The amount immersed doesn't matter (unless there's a hole for the water
to poor in, but that'll change what's being immersed by filling it with
water and thus changing its density.

It's a function of mass and volume. An iron bar will sink, yet if you
make that same iron bar into a hollow ball large enough that it's
density is less than that of the water (for whatever unit of measurement
of density that you choose) then it will float. The hip replacements are
solid, and much denser than water. If the tissue surrounding them isn't
sufficiently less dense than water and in sufficient quantity to
counterbalance the density increase that comes with solid metal implants
being put in you, then your hips will sink (but you'll be like a bobber,
because your lungs reduce the density of your torso massively). Muscle
is pretty dense compared to fat and other types of tissue, which is why
in Twain's Huckleberry Finn Huck decides that the body in the river was
not that of his father and must have been a woman: it was floating face
up (breasts are not very dense). Density is also why a body can sink
(lungs full of water) and then float again later: as decomposition
ensues the gases formed inside the corpse lower it's density...so up it
comes :-/ Solutes in the water can also change it's density, and thus
change how dense things must be to float on that water.