Although association analysis is a useful tool for uncovering the genetic u
nderpinnings of complex traits, its utility is diminished by population sub
structure, which can produce spurious association between phenotype and gen
otype within population-based samples. Because family-based designs are rob
ust against substructure, they have risen to the fore of association analys
is. Yet, if population substructure could be ignored, this robustness can c
ome at the price of power. Unfortunately it is rarely evident when populati
on substructure can be ignored. Devlin and Roeder recently have proposed a
method, termed "genomic control" (GC), which has the robustness of family-b
ased designs even though it uses population-based data. GC uses the genome
itself to determine appropriate corrections for population-based associatio
n tests. Using the GC method, we contrast the power of two study designs, f
amily trios (i.e., father, mother, and affected progeny) versus case-contro
l. For analysis of trios, we use the TDT test. When population substructure
is absent, we find GC is always more powerful than TDT; furthermore, contr
ary to previous results, we show that as a disease becomes more prevalent t
he discrepancy in power becomes more extreme. When population substructure
is present, however, the results are more complex: TDT is more powerful whe
n population substructure is substantial, and GC is more powerful otherwise
. We also explore general issues of power and implementation of GC within t
he case-control setting and find that, economically, CC is at least compara
ble to and often less expensive than family-based methods. Therefore, CC me
thods should prove a useful complement to family-based methods for the gene
tic analysis of complex traits.