Cross-Sectional Surveys: Inferring Total Eventual Time in Current State Using Only Elapsed Time-to-Date

We focus on snapshot surveying of sub-populations whose members are in a temporary state and where one of the questions asked is the elapsed time already spent in that state. From these answers we develop probabilistic and statistical procedures to estimate the distribution of total time that will eventually be spent in that state by any random individual who enters the state. The method relies on a selection bias often found in temporal sampling, sometimes called "random incidence" or "longevity bias." We develop results for several types of sampling, including random and fixed times of surveying, random and fixed times of entering the state, and sampling only those who have already spent some minimal specified time in the targeted state. An example with post-doc data is included to demonstrate the steps.