find.matches: Find Close Matches

Description

Compares each row in x against all the rows in y, finding rows in y with all columns within a tolerance of the values a given row of x. The default tolerance tol is zero, i.e., an exact match is required on all columns. For qualifying matches, a distance measure is computed. This is the sum of squares of differences between x and y after scaling the columns. The default scaling values are tol, and for columns with tol=1 the scale values are set to 1.0 (since they are ignored anyway). Matches (up to maxmatch of them) are stored and listed in order of increasing distance.
The summary method prints a frequency distribution of the number of matches per observation in x, the median of the minimum distances for all matches per x, as a function of the number of matches, and the frequency of selection of duplicate observations as those having the smallest distance. The print method prints the entire matches and distance components of the result from find.matches.
matchCases finds all controls that match cases on a single variable x within a tolerance of tol. This is intended for prospective cohort studies that use matching for confounder adjustment (even though regression models usually work better).

Usage

find.matches(x, y, tol=rep(0, ncol(y)), scale=tol, maxmatch=10)
# S3 method for find.matches
summary(object, ...)
# S3 method for find.matches
print(x, digits, ...)
matchCases(xcase,    ycase,    idcase=names(ycase),
           xcontrol, ycontrol, idcontrol=names(ycontrol),
           tol=NULL,
           maxobs=max(length(ycase),length(ycontrol))*10,
           maxmatch=20, which=c('closest','random'))

Arguments

Value

find.matches returns a list of class find.matches with elements matches and distance. Both elements are matrices with the number of rows equal to the number of rows in x, and with k columns, where k is the maximum number of matches (<= maxmatch) that occurred. The elements of matches

are row identifiers of y that match, with zeros if fewer than maxmatch matches are found (blanks if y had row names). matchCases returns a data frame with variables idcase (id of case currently being matched), type (factor variable with levels "case"

and "control"), id (id of case if case row, or id of matching case), and y.

References

Ming K, Rosenbaum PR (2001): A note on optimal matching with variable controls using the assignment algorithm. J Comp Graph Stat 10:455--463.

Cepeda MS, Boston R, Farrar JT, Strom BL (2003): Optimal matching with a variable number of controls vs. a fixed number of controls for a cohort study: trade-offs. J Clin Epidemiology 56:230-237. Note: These papers were not used for the functions here but probably should have been.

Examples

Run this code

y <- rbind(c(.1, .2),c(.11, .22), c(.3, .4), c(.31, .41), c(.32, 5))
x <- rbind(c(.09,.21), c(.29,.39))
y
x
w <- find.matches(x, y, maxmatch=5, tol=c(.05,.05))


set.seed(111)       # so can replicate results
x <- matrix(runif(500), ncol=2)
y <- matrix(runif(2000), ncol=2)
w <- find.matches(x, y, maxmatch=5, tol=c(.02,.03))
w$matches[1:5,]
w$distance[1:5,]
# Find first x with 3 or more y-matches
num.match <- apply(w$matches, 1, function(x)sum(x > 0))
j <- ((1:length(num.match))[num.match > 2])[1]
x[j,]
y[w$matches[j,],]


summary(w)


# For many applications would do something like this:
# attach(df1)
# x <- cbind(age, sex) # Just do as.matrix(df1) if df1 has no factor objects
# attach(df2)
# y <- cbind(age, sex)
# mat <- find.matches(x, y, tol=c(5,0)) # exact match on sex, 5y on age


# Demonstrate matchCases
xcase     <- c(1,3,5,12)
xcontrol  <- 1:6
idcase    <- c('A','B','C','D')
idcontrol <- c('a','b','c','d','e','f')
ycase     <- c(11,33,55,122)
ycontrol  <- c(11,22,33,44,55,66)
matchCases(xcase, ycase, idcase,
           xcontrol, ycontrol, idcontrol, tol=1)


# If y is a binary response variable, the following code
# will produce a Mantel-Haenszel summary odds ratio that 
# utilizes the matching.
# Standard variance formula will not work here because
# a control will match more than one case
# WARNING: The M-H procedure exemplified here is suspect 
# because of the small strata and widely varying number
# of controls per case.


x    <- c(1, 2, 3, 3, 3, 6, 7, 12,  1, 1:7)
y    <- c(0, 0, 0, 1, 0, 1, 1,  1,  1, 0, 0, 0, 0, 1, 1, 1)
case <- c(rep(TRUE, 8), rep(FALSE, 8))
id   <- 1:length(x)


m <- matchCases(x[case],  y[case],  id[case],
                x[!case], y[!case], id[!case], tol=1)
iscase <- m$type=='case'
# Note: the first tapply on insures that event indicators are
# sorted by case id.  The second actually does something.
event.case    <- tapply(m$y[iscase],  m$idcase[iscase],  sum)
event.control <- tapply(m$y[!iscase], m$idcase[!iscase], sum)
n.control     <- tapply(!iscase,      m$idcase,          sum)
n             <- tapply(m$y,          m$idcase,          length)
or <- sum(event.case * (n.control - event.control) / n) /
      sum(event.control * (1 - event.case) / n)
or


# Bootstrap this estimator by sampling with replacement from
# subjects.  Assumes id is unique when combine cases+controls
# (id was constructed this way above).  The following algorithms
# puts all sampled controls back with the cases to whom they were
# originally matched.


ids <- unique(m$id)
idgroups <- split(1:nrow(m), m$id)
B   <- 50   # in practice use many more
ors <- numeric(B)
# Function to order w by ids, leaving unassigned elements zero
align <- function(ids, w) {
  z <- structure(rep(0, length(ids)), names=ids)
  z[names(w)] <- w
  z
}
for(i in 1:B) {
  j <- sample(ids, replace=TRUE)
  obs <- unlist(idgroups[j])
  u <- m[obs,]
  iscase <- u$type=='case'
  n.case <- align(ids, tapply(u$type, u$idcase, 
                              function(v)sum(v=='case')))
  n.control <- align(ids, tapply(u$type, u$idcase,
                                 function(v)sum(v=='control')))
  event.case <- align(ids, tapply(u$y[iscase],  u$idcase[iscase],  sum))
  event.control <- align(ids, tapply(u$y[!iscase], u$idcase[!iscase], sum))
  n <- n.case + n.control
  # Remove sets having 0 cases or 0 controls in resample
  s             <- n.case > 0 & n.control > 0
  denom <- sum(event.control[s] * (n.case[s] - event.case[s]) / n[s])
  or <- if(denom==0) NA else 
   sum(event.case[s] * (n.control[s] - event.control[s]) / n[s]) / denom
  ors[i] <- or
}
describe(ors)