Though it sounds like a strange question to ask, it seems that over the years, evidence has emerged supporting the claim that redheads may sometimes require up to twice the amount of anesthetics for procedures than that of their blonde and brunette counterparts.
Redheads experience more pain and require about 20 percent more anesthesia when going into surgery because a gene that influences their red hair color also influences pain receptors in the body. The melanocortin-1 receptor (MC1R) gene is responsible for the production of pigments in the body. Redheads' bodies produce the red pigment pheomelanin in increased amounts, and under produce the dark pigment eumelanin. It's because of their levels of these pigments that redheads have red hair and their skin doesn't tan well. The MC1R gene is also involved in hormones that stimulate pain receptors in the brain. The same mutation that inhibits the production of one pigment and increases another could also overproduce a pain-related hormone, making redheads more sensitive to pain.
It's not just redheads, and it's not just anesthetics either. Individuals with more melanin (darker skin, brown eyes) have faster drug uptake rates than those with less melanin (paler skin, blue eyes). This has been noticed at least as far back as 1988, and we still don't really know why.
This affects not only anesthetics, but other drugs too. Ever gotten your pupils dilated? If you have blue eyes, you probably had to wait a lot longer than brown-eyed patients for the drops to take effect. These effects also seem to be present in how our bodies consume alcohol. Brown-eyed people will absorb alcohol into their bloodstream more quickly than their equal-sized blue-eyed counterparts, making them prone to quicker intoxication.
Source: Parker-Pope, Tara (2009, August 6). The pain of being a redhead. The New York Times. Retrieved from http://well.blogs.nytimes.com