles of ciprofol. No dose adjustment is required in patients with mild and moderate renal impairment.

Relationships between body- and udder-related type traits with somatic cell counts and potential use for an early selection method for water buffaloes (Bubalus bubalis)

Water buffalo milk is a reliable source of high-quality nutrients; however, the susceptibility of mastitis in buffaloes must be taken into consideration. An animal with somatic cell count (SCC) of greater than 250,000 cells/mL is reported to be likely to have mastitis which has serious adverse effects on animal health, reproduction, milk yield, and milk quality. Type traits (TTs) of water buffalo can affect SCC in animal milk to some extent, but few reports on the correlation between SCC and TTs are available. In this study, a total of 1908 records collected from 678 water buffaloes were investigated. The general linear model was used to identify factors associated with phenotypic variation of the somatic cell score (SCS) trait, including parity, lactation length, calving year, and calving season as fixed effects. Using PROC CORR analysis method, taking calving year and lactation length as covariates, the correlation co-efficient between TT and SCS was obtained. Our results showed that correlation co-efficients between the 45 TTs with SCS ranged from 0.003 to 0.443 (degree of correlation). The correlation between udder traits and SCS was greater than that between body structure traits and SCS. Among udder traits, distance between teats (including front and rear teat distance [r = 0.308], front teat distance [r = 0.211], and teat crossing distance [r = 0.412]) and teat circumference (r = 0.443) had the highest correlation with SCS, followed by the leg traits including rear leg height (r = -0.354) and hock bend angle (r = -0.170). Animal with high rear legs (>48 cm) and short teat crossing distance (<17 cm), and narrow teat circumference (<11 cm) exhibited low SCS. Using four nonlinear models (Von Bertalanffy, Brody, Logistic, and Gompertz), the optimal growth curves of the TTs highly correlated with the SCS (rear leg height and teat crossing distance) were fitted, and the correction co-efficients of these two TTs rear leg height and teat crossing distance of animal from young age (2 mo old) to first lactation (35 mo old) were attained for establishment of early selection method for water buffaloes with low SCS. This study provides theoretical support for early selection of low-SCS water buffaloes and lays a foundation for improving milk quality and promoting healthy development of water buffalo's dairy industry.

Growth and growth curve analysis in Dorper × Tumele crossbred sheep under a smallholder management system

This study aimed to evaluate the growth performance and Kleiber ratio (KR) and to determine the growth curve of Dorper × Tumele sheep under a smallholder management system. Growth and efficiency-related traits were analyzed by using the general linear model (GLM) procedure of SAS. Gompertz, Logistics, Brody, Monomolecular, and Negative exponential models were used to determine the growth curve, and growth curve parameters were estimated via the nonlinear regression model (NLIN) procedure of SAS. The overall least-squares means of the birth weight, weaning weight, 6-month weight, and yearling weight were 3.29, 13.7, 17.3, and 23.4 kg, respectively. Dorper × Tumele lambs grew faster during the preweaning period (115.3 ± 1.19 g day^-1) than during the postweaning periods (44.1 ± 1.26 g day^-1 to 33.5 ± 1.13 g day^-1). Likewise, a higher KR was observed during the pre-weaning age (16.1 ± 0.08 g/day/kg^0.75) than during postweaning periods (5.08 ± 0.13 g/day/kg^0.75 to 3.10 ± 0.09 g/day/kg^0.75). Brody, a model without an inflection point was the best-fitted growth function for Dorper × Tumele sheep under a smallholder management system. The highest and lowest asymptotic weight was observed for Brody (23.8 ± 0.22 kg) and Logistics (20.7 ± 0.11 kg) models, respectively. The maturation rate ranged between 0.21 (Brody) and 0.66 (Logistics). Based on the Brody model, the correlation between asymptotic weight and maturity rate was -0.92. The growth parameter estimate in this study indicates that Dorper × indigenous sheep had a better speed to achieve mature weight and the early mature crossbred sheep are less likely to exhibit high adult weight. The rapid growth of crossbred sheep during the early period can provide more profit to the farmer by reducing the cost of sheep production inputs. Therefore, crossing Tumele with Dorper sheep and integrating with improved management would be suggested to improve productivity and profit from sheep production.

Temperature-Dependent Development Models Describing the Effects of Temperature on the Development of the Fall Armyworm Spodoptera frugiperda (J. E. Smith) (Lepidoptera: Noctuidae)

The fall armyworm Spodoptera frugiperda (J.E. Smith) is an economically important pest that recently invaded Africa and Asia; however, information regarding its biological capacity to establish itself in newly invaded environments is largely unknown. We investigated the effects of temperature on the development and survival of the invaded populations of S. frugiperda and selected mathematical models to evaluate its development in a new environment. S. frugiperda exhibited optimum survival and growth at temperatures between 28 °C and 30 °C. The lower and upper thermal thresholds for the egg-to-adult life cycle were 13.51 °C and 34.13 °C, respectively. We compared seven mathematical models and found that the Shi model was the most suitable for describing the temperature-dependent development rate of S. frugiperda. Therefore, the Shi mathematical model may be used to predict both the occurrence of particular developmental stages and the geographic distribution to implement measures for the management of S. frugiperda in agricultural fields.

Multibody-Based Input and State Observers Using Adaptive Extended Kalman Filter

The aim of this work is to explore the suitability of adaptive methods for state estimators based on multibody dynamics, which present severe non-linearities. The performance of a Kalman filter relies on the knowledge of the noise covariance matrices, which are difficult to obtain. This challenge can be overcome by the use of adaptive techniques. Based on an error-extended Kalman filter with force estimation (errorEKF-FE), the adaptive method known as maximum likelihood is adjusted to fulfill the multibody requirements. This new filter is called adaptive error-extended Kalman filter (AerrorEKF-FE). In order to present a general approach, the method is tested on two different mechanisms in a simulation environment. In addition, different sensor configurations are also studied. Results show that, in spite of the maneuver conditions and initial statistics, the AerrorEKF-FE provides estimations with accuracy and robustness. The AerrorEKF-FE proves that adaptive techniques can be applied to multibody-based state estimators, increasing, therefore, their fields of application.

Time-Delay Identification Using Multiscale Ordinal Quantifiers

Time-delayed interactions naturally appear in a multitude of real-world systems due to the finite propagation speed of physical quantities. Often, the time scales of the interactions are unknown to an external observer and need to be inferred from time series of observed data. We explore, in this work, the properties of several ordinal-based quantifiers for the identification of time-delays from time series. To that end, we generate artificial time series of stochastic and deterministic time-delay models. We find that the presence of a nonlinearity in the generating model has consequences for the distribution of ordinal patterns and, consequently, on the delay-identification qualities of the quantifiers. Here, we put forward a novel ordinal-based quantifier that is particularly sensitive to nonlinearities in the generating model and compare it with previously-defined quantifiers. We conclude from our analysis on artificially generated data that the proper identification of the presence of a time-delay and its precise value from time series benefits from the complementary use of ordinal-based quantifiers and the standard autocorrelation function. We further validate these tools with a practical example on real-world data originating from the North Atlantic Oscillation weather phenomenon.

Identifying treatment effect heterogeneity in dose-finding trials using Bayesian hierarchical models

An important task in drug development is to identify patients, which respond better or worse to an experimental treatment. Identifying predictive covariates, which influence the treatment effect and can be used to define subgroups of patients, is a key aspect of this task. Analyses of treatment effect heterogeneity are however known to be challenging, since the number of possible covariates or subgroups is often large, while samples sizes in earlier phases of drug development are often small. In addition, distinguishing predictive covariates from prognostic covariates, which influence the response independent of the given treatment, can often be difficult. While many approaches for these types of problems have been proposed, most of them focus on the two-arm clinical trial setting, where patients are given either the treatment or a control. In this article we consider parallel groups dose-finding trials, in which patients are administered different doses of the same treatment. To investigate treatment effect heterogeneity in this setting we propose a Bayesian hierarchical dose-response model with covariate effects on dose-response parameters. We make use of shrinkage priors to prevent overfitting, which can easily occur, when the number of considered covariates is large and sample sizes are small. We compare several such priors in simulations and also investigate dependent modeling of prognostic and predictive effects to better distinguish these two types of effects. We illustrate the use of our proposed approach using a Phase II dose-finding trial and show how it can be used to identify predictive covariates and subgroups of patients with increased treatment effects.

Genetic and phenotypic parameters for body weights, harvest length, and growth curve parameters in American mink

Understanding the genetics underlying growth curve is important for selection of animals with better growth potential, but little is known about the genetics of growth curve parameters in mink. This study estimated the genetic parameters for body weights (BWs), harvest length (HL), and growth parameters derived from the Richards model. For this purpose, individual BW of 1,088 mink measured seven times in 3-wk intervals (weeks 13 to 31 of life) were used for growth curve modeling using the Richards model. The BW traits included BW at week 13 (BW13), 16 (BW16), 19 (BW19), 22 (BW22), 25 (BW25), 28 (BW28), and 31 (BW31). Univariate analyses indicated that sex and birth-year had significant effects (P < 0.05) on BW, HL, asymptotic weight (α), growth rate at mature (k), shape parameter (m), weight at the inflection point (WIP), and age at the inflection point (AIP). In contrast, the color type had only significant effect (P < 0.05) on BW31 and HL. Estimated heritabilities (±SE) were ranged from 0.36 ± 0.13 (BW13) to 0.46 ± 0.10 (BW22) for BW and were 0.51 ± 0.09, 0.29 ± 0.09, 0.30 ± 0.09, 0.33 ± 0.1, 0.44 ± 0.10, and 0.47 ± 0.10 for HL, α, k, m, WIP, and AIP, respectively. The parameter α had non-significant (P > 0.05) genetic correlations (±SE) with k (-0.21 ± 0.23) and m (-0.10 ± 0.22), suggesting that changing shape parameters (k and m) will not influence asymptotic weight (α). Strong significant (P < 0.05) phenotypic (from 0.46 ± 0.03 to 0.60 ± 0.03) and genetic (0.70±0.13 to 0.88±0.09) correlations were observed between HL and different BW measures. The α, AIP, and WIP parameters had significant (P < 0.05) genetic correlations with HL indicated that selection for higher α, AIP, and WIP values would increase HL. Parameters k and m had nonsignificant (P > 0.05) genetic correlations with HL, indicating the change of the curve shape could not influence HL. Overall, the results suggest that growth curve parameters are heritable and can respond to genetic or genomic selection for optimizing the performance in mink.

Associations between developmental trajectories of peer victimization, hair cortisol, and depressive symptoms: a longitudinal study

BACKGROUND

Peer victimization has been associated with long-lasting risks for mental health. Prior research suggests that stress-related systems underlying adaptation to changing environments may be at play. To date, inconsistent findings have been reported for the hypothalamic-pituitary-adrenal (HPA) axis, and its end product cortisol. This study tested whether peer victimization was associated with hair cortisol concentrations (HCC), and whether this association varied according to sex, timing, and changes in exposure. We also examined whether peer victimization differentially predicted depressive symptoms according to HCC.

METHODS

The sample comprised 556 adolescents (42.0%; 231 males) who provided hair for cortisol measurement at 17 years of age. Peer victimization was reported at seven occasions between the ages of 6 and 15 years.

RESULTS

Peer victimization was nonlinearly associated with HCC for boys only, whereas changes in peer victimization were related to HCC for boys and girls. Peer victimization predicted more depressive symptoms for all participants, except those with lower HCC.

CONCLUSIONS

Our findings provide further support for persistent dysregulation of the HPA axis following exposure to chronic adversity, of which the expression may change according to sex and the severity of victimization.

A review on nonlinear DNA physics

The study and the investigation of structural and dynamical properties of complex systems have attracted considerable interest among scientists in general and physicists and biologists in particular. The present review paper represents a broad overview of the research performed over the nonlinear dynamics of DNA, devoted to some different aspects of DNA physics and including analytical, quantum and computational tools to understand nonlinear DNA physics. We review in detail the semi-discrete approximation within helicoidal Peyrard-Bishop model and show that localized modulated solitary waves, usually called breathers, can emerge and move along the DNA. Since living processes occur at submolecular level, we then discuss a quantum treatment to address the problem of how charge and energy are transported on DNA and how they may play an important role for the functioning of living cells. While this problem has attracted the attention of researchers for a long time, it is still poorly understood how charge and energy transport can occur at distances comparable to the size of macromolecules. Here, we review a theory based on the mechanism of 'self-trapping' of electrons due to their interaction with mechanical (thermal) oscillation of the DNA structure. We also describe recent computational models that have been developed to capture nonlinear mechanics of DNA in vitro and in vivo, possibly under topological constraints. Finally, we provide some conjectures on potential future directions for this field.

Architectures for Combined Transcriptional and Translational Resource Allocation Controllers

Recent work on engineering synthetic cellular circuitry has shown that non-regulatory interactions mediated by competition for gene expression resources can result in degraded performance or even failure. Transcriptional and translational resource allocation controllers based on orthogonal circuit-specific gene expression machinery have separately been shown to improve modularity and circuit performance. Here, we investigate the potential advantages, challenges, and design trade-offs involved in combining transcriptional and translational controllers into a "dual resource allocation control system." We show that separately functional, translational, and transcriptional controllers cannot generally be combined without extensive redesign. We analyze candidate architectures for direct design of dual resource allocation controllers and propose modifications to improve their performance (in terms of decoupling and expression level) and robustness. We show that dual controllers can be built that are composed only of orthogonal gene expression resources and demonstrate that such designs offer both superior performance and robustness characteristics.

Bayesian pooling versus sequential integration of small preclinical trials: a comparison within linear and nonlinear modeling frameworks

Bayesian sequential integration is an appealing approach in drug development, as it allows to recursively update posterior distributions as soon as new data become available, thus considerably reducing the computation time. However, preclinical trials are often characterized by small sample sizes, which may affect the estimation process during the first integration steps, particularly when complex PK-PD models are used. In this case, sequential integration would not be practicable, and trials should be pooled together. This work is aimed at comparing simple Bayesian pooling with sequential integration through a simulation study. The two techniques are compared under several scenarios using linear as well as nonlinear models. The results of our simulation study encourage the use of Bayesian sequential integration with linear models. However, in the case of nonlinear models several caveats arise. This paper outlines some important recommendations and precautions in that respect.

Genomic predictions of growth curves in Holstein dairy cattle based on parameter estimates from nonlinear models combined with different kernel functions

Availability of longitudinal body weight (BW) records allows the application of nonlinear models (NLINM) to predict phenotypic and genomic growth curves in dairy cattle. In this regard, we considered a data set including 31,722 BW records from 4,952 female Holstein cattle, during the period from birth (mo 0) to approximately age at first calving (mo 24). Parameters of the growth curves were estimated using 3 NLINM: the logistic (LOG), the Gompertz (GOM), and the Richards (RICH) functions. Residuals for the growth curve parameters from the NLINM applications were used as pseudo-phenotypes in the ongoing genomic analyses with different similarity matrices, including 2 genomic relationship matrices (G1 and G2), a combined pedigree and genomic relationship matrix (H), and 3 kernel matrices. The kernels were a weighted "alike by state" kernel function (K1), an exponential dissimilarity kernel (K2), and a Gaussian kernel (K3). On the basis of G1 and G2 matrices, genomic heritabilities for the growth curve parameters birth weight (W₀), mature weight (W_m), and growth rate (k), and the shape parameter (m; only available from RICH) were moderate to large, in the range from 0.29 (m from RICH) to 0.46 (k from RICH). Fitting the similarity matrices based on kernel functions contributed to an increase of the ratio of the variance explained by the similarity matrix in relation to the total variance (compared with the heritability when modeling G1 or G2). Genetic correlations between W₀, W_m, and k were always positive (>0.30), especially for the same growth curve parameters estimated from different NLINM (>0.90). The shape parameter m from RICH was negatively correlated with other growth curve parameters, from -0.29 to -0.95. In a next step, estimated genomic breeding values for growth curve parameters were input data for the respective NLINM, aiming to construct genomic growth curves. Prediction accuracies were correlations between genomic growth curves and genomic breeding values from random regression models for sires and female cattle. Considering all genotyped female cattle with pseudo-phenotypes, prediction accuracies were larger from RICH than from LOG and GOM. However, differences in prediction accuracies from the NLINM × similarity matrix combinations were quite small. Accordingly, in 5-fold cross-validations using heifer groups with masked phenotypes, very similar prediction accuracies across modeling approaches were identified. Especially for specific age months, genomic growth curve predictions were more accurate for sires than for female cattle, indicating that the relationships between animals in training and validation sets are more important than the selection of specific NLINM × similarity matrix combinations.

Application of conditional robust calibration to ordinary differential equations models in computational systems biology: a comparison of two sampling strategies

Mathematical modelling is a widely used technique for describing the temporal behaviour of biological systems. One of the most challenging topics in computational systems biology is the calibration of non-linear models; i.e. the estimation of their unknown parameters. The state-of-the-art methods in this field are the frequentist and Bayesian approaches. For both of them, the performance and accuracy of results greatly depend on the sampling technique employed. Here, the authors test a novel Bayesian procedure for parameter estimation, called conditional robust calibration (CRC), comparing two different sampling techniques: uniform and logarithmic Latin hypercube sampling. CRC is an iterative algorithm based on parameter space sampling and on the estimation of parameter density functions. They apply CRC with both sampling strategies to the three ordinary differential equations (ODEs) models of increasing complexity. They obtain a more precise and reliable solution through logarithmically spaced samples.

Comparison of four nonlinear growth models in Creole chickens of Mexico

Animal growth is a complex and dynamic process that involves physiological and morphological changes from hatching to maturity. It is defined as the increase in body size per time unit. Mathematical functions, called growth models, have been used to explain growth patterns. The aim of this study was to compare the Gompertz-Laird, logistic, Richards, and Von Bertalanffy growth models to determine which best fits the data of the Creole chickens (CC). Three hundred forty-seven CC were individually weighed from hatching until 177 D of age. Birds were fed a starter diet (0–18 D of age; 19% crude protein (CP) and 3,000 kcal of ME/kg) and grower diet (19–177 D of age; 18% CP and 2,800 kcal of ME/kg). Data were analyzed using PROC NLIN to fit the nonlinear growth curve. The coefficient of determination (R²), Akaike information criteria (AIC), and Bayesian information criteria (BIC) were used to compare the goodness of fit of the models. The Von Bertalanffy (R²: 0.9382, 0.9415; AIC: 2,224.1, 2,424.8; BIC: 2,233.5, 2,434.3, for females and males, respectively) was the model that best explained growth of the birds. On the other hand, both the Gompertz-Laird and logistic models overestimated hatching BW and underestimated the final BW of CC. Females reached age of maximum growth faster than males. The asymptotic weight was higher in males (3,011 g) than in females (2,011 g). Body weight at inflection point was 892 g at 64 D of age for males and 596 g at 54 D for females. In conclusion, the best fit of the data was obtained with the Von Bertalanffy growth model; the information is intended to serve as the basis for utilizing CC.

Nonlinear Structural Vector Autoregressive Models with Application to Directed Brain Networks

Structural equation models (SEMs) and vector autoregressive models (VARMs) are two broad families of approaches that have been shown useful in effective brain connectivity studies. While VARMs postulate that a given region of interest in the brain is directionally connected to another one by virtue of time-lagged influences, SEMs assert that directed dependencies arise due to instantaneous effects, and may even be adopted when nodal measurements are not necessarily multivariate time series. To unify these complementary perspectives, linear structural vector autoregressive models (SVARMs) that leverage both instantaneous and time-lagged nodal data have recently been put forth. Albeit simple and tractable, linear SVARMs are quite limited since they are incapable of modeling nonlinear dependencies between neuronal time series. To this end, the overarching goal of the present paper is to considerably broaden the span of linear SVARMs by capturing nonlinearities through kernels, which have recently emerged as a powerful nonlinear modeling framework in canonical machine learning tasks, e.g., regression, classification, and dimensionality reduction. The merits of kernel-based methods are extended here to the task of learning the effective brain connectivity, and an efficient regularized estimator is put forth to leverage the edge sparsity inherent to real-world complex networks. Judicious kernel choice from a preselected dictionary of kernels is also addressed using a data-driven approach. Numerical tests on ECoG data captured through a study on epileptic seizures demonstrate that it is possible to unveil previously unknown directed links between brain regions of interest.

A Fractional-Order Partially Non-Linear Model of a Laboratory Prototype of Hydraulic Canal System

This article addresses the identification of the nonlinear dynamics of the main pool of a laboratory hydraulic canal installed in the University of Castilla La Mancha. A new dynamic model has been developed by taking into account the measurement errors caused by the different parts of our experimental setup: (a) the nonlinearity associated to the input signal, which is caused by the movements of the upstream gate, is avoided by using a nonlinear equivalent upstream gate model, (b) the nonlinearity associated to the output signal, caused by the sensor’s resolution, is avoided by using a quantization model in the identification process, and (c) the nonlinear behaviour of the canal, which is related to the working flow regime, is taken into account considering two completely different models in function of the operating regime: the free and the submerged flows. The proposed technique of identification is based on the time-domain data. An input pseudo-random binary signal (PRBS) is designed depending on the parameters of an initially estimated linear model that was obtained by using a fundamental technique of identification. Fractional and integer order plus time delay models are used to approximate the responses of the main pool of the canal in its different flow regimes. An accurate model has been obtained, which is composed of two submodels: a first order plus time delay submodel that accurately describes the dynamics of the free flow and a fractional-order plus time delay submodel that properly describes the dynamics of the submerged flow.

Nonlinear Predictive Models for Multiple Mediation Analysis: With an Application to Explore Ethnic Disparities in Anxiety and Depression Among Cancer Survivors

Mediation analysis allows the examination of effects of a third variable (mediator/confounder) in the causal pathway between an exposure and an outcome. The general multiple mediation analysis method (MMA), proposed by Yu et al., improves traditional methods (e.g., estimation of natural and controlled direct effects) to enable consideration of multiple mediators/confounders simultaneously and the use of linear and nonlinear predictive models for estimating mediation/confounding effects. Previous studies find that compared with non-Hispanic cancer survivors, Hispanic survivors are more likely to endure anxiety and depression after cancer diagnoses. In this paper, we applied MMA on MY-Health study to identify mediators/confounders and quantify the indirect effect of each identified mediator/confounder in explaining ethnic disparities in anxiety and depression among cancer survivors who enrolled in the study. We considered a number of socio-demographic variables, tumor characteristics, and treatment factors as potential mediators/confounders and found that most of the ethnic differences in anxiety or depression between Hispanic and non-Hispanic white cancer survivors were explained by younger diagnosis age, lower education level, lower proportions of employment, less likely of being born in the USA, less insurance, and less social support among Hispanic patients.

Novel Modelling Approaches to Characterize and Quantify Carryover Effects on Sensory Acceptability

Sensory biases caused by the residual sensations of previously served samples are known as carryover effects (COE). Contrast and convergence effects are the two possible outcomes of carryover. COE can lead to misinterpretations of acceptability, due to the presence of intrinsic psychological/physiological biases. COE on sensory acceptability (hedonic liking) were characterized and quantified using mixed and nonlinear models. N = 540 subjects evaluated grape juice samples of different acceptability qualities (A = good, B = medium, C = poor) for the liking of color (C), taste (T), and overall (OL). Three models were used to quantify COE: (1) COE as an interaction effect; (2) COE as a residual effect; (3) COE proportional to the treatment effect. For (1), COE was stronger for C than T and OL, although COE was minimal. For (2), C showed higher estimates (−0.15 to +0.10) of COE than did T and OL (−0.09 to +0.07). COE mainly took the form of convergence. For (3), the absolute proportionality parameter estimate (λ) was higher for C than for T and OL (−0.155 vs. −0.004 to −0.039), which represented −15.46% of its direct treatment effect. Model (3) showed a significant COE for C. COE cannot be ignored as they may lead to the misinterpretation of sensory acceptability results.

Modeling the dependence of the distortion product otoacoustic emission response on primary frequency ratio

When measured as a function of primary frequency ratio r = f₂/f₁, using a constant f₂, distortion product otoacoustic emission (DPOAE) response demonstrates a bandpass shape, previously interpreted as the evidence for a cochlear "second filter." In this study, an alternate, interference-based explanation, previously advanced in variants, is forwarded on the basis of experimental data along with numerical and analytical solutions of nonlinear and linear cochlear models. The decrease of the DPOAE response with increasing and decreasing ratios is explained by a diminishing "overlap" generation region and the onset of negative interference among wavelets of different phase, respectively. In this paper, the additional quantitative hypothesis is made that negative interference becomes the dominant effect when the spatial width of the generation (overlap) region exceeds half a wavelength of the DPOAE wavelets. Therefore, r is predicted to be optimal when this condition is matched. Additionally, the minimum on the low-ratio side of the DPOAE curve is predicted to occur as the overlap region width equals one wavelength. As the width of the overlap region depends on both tuning and ratio, while wavelength depends on tuning only, an experimental method for estimating tuning from either the width of the pass band or the optimal ratio of the DPOAE vs. ratio curve has been theoretically formulated and evaluated using numerical simulations. A linear model without the possibility of nonlinear suppression is shown to reasonably approximate data from human subjects at low ratios reinforcing the relevance of the proposed negative interference effect. The different dependence of the distortion and reflection DPOAE components on r as well as the nonmonotonic behavior of the distortion component observed at very low ratios are also in agreement with this interpretation.

A general approach to evaluating the bias of 2-stage instrumental variable estimators

Unmeasured confounding is a common concern when researchers attempt to estimate a treatment effect using observational data or randomized studies with nonperfect compliance. To address this concern, instrumental variable methods, such as 2-stage predictor substitution (2SPS) and 2-stage residual inclusion (2SRI), have been widely adopted. In many clinical studies of binary and survival outcomes, 2SRI has been accepted as the method of choice over 2SPS, but a compelling theoretical rationale has not been postulated. We evaluate the bias and consistency in estimating the conditional treatment effect for both 2SPS and 2SRI when the outcome is binary, count, or time to event. We demonstrate analytically that the bias in 2SPS and 2SRI estimators can be reframed to mirror the problem of omitted variables in nonlinear models and that there is a direct relationship with the collapsibility of effect measures. In contrast to conclusions made by previous studies (Terza et al, 2008), we demonstrate that the consistency of 2SRI estimators only holds under the following conditions: (1) when the null hypothesis is true; (2) when the outcome model is collapsible; or (3) when estimating the nonnull causal effect from Cox or logistic regression models, the strong and unrealistic assumption that the effect of the unmeasured covariates on the treatment is proportional to their effect on the outcome needs to hold. We propose a novel dissimilarity metric to provide an intuitive explanation of the bias of 2SRI estimators in noncollapsible models and demonstrate that with increasing dissimilarity between the effects of the unmeasured covariates on the treatment versus outcome, the bias of 2SRI increases in magnitude.

Application of Artificial Neural Networks for Dengue Fever Outbreak Predictions in the Northwest Coast of Yucatan, Mexico and San Juan, Puerto Rico

Modelling dengue fever in endemic areas is important to mitigate and improve vector-borne disease control to reduce outbreaks. This study applied artificial neural networks (ANNs) to predict dengue fever outbreak occurrences in San Juan, Puerto Rico (USA), and in several coastal municipalities of the state of Yucatan, Mexico, based on specific thresholds. The models were trained with 19 years of dengue fever data for Puerto Rico and six years for Mexico. Environmental and demographic data included in the predictive models were sea surface temperature (SST), precipitation, air temperature (i.e., minimum, maximum, and average), humidity, previous dengue cases, and population size. Two models were applied for each study area. One predicted dengue incidence rates based on population at risk (i.e., numbers of people younger than 24 years), and the other on the size of the vulnerable population (i.e., number of people younger than five years and older than 65 years). The predictive power was above 70% for all four model runs. The ANNs were able to successfully model dengue fever outbreak occurrences in both study areas. The variables with the most influence on predicting dengue fever outbreak occurrences for San Juan, Puerto Rico, included population size, previous dengue cases, maximum air temperature, and date. In Yucatan, Mexico, the most important variables were population size, previous dengue cases, minimum air temperature, and date. These models have predictive skills and should help dengue fever mitigation and management to aid specific population segments in the Caribbean region and around the Gulf of Mexico.

Simulation-Extrapolation with Latent Heteroskedastic Error Variance

This article considers the application of the simulation-extrapolation (SIMEX) method for measurement error correction when the error variance is a function of the latent variable being measured. Heteroskedasticity of this form arises in educational and psychological applications with ability estimates from item response theory models. We conclude that there is no simple solution for applying SIMEX that generally will yield consistent estimators in this setting. However, we demonstrate that several approximate SIMEX methods can provide useful estimators, leading to recommendations for analysts dealing with this form of error in settings where SIMEX may be the most practical option.

Comparison on accuracy of different nonlinear models in predicting growth of Podolica bulls

Animal growth does not follow a linear pattern, being explained mathematically by functions that have parameters with biological meaning. These parameters are used to estimate the expected weight of animals at specific ages. Several nonlinear models have been used to describe growth. This study was carried out to estimate the parameters of logistic, Gompertz, Richards and von Bertalanffy growth curve models in a sample of Podolica young bulls to determine the goodness of fit. Animals were weighed every 3 months from birth to 810 days of age. The results indicate that all the growth models used were easily fitted to the observed data with Gompertz and logistic functions presenting less computational difficulty in terms of number of iterations to achieve convergence. Moreover, logistic and Richards equations provided the best overall fit being useful to describe the growth of Podolica bulls. Considering that the literature lacks information on growth curves in Podolica breed, the study of a mathematical model for growth describing the developmental pattern of a specific population within a peculiar environment is a useful tool to improve Podolica breed production.

Challenges of Prolonged Follow-up and Temporal Imbalance in Pragmatic Trials: Analysis of the ENCOURAGE Trial

PURPOSE

Peer support intervention trials are typically conducted in community-based settings and provide generalizable results. The logistic challenges of community-based trials often result in unplanned temporal imbalances in recruitment and follow-up. When imbalances are present, as in the ENCOURAGE trial, appropriate statistical methods must be used to account for these imbalances. We present the design, conduct, and analysis of the ENCOURAGE trial as a case study of a cluster-randomized, community-based, peer-coaching intervention.

METHODS

Preliminary data analysis included examination of study data for imbalances in participant characteristics at baseline, the presence of both secular and seasonal trends in outcome measures, and imbalances in time from baseline to follow-up. Additional examination suggested the presence of nonlinear trends in the intervention effect. The final analyses adjusted for all identified imbalances with accounting for community clustering by supplementing linear mixed effect models with generalized additive mixed models (GAMM) to examine nonlinear trends.

RESULTS

Largely due to the location of participants across a considerable geographic area, temporal imbalances were discovered in recruitment, baseline, and follow-up data collection, along with evidence for both secular and seasonal trends in study outcome measures. Using the standard analytical approach, ENCOURAGE appeared to be a null trial. After incorporating adjustment for these temporal imbalances, linear regression analyses still showed no intervention effect. Upon further analyses using GAMM to consider nonlinear intervention trends, we observed intervention effects that were both significant (P <.05) and nonlinear.

DISCUSSION

In community-based trials, recruitment and follow-up may not occur as planned, and complex temporal imbalance may greatly influence the analysis. Real-world trials should use careful logistic planning and monitoring to avoid temporal imbalance. If imbalance is unavoidable, sophisticated statistical methods may nevertheless extract useful information, although the potential problem of residual confounding due to other unmeasured imbalances must be considered.

Finding Bayesian Optimal Designs for Nonlinear Models: A Semidefinite Programming-Based Approach

This paper uses semidefinite programming (SDP) to construct Bayesian optimal design for nonlinear regression models. The setup here extends the formulation of the optimal designs problem as an SDP problem from linear to nonlinear models. Gaussian quadrature formulas (GQF) are used to compute the expectation in the Bayesian design criterion, such as D-, A- or E-optimality. As an illustrative example, we demonstrate the approach using the power-logistic model and compare results in the literature. Additionally, we investigate how the optimal design is impacted by different discretising schemes for the design space, different amounts of uncertainty in the parameter values, different choices of GQF and different prior distributions for the vector of model parameters, including normal priors with and without correlated components. Further applications to find Bayesian D-optimal designs with two regressors for a logistic model and a two-variable generalised linear model with a gamma distributed response are discussed, and some limitations of our approach are noted.

Threshold effects in nonlinear models with an application to the social capital-retirement-health relationship

This paper considers the relationship between social capital and health in the years before, at and after retirement. This adds to the current literature that only investigates this relationship in either the population as a whole or two subpopulations, pre-retirement and post-retirement. We now investigate if there are further additional subpopulations in the years to and from retirement. We take an information criteria approach to select the optimal model of subpopulations from a full range of potential models. This approach is similar to that proposed for linear models. Our contribution is to show how this may also be applied to nonlinear models and without the need for estimating subsequent subpopulations conditional on previous fixed subpopulations. Our main finding is that the association of social capital with health diminishes at retirement, and this decreases further 10 years after retirement. We find a strong positive significant association of social capital with health, although this turns negative after 20 years, indicating potential unobserved heterogeneity. The types of social capital may differ in later years (e.g., less volunteering) and hence overall social capital may have less of an influence on health in later years.

Melting of DNA oligomers: dynamical models and comparison with experimental results

We compare experimental melting curves of short heterogeneous DNA oligomers with theoretical curves derived from statistical mechanics. Partition functions are computed with the one-dimensional Peyrard-Bishop (PB) Hamiltonian, already used in the study of the melting of long DNA chains. Working with short chains we take into account, in the computations, not only the breaking of the interstrand hydrogen bonds, but also the complete dissociation of the double helix into separate single strands. Since this dissociation equilibrium is of general relevance, independent of the particular microscopic model, we give some details of its treatment. We discuss how the non bonded three-dimensional interactions, not explicitly considered in the one-dimensional PB model, are taken into account through the treatment of the dissociation equilibrium. We also evaluate the relevance of the dissociation as a function of the chain length.

Statistical methods in randomised controlled trials for delirium

OBJECTIVE

The analysis of clinical trials in delirium is typically complicated by treatment dropouts and by the fact that even untreated individuals may have a good prognosis. These features of delirium trials warrant special statistical attention; implications for each stage of a trial planning process are described.

METHODS

Choice of outcome, patient sample, and data collection in delirium trials are discussed. Descriptions are given, together with examples, of time-to-event, imputation-based, linear and nonlinear models for the analysis of randomised controlled trials for delirium.

RESULTS

Imputation allows evaluation of the plausibility of individual recovery trajectories, but some simple imputations are found to be unsuitable for delirium research. Time-to-event and nonlinear models encourage a global perspective on analysis, which is often preferable to cross-sectional end-of-trial assessments. It is suggested that nonlinear random effects models for longitudinal trajectories are particularly suitable in a delirium context.

CONCLUSION

It is hoped that the methods described, and nonlinear models in particular, will play a part in convincing analyses of future delirium research.

Corrected score estimation in the proportional hazards model with misclassified discrete covariates

We consider Cox proportional hazards regression when the covariate vector includes error-prone discrete covariates along with error-free covariates, which may be discrete or continuous. The misclassification in the discrete error-prone covariates is allowed to be of any specified form. Building on the work of Nakamura and his colleagues, we present a corrected score method for this setting. The method can handle all three major study designs (internal validation design, external validation design, and replicate measures design), both functional and structural error models, and time-dependent covariates satisfying a certain 'localized error' condition. We derive the asymptotic properties of the method and indicate how to adjust the covariance matrix of the regression coefficient estimates to account for estimation of the misclassification matrix. We present the results of a finite-sample simulation study under Weibull survival with a single binary covariate having known misclassification rates. The performance of the method described here was similar to that of related methods we have examined in previous works. Specifically, our new estimator performed as well as or, in a few cases, better than the full Weibull maximum likelihood estimator. We also present simulation results for our method for the case where the misclassification probabilities are estimated from an external replicate measures study. Our method generally performed well in these simulations. The new estimator has a broader range of applicability than many other estimators proposed in the literature, including those described in our own earlier work, in that it can handle time-dependent covariates with an arbitrary misclassification structure. We illustrate the method on data from a study of the relationship between dietary calcium intake and distal colon cancer.

Targeted social distancing design for pandemic influenza

Targeted social distancing to mitigate pandemic influenza can be designed through simulation of influenza's spread within local community social contact networks. We demonstrate this design for a stylized community representative of a small town in the United States. The critical importance of children and teenagers in transmission of influenza is first identified and targeted. For influenza as infectious as 1957-58 Asian flu (=50% infected), closing schools and keeping children and teenagers at home reduced the attack rate by >90%. For more infectious strains, or transmission that is less focused on the young, adults and the work environment must also be targeted. Tailored to specific communities across the world, such design would yield local defenses against a highly virulent strain in the absence of vaccine and antiviral drugs.