Title: Unbiased Penetrance Estimates with Unknown Ascertainment Strategies
Description: Allelic variation in the genome leads to variation in individuals' production of proteins. This, in turn, leads to variation in traits and development, and, in some cases, to diseases. Understanding the genetic basis for disease can aid in the search for therapies and in guiding genetic counseling. Thus, it is of interest to discover the genes with mutations responsible for diseases and to understand the impact of allelic variation at those genes. A subject's genetic composition is commonly referred to as the subject's genotype. Subjects who carry the gene mutation of interests are referred to as carriers. Subjects who are afflicted with a disease under study (that is, subjects who exhibit the phenotype) are termed affected carriers. The age-specific probability that a given subject will exhibit a phenotype of interest, given mutation status at a gene is known as penetrance. Understanding penetrance is an important facet of genetic epidemiology. Penetrance estimates are typically calculated via maximum likelihood from family data.

However, penetrance estimates can be biased if the nature of the sampling strategy is not correctly reflected in the likelihood. Unfortunately, sampling of family data may be conducted in a haphazard fashion or, even if conducted systematically, might be reported in an incomplete fashion. Bias is possible in applying likelihood methods to reported data if (as is commonly the case) some unaffected family members are not represented in the reports. The purpose here is to present an approach to find efficient and unbiased penetrance estimates in cases where there is incomplete knowledge of the sampling strategy and incomplete information on the full pedigree structure of families included in the data. The method may be applied with different conjectural assumptions about the ascertainment strategy to balance the possibly biasing effects of wishful assumptions about the sampling strategy with the efficiency gains that could be obtained through valid assumptions.