mahal {DOS}

Mahalanobis Distance Matrix for Optimal Matching

Description

Computes a Mahalanobis distance matrix between treated individuals and potential controls. The method is discussed in Chapter 8 of Design of Observational Studies (2010).

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).

Author(s)

Paul R. Rosenbaum

References

Hansen, B. B. and Klopfer, S. O. (2006). 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). Flexible, optimal matching for observational studies. R News, 7, 18-24. (optmatch package)

Rosenbaum, P. R. (2010). Design of Observational Studies. New York: Springer. The method and example are discussed in Chapter 8.

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

Rubin, D. B. (1980). Bias reduction using Mahalanobis-metric matching. Biometrics, 36, 293-298.

Examples

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 8.5 in Design of Observational Studies (2010)
# 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 8.5 in Design of Observational Studies (2010)
## Not run: 
# Find the minimum distance match within propensity score calipers.
optmatch::pairmatch(dmat,data=costa)

## End(Not run)
# Conceptual versions with infinite distances for violations of propensity caliper.
dmat[dmat>20]<-Inf
round(dmat[,1:6],2) # Compare with Table 8.5 in Design of Observational Studies (2010)