Built-in selection in period-by-period hazard ratios

Two risk types with per-period reconviction probabilities h (high) and l (low), initial high-risk share s. Whatever the programme does in period 1, the period-2 hazard among survivors is a weighted average of h and l with weight the surviving high-risk share (Research.P5.survivor_hazard_mono); an arm that depletes the high-risk type less in period 1 has a higher period-2 hazard with no individual effect in period 2 at all (hr2_gt_one_of_depletion, hr2_witness). A period-specific hazard ratio is therefore not a causal contrast; fixed-horizon risk differences are.

Usage

morie_hazard_selection(s, h, l, survive_high, survive_low)

Arguments

s

Initial high-risk share in (0, 1).

h, l

Per-period hazards of the high- and low-risk types, l < h.

survive_high, survive_low

Period-1 survival probabilities of the two types in each arm, as length-2 vectors c(control, treated).

Value

A list with surviving_high_share per arm, period2_hazard per arm, period2_hazard_ratio (treated over control) and theorems.

Examples

morie_hazard_selection(s = 0.5, h = 0.5, l = 0.1,
                       survive_high = c(control = 0.5, treated = 0.8),
                       survive_low = c(control = 0.9, treated = 0.9))
#> $surviving_high_share
#>   control   treated 
#> 0.3571429 0.4705882 
#> 
#> $period2_hazard
#>   control   treated 
#> 0.2428571 0.2882353 
#> 
#> $period2_hazard_ratio
#> [1] 1.186851
#> 
#> $theorems
#> [1] "Research.P5.survivor_hazard_mono"    "Research.P5.hr2_gt_one_of_depletion"
#> [3] "Research.P5.hr2_witness"            
#>