separable1f {sensitivityfull}

Computes the Separable Approximation.

Description

Of limited interest to most users, separable1f() is called by the main function, senfm(), in computing the sensitivity analysis. separable1f() is given scores produced by mscoref() and computes the separable approximation to the upper bound on the P-value.

Usage

separable1f(ymat, gamma = 1)

Arguments

ymat

A matrix of scores produced by mscoref.

gamma

The sensitivity parameter \Gamma \ge 1.

Details

See Gastwirth, Krieger and Rosenbaum (2000) and Rosenbaum (2007, section 4) for discussion of the separable approximation.

Value

pval

The upper bound on the 1-sided P-value.

deviate

The deviate that was compared to the Normal distribution to produce pval.

statistic

The value of the score-statistic.

expectation

The maximum expectation of the score-statistic for the given \Gamma.

variance

The maximum variance of the score-statistic among treatment assignments that achieve the maximum expectation. Part of the separable approximation.

Author(s)

Paul R. Rosenbaum

References

Gastwirth, J. L., Krieger, A. M. and Rosenbaum, P. R. (2000). Asymptotic separability in sensitivity analysis. J. Roy. Statist. Soc. B. 62 545-555.

Rosenbaum, P. R. (2007). Sensitivity analysis for m-estimates, tests and confidence intervals in matched observational studies. Biometrics 63 456-64. (See section 4.) (R package sensitivitymv)

Examples

# The artificial example that follows has I=9
# matched sets.  The first 3 sets have one treated
# individual and two controls with treated subjects
# in column 1.  The next 3 sets are
# matched pairs, with treated subjects in column 1.
# The next 3 sets have one control and two treated
# subjects, with the control in column 1.  Simulated
# from a Normal distribution with an additive effect
# of tau=1.

y<-c(2.2, 1.4, 1.6, 2.4, 0.7, 1.3, 1.2, 0.6, 0.3,
0.5, -0.1, -1.3, -0.3, 0.1, 0.4, 3.0, 1.1, 1.4, -0.8,
0.1, 0.8, NA, NA, NA, 1.1, 0.5, 1.8)
y<-matrix(y,9,3)
treated1<-c(rep(TRUE,6),rep(FALSE,3))

# The same calculation done in two equivalent ways.
separable1f(mscoref(y,treated1),gamma=2)
senfm(y,treated1,gamma=2)