Mapping the drivers of within-host pathogen evolution using massive data sets

Palmer, Duncan S.; Turner, Isaac; Fidler, Sarah; Frater, John; Goedhals, Dominique; Goulder, Philip; Huang, Kuan-Hsiang Gary; Oxenius, Annette; Phillips, Rodney; Shapiro, Roger; Vuuren, Cloete van; McLean, Angela R.; McVean, Gil

Felsenstein's peeling algorithm [13] is then used to evaluate the likelihood L(λ, π|D, G max ) and maximised, where D is the combination of simulated query sequences and associated host HLA data. So called 'leaf-distributions' are then potentially added using forward selection. This involves the inclusion of further hidden states -estimates of the transmitted sequence for each subsequently sampled member of the query sequences set. This transmitted sequence is then potentially modified conditional on the hosts' HLA. In the case of escape, the probability of an instantaneous switch from wild-type to escape is parameterised by a probability; p. Thus, given Q above for the remainder of the tree, and probabilities of switching between states between the hidden 'transmitted sequence' and the query sequences at the leaves, we can evaluate L(λ, π, p|D, G max ) using tree peeling. Maximising this likelihood and comparing to the current null model, parameters are added if the p-value for the associated likelihood ratio test is lower than 0.05. Whereas in Carlson et al. maximum likelihood parameterisations are obtained by either coordinate descent [14] or expectation-maximisation [9] , we take a pragmatic approach, as often certain optimisation schemes fail under different scenarios. To this end, we simultaneously run six different optimisation schemes built into the optimx R package [15] : Nelder-Mead [16] , L-BFGS-B [17] , ucminf [18] , nmkb [19] , newuoa [20] , bobyqa [21] . We stipulate that at least two schemes must converge, and choose the likelihood parameterisation of the scheme with the highest likelihood. If less than two schemes converge, new starting parameters are chosen at random and estimates are re-evaluated.