profmatch {designmatch}

Optimal profile matching

Description

Function for optimal profile matching to construct matched samples that are balanced toward a user-specified covariate profile. This covariate profile can represent a specific population or a target individual, facilitating the generalization and personalization of causal inferences (Cohn and Zubizarreta 2022). For each treatment group reservoir, profmatch finds the largest sample that is balanced relative to the profile. The formulation of profmatch has been simplified to handle larger data than bmatch or nmatch. Similar to bmatch or nmatch, the performance of profmatch is greatly enhanced by using the solver options cplex or gurobi.

Usage

	profmatch(t_ind, mom, solver = NULL)

Arguments

t_ind

treatment indicator: a vector indicating treatment group of each observation.

mom

moment balance parameters: a list with three arguments,

mom = list(targets = mom_targets, covs = mom_covs, tols = mom_tols).

mom_targets is the profile, i.e. a vector of target moments (e.g., means) of a distribution or a vector of characteristics of an individual toward which to balance the treatment groups. mom_covs is a matrix where each column is a covariate whose mean is to be balanced toward mom_targets. mom_tols is a vector of tolerances for the maximum difference in means between the covariates in mom_covs and the elements of mom_targets. profmatch will select units from each treatment group so that each matched group differs at most by mom_tols from the respective elements of mom_targets. As a result, the matched groups will differ at most mom_tols * 2 from each other. Under certain assumptions, mom_targets can be used for constructing a representative matched sample. The lengths of mom_tols and mom_target have to be equal to the number of columns of mom_covs. Note that the columns of mom_covs can be transformations of the original covariates to balance higher order single-dimensional moments like variances and skewness, and multidimensional moments such as correlations (Zubizarreta 2012).

solver

Optimization solver parameters: a list with four objects,

solver = list(name = name, t_max = t_max, approximate = 1, round_cplex = 0,
trace_cplex = 0).

solver is a string that determines the optimization solver to be used. The options are: cplex, glpk, gurobi, highs, and symphony. The default solver is highs with approximate = 1. For an exact solution, we strongly recommend using cplex or gurobi as they are much faster than the other solvers, but they do require a license (free for academics, but not for people outside universities). Between cplex and gurobi, note that installing the R interface for gurobi is much simpler.

t_max is a scalar with the maximum time limit for finding the matches. This option is specific to cplex, gurobi, and highs. If the optimal matches are not found within this time limit, a partial, suboptimal solution is given.

approximate is a scalar that determines the method of solution. If approximate = 1 (the default), an approximate solution is found via a relaxation of the original integer program. This method of solution is faster than approximate = 0, but some balancing constraints may be violated to some extent. This option works only with n_controls = 1, i.e. pair matching.

round_cplex is binary specific to cplex. round_cplex = 1 ensures that the solution found is integral by rounding and all the constraints are exactly statisfied; round_cplex = 0 (the default) encodes there is no rounding which may return slightly infeasible integer solutions.

trace is a binary specific to cplex and gurobi. trace = 1 turns the optimizer output on. The default is trace = 0.

Value

A list containing the optimal solution, with the following objects:

obj_totals

values of the objective functions at the optima (one value for each treatment group matching problem);

ids

indices of the matched units at the optima;

times

time elapsed to find the optimal solutions (one value for each treatment group matching problem).

Author(s)

Eric R. Cohn <[e-mail]>, Jose R. Zubizarreta <[e-mail]>, Cinar Kilcioglu <[e-mail]>, Juan P. Vielma <[e-mail]>.

References

Zubizarreta, J. R. (2012), "Using Mixed Integer Programming for Matching in an Observational Study of Kidney Failure after Surgery," Journal of the American Statistical Association, 107, 1360-1371.

Cohn, E. R. and Zubizarreta, J. R. (2022) "Profile Matching for the Generalization and Personalization of Causal Inferences," Epidemiology

See Also

sensitivitymv, sensitivitymw.

Examples

	
### Load, sort, and attach data
#data(lalonde)
#lalonde = lalonde[order(lalonde$treatment, decreasing = TRUE), ]
#attach(lalonde)

### Specify covariates
#covs = c("age", "education", "black", "hispanic", "married", "nodegree", "re74", "re75")

### Vector of treatment group indicators
#t_ind = lalonde$treatment

### Covariate matrix
#mom_covs = as.matrix(lalonde[, covs])

### Tolerances will be 0.05 * each covariate's standard deviation
#mom_sds = apply(lalonde[, covs], 2, sd)
#mom_tols = 0.05 * mom_sds

### Target moments will be the overall means in the sample
#mom_targets = colMeans(lalonde[, covs])

### Solver options
#t_max = 60*30
#solver = "gurobi"
#approximate = 0
#solver = list(name = solver, t_max = t_max, approximate = approximate, round_cplex = 0, trace = 0)

#mom = list(covs = mom_covs, tols = mom_tols, targets = mom_targets)
#pmatch_out = profmatch(t_ind, mom, solver)

### Selecting the matched units
#lalonde.matched = lalonde[pmatch_out$id,]

### Comparing TASMDs before and after matching
#TASMD.0.2 = abs(colMeans(lalonde.matched[which(lalonde.matched$treatment == 0), covs]) 
#                    - mom_targets) / mom_sds
#TASMD.1.2 = abs(colMeans(lalonde.matched[which(lalonde.matched$treatment == 1), covs]) 
#                    - mom_targets) / mom_sds

#TASMD.0.1 = abs(colMeans(lalonde[which(lalonde$treatment == 0), covs]) - mom_targets) / mom_sds
#TASMD.1.1 = abs(colMeans(lalonde[which(lalonde$treatment == 1), covs]) - mom_targets) / mom_sds

### For each treatment group, ASAMDs are reduced after matching (i.e., balance is achieved)
#cbind(TASMD.0.1, TASMD.0.2)
#cbind(TASMD.1.1, TASMD.1.2)