En parallèle des facteurs cliniques et biologiques, de nombreux déterminants psychologiques, dont l’adhésion et la qualité de vie, peuvent influencer la survie des greffons et des patients transplantés. Dans ce contexte notre objectif était d’étudier l’hétérogénéité des profils d’évolution de la qualité de vie et d’adhésion chez les patients transplantés rénaux et d’en identifier les déterminants. Dans un premier temps, l’étude de la qualité de vie a permis d’identifié deux sous-populations homogènes de patients: une majorité présentaient une qualité de vie semblable à la population générale alors que 40% des patients montraient une qualité de vie dégradée associé à une augmentation d’épisodes d’anxiété et de faiblesse musculaire. Nous avons pu montrer, dans un deuxième temps, qu’il existait deux profils d’évolution de l’adhésion : la majorité des patients étaient adhérents alors que 15 % des patients présentaient une non-adhésion en constante augmentation, une qualité de vie mentale dégradée et de plus nombreux épisodes de dépression. Enfin, nous présentons dans ce travail un nouvel outil dédié à l'évaluation de l’adhésion aux immunosuppresseurs des patients transplantés francophones. Cette thèse fournit de nouveaux outils, facile à utiliser précocement ou à distance de la greffe, permettant de détecter les patients présentant une qualité de vie et/ou une adhésion dégradée afin de mettre en place, pour ces patients, une prise en charge personnalisée. / In parallel to clinical and biological factors, many psychological determinants could influence transplant patient grafts survival and contributes to patients’ morbidity and mortality. Among them, adherence and quality of life were largely reported. In this context, our objective was to study, in kidney transplant patients, quality of life and adherence time-profiles heterogeneity and to identify determinants of distinct time-course. First, we identified two homogeneous subpopulations of patients: a majority presented a quality of life similar to the general population, while 40% of patients showed a poor quality of life associated with more episodes of anxiety and muscle weakness. Secondly, we found two distinct adherence time-profiles: the majority of patients were adherent while 15% presented a non-adherence constantly increasing associated with a poor mental quality of life and more depressive episodes. Finally, we proposed in this work a new tool dedicated to the evaluation of adherence in French-speaking transplant patients. This thesis provides new tools, easy to use even early on after transplantation, to detect patients with poor quality of life and / or adhesion in order to individualize the management of these patients with appropriate interventions.

Dengue fever affects over 390 million people annually worldwide and is of particu- lar concern in Southeast Asia where it is one of the leading causes of hospitalization. Modeling trends in dengue occurrence can provide valuable information to Public Health officials, however many challenges arise depending on the data available. In Thailand, reporting of dengue cases is often delayed by more than 6 weeks, and a small fraction of cases may not be reported until over 11 months after they occurred. This study shows that incorporating data on Google Search trends can improve dis- ease predictions in settings with severely underreported data. We compare penalized regression approaches to seasonal baseline models and illustrate that incorporation of search data can improve prediction error. This builds on previous research show- ing that search data and recent surveillance data together can be used to create accurate forecasts for diseases such as influenza and dengue fever. This work shows that even in settings where timely surveillance data is not available, using search data in real-time can produce more accurate short-term forecasts than a seasonal baseline prediction. However, forecast accuracy degrades the further into the future the forecasts go. The relative accuracy of these forecasts compared to a seasonal average forecast varies depending on location. Overall, these data and models can improve short-term public health situational awareness and should be incorporated into larger real-time forecasting efforts.

Syndromic surveillance is defined generally as the collection and statistical analysis of data which are believed to be leading indicators for the presence of deleterious activities developing within a system. Conceptually, syndromic surveillance can be applied to any discipline in which it is important to know when external influences manifest themselves in a system by forcing it to depart from its baseline. Comparing syndromic surveillance systems have led to mixed results, where models that dominate in one performance metric are often sorely deficient in another. This results in a zero-sum trade off where one performance metric must be afforded greater importance for a decision to be made. This thesis presents a dynamic pooling technique which allows for the combination of competing syndromic surveillance models in such a way that the resulting detection algorithm offers a superior combination of sensitivity and specificity, two of the key model metrics, than any of the models individually. We then apply this methodology to a simulated data set in the context of detecting outbreaks of disease in an animal population. We find that this dynamic pooling methodology is robust in the sense that it is capable of superior overall performance with respect to sensitivity, specificity, and mean time to detection under varying conditions of baseline data behavior, e.g. controlling for the presence or absence of various levels of trend and seasonality, as well as in simulated out-of-sample performance tests.

Infectious disease forecasting efforts underwent rapid growth during the COVID-19 pandemic, providing guidance for pandemic response and about potential future trends. Yet despite their importance, short-term forecasting models often struggled to produce accurate real-time predictions of this complex and rapidly changing system. This gap in accuracy persisted into the pandemic and warrants the exploration and testing of new methods to glean fresh insights. In this work, we examined the application of the temporal hierarchical forecasting (THieF) methodology to probabilistic forecasts of COVID-19 incident hospital admissions in the United States. THieF is an innovative forecasting technique that aggregates time-series data into a hierarchy made up of different temporal scales, produces forecasts at each level of the hierarchy, then reconciles those forecasts using optimized weighted forecast combination. While THieF's unique approach has shown substantial accuracy improvements in a diverse range of applications, such as operations management and emergency room admission predictions, this technique had not previously been applied to outbreak forecasting. We generated candidate models formulated using the THieF methodology, which differed by their hierarchy schemes and data transformations, and ensembles of the THieF models, computed as a mean of predictive quantiles. The models were evaluated using weighted interval score (WIS) as a measure of forecast skill, and the top-performing subset was compared to several benchmark models. These models included simple ARIMA and seasonal ARIMA models, a naive baseline model, and an ensemble of operational incident hospitalization models from the US COVID-19 Forecast Hub. The THieF models and THieF ensembles demonstrated improvements in WIS and MAE, as well as competitive prediction interval coverage, over many benchmark models for both the validation and testing phases. The best THieF model generally ranked second out of nine total models during the testing evaluation. These accuracy improvements suggest the THieF methodology may serve as a useful addition to the infectious disease forecasting toolkit.

<p>Postpartum depression has become a major public health concern for women within a specific time period after delivery. Depression is possibly associated with some risk factors such as socioeconomic status, social support, maternal mental and physical health, and history of anxiety. TOMIS III, funded by the Canadian Institutes of Health Research, is a prospective cohort to study the associations between delivery method and health and health resource utilization.</p> <p>Clinically, we investigated the associations between mode of delivery and outcome of postnatal depression, maternal and infant health, and we implied the risk predictors for outcomes by statistical methodology of marginal model with generalized estimating equations (GEE). Statistically, a variety of regression models, namely, generalized linear mixed effect model (GLMM), hierarchical generalized linear model (HGLM) and Bayesian hierarchical model were applied for this analysis and results were compared with GEEs. Some imputation strategies, namely, mean imputation, last observation carrying forward (LOCF), hot-deck imputation and multiple imputation were employed for handling missing values in this study.</p> <p>Analysis results demonstrated that there was no statistically significant association between mode of delivery and postpartum depression [OR 0.99, 95% CI (0.73, 1.34)]. However, the development of postpartum depression was found to be associated with low income, low mental and physical health functioning, lack of social support, the low number of unmet learning needs in hospital, and English or French spoken at home. Results were consistent for all regression models but GEE provided the best fit and an excellent discriminative ability. GEE models were constructed on different datasets imputed by mean, LOCF, hot-deck and multiple imputation, and LOCF was recommended to handle the missing data in this longitudinal study.</p> <p>Analyses on the outcome of maternal health and infant health stated that method of delivery had a statistically significant influence on maternal health but no significant impact on infant health. Risks of maternal health problems were associated with cesarean delivery, good/fair/poor infant health, low maternal mental and physical health functioning, lack of care for maternal mental health, and good/fair/poor health before pregnancy. Risks of infant health problems were associated with good/fair/poor maternal health before pregnancy and after discharge, inadequate care or help for infant health, fair/poor community services after discharge, low maternal mental health functioning, non-English or non-French spoken at home, and mothers born outside of Canada.</p> / Master of Science (MSc)

<p>Correlated data with complex association structures arise from longitudinal studies and cluster randomized trials. However, some methodological challenges in the design and analysis of such studies or trials have not been overcome. In this thesis, we address three of the challenges: 1) <em>Power analysis for population based longitudinal study investigating gene-environment interaction effects on chronic disease:</em> For longitudinal studies with interest in investigating the gene-environment interaction in disease susceptibility and progression, rigorous statistical power estimation is crucial to ensure that such studies are scientifically useful and cost-effective since human genome epidemiology is expensive. However conventional sample size calculations for longitudinal study can seriously overestimate the statistical power due to overlooking the measurement error, unmeasured etiological determinants, and competing events that can impede the occurrence of the event of interest. 2) <em>Comparing the performance of different multiple imputation strategies for missing binary outcomes in cluster randomized trials</em>: Though researchers have proposed various strategies to handle missing binary outcome in cluster randomized trials (CRTs), comprehensive guidelines on the selection of the most appropriate or optimal strategy are not available in the literature. 3) <em>Comparison of population-averaged and cluster-specific models for the analysis of cluster randomized trials with missing binary outcome</em>: Both population-averaged and cluster-specific models are commonly used for analyzing binary outcomes in CRTs. However, little attention has been paid to their accuracy and efficiency when analyzing data with missing outcomes. The objective of this thesis is to provide researchers recommendations and guidance for future research in handling the above issues.</p> / Doctor of Philosophy (PhD)

Os modelos mistos são apropriados na análise de dados longitudinais, agrupados e hierárquicos, permitindo descrever e comparar os perfis médios de respostas, levando em conta a variabilidade e a correlação entre as unidades experimentais de um mesmo grupo e entre os valores observados na mesma unidade experimental ao longo do tempo, assim como a heterogeneidade das variâncias. Esses modelos possibilitam a análise de dados desbalanceados, incompletos ou irregulares com relação ao tempo. Neste trabalho, buscou-se mostrar a flexibilidade dos modelos lineares mistos e a sua importância na análise de dados toxicológicos longitudinais. Os modelos lineares mistos foram utilizados para analisar os efeitos de dose no ganho de peso de ratos adultos machos e fêmeas, em teste de toxicidade por doses repetidas e também os efeitos de fase de gestação e dose nos perfis de pesos de filhotes de ratas tratadas. Foram comparados os modelos lineares mistos de regressão polinomial de grau 3, spline e de regressão por partes, ambos com um único ponto de mudança na idade média de abertura dos olhos dos filhotes, buscando o mais apropriado para descrever o crescimento dos mesmos ao longo do período de amamentação. São apresentados os códigos escritos no SAS/STAT para a análise exploratória dos dados, ajuste, comparação e validação dos modelos. Espera-se que o detalhamento da teoria e das aplicações apresentado contribua para a compreensão, interesse e uso desta metodologia por estatísticos e pesquisadores da área. / Mixed models are appropriate in the analysis of longitudinal, grouped and hierarchical data, allowing describe and compare the average response profiles, taking into account the variability and correlation among the experimental units of the same group and among the values observed over the time in the same experimental unit, as well as the heterogeneity of variances. These models allow the analysis of unbalanced, incomplete or irregular data with respect to time. This work aimed to show the flexibility of linear mixed models and its importance in the analysis of longitudinal toxicological data. Linear mixed models were used to evaluate the effects of doses in the body weight gain of adult male and female Wistar rats, in repeated doses toxicity test and also the effects of pregnancy period and dose in the pups growth of treated dams. It were compared the linear mixed models of third degree polynomial regression, spline and piecewise regression, both with a single point of change in the average time of pups eyes opening, searching for the most appropriate one to describe their growth along the lactation period. The SAS/STAT codes used for exploratory data analysis, comparison and validation of fitted models are presented. It is expected that the detailing of the theory and of the applications presented contribute with the understanding, interest and use of this methodology by statisticians and researchers in the area.

Diversos delineamentos experimentais que são aplicados correntemente tomam como base experimentos agronômicos. Esses dados experimentais são, geralmente, analisados usando-se modelos que consideram uma variância residual constante (ou homogênea), como pressuposto inicial. Entretanto, esta pressuposição mostra-se relativamente forte quando se está diante de situações para as quais fatores ambientais ou externos exercem considerável influência nas medidas experimentais. Neste trabalho, são estudados modelos para a média e a variância, simultaneamente, com a variância estruturada de duas formas: (i) por meio de um preditor linear, que permite incorporar variáveis externas e fatores de ruído e (ii) por meio de efeitos aleatórios, que permitem acomodar tanto o efeito longitudinal quanto o efeito de superdispersão, no caso de medidas binárias repetidas no tempo. A classe de modelos lineares generalizados duplos (MLGD) foi aplicada a um estudo observacional que consistiu em medir a mortalidade de frangos de corte no fim da condição de espera pré-abate. Nesse problema, é forte a evidência de que alguns fatores influenciam a variabilidade, e consequentemente, diminuem a precisão das análises inferenciais. Outro problema agronômico relevante, associado à horticultura, são os experimentos de cultura de tecidos vegetais, em que o número de explantes que regeneram são contados. Como esse tipo de experimento apresenta um grande número de parâmetros a serem estimados, comparado ao tamanho da amostra, os modelos existente podem gerar estimativas questionáveis ou até levar a conclusões erroneas, uma vez esse que são baseados em grandes amostras para se fazer inferência estatística. Foi proposto um modelo linear generalizados duplo, para os dados de proporções, de uma perspectiva Bayesiana, visando a análise estatística sob pequenas amostras e a incorporação do conhecimento especialista no processo de estimação dos parâmetros. Um problema clínico, que envolve dados binários medidos repetidamente no tempo é apresentado e são propostos dois modelos que acomodam o efeito da superdispersão e a dependência longitudinal das medidas, utilizandos-se efeitos aleatórios. Foram obtidos resultados satisfatórios nos três problemas estudados. Os MLGD permitiram identificar os fatores associados à mortalidade das aves de corte, o que permitirá minimizar perdas e habilitar os processos de manejo, transporte e abate aos critérios de bem-estar animal e exigências da comunidade européia. O MLGD Bayesiano permitiu identificar o genótipo associado ao efeito de superdispersão, aumentando a precisão da inferência de seleção de variedades. Dois modelos combinados foram propostos logit-normal-Bernoulli-beta e o probit-normal-Bernoulli-beta, que acomodaram satisfatoriamente a superdispersão e a dependência longitudinal das medidas binárias. Esses resultados reforçam a importância de se modelar a média e a variância conjuntamente, o que aumenta a precisão na pesquisa agronômica, tanto em estudos experimentais quanto em estudos observacionais. / Several experimental designs that are currently applied are based on agricultural experiments. These experimental data are, usually, analised with statistical models that assume constant residual variance (or homogeneous), as basic assumption. However, this assumption shows hard to stand for, when environmental or external factors exert strong influence over the measurements. In this work, we study the joint modelling for the mean and the variance, the latter being structured on two ways: (i) through a linear predictor, which allows the incorporation of external variables and/or noise factors and (ii) by the use of random effects, that accommodate jointly the possible overdispersion effect and the dependence of longitudinal data in the case of binary measusurements taken over time. The class of double generalized linear models (DGLM) was applied to an observational study where the poultry mortality was measured in the preslaughter operations. With this situation, it can be observed that there is a strong influence from some environmental factors over the variability observed, and consequently, this reduces the precision of the inferential analysis. Another relevant agricultural problem, related to horticulture, is the tissue culture experiments, where the number of regenerated explants is counted. Usually, this kind of experiment use a large number of parameters to be estimated, when compared with the sample size. The current frequentist models are based on large samples for statistical inference and, under this experimental condition, can generate unreliable estimates or even lead to erroneous conclusions. A double generalized linear model was proposed to analyse proportion data, under the Bayesian perspective, which can be applied to small samples and can incorporate expert knowledge into the parameter estimation process. One clinical research, that measured binary data repeatedly through the time is presented and two models are proposed to fit the overdispersion effect and the dependence of longitudinal measurements, using random effects. It was obtained satisfactory results under these three problems studied. the DGLM allowed to identify factors associated with the poultry mortality, that will allow to minimize loss and improve the process, since the catching until lairage on slaughterhouse, agreeing with animal welfare criteria and the European community rules. The Bayesian DGLM allowed to identify the genotype associated with the overdispersion effect, increasing the precision on the inference about varieties selection. Two combined models were proposed, a logit-normal- Bernoulli-beta and a probit-normal-Bernoulli-beta, which have both addressed the overdispersion effect and the longitudinal dependence of the binary measurements. These results reinforce the importance to modelling mean and dispersion jointly, as a way to increase the precision of agricultural experimentation, be it on experimental studies or observational studies.

Dados consistindo de medidas repetidas tomadas em um mesmo indivíduo são muito comuns na agricultura e biologia. A modelagem de dados desta natureza usualmente envolve a caracterização da relação entre medidas repetidas e covariáveis. Em muitas aplicações, a relação proposta entre as medidas repetidas tem um comportamento não-linear nos parâmetros desconhecidos de interesse. Por exemplo, em estudo de crescimento de arvores, geralmente o comportamento da variável resposta e melhor descrito por um modelo não-linear nos parâmetros porque estes modelos caracterizam melhor a realidade dos fenômenos biológicos em estudo e porque e possvel uma interpretação biológica dos parâmetros. A presença de medidas repetidas em um indivíduo requer um cuidado particular na caracterização da variac~ao entre medidas dentro de uma mesma unidade experimental e entre unidades. Dados observados na mesma unidade experimental são correlacionados, e é provável que essa correlação decaia ao longo do tempo e que haja variações entre as medidas. Neste trabalho considera-se duas estruturas de covariâncias: erros aleatórios e independentes com media zero e variância 2, esta formulação não incorpora uma possível dependência entre as observações tomadas no mesmo indivíduo, que e comum em estudos longitudinais. Portanto, e importante ter modelos que acomodem a dependência (entre e dentre dos indivíduos) e a heterocedasticidade na sua formulação. Então, considerou-se outra estrutura de covariância, chamada não-estruturada, com a nulidade de permitir que os dados \"contribuam\" na estrutura da matriz de covariâncias. Neste trabalho analisou-se um delineamento em blocos casualizados assumindo um modelo bayesiano hierárquico de três estágios. No primeiro estagio, modelou-se a variação dentro do indivíduo, no segundo estagio a variação entre indivíduos. Este estágio da hierarquia da uma relação explícita entre os parâmetros aleatórios do modelo. No terceiro estagio foi incorporada a incerteza relativa as quantidades desconhecidas no modelo. Para a analise estatística, utilizou-se um conjunto de dados de um experimento conduzido pela Klabin Fabricadora de Papel e Celulose S.A., do Paraná, Brasil, envolvendo duas espécies de eucaliptos e espaçamentos 10 que foram completamente aleatorizados em blocos; em que a variável resposta, definida como o volume solido com casca, foi observada em 16 indivíduos, e quatro indivíduos foram aleatorizados para cada um dos quatro tratamentos. O modelo de Gompertz foi utilizado para representar o crescimento esperado das arvores de eucaliptos. Usando o modelo de Gompertz e possível ter uma interpretação biológica dos parâmetros. Considerando diferentes estruturas de covariância entre as observações, um programa para a analise de dados foi implementado no WinBUGS. / Data consisting of repeated measurements taken on each of a number of individual arise commonly in agricultural and biological applications. Modeling data of this kind usually involves the characterization of the relationship between the measured response and covariate. In many application,the proposed systematic relationship between the measured response is nonlinear in unknown parameters of interest. For example, in growing studies of trees, generally the behavior of the response variable over time is best described by a nonlinear model in the parameters of interest because this model characterizes better the reality of biological phenomenon in study and because is possible to do a biological interpretation of the parameters. The presence of repeated observations on an individual requires particular care in characterizing the random variation among measurements within a given individual and random variation among individuals. Likely the observations made on the same unit are correlated, probability decreasing over time and possible the variances are growth among the serial measurements. In this work we considerer two covariance structure namely: independent random error vectors whose elements are also independent with mean zero and variance 2, but this formulation does not incorporate possible dependence among the observation taken on the same subject neither that in longitudinal studies it is quite common to have the variances varying along the ordered dimension. Therefore, it is important to have models that allow for both dependences (within and between subjects) and also for heteroscedasticity in their formulations. Then we considerer other covariance structure namely: the structure is a non structure which permit that the data set \\tells\"about the covariance structure. In this work we analyzed a randomized block design assuming a three-stage Bayesian hierarchical model. On the rst stage, we model the intra-individual variation, on the second stage, we model the inter-individual variation. This stage of hierarchy gives an explicit relationship between the random parameters. On the third stage, we dene the hyperprior distribution to incorporate the uncertainty about the unknown parameters. For the statistical analysis we used a data set 12 from a experiment conducted at Klabin Fabricadora de Papel e Celulose S.A. from Parana, Brazil, involving two Eucalyptus species and two spacings in a complete randomized design; where the response variable, dened as the solid volume with bark, was evaluated for each of 16 subjects (groups of Eucalyptus trees), and four subjects were randomly assigned to one of four treatments. To represent the expected growing function of the Eucalyptus\'s tree Gompertz nonlinear model was used. Using the Gompertz nonlinear model is possible to a biological interpretation of the parameters. Considering dierent structures covariance within subjects, a program for the analysis of the data set was implemented in WinBUGS.

Dados consistindo de medidas repetidas tomadas em um mesmo indivíduo são muito comuns na agricultura e biologia. A modelagem de dados desta natureza usualmente envolve a caracterização da relação entre medidas repetidas e covariáveis. Em muitas aplicações, a relação proposta entre as medidas repetidas tem um comportamento não-linear nos parâmetros desconhecidos de interesse. Por exemplo, em estudo de crescimento de arvores, geralmente o comportamento da variável resposta e melhor descrito por um modelo não-linear nos parâmetros porque estes modelos caracterizam melhor a realidade dos fenômenos biológicos em estudo e porque e possvel uma interpretação biológica dos parâmetros. A presença de medidas repetidas em um indivíduo requer um cuidado particular na caracterização da variac~ao entre medidas dentro de uma mesma unidade experimental e entre unidades. Dados observados na mesma unidade experimental são correlacionados, e é provável que essa correlação decaia ao longo do tempo e que haja variações entre as medidas. Neste trabalho considera-se duas estruturas de covariâncias: erros aleatórios e independentes com media zero e variância 2, esta formulação não incorpora uma possível dependência entre as observações tomadas no mesmo indivíduo, que e comum em estudos longitudinais. Portanto, e importante ter modelos que acomodem a dependência (entre e dentre dos indivíduos) e a heterocedasticidade na sua formulação. Então, considerou-se outra estrutura de covariância, chamada não-estruturada, com a nulidade de permitir que os dados \"contribuam\" na estrutura da matriz de covariâncias. Neste trabalho analisou-se um delineamento em blocos casualizados assumindo um modelo bayesiano hierárquico de três estágios. No primeiro estagio, modelou-se a variação dentro do indivíduo, no segundo estagio a variação entre indivíduos. Este estágio da hierarquia da uma relação explícita entre os parâmetros aleatórios do modelo. No terceiro estagio foi incorporada a incerteza relativa as quantidades desconhecidas no modelo. Para a analise estatística, utilizou-se um conjunto de dados de um experimento conduzido pela Klabin Fabricadora de Papel e Celulose S.A., do Paraná, Brasil, envolvendo duas espécies de eucaliptos e espaçamentos 10 que foram completamente aleatorizados em blocos; em que a variável resposta, definida como o volume solido com casca, foi observada em 16 indivíduos, e quatro indivíduos foram aleatorizados para cada um dos quatro tratamentos. O modelo de Gompertz foi utilizado para representar o crescimento esperado das arvores de eucaliptos. Usando o modelo de Gompertz e possível ter uma interpretação biológica dos parâmetros. Considerando diferentes estruturas de covariância entre as observações, um programa para a analise de dados foi implementado no WinBUGS. / Data consisting of repeated measurements taken on each of a number of individual arise commonly in agricultural and biological applications. Modeling data of this kind usually involves the characterization of the relationship between the measured response and covariate. In many application,the proposed systematic relationship between the measured response is nonlinear in unknown parameters of interest. For example, in growing studies of trees, generally the behavior of the response variable over time is best described by a nonlinear model in the parameters of interest because this model characterizes better the reality of biological phenomenon in study and because is possible to do a biological interpretation of the parameters. The presence of repeated observations on an individual requires particular care in characterizing the random variation among measurements within a given individual and random variation among individuals. Likely the observations made on the same unit are correlated, probability decreasing over time and possible the variances are growth among the serial measurements. In this work we considerer two covariance structure namely: independent random error vectors whose elements are also independent with mean zero and variance 2, but this formulation does not incorporate possible dependence among the observation taken on the same subject neither that in longitudinal studies it is quite common to have the variances varying along the ordered dimension. Therefore, it is important to have models that allow for both dependences (within and between subjects) and also for heteroscedasticity in their formulations. Then we considerer other covariance structure namely: the structure is a non structure which permit that the data set \\tells\"about the covariance structure. In this work we analyzed a randomized block design assuming a three-stage Bayesian hierarchical model. On the rst stage, we model the intra-individual variation, on the second stage, we model the inter-individual variation. This stage of hierarchy gives an explicit relationship between the random parameters. On the third stage, we dene the hyperprior distribution to incorporate the uncertainty about the unknown parameters. For the statistical analysis we used a data set 12 from a experiment conducted at Klabin Fabricadora de Papel e Celulose S.A. from Parana, Brazil, involving two Eucalyptus species and two spacings in a complete randomized design; where the response variable, dened as the solid volume with bark, was evaluated for each of 16 subjects (groups of Eucalyptus trees), and four subjects were randomly assigned to one of four treatments. To represent the expected growing function of the Eucalyptus\'s tree Gompertz nonlinear model was used. Using the Gompertz nonlinear model is possible to a biological interpretation of the parameters. Considering dierent structures covariance within subjects, a program for the analysis of the data set was implemented in WinBUGS.