We illustrate data analytic concerns that arise in the context of relating
genotype, as represented by amino acid sequence, to phenotypes (outcomes).
The present application examines whether peptides that bind to a particular
major histocompatibility complex (MHC) class I molecule have characteristi
c amino acid sequences. However, the concerns identified and addressed are
considerably more general. It is recognized that simple rules for predictin
g binding based solely on preferences for specific amino acids in certain (
anchor) positions of the peptide's amino acid sequence are generally inadeq
uate and that binding is potentially influenced by all sequence positions a
s well as between-position interactions. The desire to elucidate these more
complex prediction rules has spawned various modeling attempts, the shortc
omings of which provide motivation for the methods adopted here. Because of
(i) this need to model between-position interactions, (ii) amino acids con
stituting a highly (20) multilevel unordered categorical covariate, and (ii
i) there frequently being numerous such covariates (i.e., positions) compri
sing the sequence, standard regression/classification techniques are proble
matic due to the proliferation of indicator variables required for encoding
the sequence position covariates and attendant interactions. These difficu
lties have led to analyses based on (continuous) properties (e.g., molecula
r weights) of the amino acids. However, there is potential information loss
in such an approach if the properties used are incomplete and/or do not ca
pture the mechanism underlying association with the phenotype. Here we demo
nstrate that handling unordered categorical covariates with numerous levels
and accompanying interactions can be done effectively using classification
trees and recently devised bump-hunting methods. We further tackle the que
stion of whether observed associations are attributable to amino acid prope
rties as well as addressing the assessment and implications of between-posi
tion covariation.