# senmscores: Computes M-scores for M-tests. In informedSen: Sensitivity Analysis Informed by a Test for Bias

## 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

 `1` ```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 condence 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

 ```1 2 3``` ```data(HDL) shdl<-senmscores(HDL\$hdl,HDL\$z,HDL\$mset) plot(HDL\$hdl,shdl) ```

informedSen documentation built on Aug. 4, 2021, 5:06 p.m.