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

Abstract

Cancers exhibit substantial genetic diversity between individual cells. Previous work shows greater overall diversity that also increases more quickly during a patients clinical course than heretofore expected. Rare subclones will harbor pre-existing resistance to any single agent and may cause medium to late term relapse, which may evolve further variants that have simultaneous resistance to non-cross resistant therapies. In this work, we present a probability distribution function (PDF) of the variant allele fraction (VAF), or prevalence, of a rare subclone, derived from previous evolutionary theory. We show that current clinical sequencing protocols fail to detect the vast majority of these rare subclones and that by the time of detection, simultaneous multiple resistance may already evolve. We apply the PDF to simulation of dynamic precision medicine (DPM), 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 the simulated benefit of DPM with perfect information is hampered by an inability to detect rare subclones if they are assumed to be absent when undetectable. However, the DPM 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. Two 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. Significance StatementCancers contain many cells, each genetically unique. These variations can include pre-existing resistance to therapy, enabling relapse. DNA sequencing cannot detect minority cellular populations (subclones) below a certain size, by which time they may have already evolved simultaneous resistance to multiple therapies. We present a mathematical approach that assigns a risk that a subclone is present, and at what prevalence in the cellular population, even when undetected. We simulate applying this approach to dynamic precision medicine (DPM), which attempts to proactively eliminate singly resistant cells before they become resistant to multiple therapies. Using this probability distribution, we can retain the benefit of DPM even when most rare subclones are undetectable, in contrast to just assuming undetected subclones are absent.