Appreciation of medical treatments through confidence intervals

The typical way of judging about either the efficacy of a new treatment or, on the contrary, the damage of a pollutant agent is through a test of hypothesis having its ineffectiveness as null hypothesis. This is the typical operational field of Kolmogorov's statistical framework where wastes of data (for instance non significant deaths in a polluted region) represent the main drawback. Instead, confidence intervals about treatment/pollution effectiveness are a way of exploiting all data, whatever their number is. We recently proposed a new statistical framework, called Algorithmic Inference, for overcoming crucial difficulties usually met when computing these intervals and abandoning general simplifying hypotheses such as errors' Gaussian distribution. When effectiveness is expressed in terms of regression curves between observed data we come to a learning problem that we solve by identifying a region where the whole curve lies with a given confidence. The approach to inference we propose is very suitable for identifying these regions with great accuracy, even in the case of nonlinear regression models and/or a limited size of the observed sample, provided that a normally powered computing station is available. In the paper we discuss this new way of extracting functions from the experimental data and drawing conclusions about the treatments originating them. From an operational perspective, we give the general layout of the procedure for computing confidence regions as well as some applications on real data.