  Intrahost simian immunodeficiency virus (SIV) evolution is marked by repeated
viral escape from cytotoxic T-lymphocyte (CTLs) response. Typically, the first
such CTL escape occurs in a matter of days, starting around the time of peak
viral load. Many authors have developed methods to quantify the strength of CTL
response by measuring the rate at which CTL escape occurs, but such methods
usually depend on sampling at two or more timepoints, while many datasets
capture the dynamics of the first CTL escape at only a single timepoint. Here,
we develop inference methods for CTL escape rates applicable to single
timepoint datasets. Through a model of early infection dynamics, we construct
confidence intervals for escape rates, but since early infection dynamics are
not completely understood, we also develop a one-sided confidence interval
serving as a lower bound for escape rates over a collection of early infection
models. We apply our methods to two SIV datasets, using our lower bounds and
existing methods to show that escape rates are relatively high during the
initial days of the first CTL escape and then drop to lower levels as the
escape proceeds. We also compare escape in the lymph nodes and the rectal
mucosa, showing that escape in the lymph nodes is initially faster, but as the
first escape proceeds, the rate of escape in the lymph nodes drops below the
rate seen in the rectal mucosa.
