submax (version 1.1.1)

separable1fc: Computes the Separable Approximation.

Description

Of limited interest to most users, separable1fc() is called by the main function, submax().

Usage

separable1fc(ymat, gamma = 1)

Value

tstat

Vector of length I = dim(ymat)[1] giving the values of the test statistic in the I matched sets.

expect

Vector of length I giving the maximum expectations in the I matched sets.

vari

Vector of length I giving the maximum variances at the maximum expectations in the I matched sets.

Arguments

ymat

A matrix of scores produced by mscoref.

gamma

The sensitivity parameter \(\Gamma \ge 1\).

Author

Paul R. Rosenbaum

Details

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

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. <doi:10.1111/1467-9868.00249>

Rosenbaum, P. R. (2007). Sensitivity analysis for m-estimates, tests and confidence intervals in matched observational studies. Biometrics 63 456-64. (See section 4.) <doi:10.1111/j.1541-0420.2006.00717.x>

Examples

# The following artificial example computes mscores for a
# full matching, then applies separable1fc() to
# perform a sensitivity analysis.  Compare with
# the example below from the sensitivityfull package.

# 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))

s<-separable1fc(sensitivityfull::mscoref(y,treated1),gamma=2)
1-pnorm((sum(s$tstat)-sum(s$expect))/sqrt(sum(s$vari)))
sensitivityfull::senfm(y,treated1,gamma=2)
s