The problem of construction of non-linear prognostic models is dealt with. A method of by-piece approximation is suggested as a means of increasing the reliability of predictions. In this case the procedure of making a prediction consists of two stages: first subjects are divided by types, then a particular prognostic equation is composed for each type. A complex function is therefore represented by a composition of "simple" functions (e. g. linear functions or constant functions) each corresponding to a particular sub-sample. Efficiency of the approach is illustrated by exemplary instances of prediction of outcomes of clinical treatment of chronic alcoholics on the basis of their personality characteristics.