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Design sensitivity: the Gamma at which a sensitivity analysis's limiting power turns

Source: R/ledger_scan2.R
morie_design_sensitivity.Rd

Along a sequence of studies with \(T_n/n \to \mu\) and worst-case critical values \(c_n/n \to \mu_\Gamma\), the test rejects for all large \(n\) when \(\mu > \mu_\Gamma\) and never when \(\mu < \mu_\Gamma\) (Research.P5.DesignSensitivity.eventually_reject, eventually_accept); the design sensitivity is the unique root of \(\mu_\Gamma = \mu\) when \(\Gamma \mapsto \mu_\Gamma\) is continuous and strictly increasing (design_sensitivity_exists_unique).

Usage

morie_design_sensitivity(mu, mu_gamma = function(G) G/(1 + G), upper = 10000)

Arguments

mu

Limiting standardised statistic under the alternative.

mu_gamma

Function of \(\Gamma\) giving the worst-case limit; the default is the sign-score form \(\Gamma/(1+\Gamma)\).

upper

Upper end of the search interval.

Value

A list: gamma_tilde and the limiting power at a few \(\Gamma\).

References

Rosenbaum PR (2004). Design sensitivity in observational studies. Biometrika 91(1).

Examples

morie_design_sensitivity(mu = 0.7)
#> $gamma_tilde
#> [1] 2.333333
#> 
#> $limiting_power
#>      Gamma power
#> 1 1.000000     1
#> 2 1.666667     1
#> 3 4.666667     0
#> 
#> attr(,"theorem")
#> [1] "Research.P5.DesignSensitivity.design_sensitivity_exists_unique"