iTOS (version 1.0.3)

addcaliper: Add a Caliper to an Existing Cost Matrix

Description

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

Usage

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

Value

A penalized costmatrix.

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.

Author

Paul R. Rosenbaum

Details

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

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.

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)