Modelos mistos semiparamétricos parcialmente não lineares

Abstract

Correlated data sets with nonlinear structure are common in many areas such as biostatistics, pharmacokinetics and longitudinal studies. Nonlinear mixed-effects models are useful tools to analyse those type of problems. In this dissertation, a generalization to this models is proposed, namely by semiparametric partially nonlinear mixed-effects model (MMSPNL), with a nonparametric function to model the mean of the response variable. It assumes that the mean of the interest variable is explained by a nonlinear function, which depends on fixed effects parameters and explanatory variables, and by a nonparametric function. Such nonparametic function is quite flexible, allowing a better adequacy to the functional form that underlies the data. The random effects are included linearly to the model, which simplify the expression of the response variable distribution and enables the model to take into account the within-group correlation structure. It is assumed that the random errors and the random effects jointly follow a multivariate normal distribution. Relate to the nonparametric function, it is deal with the P-splines smoothing technique. The methodology to obtain the parameters estimates is penalized maximum likelihood method. The random effects may be obtained by using the Empirical Bayes method. The goodness of the model and identification of potencial influent observation is verified with the local influence method and a residual analysis. The pharmacokinetic data set, in which the anti-asthmatic drug theophylline was administered to 12 subjects and serum concentrations were taken at 11 time points over the 25 hours (after being administered), was re-analysed with the proposed model, exemplifying its uses and properties.