Estimating the predictability of cancer evolution

Abstract

Motivation How predictable is the evolution of cancer? This fundamental question is of immense relevance for the diagnosis, prognosis and treatment of cancer. Evolutionary biologists have approached the question of predictability based on the underlying fitness landscape. However, empirical fitness landscapes of tumor cells are impossible to determine in vivo. Thus, in order to quantify the predictability of cancer evolution, alternative approaches are required that circumvent the need for fitness landscapes. Results We developed a computational method based on conjunctive Bayesian networks (CBNs) to quantify the predictability of cancer evolution directly from mutational data, without the need for measuring or estimating fitness. Using simulated data derived from >200 different fitness landscapes, we show that our CBN-based notion of evolutionary predictability strongly correlates with the classical notion of predictability based on fitness landscapes under the strong selection weak mutation assumption. The statistical framework enables robust and scalable quantification of evolutionary predictability. We applied our approach to driver mutation data from the TCGA and the MSK-IMPACT clinical cohorts to systematically compare the predictability of 15 different cancer types. We found that cancer evolution is remarkably predictable as only a small fraction of evolutionary trajectories are feasible during cancer progression. Availability and implementation https://github.com/cbg-ethz/predictability\_of\_cancer\_evolution Supplementary information Supplementary data are available at Bioinformatics online.

Every which way? On predicting tumor evolution using cancer progression models

“…Under representable fitness landscapes, H-CBN, the best performing model also for this task (Fig 6B), returned values of S c very similar to S p , the evolutionary unpredictability estimated from the diversity of paths, and this held over detection regimes and sample sizes. Hosseini et al [36] also find that the estimates of predictability from H-CBN correlate well with the fitness landscape-based evolutionary predictability (estimated assuming SSWM in fitness landscapes where the fully mutated genotype has largest fitness), with slopes of the regression of CPM-based on landscape-based predictability generally slightly below 1, similar to our findings (Fig 6C). These good results do not hold under the other two types of fitness landscapes that we analyzed: evolutionary unpredictability is overestimated and increasing sample size made the problems worse, and different evolutionary scenarios, sample sizes, and detection regimes have different relationships of estimated and true unpredictability (Fig 6C).…”

“…Hosseini et al [36] reanalized the DAG-derived representable and a subset (those where the fully mutated genotype has the largest fitness) of the DAG-derived non-representable fitness landscapes in [31]. They find good agreement between the distributions of paths to the maximum from H-CBN and the fitness landscape-based probability distribution of paths to the maximum computed assuming SSWM.…”

“…Two differences in the studies explain the differences. First, [36] computes the fitness landscape-based probability of paths assuming a SSWM regime and restricting the analysis to fitness landscapes where the fully mutated genotype has the largest fitness, while our analyses directly examine the distribution of the paths to the maximum in each simulation (LODs), without restricting the evolutionary regime and the fitness landscapes; second, [36] uses H-CBN with the very large sample size of 20000 (the full data sets in [31]), while we use a more realistic range of sample sizes.…”

“…This we did for all models. From H-CBN and MCCBN we can also obtain the estimated probability of each path of tumor progression to the fitness maximum, since both H-CBN and MCCBN return the parameters of the waiting time to occurrence of each mutation (given its restrictions are satisfied; e.g., [11, p. i729], [9, section 2.2], or [36]; details and example in section 3 of S4 Text). It is also possible to perform a similar operation with the output of OT, and use the edge weights from the fits of OT to obtain the probabilities of transition to each descendant genotype and, from them, the probabilities of the different paths to the single fitness maximum.…”

“…Evolutionary unpredictability, as estimated by the CPMs, will analogously be defined as S c = −∑ q j ln q j , where q j is the probability of each path to the maximum according to the cancer progression model considered, and the sum is over all paths predicted by the CPMs. ([36] normalizes predictability by dividing by the maximum entropy, similar to dividing by the prior entropy in the “information gain” statistic in [5]; but the maximum entropy is a constant for each number of genes, i.e., 7! or 10!…”