For ${X_1,X_2,...,X_n}$ are independent random variables with the normal distribution $X_i \sim N(0,1)$, $$ Y = \sum_{i=1}^{n} X_i^2 \sim \chi^2(n) $$
For a allel sample $$ \sum_{i=1}^{M} \sum_{j=1}^{N} \frac {(O_{ij}-E_{ij})^2} {E_{ij}} \sim \chi^2_p((M-1)(N-1))$$ where $p=1-\alpha$, $M$ means type, $N$ means the individual amount of specific type。 $p$ will determine the level of relationship between specific type and final result.
Bonferroni correction
For allel, there are two types ${A,T}$, we have ill samples $n_A$ with $A$, $n_T$ with $T$, healthy samples $m_A$ with $A$, $m_T$ with $T$, we have OR: $$ OR = \frac {n_A} {m_A} / \frac {n_T} {m_T} = \frac {n_A m_T} {n_T m_A} $$ $ OR > 1$ means $A$ make bigger influence, while $OR < 1$ means $A$ make less influence.
$$ OR' = max(OR,\frac{1}{OR}) $$means the level of relationship among allel and phenotype
If $A$ and $B$ are independent random variables with frequency $f(A)$ and $f(B)$, we will have: $$ f(A,B) = f(A)f(B) $$
If $A$ and $B$ are linked, so we will have: $$ f(A,B) = f(A)f(B) + LD $$ meanwhile, $f(A|B) \ne f(A)$.
The relevant coefficient: $$ r^2 = \frac {LD^2} {f(A)f(a)f(B)f(b)} $$ Strong LD when $r^2$ is high
The $p$ value of all SNPs of gene, ${p_i}$, we will have: $$ X = -2 ln\left(\prod_{i=1}^{n} p_i\right) = -2 \sum_{i=1}^{n} ln(p_i) \sim \chi^2(2n) $$
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