DOS2 (version 0.5.2)

mahal: Mahalanobis Distance Matrix for Optimal Matching

Description

Computes a Mahalanobis distance matrix between treated individuals and potential controls; see Rubin (1980) and Rosenbaum and Rubin (1985). The method is discussed in Section 9.3 of "Design of Observational Studies", second edition.

Usage

mahal(z, X)

Arguments

z

z is a vector that is 1 for a treated individual and 0 for a control.

X

A matrix of continuous or binary covariates. The number of rows of X must equal the length of z.

Value

The distance matrix has one row for each treated individual (z=1) and one column for each potential control (z=0). The row and column names of the distance matrix refer to the position in z, 1, 2, ..., length(z).

References

Hansen, B. B. and Klopfer, S. O. (2006) <doi:10.1198/106186006X137047> "Optimal full matching and related designs via network flows". Journal of computational and Graphical Statistics, 15(3), 609-627. ('optmatch' package)

Hansen, B. B. (2007) <https://www.r-project.org/conferences/useR-2007/program/presentations/hansen.pdf> "Flexible, optimal matching for observational studies". R News, 7, 18-24. ('optmatch' package)

Rosenbaum, P. R. and Rubin, D. B. (1985) <doi:10.1080/00031305.1985.10479383> "Constructing a control group using multivariate matched sampling methods that incorporate the propensity score". The American Statistician, 39, 33-38.

Rubin, D. B. (1980) <doi:10.2307/2529981> "Bias reduction using Mahalanobis-metric matching". Biometrics, 36, 293-298.

Examples

# NOT RUN {
data(costa)
z<-1*(costa$welder=="Y")
aa<-1*(costa$race=="A")
smoker=1*(costa$smoker=="Y")
age<-costa$age
x<-cbind(age,aa,smoker)
dmat<-mahal(z,x)
# Mahalanobis distances
round(dmat[,1:6],2)
# Compare with Table 9.5 in "Design of Observational Studies", 2nd ed.
# Impose propensity score calipers
prop<-glm(z~age+aa+smoker,family=binomial)$fitted.values # propensity score
# Mahalanobis distanced penalized for violations of a propensity score caliper.
# This version is used for numerical work.
dmat<-addcaliper(dmat,z,prop,caliper=.5)
round(dmat[,1:6],2)
# Compare with Table 9.5 in "Design of Observational Studies", 2nd ed.
# }
# NOT RUN {
# Find the minimum distance match within propensity score calipers.
# You must load the 'optmatch' package to try this example
optmatch::pairmatch(dmat,data=costa)
# }
# NOT RUN {
# Conceptual versions with infinite distances for violations of propensity caliper.
dmat[dmat>20]<-Inf
round(dmat[,1:6],2)
# Compare with Table 9.5 in "Design of Observational Studies", 2nd ed.
# }