# fGWAS: Dynamic Model for GWAS

##### Posted on (Update: )

In the fGWAS of clinical data sets, longitudinal traits are measured at irregular and possibly subject-specific time points.

\[y_i(t_{i\tau}) = \sum_{j=1}^3\xi_i\mu_j(t_{i\tau}) + \beta^T(t_{i\tau})x_i + e_i(t_{i\tau}) + \varepsilon_i(t_{i\tau})\]where

- $\mu_j(t_{i\tau})$: mean value for genotype $j$ at time $t_{i\tau}$

## another GWAS

\[y_i(t_{i\ell}) = \mu(t_{i\ell}) + \alpha(t_{i\ell})^TX_i + a(t_{i\ell})^T\xi_i + d(t_{i\ell})^T\zeta_i + e_i(t_{i\ell})\]where

- $\xi_{ij} = 1 I(AA) + 0 I(Aa) - 1 I(aa)$
- $\zeta_{ij} = I(Aa) + 0 I(AA) + 0 I(aa)$