The NHS Evidence Update on cancer rates has been published, and gives you an idea of the accumulated evidsence on what kinds of cancer differentially affect particular minority ethnic groups. It says:

Overall cancer incidence was found to be lower in South Asian, Chinese and mixed race groups than whites.  However, some important specific differences were also identified:

• Black males of all ages were more likely to have a diagnosis of prostate cancer than white males. (Age standardised Relative Risk (RR) between 1.26 and 2.48, based on different assumptions regarding patients with unknown ethnicity)

• Black males and black females had higher rates of cancers o f the stomach. (RR 1.14 – 1.74)
• Black males and black females had a higher rate of liver cancer than white males and females. (RR 1.47 – 2.67)
• Black males and black females had a higher rate of myeloma than white males and females. (RR 1.79 – 2.80)
• Black females aged 65 and over were at a higher risk of cervical cancer than white females of the same age. (RR 1.13 – 2.50)
• South Asian men and women had a higher rate of liver cancer than white males and females. (RR 1.47 – 2.43)
• South Asian females 65 and over had an increased risk of cancer of the mouth (RR 1.18 – 1.97), whereas South Asian men may have a lower risk of getting cancer of the mouth than white men.
• South Asian females aged 65 and over had a higher risk of cervical cancer than white females. (RR 1.15 – 2.29)

Worth a look at the whole thing and links to the evidence:

http://www.library.nhs.uk/ETHNICITY/ViewResource.aspx?resID=326764&tabID=290