# Add a Caliper to an Existing Cost Matrix For one covariate, adds a caliper to an existing cost matrix. ```r 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. Directional penalties for optimal matching in observational studies. Biometrics 2019;75:1380-1390. ## Author(s) Paul R. Rosenbaum ## Examples ```r 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) ```

addcaliper function