During the first weeks of human immunodeficiency virus-1 (HIV-1) infection, cytotoxic T-lymphocytes (CTLs) select for multiple escape mutations in the infecting HIV population. In recent years, methods that use escape mutation data to estimate rates of HIV escape have been developed, thereby providing a quantitative framework for exploring HIV escape from CTL response. Current methods for escape-rate inference focus on a specific HIV mutant selected by a single CTL response. However, recent studies have shown that during the first weeks of infection, CTL responses occur at one to three epitopes and HIV escape occurs through complex mutation pathways. Consequently, HIV escape from CTL response forms a complex, selective sweep that is difficult to analyze. In this work, we develop a model of initial infection, based on the well-known standard model, that allows for a description of multi-epitope response and the complex mutation pathways of HIV escape. Under this model, we develop Bayesian and hypothesis-test inference methods that allow us to analyze and estimate HIV escape rates. The methods are applied to two HIV patient data sets, concretely demonstrating the utility of our approach.A CUTE HIV-1 infection is marked by an initial period of 2-4 weeks in which the viral population expands from one to five infected cells to 10 9 infected cells. Following this expansion period, in the subsequent 1-2 months, the viral load drops and reaches a setpoint (Fiebig et al. 2003;Mehandru et al. 2004Mehandru et al. , 2007Keele et al. 2008). Cytotoxic T lymphocytes (CTLs) are thought to play an important role in shaping acute infection (Goulder and Watkins 2004;Cohen et al. 2011). The onset of CTL response is temporally correlated with the end of the expansion period, suggesting a role for CTLs in controlling viral load. Numerous studies have shown that during acute infection, specific HIV mutations on CTL targeted epitopes sweep to fixation, providing more direct evidence that CTL response shapes the infecting HIV population; see Goulder and Watkins (2004) for a review.In recent years, full-genome sequencing studies have provided an increasingly detailed description of CTL response during acute infection, e.g., Fernandez et al. Recent deep-sequencing data sets have provided a picture of HIV escape at the CTL targeted epitopes, e.g., Fisher et al. (2010), Henn et al. (2012), Bimber et al. (2009). HIV escape mutations at the first CTL targeted epitope rise to significant proportions 1-3 weeks after peak viral load. Escape mutations at the next series of epitopes targeted rise to significant proportion within roughly 4-6 weeks of peak viral load. Importantly, deep-sequencing studies have shown that HIV escape at a targeted epitope often occurs along multiple mutation pathways. The different mutation pathways are simply different nucleotide substitutions in the targeted epitope. During an HIV escape, these different mutations sweep to significant frequencies simultaneously, thereby replacing an HIV population typically ...