An Application of a General Branching Process in the Study of the Genetics of Aging

A general branching process model is developed to analyse familial dependence in longevity data. A general formula for the survival function of a randomly chosen sibling of an individual of a specified age is derived. The branching process model takes into account that siblingsʹ ages may be censored. This is applied to a data set consisting of lifelengths of siblings of centenarians. Age distributions used in the branching process model are estimated from US Census data from the relevant period. It is demonstrated that there is a marked difference in the survival function according to the formula assuming no familial effect and the empirical survival function estimated from the data; thus, indicating a strong familial component.