  In genetic studies of complex diseases, the underlying mode of inheritance is
often not known. Thus, the most powerful test or other optimal procedure for
one model, e.g. recessive, may be quite inefficient if another model, e.g.
dominant, describes the inheritance process. Rather than choose among the
procedures that are optimal for a particular model, it is preferable to see a
method that has high efficiency across a family of scientifically realistic
models. Statisticians well recognize that this situation is analogous to the
selection of an estimator of location when the form of the underlying
distribution is not known. We review how the concepts and techniques in the
efficiency robustness literature that are used to obtain efficiency robust
estimators and rank tests can be adapted for the analysis of genetic data. In
particular, several statistics have been used to test for a genetic association
between a disease and a candidate allele or marker allele from data collected
in case-control studies. Each of them is optimal for a specific inheritance
model and we describe and compare several robust methods. The most suitable
robust test depends somewhat on the range of plausible genetic models. When
little is known about the inheritance process, the maximum of the optimal
statistics for the extreme models and an intermediate one is usually the
preferred choice. Sometimes one can eliminate a mode of inheritance, e.g. from
prior studies of family pedigrees one may know whether the disease skips
generations or not. If it does, the disease is much more likely to follow a
recessive model than a dominant one. In that case, a simpler linear combination
of the optimal tests for the extreme models can be a robust choice.
