informedSen (version 1.0.7)

senmscores: Computes M-scores for M-tests.

Description

Computes M-scores for an M-test with one outcome in 1-to-k matched sets, for fixed k>=1. For the one-sample problem or matched pairs, Maritz (1979) proposed robust tests and confidence intervals based on Huber's (1981) M-estimates. These tests are extended to matching with several controls in Rosenbaum (2007).

Usage

senmscores(y, z, mset, inner = 0, trim = 3, lambda = 1/2)

Arguments

y

A vector of length N for one outcome.

z

A vector whose N coordinates are 1 for treated, 0 for control.

mset

A vector of length N giving the matched set.

inner

See trim.

trim

The two values, inner and trim, define the M-statistic's psi-function. The psi-function is an odd function, psi(y) = -psi(-y), so it suffices to define it for nonnegative y. For nonnegative y, psi(y) equals 0 for y between 0 and inner, rises linearly from 0 to 1 for y between inner and trim, and equals 1 for y greater than trim. There are two requirements: inner must be nonnegative, and trim must be larger than inner.

lambda

A number strictly between 0 and 1. The M-scores are psi(y/s) where s is the lambda quantile of the within-set absolute pair differences.

Value

A vector of length N containing the M-scores.

Details

The choice of psi-function to increase insensitivity to unmeasured bias is discussed in Rosenbaum (2013), where the parameter inner is proposed.

References

Huber, P. (1981). Robust Statistics. NY: Wiley.

Maritz, J. S. (1979). A note on exact robust condence intervals for location. Biometrika 66, 163-170.

Rosenbaum, P. R. (2007) Sensitivity analysis for m-estimates, tests and confidence intervals in matched observational studies. Biometrics, 2007, 63, 456-464. <doi:10.1111/j.1541-0420.2006.00717.x>

Rosenbaum, P. R. (2013). Impact of multiple matched controls on design sensitivity in observational studies. Biometrics 69 118-127. (Introduces inner trimming.) <doi:10.1111/j.1541-0420.2012.01821.x>

Rosenbaum, P. R. (2015). Two R packages for sensitivity analysis in observational studies. Observational Studies, v. 1. (Free on-line.)

Examples

# NOT RUN {
data(HDL)
shdl<-senmscores(HDL$hdl,HDL$z,HDL$mset)
plot(HDL$hdl,shdl)
# }