Proposals of models for new formulations of the current complication-free cure (P+) and uncomplicated tumor control probability (UTCP) concepts, and total normal tissue complication probability of late complications.

This study proposes phenomenological models for total normal tissue complication probability (TNTCP) and NTCP0. NTCP0 is a new acronym for reformulating the current complication-free cure (P+) and uncomplicated tumor control probability (UTCP) concepts, and TNTCP will reformulate the current NTCP involving multiple organs at risks. The current probabilistic concepts are incoherently formulated with mathematical operations of tumor control probability (TCP) and normal tissue complication probability (NTCP) that are associated with different stochastic processes and random variables. NTCP0 is equal to NTCP0 (normal tissue non-complication probability) that is calculated as the ratio of a number of patients of a population without late complications and a total of them. As a cumulative distribution function (CDF) of late complications, TNTCP = sum(NTCPi), where NTCPi is the NTCP of the ith late complication. TNTCP is also a new acronym, and the probabilistic complement of NTCP0, then NTCP0 = 100% - TNTCP. The NTCP0/TNTCP (D(d)) proposing models are based on the relationship between the NTCP0/TNTCP and total dose (D = n×d; where d = dose per fraction, and n = number of fractions). TNTCP(D) model will be correlated with LKB model (the normal CDF) that is an increasing function; and NTCP0(D) model with a decreasing function, which additionally will define clear limits of three possible regions for NTCP0: 0 and 100% deterministic, and a stochastic. These models are function D, which is widely used for characterizing radiation therapies.