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The budget-constrained optimal rule is a threshold on the conditional effect

Source: R/ledger_scan2.R
morie_budget_rule.Rd

Covariate cells with masses m and effects tau, budget kappa: treat cells above the threshold, none below, and a fraction of the tied cell so the budget binds; this maximises the total effect over all feasible fractional rules (Research.P5.BudgetRule.threshold_optimal). When the tied cell is only partly treated no deterministic rule attains the optimum (stochastic_needed).

Usage

morie_budget_rule(m, tau, kappa)

Arguments

m

Cell masses, positive.

tau

Cell effects.

kappa

Budget.

Value

A list: rule (treated share per cell), threshold, value, best_deterministic (the best over all-or-nothing rules when the number of cells is at most 15) and stochastic_needed.

References

Luedtke AR, van der Laan MJ (2016). Optimal individualized treatments in resource-limited settings. International Journal of Biostatistics 12(1).

Examples

morie_budget_rule(m = c(1, 1, 1), tau = c(0.5, 0.2, -0.1), kappa = 1.5)
#> $rule
#> [1] 1.0 0.5 0.0
#> 
#> $threshold
#> [1] 0.2
#> 
#> $value
#> [1] 0.6
#> 
#> $best_deterministic
#> [1] 0.5
#> 
#> $stochastic_needed
#> [1] TRUE
#> 
#> attr(,"theorem")
#> [1] "Research.P5.BudgetRule.threshold_optimal"