Probability Distribution for Rare Neutral Mutations in Cancers and Application to Dynamic Precision Medicine of Cancer

Cancers exhibit genetic diversity between individual cancer cells. Previous work shows greater diversity than heretofore expected (1) and that also increases more quickly during a patient’s clinical course than previously thought (1, 2). Rare subclones will harbor pre-existing resistance to any single agent and may cause medium to late term relapse (1), which may evolve further variants that have simultaneous resistance to non-cross resistant therapies (3, 4). We now present a probability distribution function (PDF) of the variant allele fraction (VAF) or prevalence of a rare subclone, derived from previous evolutionary theory (1, 2). We show that current clinical sequencing protocols fail to detect the vast majority of rare subclones. By the time of detection, simultaneous multiple resistance may evolve. We then apply the PDF to simulation of dynamic precision medicine (DPM) (3), an evolutionary guided precision medicine paradigm that attempts to proactively eliminate singly-resistant subclones before they evolve multiple resistance, with significant potential to extend survival. We show that the simulated benefit of DPM with perfect information is degraded by inability to detect rare subclones if they are assumed to be absent when undetectable. But this benefit is restored if the PDF is used to calculate the likelihood of the subclone being present below the level of detection and incorporated into the DPM simulation and therapy recommendations in a probabilistic fashion. Moreover, other common statistical distributions are less effective. This theoretical advance facilitates DPM and potentially other evolutionary guided approaches to precision cancer medicine in spite of the limitations of clinical sequencing.