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# BIOMATHEMATICS & APPLIED STATISTICS

### Rationale

With the development of increasingly accelerated technology, mathematics are considered nowadays as a complex and abstract science with little use. Yet mathematics, through the development of theories and methodological tools are unquestionably those who have the most advanced human knowledge of our environment. The development of practical applications of mathematics in different scientific fields should help in renewing interest in mathematics. Biomathematics can be viewed as the combination of two sciences: biology and mathematics and are interested in applications of mathematics in the field of biology. The research unit on biomathematics and applied statistics falls into this perspective. This unit is interested not only in the use of mathematical theories in biology but especially publishing scientific notes describing the application of different mathematical tools in life sciences.

### Foci

• Biostatistics
• quantitative genetics
• agricultural and health econometrics
• bioinformatics.

### MSc. research

Estimation of population pharmacokinetic parameters with sparse data in Nonparametric nonlinear mixed effect model

Several models are used to study the pharmacokinetics and pharmacodynamics of a drug. Estimation of the parameters of these models is delicate due to the digital nature of the assessment of their quality. Indeed, these models generally correspond to dynamic systems described by differential equations which are not analytically integrable. Thereby, the calibration is expensive in calculation time, and in the convergence of the proposed algorithms. Recently, new approaches have been developed to estimate the dynamic system parameters, which could offer interesting alternatives. These include the method of SMC-ABC (Approximate Bayesian Computing by Sequential Monte Carlo) and approaches by particles convolution filtering. This research aims to (i) explore PK/PD models and the more conventional data sets typically used to estimate their parameters, identifying similarities and differences; (ii) review the parameters estimation methods currently used on PK/PD models; (iii) explore the recently proposed algorithms for type SMC-ABC methods and approaches by particles convolution filtering and (iv) compare the methods implemented on PK/PD data of the eflavirance Beninese subjects to antiretroviral (ART). For more details please contact Castro HOUNMENOU [Defended]

Longitudinal data analysis: fitting an optimal variance-covariance structure under linear mixed effects models framework

With longitudinal data, measures on the same subject at different times tend to be correlated. Hence, taking this dependency into account by specifying right covariance structure for observations within each subject becomes an important issue. Contrary to standard multivariate models, multilevel models are more flexible to model these data. The purpose of this study is to evaluate the performance of five fit statistics i.e. Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Consistent Akaike Information Criterion (CAIC), Hannan and Quin Information Criterion (HQIC) and Akaike Information Criterion – Corrected (AICC) in identifying the correct within subject covariance structure. We will focus on the sample size at each level of the model, magnitudes of growth parameter of the model and between and within subject covariance matrices. Moreover, the consequence of simultaneous misspecification in both within and between subject covariance structures will be investigated. Applications to real-word data will be done on appropriate ecological data. For more details please contact Aubin AMAGNIDE [Defended]

Generalized linear models with Poisson family: applications in ecology
Ecological data are often discrete. Such data often do not meet the assumptions of the General linear model and its variants. Putting in relation count data and covariates by classical general linear model requires some assumptions that are frequently violated. To solve these problems, GLM (Generalized Linear Models) have been more recently developed. The GLMs are a generalization of linear regression to response types other than Gaussian, as long as the distribution of that response is a member of the exponential family. The basic GLM for count data is the Poisson model with log link. The main assumption of Poisson model is the equality of mean and variance. Frequently, however, count data are often ‘‘overdispersed’’ i.e. a greater variance than the mean. Some extensions of Poisson model are usually used to deal with overdispersion, including the negative binomial, quasi-Poisson and zero-inflated models. Thus, the main question in ecological studies is: which Poisson extension model should be used according to some characteristics of the data sample considered? This Msc. thesis seeks to assess, using Monte Carlo methods, the relative performance of Poisson extension models to solve problem of overdispersion in ecological count data. For more details, contact Bruno LOKONON [Defended]

Empirical assessment of relative performance of three permutation methods in one way analysis of variance framework

In inferential statistic field, the ANOVA is by far the most used statistical method by biologists. Its use is conditioned by the normality of the data, equal populations’ variances and independence of observations. The Permutation-ANOVA (P-ANOVA) is one of the methods broadly proposed as the best non parametric alternatives when these assumptions do not hold. However when the homogeneity is violated the type I error is not maintaining and then lower the power of P-ANOVA. This work aims thus at improving the method of P-ANOVA through the control of Type I error and the power of the test. Specifically, we will control type I error and power of the test after the application of Box and Cox transformations. Performance of Box and Cox P-ANOVA will be assessed in comparison with P-ANOVA, Box and Cox ANOVA and ANOVA. Monte Carlo methods will be used to generate 100 data samples for each combination of factors considered (sample size, heteroscedasticity degree, degree of normality of the data sample). During this process each data sample generated will be run 10000 times to assess the relative performance of the 3 ANOVA methods considered. For more details, contact Merveille KOISSI [Defended]