  Cytotoxic T-lymphocytes (CTLs) recognize viral protein fragments displayed by
major histocompatibility complex (MHC) molecules on the surface of virally
infected cells and generate an anti-viral response that can kill the infected
cells. Virus variants whose protein fragments are not efficiently presented on
infected cells or whose fragments are presented but not recognized by CTLs
therefore have a competitive advantage and spread rapidly through the
population. We present a method that allows a more robust estimation of these
escape rates from serially sampled sequence data. The proposed method accounts
for competition between multiple escapes by explicitly modeling the
accumulation of escape mutations and the stochastic effects of rare multiple
mutants. Applying our method to serially sampled HIV sequence data, we estimate
rates of HIV escape that are substantially larger than those previously
reported. The method can be extended to complex escapes that require
compensatory mutations. We expect our method to be applicable in other contexts
such as cancer evolution where time series data is also available.
