A study by I. Rudan of School of Public Health at University of Zagreb, Croatia claims that there is a higher incidence of cancer in both males and females in inbred island population. The article was not available for downloading thus, no additional details are available at this time. However, the cancers that seems to have increased in island populations are the recessive ones that is the cancers that are caused due to recessive mutations in anti cancer genes. If an individual is homozygous for these genes (both copies mutated) then they will have the cancer.
Whether or not this particular study in humans establishes a clear link between inbreeding and cancer (I say this because I cannot read this paper), ample reports have shown that low genetic diversity caused by inbreeding will make populations susceptible to new cancers. For example, a recent report in
Science and in other newspapers (click the image) show that facial cancer is pushing Tasmanian Devils to extinction. Inbreeding reduces genetic diversity and makes one susceptible not only to cancer but also to any other infectious agents.