We propose two extensions of the Logical Analysis of Data (LAD) methodology, designed in the context of diagnosing growth hormone deficiencies. On the one hand, combinatorial regression extends the standard methodology from classification problems to regression problems; it permits to predict the final height of children with particular growth troubles. On the other hand, function-based patterns extend the standard notion of pattern, leading to both accurate and simple models; it allows to produce an efficient diagnosis, straightforwardly usable by a general practitioner, that settles most of the doubtful cases of growth hormone deficiencies among short children. In both cases, we show the interest of the LAD extensions for each application, and we also point out the more general use that can be achieved through the two proposed approaches.