On survival assumptions between integer ages in the theory of competing risks

Calculating survival probabilities based on a multiple decrement life table often requires additional information at arbitrary non-integer ages or conversion formula between multiple decrement probabilities and absolute decrement rates. However, due to the discrete characteristic of the table, it is necessary to impose a certain distributional assumption about the decrements between integer ages such as the uniform distribution of decrements (UDD) or the constant forces (CF) of decrement. In this paper, inspired by the fractional independence (FI) assumption in Willmot (1997), we intend to generalize the commonly used fractional age assumptions and investigate their relationships. In particular, we are interested in relaxing the assumptions while inheriting the same conversion formula from the UDD or the CF assumption. Numerical examples show that our generalization facilitates the investigation of conversion errors caused by incorrectly using the formula when the fractional age assumption is misspecified.