Can the allelic test be retired from analysis of case-control association studies?

It has been stated that, when Hardy-Weinberg equilibrium (HWE) holds in the combined case-control samples, the allelic test is asymptotically equivalent to the trend test (for the additive model) for testing genetic association, and hence the allelic test should not be used. A recent publication shows that the allelic test and the trend test are asymptotically equivalent when HWE holds in the population. It is known that, when HWE does not hold, the trend test can still be used while the allelic test is no longer valid. Therefore, the allelic test is either not valid or is asymptotically equivalent to the trend test. It appears that the allelic test is a nuisance test. Can it be retired from the analysis of case-control association studies? It all depends on data and model assumptions. We give conditions under which the allelic test and the trend test are asymptotically equivalent under both null and alternative hypotheses.