Isobutanol is a prototype biofuel, and sorting out the mechanism of its combustion is an important objective where theoretical modeling can provide information that is unavailable and not easily obtained by experiment. In the present work the rate constants and branching ratios for the hydrogen abstraction reactions from isobutanol by hydroxyl radical have been calculated using multi-path variational transition-state theory with small-curvature tunneling. We use hybrid degeneracy-corrected vibrational perturbation theory to show that it is critical to consider the anharmonicity difference of high-frequency modes between reactants and transition states. To obtain accurate rate constants, we must apply different scaling factors to the calculated harmonic vibrational frequencies at the reactants and at the transition states. The factors determining the reaction rate constants have been analyzed in detail, including variational effects, tunneling contributions, the effect of multiple reaction paths on transmission coefficients, and anharmonicities of low- and high-frequency vibrational modes. The analysis quantifies the uncertainties in the rate calculations. A key result of the paper is a prediction for the site dependence of hydrogen abstraction from isobutanol by hydroxyl radical. This is very hard to measure experimentally, although it is critical for combustion mechanism modeling. The present prediction differs considerably from previous theoretical work.