FRAILTY MODELS FOR ARBITRARILY CENSORED AND TRUNCATED DATA C. HUBER-CAROL, University of Paris V, and F. VONTA University of Cyprus   Abstract:  We propose statistical inference for a regression model including frailty for survival data that are arbitrarily censored and truncated. Our results extend those of Alioum and Commenges (1996) who developed a method of fitting a proportional hazards model to data of this kind. We discuss the identifiability of the regression coefficients which are the parameters of interest, as well as the identifiability of the baseline cumulative hazard function of the model which plays the role of the infinite dimensional nuisance parameter. We illustrate our method with a set of real data on transfusion-related AIDS.