Based on data from a randomized, controlled vaccine efficacy trial, this article develops statistical methods for assessing vaccine efficacy (VE) to prevent COVID-19 infections by a discrete set of genetic strains of SARS-CoV-2. Strain-specific VE adjusting for possibly time-varying covariates is estimated using augmented inverse probability weighting to address missing viral genotypes under a competing risks model that allows separate baseline hazards for different risk groups. Hypothesis tests are developed to assess whether the vaccine provides at least a specified level of VE against some viral genotypes and whether VE varies across genotypes. Asymptotic properties providing analytic inferences are derived and finite-sample properties of the estimators and hypothesis tests are studied through simulations. This research is motivated by the fact that previous analyses of COVID-19 vaccine efficacy did not account for missing genotypes, which can cause severe bias and efficiency loss. The theoretical properties and simulations demonstrate superior performance of the new methods. Application to the Moderna COVE trial identifies several SARS-CoV-2 genotype features with differential vaccine efficacy across genotypes, including lineage (Reference, Epsilon, Gamma, Zeta), indicators of residue match vs. mismatch to the vaccine-strain residue at Spike amino acid positions (identifying signatures of differential VE), and a weighted Hamming distance to the vaccine strain. The results show VE decreases against genotypes more distant from the vaccine strain, highlighting the need to update COVID-19 vaccine strains.