addcaliper function

Add a caliper, that need not be symmetric, to a distance object.

Imposes a caliper, that need not be symmetric, on p using a penalty function, adding the penalty to a distance matrix dmat and returning a new distance matrix. The symmetric version of this function is discussed in Rosenbaum (2010).

addcaliper(dist, z, dx, rg, stdev = FALSE, penalty = 1000)

Arguments

• dist: A distance object with three components: d, start, end, typically created by maha_dense or maha_sparse. d[i] gives the distance between the (start[i])th treated and the (end[i]-sum(z))th control.
• z: A vector whose ith coordinate is 1 for a treated unit and is 0 for a control. Must have treated subjects (z = 1) before controls (z = 0).
• dx: A vector of with length(z)=length(dx) giving the variable used to define the caliper. For instance, dx might be the propensity score.
• rg: A vector with length(rg) = 2 such that rg[1] <= 0 <= rg[2]. If the treated-minus-control difference in dx is < rg[1] or > rg[2], then penalty is added to the distance. If treated individuals have dx higher than controls, then you want to set rg[2] < -rg[1], so that you tolerate smaller positive differences and larger negative differences.
• stdev: If stdev = TRUE, rg is interpreted in units of an equally weighted pooled standard deviation; that is,rg is replaced by rg*sp where sp is sqrt((var(dx[z==1])+var(dx[z==0]))/2).
• penalty: The number added to a distance when the caliper is violated. A large penalty, like the default value of penalty = 1000, will try to enforce the caliper to the extent that this is feasible. Small penalties can slightly tilt a match in a desired direction.

Returns

Returns a new distance object whose distance component d is updated by the sum of d and the penalties for caliper violations.

Examples

data("nh0506Homocysteine")
attach(nh0506Homocysteine)
X<-cbind(female, age, black, education, povertyr, bmi)
p<-glm(z ~ female + age + black + education + povertyr + bmi,
        family = binomial)$fitted.values
d<-cbind(nh0506Homocysteine, p)
detach(nh0506Homocysteine)
dist0<-maha_dense(d$z, X)
#symmetric caliper
dist1<-addcaliper(dist0, d$z, d$p, c(-.3,.3), stdev = TRUE,
                    penalty = 1000)
head(dist1$d)
#asymmetric caliper
dist2<-addcaliper(dist0, d$z, d$p, c(-.5,.1), stdev = TRUE,
                    penalty = 1000)
head(dist2$d)

References

Yu, R., & Rosenbaum, P. R. (2019). Directional penalties for optimal matching in observational studies. Biometrics, 75(4), 1380-1390.

Rosenbaum, P. R. (2010) Design of Observational Studies. New York: Springer.