Increment-decrement life-tables

The increment-decrement life-table appears to be a birth-death life-table or more generally an open-population life-table.

This could be appropriate for the hospital acquired infection length of stay calculations because the risk set in the infected state changes over time as new patients become infected and infected patients die in-hospital or are discharged alive.

So potentially we can calculate a life-table for the infected state and a separate life-table for the non-infected state, and then make a comparison.

This would require us to account for censoring.