# Significance cutoff point for multiple testing

I have some results from a genome wide association study, which basically fits $n$ linear models for one trait $y$ and $n$ genotypes $x_1, x_2, \cdots, x_n$:

\begin{align*} y &\sim b_{10} + b_{11} x_1 \\ y &\sim b_{20} + b_{21} x_2 \\ &\vdots \\ y &\sim b_{n0} + b_{n1} x_n \\ \end{align*}

after which we get $n$ p values: $p_1, p_2, \cdots, p_n$. Normally $n$ is in the order of $10^6$, and the $\alpha$ level is usually set at $5 \times 10^{-8}$ in the literature, roughly following the Bonferroni correction.

Now based on these p values we have spotted an interesting region for which we have built a series of different models and conducted around 10000 more tests, the problem is how do we determine the significance cutoff point this time?

Someone has suggested to set it at $5 \times 10^{-8} / 10^4 = 5 \times 10^{-12}$, but apparently this is not quite reasonable, the 10000 tests are only a small number compared to the millions of test conducted previously.

3. Use another sub-set of the data to test your explorative hypotheses built on the first set of the data. Now use a new Bnonferroni correction, e.g. by $10^4$.