Genome-wide association studies (GWASs) aim to genotype enough single nucleotide polymorphisms (SNPs) to effectively capture common genetic variants across the genome. Even though the number of SNPs genotyped in such studies can exceed a million, there is still interest in testing association with SNPs that were not genotyped in the study sample. Analyses of such untyped SNPs can assist in signal localization, permit cross-platform integration of samples from separate studies, and can improve power - especially for rarer SNPs. External information on a larger collection of SNPs from an appropriate reference panel, comprising both SNPs typed in the sample and the untyped SNPs we wish to test for association, is necessary for an untyped variant analysis to proceed. Linkage disequilibrium patterns observed in the reference panel are then used to infer the likely genotype at the untyped SNPs in the study sample. We propose here a novel statistical approach for testing untyped SNPs in case-control GWAS, based on an efficient score function derived from a prospective likelihood, that automatically accounts for the variability in the process of estimating the untyped variant. Computationally efficient methods of phasing can be used without affecting the validity of the test, and simple measures of haplotype sharing can be used to infer genotypes at the untyped SNPs, making our approach computationally much faster than existing approaches for untyped analysis. At the same time, we show, using simulated data, that our approach often has performance nearly equivalent to hidden Markov methods of untyped analysis. The software package 'untyped' is available to implement our approach.