senmscores {informedSen}

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.

Details

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

Value

A vector of length N containing the M-scores.

Note

The function is essentially a wrapper for the mscoresv function in the sensitivitymult package. It is easier to use senmscores when using the informedSen package.

Author(s)

Paul R. Rosenbaum

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

data(HDL)
shdl<-senmscores(HDL$hdl,HDL$z,HDL$mset)
plot(HDL$hdl,shdl)