Monte Carlo simulation of detection sensitivity

We used Monte Carlo simulation to estimate the probability of detecting a molecule with a tumor-derived alteration. Briefly, we generated 1 million molecules from a multinomial distribution. For a simulation with m alterations, wild-type molecules were simulated with probability p and each of the m tumor alterations were simulated with probability (1-p)/m. Next, we sampled g * m molecules randomly with replacement, where g denotes the number of genome equivalents in 1 ml of plasma. If a tumor alteration was sampled s or more times, we classified the sample as cancer-derived. We repeated the simulation 1000 times, estimating the probability that the in silico sample would be correctly classified as cancer by the mean of the cancer indicator. Setting g = 2000 and s = 5, we varied the number of tumor alterations by powers of 2 from 1 to 256 and the fraction of tumor-derived molecules from 0.0001% to 1%.