High-energy proton- and deuteron-nucleus collisions provide an excellent tool for studying a wide array of physics effects, including modifications of parton distribution functions in nuclei, gluon saturation, and color neutralization and hadronization in a nuclear environment, among others. All of these effects are expected to have a significant dependence on the size of the nuclear target and the impact parameter of the collision, also known as the collision centrality. In this article, we detail a method for determining centrality classes in p(d) + A collisions via cuts on the multiplicity at backward rapidity (i.e., the nucleus-going direction) and for determining systematic uncertainties in this procedure. For d + Au collisions at root s(NN) = 200 GeV we find that the connection to geometry is confirmed by measuring the fraction of events in which a neutron from the deuteron does not interact with the nucleus. As an application, we consider the nuclear modification factors Rp(d)+A, for which there is a bias in the measured centrality-dependent yields owing to auto correlations between the process of interest and the backward-rapidity multiplicity. We determine the bias-correction factors within this framework. This method is further tested using the HIJING Monte Carlo generator. We find that for d + Au collisions at root s(NN) = 200 GeV, these bias corrections are small and vary by less than 5% (10%) up to p(T) = 10 (20) GeV/c. In contrast, for p + Pb collisions at v root s(NN) = 5.02 TeV we find that these bias factors are an order of magnitude larger and strongly pT dependent, likely attributable to the larger effect of multiparton interactions.