window_intersect

given two intervals, figure out the intersection between the first and the second

NOTE that the intervals are treated as half-open, closed on the left and open on the right, so that an event happening exactly at time b is counted in the window starting at b and not in the one ending at b.

The left-closed form matters at the edges of the observation period. An event in the very first month of a window contributes exposure to that window, so it must also be able to be counted there; closing on the right instead would take the exposure and drop the event, leaving the numerator and denominator disagreeing about whether that month is in the window. It also puts an event exactly on an age-group boundary into the later group, which is what floor((death - dob)/width) does and what The DHS Program's own tabulation code assumes.

Usage

window_intersect(a, b)

Arguments

a

the first window; here, we use all three components (start, finish, event)

b

the second window; here, we only use the start and finish time, and ignore any events

Value

a window containing the exposure and events from a that takes place during the time given by b; also, if a has an event and it takes place during b, it is included

Details

TODO - should write a more detailed description