exteriorMatch (version 1.0.0)

exterior: Constructs the Exterior Match from Two Matched Control Groups

Description

If one treated group is matched to one control reservoir in two different ways to produce two sets of treated-control matched pairs, then the two control groups may be entwined, in the sense that some control individuals are in both control groups. The exterior match is used to compare the two control groups.

Usage

exterior(id1, id2)

Arguments

id1

id1 and id2 are vectors of the same length containing unique identifiers for the controls in control group 1 and control group 2. The first treated individual is paired with control id1[1] in the first control group, and with control id2[1] in the second control group. The ith treated individual is paired with control id1[i] in the first control group and with control id2[i] in the second control group, for i = 1, 2, ..., length(id1).

id2

See id1.

Value

The value is a list containing a revised id1 and id2 with revised pairing and the removal of duplicates.

Details

The identifiers in id1 are unique, length(id1) == length(unique(id1)), and the identifiers in id2 are unique, length(id2) == length(unique(id2)); however, some controls in id1 may also be in id2. The exterior match minimally adjusts the match to remove duplicates. It is used to compare the two control groups. The exterior match was proposed in Rosenbaum and Silber (2013), and the example below reproduces the example in Figure 3 of that paper.

References

Daniel, S.R., Armstrong, K., Silber, J.H. and Rosenbaum, P.R., 2008. An algorithm for optimal tapered matching, with application to disparities in survival. Journal of Computational and Graphical Statistics, 17(4), pp.914-924.

Pimentel, S.D., Small, D.S. and Rosenbaum, P.R., 2016. Constructed second control groups and attenuation of unmeasured biases. Journal of the American Statistical Association, 111(515), pp. 1157-1167.

Rosenbaum, P.R. and Silber, J.H., 2013. Using the exterior match to compare two entwined matched control groups. The American Statistician, 67(2), pp.67-75.

Silber, J.H., Rosenbaum, P.R., Clark, A.S., Giantonio, B.J., Ross, R.N., Teng, Y., Wang, M., Niknam, B.A., Ludwig, J.M., Wang, W. and Even-Shoshan, O., 2013. Characteristics associated with differences in survival among black and white women with breast cancer. JAMA, 310(4), pp.389-397.

Silber, J.H., Rosenbaum, P.R., Ross, R.N., Niknam, B.A., Ludwig, J.M., Wang, W., Clark, A.S., Fox, K.R., Wang, M., Even-Shoshan, O. and Giantonio, B.J., 2014. Racial disparities in colon cancer survival: a matched cohort study. Annals of Internal Medicine, 161(12), pp.845-854.

Examples

#The example is Figure 3 in Rosenbaum and Silber (2013).
g1<-c("A", "C", "D", "E", "G", "H", "I", "K", "L")
g2<-c("B", "C", "E", "F", "H", "I", "J", "L", "K")
exterior(g1,g2)

## The function is currently defined as
function (id1, id2)
{
    stopifnot(is.vector(id1))
    stopifnot(is.vector(id2))
    stopifnot(length(id1) == length(id2))
    stopifnot(length(id1) == length(unique(id1)))
    stopifnot(length(id2) == length(unique(id2)))
    n <- length(id1)
    ident <- id1 == id2
    nident <- sum(ident)
    id1 <- id1[!ident]
    id2 <- id2[!ident]
    inter <- intersect(id1, id2)
    while (length(inter) >= 1) {
        dup <- inter[1]
        w1 <- which(id1 == dup)
        w2 <- which(id2 == dup)
        id1 <- c(id1[w2], id1[-c(w1, w2)])
        id2 <- c(id2[w1], id2[-c(w1, w2)])
        if (id1[1] == id2[1]) {
            id1 <- id1[-1]
            id2 <- id2[-1]
        }
        inter <- intersect(id1, id2)
    }
    o <- order(id1)
    id1 <- id1[o]
    id2 <- id2[o]
    list(id1 = id1, id2 = id2)
  }