Here's a possible approach.
Buy n = 1024 doses of your insulin or whatever, D(0, i) for i from 0 to n - 1 = 1023, homogenize each dose, and divide each one in half into half-doses called E(0, i) and F(0, i).
Mix pairs F(0, 2*i) and F(0, 2*i + 1) into 512 new doses D(1, i) for i from 0 to 511. Homogenize these new doses and divide each one in half into half-doses called E(1, i) and F(1, i).
Mix pairs F(1, 2*i) and F(1, 2*i + 1) into 256 new doses D(2, i) for i from 0 to 255.
And so on, until in step k = lg n = 10 step you mix the half-doses F(k - 1 = 9, 0) and F(9, 1) into a single dose D(k = 10, 0). Send this D(k, 0) off to the lab to be analyzed.
If the lab is equipped to detect dangerous impurities in your insulin at one-thousandth the danger level, which is reasonable for many contaminants, and the sample comes back clean, then you know that all 1024 doses were safe, though some of them may have the wrong dose. Mix the remaining 1023 doses well so that they all have the same dose and store them safely.
If not, you need to track down the contamination (or massive dilution), so in the next iteration, you send E(9, 0) and E(9, 1) to the lab for analysis. If one of them comes back safe, you know the 511 doses that were mixed into it were okay, and you can mix them well and store them safely, then repeat the process on the contaminated subtree.
Depending on your cost function (latency, shipping and handling costs, etc.) and your priors for correlation among the samples, it might be worthwhile to recurse more deeply on failure: instead of sending E(9, i) for i from 0 to 1 to the lab, you might instead send them E(6, i) for i from 0 to 15. If one out of 30 doses was randomly contaminated, for example, about 14 out of the 16 groups will be bad on average, while if it's one out of 100, then you'll have about 7 bad groups out of 16. At some point you need to give up on the recursion, too, or you'll end up testing almost all 1024 doses when they're all bad.
This of course doesn't solve the problem of future buys, just reduces it by the factor of n.