Amplification of a sensitivity parameter: one Gamma is a curve of (Lambda, Delta)

\(\Gamma = (\Lambda\Delta + 1)/(\Lambda + \Delta)\) with \(\Lambda\) the odds of treatment and \(\Delta\) the odds of a positive outcome attributable to the unobserved covariate. The map is symmetric, at least one, at most \(\min(\Lambda, \Delta)\) and non-decreasing in each argument (Research.P11.Amplification.symmetric, ge_one, le_min, mono_left); every \(\Gamma \ge 1\) is a curve, parametrised by \(\Lambda > \Gamma\) through \(\Delta = (\Lambda\Gamma - 1)/(\Lambda - \Gamma)\) (level_curve). Give any two of the three.

Usage

morie_sensitivity_amplification(Lambda = NULL, Delta = NULL, Gamma = NULL)

Arguments

Lambda, Delta, Gamma

Two of the three (each at least 1); the third is computed. Lambda and Delta may be vectors.

Value

A data frame with columns Lambda, Delta, Gamma.

References

Rosenbaum PR, Silber JH (2009). Amplification of sensitivity analysis in matched observational studies. JASA 104(488).

Examples

morie_sensitivity_amplification(Lambda = c(2, 3, 5), Delta = 4)
#>   Lambda Delta    Gamma
#> 1      2     4 1.500000
#> 2      3     4 1.857143
#> 3      5     4 2.333333
morie_sensitivity_amplification(Gamma = 2, Lambda = c(3, 4, 10))
#>   Lambda Delta Gamma
#> 1      3 5.000     2
#> 2      4 3.500     2
#> 3     10 2.375     2