find.matches {Hmisc}

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 class 'find.matches'
summary(object, ...)
## S3 method for class '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

x

a numeric matrix or the result of find.matches

y

a numeric matrix with same number of columns as x

xcase

numeric vector to match on for cases

xcontrol

numeric vector to match on for controls, not necessarily the same length as xcase

ycase

a vector or matrix

ycontrol

ycase and ycontrol are vectors or matrices, not necessarily having the same number of rows, specifying a variable to carry along from cases and matching controls. If you instead want to carry along rows from a data frame, let ycase and ycontrol be non-overlapping integer subscripts of the donor data frame.

tol

a vector of tolerances with number of elements the same as the number of columns of y, for find.matches. For matchCases is a scalar tolerance.

scale

a vector of scaling constants with number of elements the same as the number of columns of y.

maxmatch

maximum number of matches to allow. For matchCases, maximum number of controls to match with a case (default is 20). If more than maxmatch matching controls are available, a random sample without replacement of maxmatch controls is used (if which="random").

object

an object created by find.matches

digits

number of digits to use in printing distances

idcase

vector the same length as xcase

idcontrol

idcase and idcontrol are vectors the same length as xcase and xcontrol respectively, specifying the id of cases and controls. Defaults are integers specifying original element positions within each of cases and controls.

maxobs

maximum number of cases and all matching controls combined (maximum dimension of data frame resulting from matchControls). Default is ten times the maximum of the number of cases and number of controls. maxobs is used to allocate space for the resulting data frame.

which

set to "closest" (the default) to match cases with up to maxmatch controls that most closely match on x. Set which="random" to use randomly chosen controls. In either case, only those controls within tol on x are allowed to be used.

...

unused

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.

Author(s)

Frank Harrell
Department of Biostatistics
Vanderbilt University
[e-mail]

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.

See Also

scale, apply

Examples

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)