## Time Spent and Left of Transient States in Stationary Populations

**Francisco Villavicencio**, *Department of Public Health, University of Southern Denmark*

**Tim Riffe**, *Max Planck Institute for Demographic Research*

**Nicolas Brouard**, *INED*

Background: The Brouard-Carey equality establishes equality between the distributions of years-lived and years-left in stationary populations.

Objective: We aim to generalize this equality to account for time spent and time left in states within multistate stationary populations.

Results: We provide two intuitive proofs that the distribution of time spent and left in transient states is equal in multistate stationary populations.

Conclusions: This equality may be helpful under certain constraints to estimate the distribution of otherwise unobserved onset timing for health or other states.

Objective: We aim to generalize this equality to account for time spent and time left in states within multistate stationary populations.

Results: We provide two intuitive proofs that the distribution of time spent and left in transient states is equal in multistate stationary populations.

Conclusions: This equality may be helpful under certain constraints to estimate the distribution of otherwise unobserved onset timing for health or other states.

Presented in Session 1066: Data and Methods