addcaliper function

Add a Caliper to an Existing Cost Matrix

For one covariate, adds a caliper to an existing cost matrix.

addcaliper(costmatrix, z, p, caliper = NULL, penalty = 1000, twostep = TRUE)

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.
• p: A vector with the same length as p. The vector p is the covariate for which a caliper is needed.
• caliper: Determines the type and length of the caliper. The caliper becomes a vector cvex with length 2. If is.null(caliper), then the caliper is +/- 0.2 times the standard deviation of p, namely cvec = c(-.2,.2)*sd(p). If caliper is a single number, then the caliper is +/- caliper, or cvec = c(-1,1)*abs(caliper). If caliper is a vector of length 2, then an asymmetric caliper is used, cvec = c(min(caliper),max(caliper)), where min(caliper) must be negative and max caliper must be positive.
• penalty: Let I be the index of ith treated individual, 1,...,sum(z), and J be the index of the jth control, j=1,...,sum(1-z), so 1 <= I <= length(z) and so 1 <= J <= length(z). The penality added to costmatrix[i,j] is 0 if cvec[1] <= p[I]-p[J] <= cvex[2].
• twostep: If twostep is FALSE, then no action is taken. If twostep is true, no action is take if 2 cvec[1] <= p[I]-p[J] <= 2 cvex[2], and otherwise costmatrix[i,j] is further increased by adding penalty. In words, the penalty is doubled if p[I]-p[J] falls outside twice the caliper.

Details

For discussion of directional calipers, see Yu and Rosenbaum (2019).

Returns

A penalized costmatrix.

References

Cochran, William G., and Donald B. Rubin. Controlling bias in observational studies: A review. Sankhya: The Indian Journal of Statistics, Series A 1973;35:417-446.

Yu, Ruoqi, and Paul R. Rosenbaum. doi:10.1111/biom.13098 Directional penalties for optimal matching in observational studies. Biometrics 2019;75:1380-1390.

Author(s)

Paul R. Rosenbaum

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

# Ten-year age caliper
addcaliper(dist,z,x$age,caliper=10,twostep=FALSE)

# Ten-year age caliper with twostep=TRUE
addcaliper(dist,z,x$age,caliper=10,twostep=TRUE)

# Same ten-year age caliper with twostep=TRUE
addcaliper(dist,z,x$age,caliper=c(-10,10))

# Asymmetric, directional age caliper with twostep=TRUE
addcaliper(dist,z,x$age,caliper=c(-2,10))
# Treated 109315 aged 30 is more than 2 years younger
# than control 109273 aged 36, 30-36<(-2), so
# row 109315 column 109273 is penalized, indeed
# double penalized, as 30-36<2*(-2)

rm(z,x,dist,d)