Multi-period sampling bias arises when the imposition of a minimum history requirement on time-series data excludes some data. For example, when looking at the returns generated by funds, investments that have been in existence for less than a minimum period may be excluded. This may give different results because the more recently launched funds may have performed better or worse.
Studies suggest that this causes a small overestimation of the the returns generated by hedge funds, but it is small enough that is is probably generally not significant. It is all the less important given the much bigger problems of survivorship bias (which affects almost all studies of returns), look ahead benchmark bias (which is common) and backfill bias (which mostly affects hidge fund indices) and self-selection bias.