For each SNP the Cochrane-Armitage trend-test statistic is computed from a 3x2 contingency table

	Cases	Controls	Row totals
AA	$N_{11}$	$N_{12}$	$N_{1*}$
AB	$N_{21}$	$N_{22}$	$N_{2*}$
BB	$N_{31}$	$N_{32}$	$N_{3*}$
Column totals	$N_{*1}$	$N_{*2}$	$N$

$N_{11}$ ($N_{12}$) and $N_{21}$ ($N_{22}$) and $N_{31}$ ($N_{32}$) are the total number of occurrences of genotype AA, AB and BB, respectively, for the cases (controls), and

$$\begin{eqnarray*} N_{*1} &=& N_{11} + N_{21} + N_{31},\\ N_{*2} &=& N_{12} + N_... ... \\ N &=& N_{11} + N_{12} + N_{21} + N_{22} + N_{31} + N_{32}. \end{eqnarray*}$$

The Cochrane-Armitage trend-test statistic with weights $(x_1, x_2, x_3)$ is defined as

$$\begin{eqnarray*} \frac{ (\frac{1}{N} \cdot (x_1\cdot( N_{*2}\cdot N_{11} - N_... ...*}) -( x_1\cdot N_{1*} +x_2\cdot N_{2*} + x_3\cdot N_{3*})^2)}, \end{eqnarray*}$$

The MAX statistics is equal to the maximum of the three Cochrane-Armitage trend-test statistic obtained when assuming a recessive ( $(x_1, x_2, x_3)=(0,0,1)$) model, a dominant model ( $(x_1, x_2, x_3)=(0,1,1)$) and an additive model ( $(x_1, x_2, x_3)=(0,1,2)$). When assuming an additive model( $(x_1, x_2, x_3)=(0,1,2)$), the Cochrane-Armitage trend-test statistic is equal to

$$\begin{eqnarray*} \frac{N \cdot ( N\cdot E_{1} - N_{*1}\cdot E_{2} )^2}{N_{*1} \cdot ( N - N_{*1} ) \cdot (N\cdot E_{3}-(E_{2})^2)}, \end{eqnarray*}$$

where $E_{1} &=& N_{21} + 2\cdot N_{31}$, $E_{2} &=& N_{2*} + 2\cdot N_{3*}$ and $E_{3} &=& N_{2*} + 4\cdot N_{3*}$.