#Partial Answer
I think the answer may be
A
Reasoning:
If you look at each diagonal going from top left to bottom right, there appears to be a pattern of reflective ratios.
Let $\rm B : W$ be the ratio of Black shapes to White shapes, then the first diagonal (bottom left corner) is $1 : 3$.
Next diagonal (left middle box and bottom middle box) is $4 : 0$ and $0 : 4$ respectively.
Next diagonal (the middle diagonal with the missing box) have the ratios $1 : 3$ and $3 : 1$, so to me it makes sense that the missing box has a ratio of $1 : 3$.
That leaves either
A or F
Due to how the shapes in these boxes are positioned, I am going with
A
However, my answer does no explain why the shapes are the way they are, but I think
It not only has to do with the ratio between colour, but also the ratio between edges. I noticed that when comparing boxes in the same diagonal, if a white circle (or donut) was in the same position as a black shape in another box, then that black shape is a diamond.
Hence, this answer is partial.