STIMA DI FUNZIONI NON-LINEARI DI RISPOSTA DIPENDENTI DAL TEMPO O DALLA DOSE QUANDO I PROFILI DI RISPOSTA NON POSSONO ESSERE INTERPOLATI SINGOLARMENTE

Statistical models aiming to establish the relationship of a biological response (or effect) to increasing values of dose (or time) must take into account the differences in shape that such a relationship presents between individuals. These models involve two levels of variability: a within-individual level 1 including measurement errors and random deviations from the individual dose-response function, and a between-individuals level 2 expressing the biological differences between individuals belonging to the same population. At level 1, random terms usually have a simple covariance structure (i.e. are uncorrelated). The parameters of individual functions are regarded as random variables whose means are the parameters of the function at level 2 (or population level) and whose covariance may be expressed by any Gramian. Since dose-response functions are typically nonlinear, two-stage models properly apply to this kind of problems. Unfortunately, in many situations the observed response profiles are so irregular that only mean profiles can be successfully fitted. This approach may result in a severe underestimation of the standard errors of parameters and in a confidence level by far lower than the nominal value. In addition, the estimate of one or more parameters may be biased. The simulation studies presented in this thesis demonstrate that the first drawback can be avoided including the covariance matrix of residuals conditional on the dose into the estimate of the covariance matrix of the parameters estimates, whereas the extent of bias in the estimate of a given parameter may be derived from the structure of the model.