Bayesian longitudinal data analysis with mixed models and thick-tailed distributions using MCMC

Linear mixed effects models are frequently used to analyse longitudinal data, due to their flexibility in modelling the covariance structure between and within observations. Further, it is easy to deal with unbalanced data, either with respect to the number of observations per subject or per time period, and with varying time intervals between observations. In most applications of mixed models to biological sciences, a normal distribution is assumed both for the random effects and for the residuals. This, however, makes inferences vulnerable to the presence of outliers. Here, linear mixed models employing thick-tailed distributions for robust inferences in longitudinal data analysis are described. Specific distributions discussed include the Student-t, the slash and the contaminated normal. A Bayesian framework is adopted, and the Gibbs sampler and the Metropolis-Hastings algorithms are used to carry out the posterior analyses. An example with data on orthodontic distance growth in children is discussed to illustrate the methodology. Analyses based on either the Student-t distribution or on the usual Gaussian assumption are contrasted. The thick-tailed distributions provide an appealing robust alternative to the Gaussian process for modelling distributions of the random effects and of residuals in linear mixed models, and the MCMC implementation allows the computations to be performed in a flexible manner.

Modelling of fatigue crack growth following overloads

In variable-amplitude loading there are interaction effects between the loading history and the crack propagation rate. The most important of these effects is the retardation in the crack propagation, which may raise the life of the cracked structureconsiderably. The main objective of this research is to analyse and quantify the retardation of crack propagation in a thin plate of the high-resistance aluminium alloy 2024-T3, comparing the results obtained from the mathematical models proposed to account for the retardation effect. The specimens were tested under high-low loading sequences, for different crack sizes and overload ratios. A simplified model was developed, based on crack closure theory, that could represent the crack behaviour during retardation very well. © 1991.

Evaluation of transverse changes in the dental arches according to growth pattern: a longitudinal study

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Does hyperglycemia in pregnancy change fetal kidney growth?: a longitudinal prospective study

PURPOSE: To measure fetal renal volume in normoglycemic and hyperglycemic pregnancies. METHODS: A longitudinal prospective study was conducted and included 92 hyperglycemic and 339 normoglycemic pregnant women attended at the prenatal service of a hospital from Rio de Janeiro State. Ultrasound examinations were performed to estimate gestational age at baseline and the kidney volume was estimated using the prolate ellipsoid volume equation. RESULTS: Fetal kidney volume growth between normoglycemic and hyperglycemic pregnancies are significantly different. The fetal kidney volume growth in pregnancy is positively correlated with gestational age explained by these predictor equations, by group: normal renal volume = exp (6.186+0.09×gestational week); hyperglycemic renal volume = exp (6.978+0.071×gestational week) and an excessive growth pattern for hyperglycemic pregnancies may be established according to gestational age. CONCLUSION: This is important for early detection of abnormalities in pregnancy, particularly in diabetic mothers.

Rietveld refinement, cluster modelling, growth mechanism and photoluminescence properties of CaWO4: Eu3+ microcrystals

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Noisy Oncology: applications of bounded noise transitions in modelling tumor growth

I tumori macroscopici e microscopici, dopo la loro prima fase di crescita, sono composti da un numero medio elevato di cellule. Così, in assenza di perturbazioni esterne, la loro crescita e i punti di equilibrio possono essere descritti da equazioni differenziali. Tuttavia, il tumore interagisce fortemente col macroambiente che lo circonda e di conseguenza una descrizione del tutto deterministica risulta a volte inappropriata. In questo caso si può considerare l'interazione con fluttuazioni statistiche, causate da disturbi esterni, utilizzando le equazioni differenziali stocastiche (SDE). Questo è vero in modo particolare quando si cerca di modellizzare tumori altamente immunogenici che interagiscono con il sistema immunitario, in quanto la complessità di questa interazione risulta in fenomeni di multistabilità. Così, il rumore può provocare disturbi e indurre transizioni di stato (Noise-Induced-Transitions). E' importante notare che una NIT può avere implicazioni profonde sulla vita di un paziente, dal momento che una transizione da uno stato di equilibrio piccolo, nelle dimensioni del tumore, ad uno stato di equilibrio macroscopico, nella maggior parte dei casi significa il passaggio dalla vita alla morte. Generalmente l'approccio standard è quello di modellizzare le fluttuazioni stocastiche dei parametri per mezzo di rumore gaussiano bianco o colorato. In alcuni casi però questa procedura è altamente inadeguata, a causa della illimitatezza intrinseca dei rumori gaussiani che può portare a gravi incongruenze biologiche: pertanto devono essere utilizzati dei rumori "limitati", che, tuttavia, sono molto meno studiati di quelli gaussiani. Inoltre, l'insorgenza di NIT dipende dal tipo di rumore scelto, che rivela un nuovo livello di complessità in biologia. Lo scopo di questa tesi è quello di studiare le applicazioni di due tipi diversi di "rumori limitati" nelle transizioni indotte in due casi: interazione tra tumore e sistema immunitario e chemioterapia dei tumori. Nel primo caso, abbiamo anche introdotto un nuovo modello matematico di terapia, che estende, in modo nuovo, il noto modello di Norton-Simon.

Modelling growth dynamics and toxin production in Ostreopsis cf. ovata

The benthic dinoflagellate O. ovata represents a serious threat for human health and for the ecology of its blooming areas: thanks to its toxicity this microalga has been responsible for several cases of human intoxication and mass mortalities of benthic invertebrates. Although the large number of studies on this dinoflagellate, the mechanisms underpinning O. ovata growth and toxin production are still far to be fully understood. In this work we have enriched the dataset on this species by carrying out a new experiment on an Adriatic O. cf. ovata strain. Data from this experiment (named Beta) and from another comparable experiment previously conducted on the same strain (named Alpha), revealed some interesting aspects of this dinoflagellate: it is able to grow also in a condition of strong intracellular nutrient deficiency (C:P molar ratio > 400; C:N > 25), reaching extremely low values of chlorophyll-a to carbon ratio (0.0004). Was also found a significant inverse relationships (r > -0.7) between cellular toxin to carbon and cellular nutrient to carbon ratios of experiment Alpha. In the light of these result, we hypothesized that in O. cf. ovata nutrient-stress conditions (intended as intracellular nutrient deficiency) can cause: i) an increase in toxin production; ii) a strong decrease in chlorophyll-a synthesis; iii) a lowering of metabolism associated with the formation of a sort of resting stage. We then used a modelling approach to test and critically evaluate these hypotheses in a mechanistic way: newly developed formulation describing toxin production and fate, and ad hoc changes in the already existent formulations describing chlorophyll synthesis, rest respiration, and mortality, have been incorporated in a simplified version of the European Regional Seas Ecosystem Model (ERSEM), together with a new ad hoc parameterization. The adapted model was able to accurately reproduce many of the trends observed in the Alpha experiment, allowing us to support our hypotheses. Instead the simulations of the experiment Beta were not fully satisfying in quantitative terms. We explained this gap with the presumed different physiological behaviors between the algae of the two experiments, due to the different pre-experimental periods of acclimation: the model was not able to reproduce acclimation processes in its simulations of the experiment Beta. Thus we attempt to simulate the acclimation of the algae to nutrient-stress conditions by manual intervention on some parameters of nutrient-stress thresholds, but we received conflicting results. Further studies are required to shed light on this interesting aspect. In this work we also improve the range of applicability of a state of the art marine biogeochemical model (ERSEM) by implementing in it an ecological relevant process such as the production of toxic compounds.

Left ventricular growth from age 8 to 18 and its anthropometric determinants: Longitudinal results from Project Heartbeat!

Left ventricular mass (LVM) is a strong predictor of cardiovascular disease (CVD) in adults. However, normal growth of LVM in healthy children is not well understood, and previous results on independent effects of body size and body fatness on LVM have been inconsistent. The purpose of this study was (1) to establish the normal growth curve of LVM from age 8 to age 18, and evaluate the determinants of change in LVM with age, and (2) to assess the independent effects of body size and body fatness on LVM.^ In Project HeartBeat!, 678 healthy children aged 8, 11 and 14 years at baseline were enrolled and examined at 4-monthly intervals for up to 4 years. A synthetic cohort with continuous observations from age 8 to 18 years was constructed. A total of 4608 LVM measurements was made from M-mode echocardiography. The multilevel linear model was used for analysis.^ Sex-specific trajectories of normal growth of LVM from age 8 to 18 was displayed. On average, LVM was 15 g higher in males than females. Average LVM increased linearly in males from 78 g at age 8 to 145 g at age 18. For females, the trajectory was curvilinear, nearly constant after age 14. No significant racial differences were found. After adjustment for the effects of body size and body fatness, average LVM decreased slightly from age 8 to 18, and sex differences in changes of LVM remained constant.^ The impact of body size on LVM was examined by adding to a basic LVM-sex-age model one of 9 body size indicators. The impact of body fatness was tested by further introducing into each of the 9 LVM models (with one or another of the body size indicators) one of 4 body fatness indicators, yielding 36 models with different body size and body fatness combinations. The results indicated that effects of body size on LVM can be distinguished between fat-free body mass and fat body mass, both being independent, positive predictors. The former is the stronger determinant. When a non-fat-free body size indicator is used as predictor, the estimated residual effect of body fatness on LVM becomes negative. ^

A Longitudinal Study of Mandibular Growth Rotation

Submitted in partial fulfillment of the requirements for a Certificate in Orthodontics, Dept. of Orthodontics, University of Connecticut Health Center, 1977

In vivo longitudinal studies of spinal cord injury and vascular endothelial growth factor treatment

Approximately 12,000 new cases of spinal cord injury (SCI) are added each year to the estimated 259,000 Americans living with SCI. The majority of these patients return to society, their lives forever changed by permanent loss of sensory and motor function. While there are no FDA approved drugs for the treatment of SCI or a universally accepted standard therapy, the current though controversial treatment includes the delivery of high dosages of the corticosteroid methyliprednisolone sodium succinate, surgical interventions to stabilize the spinal column, and physical rehabilitation. It is therefore critically important to fully understand the pathology of injury and determine novel courses and rationally-based therapies for SCI. ^ Vascular endothelial growth factor (VEGF) is an attractive target for treating central nervous system (CNS) injury and disease because it has been shown to influence angiogenesis and neuroprotection. Preliminary studies have indicated that increased vasculature may be associated with functional recovery; therefore exogenous delivery of a pro-angiogenic growth factor such as VEGF may improve neurobehavioral outcome. In addition, VEGF may provide protection from secondary injury and result in increased survival and axonal sprouting. ^ In these studies, SCI rats received acute intraspinal injections of VEGF, the antibody to VEGF, or vehicle control. The effect of these various agents was investigated using longitudinalmulti-modal magnetic resonance imaging (MRI), neuro- and sensory behavioral assays, and end point immunohistochemistry. We found that rats that received VEGF after SCI had increased tissue sparing and improved white matter integrity at the earlier time points as shown by advanced magnetic resonance imaging (MRI) techniques. However, these favorable effects of VEGF were not maintained, suggesting that additional treatments with VEGF at multiple time points may be more beneficial, Histological examinations revealed that VEGF treatment may result in increased oligodendrogenesis and therefore may eventually lead to remyelination and improved functional outcome. ^ On the neurobehavioral studies, treatments with VEGF and Anti-VEGF did not significantly affect performance on tests of open-field locomotion, grid walk, inclined plane, or rearing. However, VEGF treatment resulted in significantly increased incidence of chronic neuropathic pain. This phenomenon could possibly be attributed to the fact that VEGF treatment may promote axonal sprouting and also results in tissue sparing, thereby providing a substrate for the growth of new axons. New connections made by these sprouting axons may involve components of pathways involved in the transmission of pain and therefore result in increased pain in those animals. ^