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Keywords:

  • Breast cancer;
  • Colorectal cancer;
  • EM algorithm;
  • Genetics;
  • Hardy–Weinberg;
  • Latent class;
  • Prostate cancer;
  • Twins

Summary To investigate the role of genetics in the development of cancer, we developed a new approach to analyze data on prostate, breast, and colorectal cancer from the Swedish, Danish, and Finnish twin registries on monozygotic (MZ) and same-sex dizygotic (DZ) twins. In the spirit of a sensitivity analysis, we modeled genetic inheritance as either an autosomal recessive or dominant cancer susceptibility (CS) genotype that involves either a single gene, many genes with equal allele frequencies, or three genes with a ninefold range of allele frequencies. We also modeled the joint probability of cancer incidence among five age categories, conditional on the presence or absence of the CS genotype. The main assumptions are: (1) The joint distribution of unobserved environmental effects in a twin pair conditional on the presence or absence of the CS genotype is the same for MZ and DZ twins, (2) the probability of cancer conditional on the presence or absence of the CS genotype and the unobserved environmental effects (i.e., the gene–environment interaction) is the same for MZ and DZ twins, and (3) the probability of cancer is independent between twins with the CS genotype. Estimation was maximum likelihood via a search over allele frequency and two levels of EM algorithms. Models had acceptable or good fits. Variability was estimated using a bootstrap approach, but only 50 replications were feasible. The 94th percentile of bootstrap replications for the estimated fraction of cancers with the CS genotype ranged, over the various genetic models, from 0.16 to 0.45 for prostate cancer, 0.12 to 0.30 for breast cancer, and 0.08 to 0.27 for colorectal cancer. We conclude that genetic susceptibility makes only a small to moderate contribution to the incidence of prostate, breast, and colorectal cancer.