  Background: By a new concept called "phase diagram", we compare two commonly
used genotype-based tests for case-control genetic analysis, one is a
Cochran-Armitage trend test (CAT test at $x=0.5$, or CAT0.5) and another
(called MAX2) is the maximization of two chi-square test results: one from the
two-by-two genotype count table that combines the baseline homozygotes and
heterozygotes, and another from the table that combines heterozygotes with risk
homozygotes. CAT0.5 is more suitable for multiplicative disease models and MAX2
is better for dominant/recessive models.
  Methods: We define the CAT0.5-MAX2 phase diagram on the disease model space
such that regions where MAX2 is more powerful than CAT0.5 are separated from
regions where the CAT0.5 is more powerful, and the task is to choose the
appropriate parameterization to make the separation possible.
  Results: We find that using the difference of allele frequencies ($\delta_p$)
and the difference of Hardy-Weinberg disequilibrium coefficients
($\delta_\epsilon$) can separate the two phases well, and the phase boundaries
are determined by the angle $tan^{-1}(\delta_p/\delta_\epsilon)$, which is an
improvement over the disease model selection using $\delta_\epsilon$ only.
  Conclusions: We argue that phase diagrams similar to the one for CAT0.5-MAX2
have graphical appeals in understanding power performance of various tests,
clarifying simulation schemes, summarizing case-control datasets, and guessing
the possible mode of inheritance.
