Joint modelling of longitudinal measurements and event time data

This paper formulates a class of models for the joint behaviour of a sequence of longitudinal measurements and an associated sequence of event times, including single-event survival data. This class includes and extends a number of specific models which have been proposed recently, and, in the absence of association, reduces to separate models for the measurements and events based, respectively, on a normal linear model with correlated errors and a semi-parametric proportional hazards or intensity model with frailty. Special cases of the model class are discussed in detail and an estimation procedure which allows the two components to be linked through a latent stochastic process is described. Methods are illustrated using results from a clinical trial into the treatment of schizophrenia.     

Meta-analysis of spineless cactus feeding to meat lambs: performance and development of mathematical models to predict dry matter intake and average daily gain

Spineless cactus is a useful feed for various animal species in arid and semiarid regions due to its adaptability to dry and harsh soil, high efficiency of water use and carbohydrates storage. This meta-analysis was carried out to assess the effect of spineless cactus on animal performance, and develop and evaluate equations to predict dry matter intake (DMI) and average daily gain (ADG) in meat lambs. Equations for predicting DMI and ADG as a function of animal and diet characteristics were developed using data from eight experiments. The dataset was comprised of 40 treatment means from 289 meat lambs, in which cactus was included from 0 to 75% of the diet dry matter (DM). Accuracy and precision were evaluated by cross-validation using the mean square error of prediction (MSEP), which was decomposed into mean bias, systematic bias and random error; concordance correlation coefficient, which was decomposed into accuracy (C_b) and precision (ρ); and coefficient of determination (R²). In addition, the data set was used to evaluate the predicting accuracy and precision of the main lamb feeding systems (Agricultural and Food Research Council, Small Ruminant Nutritional System, National Research Council and Institut National de la Recherche Agronomique) and also two Brazilian studies. The DMI, CP intake (CPI), metabolizable energy (ME) intake and ADG increased when cactus was included up to 499 g/kg DM (P<0.001). In contrast, animals fed high levels of cactus (>500 g/kg DM) had a decreased DMI, CPI and NDF intake, but increased feed efficiency (P<0.001) and similar ADG compared with those without cactus addition. The DMI was positively correlated with initial BW, final BW, concentrate and ADG, while it was negatively correlated with cactus inclusion and ME of the diet. On other hand, ADG was positively correlated with DMI, initial and mean BW and concentrate, and it was negatively correlated with cactus inclusion. The two developed equations had high accuracy (C_b of 0.95 for DMI and 0.94 for ADG) and the random error of MSEP was 99% for both equations. The precision of both equations was moderate, with R² values of 0.53 and 0.50 and ρ values of 0.73 and 0.71 for DMI and ADG, respectively. In conclusion, the developed equation to predict DMI had moderate precision and high accuracy, nonetheless, it was more efficient than those reported in the literature. The proposed equations can be a useful alternative to estimate intake and performance of lambs fed cactus.     

Statistical shape modelling versus linear scaling: Effects on predictions of hip joint centre location and muscle moment arms in people with hip osteoarthritis

Marker-based dynamic functional or regression methods are used to compute joint centre locations that can be used to improve linear scaling of the pelvis in musculoskeletal models, although large errors have been reported using these methods. This study aimed to investigate if statistical shape models could improve prediction of the hip joint centre (HJC) location. The inclusion of complete pelvis imaging data from computed tomography (CT) was also explored to determine if free-form deformation techniques could further improve HJC estimates. Mean Euclidean distance errors were calculated between HJC from CT and estimates from shape modelling methods, and functional- and regression-based linear scaling approaches. The HJC of a generic musculoskeletal model was also perturbed to compute the root-mean squared error (RMSE) of the hip muscle moment arms between the reference HJC obtained from CT and the different scaling methods. Shape modelling without medical imaging data significantly reduced HJC location error estimates (11.4 ± 3.3 mm) compared to functional (36.9 ± 17.5 mm, p = <0.001) and regression (31.2 ± 15 mm, p = <0.001) methods. The addition of complete pelvis imaging data to the shape modelling workflow further reduced HJC error estimates compared to no imaging (6.6 ± 3.1 mm, p = 0.002). Average RMSE were greatest for the hip flexor and extensor muscle groups using the functional (16.71 mm and 8.87 mm respectively) and regression methods (16.15 mm and 9.97 mm respectively). The effects on moment-arms were less substantial for the shape modelling methods, ranging from 0.05 to 3.2 mm. Shape modelling methods improved HJC location and muscle moment-arm estimates compared to linear scaling of musculoskeletal models in patients with hip osteoarthritis.     

Robust joint modeling of longitudinal measurements and time to event data using normal/independent distributions: A Bayesian approach

Joint modeling of longitudinal data and survival data has been used widely for analyzing AIDS clinical trials, where a biological marker such as CD4 count measurement can be an important predictor of survival. In most of these studies, a normal distribution is used for modeling longitudinal responses, which leads to vulnerable inference in the presence of outliers in longitudinal measurements. Powerful distributions for robust analysis are normal/independent distributions, which include univariate and multivariate versions of the Student's t, the slash and the contaminated normal distributions in addition to the normal. In this paper, a linear‐mixed effects model with normal/independent distribution for both random effects and residuals and Cox's model for survival time are used. For estimation, a Bayesian approach using Markov Chain Monte Carlo is adopted. Some simulation studies are performed for illustration of the proposed method. Also, the method is illustrated on a real AIDS data set and the best model is selected using some criteria.     

Using mixed silages of sweet sorghum and alfalfa in total mixed rations to improve growth performance,nutrient digestibility,carcass traits and meat quality of sheep

Combining sweet sorghum (SS) with alfalfa for ensiling has the potential to make a high-quality silage with relatively a better nutrient balance. However, the existing data are insufficient about how changes in ratios of SS to alfalfa in different silage mixtures affect animal performance and meat quality. Therefore, the objective of this study was to determine the effect of feeding total mixed rations containing mixed silages of SS and alfalfa on growth performance, nutrient digestibility, carcass traits and meat quality of Karakul sheep. Five total mixed rations were formulated with different SS proportions at 100%, 80%, 60%, 40%, and 20% on a fresh weight basis. Thirty 4-month old male Karakul sheep with 25.5 ± 1.4 kg BW were randomly allocated into five treatment groups, each with six lambs for this experiment. The results indicated that the Karakul sheep consuming total mixed rations containing SS-Alfalfa (SS-AF) silage mixtures with a lower proportion of SS tended to increase nutrient digestibility, growth performance, carcass traits, and meat quality. Feeding diets with SS at 40% and 20% inclusion rate showed a significant linear increase in the apparent digestibility of DM, CP and NDF, as well as subcutaneous fat thickness and water holding capacity (P < 0.5). Moreover, reduction in SS inclusion rate in these diets caused significant (P < 0.05) linear and quadratic increases in DM intake, final BW, average daily gain, carcass weight, and the amino acid contents of meat (P < 0.05). Conversely, feeding diet with lower SS inclusion rate led to decrease in feed conversion ratio and shear force significantly (P < 0.05) for these sheep. It appears that 40% inclusion of SS was the optimal rate in making the SS-AF silage mixture for lambs to achieve a superior production performance and high-quality meat products in Karakul sheep. However, further research is needed to investigate the effect of feeding SS-AF silage mixtures alongside contrasting ingredients on rumen function, ruminal microorganisms and digestive enzyme activity of sheep and other ruminant animals.     

Method of modelling intracellular transport in branching neurites: application to axons and dendrites of Drosophila sensory neurons

This paper develops a method of calculating the transport of intracellular organelles in neurons with branching neurites which is based on the Smith–Simmons equations of motor-assisted transport. The method is aimed at understanding the effects of microtubule (MT) polarity orientation in branching neurites on transport of organelles at the fundamental level. The method is applied to calculating the organelle transport in axons and dendrites of Drosophila neurons, using the map of MT orientation in such neurons developed by Stone et al. (Mol Biol Cell 19:4122–4129, 2008). The proximal dendrite is assumed to branch and form two distal dendrites. Two different MT polarity arrangements in a proximal dendrite are considered, and implications of these MT arrangements on organelle transport are analysed. It is demonstrated that the MT arrangement found in Drosophila dendrites (MTs have their minus ends out in a proximal dendrite) results in much more efficient motor-driven transport than the structure with a mixed MT orientation in proximal dendrites.     

Nonlinearity of photosynthetic responses to growth in rising atmospheric CO2: an experimental and modelling study

Nonlinear responses of photosynthesis to the CO₂ concentration at which plants were grown (C_g) have been often reported in the literature. This study was designed to develop mechanistic understanding of the nonlinear responses with both experimental and modelling approaches. Soybean (Glycine max) was grown in five levels of C_g (280, 350, 525, 700, 1000 ppm) with either a high or low rate of nitrogen fertilization. When the rate of nitrogen fertilization was high, the photosynthetic rate measured at C_g was highest in plants from the 700 ppm CO₂ treatment. When the rate of nitrogen fertilization was low, little variation was observed in the photosynthetic rates of plants from the different treatments measured at their respective C_g. Measurements of CO₂-induced changes in mass-based leaf nitrogen concentration (n_m, an index of changes in biochemical processes) and leaf mass per unit area (h, an index of morphological properties) were used in a model and indicate that the nonlinearity of photosynthetic responses to C_g is largely determined by relative changes in photosynthetic sensitivity, biochemical downregulation, and morphological upregulation. In order to further understand the nonlinear responses, we compiled data from the literature on CO₂-induced changes in n_m and h. These compiled data indicate that h generally increases and n_m usually decreases with increasing C_g, but that the trajectories and magnitudes of the changes in h and n_m vary with species and growth environments. Integration of these variables (n_m and h) into a biochemically based model of photosynthesis enabled us to predict diverse responses of photosynthesis to C_g. Thus a general mechanism is suggested for the highly variable, nonlinear responses of photosynthesis to C_g reported in the literature.     

Ozone effects on wheat in relation to CO2: modelling short‐term and long‐term responses of leaf photosynthesis and leaf duration

A combined stomatal–photosynthesis model was extended to simulate the effects of ozone exposure on leaf photosynthesis and leaf duration in relation to CO₂. We assume that ozone has a short‐term and a long‐term effect on the Rubisco‐limited rate of photosynthesis, A_c. Elevated CO₂ counteracts ozone damage via stomatal closure. Ozone is detoxified at uptake rates below a threshold value above which A_c decreases linearly with the rate of ozone uptake. Reduction in A_c is transient and depends on leaf age. Leaf duration decreases depending on accumulated ozone uptake. This approach is introduced into the mechanistic crop simulation model AFRCWHEAT2. The derived model, AFRCWHEAT2‐O3, is used to test the capability of these assumptions to explain responses at the plant and crop level. Simulations of short‐term and long‐term responses of leaf photosynthesis, leaf duration and plant and crop growth to ozone exposure in response to CO₂ are analysed and compared with experimental data derived from the literature. The model successfully reproduced published responses of leaf photosynthesis, leaf duration, radiation use efficiency and final biomass of wheat to elevated ozone and CO₂. However, simulations were unsatisfactory for cumulative radiation interception which had some impact on the accuracy of predictions of final biomass. There were responses of leaf‐area index to CO₂ and ozone as a result of effects on tillering which were not accounted for in the present model. We suggest that some model assumptions need to be tested, or analysed further to improve the mechanistic understanding of the combined effects of changes in ozone and CO₂ concentrations on leaf photosynthesis and senescence. We conclude that research is particularly needed to improve the understanding of leaf‐area dynamics in response to ozone exposure and elevated CO₂.     

ROS and pentose phosphate pathway: mathematical modelling of the metabolic regulation in response to xenobiotic-induced oxidative stress and the proposed Impact of the gluconate shunt

Abstract

Elevated intracellular levels of reactive oxygen species (ROS), e.g. resulting from exposure to xenobiotics, can cause severe damages. Antioxidant defence mechanisms, which involve regulation of enzyme activities, protect cells to a certain extent. Nevertheless, continuous or increased exposure can overwhelm this system resulting in an adverse cellular state. To simulate exposure scenarios and to investigate the transition to an adverse cellular state, a mathematical model for the dynamics of ROS in response to xenobiotic-induced oxidative stress has been developed. It is based on exposure experiments of human urothelial cells (RT4) to the nitrated polycyclic aromatic hydrocarbon 3-nitrobenzanthrone (3-NBA), a component of diesel engine exhaust, and takes into account the following metabolic pathways of the antioxidant defence system: glutathione redox cycle scavenging directly ROS, the pentose phosphate pathway and the gluconate shunt as NADPH supplier and the beginning of glycolysis. In addition, ROS generation due to the bioactivation of 3-NBA has been implemented. The regulation of enzyme activities plays an important role in the presented mathematical model. The in silico model consists of ordinary differential equations on the basis of enzyme kinetics and mass action for the metabolism of 3-NBA. Parameters are either estimated from performed in vitro experiments via least-squares fitting or obtained from the literature. The results underline the importance of the pentose phosphate pathway to cope with oxidative stress and suggest an important role of the gluconate shunt during low-dose exposure.     

Using adaptive traits to consider potential consequences of temporal variation in selection: male guppy colour through time and space

Temporal variation in selection is typically evaluated by estimating and comparing selection coefficients in natural populations. Meta‐analyses of these coefficients have yielded important insights, but selection coefficients are limited in several respects, including low statistical power, imperfect fitness surrogates, and uncertainty regarding consequences for trait change. A complementary approach without these limitations is to examine temporal variation in adaptive traits themselves, which is mechanistically easier and more directly relevant to evolutionary consequences. We illustrate this approach by analyzing the colour patterns of male guppies, Poecilia reticulata, from each of six sites in Trinidad in each of 6 years. This system is particularly appropriate for our study because key aspects of colour variation are genetically‐based and responsive to selection. However, although spatial patterns of colour variation have been extensively considered in this system, no study has yet formally assessed annual temporal variation in non‐manipulated populations. Matching previous conclusions for the guppy system, we find that guppies from different sites manifest different colour patterns in association with different predation regimes. We here add the new finding that, although some temporal variation is present, spatial patterns of colour variation are generally consistent across years. These results suggest that, when considering adaptive traits, spatial variation is more important than temporal variation, although our study system might be exceptional in this regard. Additional studies examining spatiotemporal variation in adaptive traits could help to improve our understanding of the role that spatiotemporal variation in selection plays in the evolutionary process. © 2014 The Linnean Society of London, Biological Journal of the Linnean Society, 2014, 112 , 108–122.     

Dynamical entropy via entropy of non-random matrices: Application to stability and complexity in modelling ecosystems

In the present paper we have first introduced a measure of dynamical entropy of an ecosystem on the basis of the dynamical model of the system. The dynamical entropy which depends on the eigenvalues of the community matrix of the system leads to a consistent measure of complexity of the ecosystem to characterize the dynamical behaviours such as the stability, instability and periodicity around the stationary states of the system. We have illustrated the theory with some model ecosystems.     

Enantioselective analysis of ibuprofen enantiomers in mice plasma and tissues by high‐performance liquid chromatography with fluorescence detection: Application to a pharmacokinetic study

A direct fluorometric high‐performance liquid chromatography (HPLC) method was developed and validated for the analysis of ibuprofen enantiomers in mouse plasma (100 μl) and tissues (brain, liver, kidneys) using liquid–liquid extraction and 4‐tertbutylphenoxyacetic acid as an internal standard. Separation of enantiomers was accomplished in a Chiracel OJ‐H chiral column based on cellulose tris(4‐methylbenzoate) coated on 5 μm silica‐gel, 250 x 4.6 mm at 22 °C with a mobile phase composed of n‐hexane, 2‐propanol, and trifluoroacetic acid that were delivered in gradient elution at a flow rate of 1 ml min⁻¹. A fluorometric detector was set at: λ_excit. = 220 nm and λ_emis. = 290 nm. Method validation included the evaluation of the selectivity, linearity, lower limit of quantification (LLOQ), within‐run and between‐run precision and accuracy. The LLOQ for the two enantiomers was 0.125 μg ml⁻¹ in plasma, 0.09 μg g⁻¹ in brain, and 0.25 μg g⁻¹ in for liver and kidney homogenates. The calibration curves showed good linearity in the ranges of each enantiomers: from 0.125 to 35 μg ml⁻¹ for plasma, 0.09–1.44 μg g⁻¹ for brain, and 0.25–20 μg g⁻¹ for liver and kidney homogenates. The method was successfully applied to a pharmacokinetic study of ibuprofen enantiomers in mice treated i.v. with 10 mg kg⁻¹ of racemate.     

River phytoplankton prediction model by Artificial Neural Network: Model performance and selection of input variables to predict time-series phytoplankton proliferations in a regulated river system

In this study, a comparison between statistical regression model and Artificial Neural Network (ANN) is given on the effectiveness of ecological model of phytoplankton dynamics in a regulated river. From the results of the study, the effectiveness of ANN over statistical method was proposed. Also feasible direction of increasing ANN models' performance was provided. A hypertrophic river data was used to develop prediction models (chlorophyll a (chl. a) 41.7 ± 56.8 μg L^− 1; n = 406). Higher time-series predictability was found from the ANN model. Failure of statistical methods would be due to the complex nature of ecological data in the regulated river ecosystems. Reduction of ANN model size by decreasing the number of input variables according to the sensitivity analysis did not have effectiveness with respect to the predictability on testing data set (RMSE of the ANN with all 27 variables, 25.7; 47.9 from using 2 highly sensitive variables; 42.9 from using 5 sensitive variables; 33.1 from using 15 variables). Even though the ANN model presented high performance in prediction accuracy, more efficient methods of selecting feasible input information are strongly requested for the prediction of freshwater ecological dynamics.     

Different ways to die in a changing world: Consequences of climate change for tree species performance and survival through an ecophysiological perspective

Anthropogenic activities such as uncontrolled deforestation and increasing greenhouse gas emissions are responsible for triggering a series of environmental imbalances that affect the Earth's complex climate dynamics. As a consequence of these changes, several climate models forecast an intensification of extreme weather events over the upcoming decades, including heat waves and increasingly severe drought and flood episodes. The occurrence of such extreme weather will prompt profound changes in several plant communities, resulting in massive forest dieback events that can trigger a massive loss of biodiversity in several biomes worldwide. Despite the gravity of the situation, our knowledge regarding how extreme weather events can undermine the performance, survival, and distribution of forest species remains very fragmented. Therefore, the present review aimed to provide a broad and integrated perspective of the main biochemical, physiological, and morpho‐anatomical disorders that may compromise the performance and survival of forest species exposed to climate change factors, particularly drought, flooding, and global warming. In addition, we also discuss the controversial effects of high CO₂ concentrations in enhancing plant growth and reducing the deleterious effects of some extreme climatic events. We conclude with a discussion about the possible effects that the factors associated with the climate change might have on species distribution and forest composition.     

Bayesian Variable Selection with Joint Modeling of Categorical and Survival Outcomes: An Application to Individualizing Chemotherapy Treatment in Advanced Colorectal Cancer

Summary Colorectal cancer is the second leading cause of cancer related deaths in the United States, with more than 130,000 new cases of colorectal cancer diagnosed each year. Clinical studies have shown that genetic alterations lead to different responses to the same treatment, despite the morphologic similarities of tumors. A molecular test prior to treatment could help in determining an optimal treatment for a patient with regard to both toxicity and efficacy. This article introduces a statistical method appropriate for predicting and comparing multiple endpoints given different treatment options and molecular profiles of an individual. A latent variable‐based multivariate regression model with structured variance covariance matrix is considered here. The latent variables account for the correlated nature of multiple endpoints and accommodate the fact that some clinical endpoints are categorical variables and others are censored variables. The mixture normal hierarchical structure admits a natural variable selection rule. Inference was conducted using the posterior distribution sampling Markov chain Monte Carlo method. We analyzed the finite‐sample properties of the proposed method using simulation studies. The application to the advanced colorectal cancer study revealed associations between multiple endpoints and particular biomarkers, demonstrating the potential of individualizing treatment based on genetic profiles.     

Contributions of leaf photosynthetic capacity, leaf angle and self-shading to the maximization of net photosynthesis in Acer saccharum: a modelling assessment

Background and Aims

Plants are expected to maximize their net photosynthetic gains and efficiently use available resources, but the fundamental principles governing trade-offs in suites of traits related to resource-use optimization remain uncertain. This study investigated whether Acer saccharum (sugar maple) saplings could maximize their net photosynthetic gains through a combination of crown structure and foliar characteristics that let all leaves maximize their photosynthetic light-use efficiency (ɛ).

Methods

A functional–structural model, LIGNUM, was used to simulate individuals of different leaf area index (LAI_ind) together with a genetic algorithm to find distributions of leaf angle (L_A) and leaf photosynthetic capacity (A_max) that maximized net carbon gain at the whole-plant level. Saplings grown in either the open or in a forest gap were simulated with A_max either unconstrained or constrained to an upper value consistent with reported values for A_max in A. saccharum.

Key Results

It was found that total net photosynthetic gain was highest when whole-plant PPFD absorption and leaf ɛ were simultaneously maximized. Maximization of ɛ required simultaneous adjustments in L_A and A_max along gradients of PPFD in the plants. When A_max was constrained to a maximum, plants growing in the open maximized their PPFD absorption but not ɛ because PPFD incident on leaves was higher than the PPFD at which ɛ_max was attainable. Average leaf ɛ in constrained plants nonetheless improved with increasing LAI_ind because of an increase in self-shading.

Conclusions

It is concluded that there are selective pressures for plants to simultaneously maximize both PPFD absorption at the scale of the whole individual and ɛ at the scale of leaves, which requires a highly integrated response between L_A, A_max and LAI_ind. The results also suggest that to maximize ɛ plants have evolved mechanisms that co-ordinate the L_A and A_max of individual leaves with PPFD availability.     

Comparing the sustainability of different action policy possibilities: Application to the issue of both household survival and forest preservation in the corridor of Fianarantsoa

A sustainability issue for the rain forest in the corridor of Fianarantsoa (Madagascar) is to preserve the forest while ensuring the development of the local population. The aim of this paper is to determine whether the current situation is sustainable or not according to different action policy possibilities. We propose a general procedure based on viability analysis: Translation of sustainability issues into constraints on the system state; elaboration of a mathematical model of system evolution rules in the form of controlled dynamical system; computations of the viability kernels according to different action policy possibilities. Among control variables, we focus on monetary transfer. Without monetary transfer, we show that the current situation of the rain forest corridor is not sustainable in our mathematical modeling framework. We then estimate the minimal maximal amount per year necessary to make the current situation sustainable.