A complex disease is caused by the interaction of multiple genes and environmental factors. Complex diseases are also called multifactorial. Examples of complex diseases include cancer and heart disease.
In a way, it's sort of funny that any disease would be called not complex, so this is one of those terms that initially seems a little odd, but in our own parlance--and geneticists have their own way of thinking about things--complex disease really is supposed to conjure up in your mind that this is not a simple Mendelian single-gene disorder. It's messier than that. A complex disease would have many genes involved, often significant environmental contributions involved. You might also say it's polygenic, another word that says multiple genes contributing. We're talking about diseases like diabetes, or the common cancers, or heart disease, where you don't expect it's going to be as simple as one glitch in the genome causing the condition.- Francis S. Collins, M.D., Ph.D.