iTOS (version 1.0.3)

addNearExact: Add a Near-exact Penalty to an Exisiting Distance Matrix.

Description

Add a Near-exact Penalty to an Exisiting Distance Matrix.

Usage

addNearExact(costmatrix, z, exact, penalty = 1000)

Value

A penalized distance matrix.

Arguments

costmatrix

An existing cost matrix with sum(z) rows and sum(1-z) columns. The function checks the compatability of costmatrix, z and p; so, it may stop with an error if these are not of appropriate dimensions. In particular, costmatrix may come from startcost().

z

A vector with z[i]=1 if individual i is treated or z[i]=0 if individual i is control. The rows of costmatrix refer to treated individuals and the columns refer to controls.

exact

A vector with the same length as z. Typically, exact take a small or moderate number of values.

penalty

One positive number.

Author

Paul R. Rosenbaum

Details

If the ith treated individual and the jth control have different values of exact, then the distance between them in costmatrix is increased by adding penalty.

References

Rosenbaum, P. R. (2020) <doi:10.1007/978-3-030-46405-9> Design of Observational Studies (2nd Edition). New York: Springer.

Yang, D., Small, D. S., Silber, J. H. and Rosenbaum, P. R. (2012) <doi:10.1111/j.1541-0420.2011.01691.x> Optimal matching with minimal deviation from fine balance in a study of obesity and surgical outcomes. Biometrics, 68, 628-636. (Extension of fine balance useful when fine balance is infeasible. Comes as close as possible to fine balance. Implemented in makematch() by placing a large near-exact penalty on a nominal/integer covariate x1 on the right distance matrix.)

Yu, R., Silber, J. H., Rosenbaum, P. R. (2020) <doi:10.1214/19-STS699> Matching Methods for Observational Studies Derived from Large Administrative Databases. Statistical Science, 35, 338-355.

Zhang, B., D. S. Small, K. B. Lasater, M. McHugh, J. H. Silber, and P. R. Rosenbaum (2023) <doi:10.1080/01621459.2021.1981337> Matching one sample according to two criteria in observational studies. Journal of the American Statistical Association, 118, 1140-1151.

Zubizarreta, J. R., Reinke, C. E., Kelz, R. R., Silber, J. H. and Rosenbaum, P. R. (2011) <doi:10.1198/tas.2011.11072> Matching for several sparse nominal variables in a case control study of readmission following surgery. The American Statistician, 65(4), 229-238.

Examples

data(binge)
# Select two treated and three controls from binge
d<-binge[is.element(binge$SEQN,c(109315,109365,109266,109273,109290)),]
z<-1*(d$AlcGroup=="B")
names(z)<-d$SEQN
attach(d)
x<-data.frame(age,female)
detach(d)
rownames(x)<-d$SEQN
dist<-startcost(z)
z
x
dist
addNearExact(dist,z,x$female)
addNearExact(dist,z,x$age<40,penalty=10)

# Combine several penalties
dist<-addNearExact(dist,z,x$female)
dist<-addNearExact(dist,z,x$age<40,penalty=10)
dist
dist<-addNearExact(dist,z,x$age<60,penalty=5)
dist
# This distance suggests pairing 109315-109266
# and 109365-109290
rm(z,x,dist,d)