The matching strategy

The idea is quite simple. We will generate a list of patients based on a recent pre-diabetes diagnosis. From that list, we will draw a single individual and then find a match from the remaining individuals. The match will be based on factors that the researchers think might be related to the outcome, such as age, gender, and one or two other relevant baseline measures. (If the number of matching characteristics grows too large, matching may turn out to be difficult.) If no match is found, the first individual is removed from the study. If a match is found, the first individual is assigned to the therapy group, and the second to the control group. Now we repeat the process, drawing another individual from the list (which excludes the first pair and any patients who have been unmatched), and finding a match. The process is repeated until everyone on the list has been matched or placed on the unmatched list.

After the pairs have been created, the research study coordinators reach out to the individuals who have been randomized to the therapy group in an effort to recruit participants. If a patient declines, she and her matched pair are removed from the study (i.e. their outcomes will not be included in the final analysis). The researchers will work their way down the list until enough people have been found to participate.

We try to eliminate the bias due to differential dropout by removing the matched patient every time a patient randomized to therapy declines to participate. We are making a key assumption here: the matched patient of someone who agrees to participate would have also agreed to participate. We are also assuming that the matching criteria are sufficient to predict participation. While we will not completely remove bias, it may be the best we can do given the baseline information we have about the patients. It would be ideal if we could ask both members of the pair if they would be willing to participate, and remove them both if one declines. However, in this particular study, this is not feasible.

The matching algorithm

I implemented this algorithm on a sample data set that includes gender, age, and BMI, the three characteristics we want to match. The data is read directly into an R data.table dsamp. I’ve printed the first six rows:

dsamp <- fread("DataMatchBias/eligList.csv")
setkey(dsamp, ID)

dsamp[1:6]
##    ID female age   BMI
## 1:  1      1  24 27.14
## 2:  2      0  29 31.98
## 3:  3      0  47 25.28
## 4:  4      0  40 24.27
## 5:  5      1  29 30.61
## 6:  6      1  38 25.69

The loop below selects a single record from dsamp and searches for a match. If a match is found, the selected record is added to drand (randomized to therapy) and the match is added to dcntl. If no match is found, the single record is added to dused, and nothing is added to drand or dcntl. Anytime a record is added to any of the three data tables, it is removed from dsamp. This process continues until dsamp has one or no records remaining.

The actual matching is done by a call to function Match from the Matching package. This function is typically used to match a group of exposed to unexposed (or treated to untreated) individuals, often using a propensity score. In this case, we are matching simultaneously on the three columns in dsamp. Ideally, we would want to have exact matches, but this is unrealistic for continuous measures. So, for age and BMI, we set the matching range to be 0.5 standard deviations. (We do match exactly on gender.)

library(Matching)
set.seed(3532)

dsamp[, rx := 0]
dused <- NULL
drand <- NULL
dcntl <- NULL

while (nrow(dsamp) > 1) {
  
  selectRow <- sample(1:nrow(dsamp), 1)
  
  dsamp[selectRow, rx := 1]
  
  myTr <- dsamp[, rx]
  myX <- as.matrix(dsamp[, .(female, age, BMI)])
  
  match.dt <- Match(Tr = myTr, X = myX, 
                    caliper = c(0, 0.50, .50), ties = FALSE)
  
  if (length(match.dt) == 1) {  # no match
    
    dused <- rbind(dused, dsamp[selectRow])
    dsamp <- dsamp[-selectRow, ]
    
  } else {                      # match
    
    trt <- match.dt$index.treated
    ctl <- match.dt$index.control
    
    drand <- rbind(drand, dsamp[trt])
    dcntl <- rbind(dcntl, dsamp[ctl])
    
    dsamp <- dsamp[-c(trt, ctl)]
    
  }
}

Matching results

Here is a plot of all the pairs that were generated (connected by the blue segment), and includes the individuals without a match (red circles). We could get shorter line segments if we reduced the caliper values, but we would certainly increase the number of unmatched patients.

The distributions of the matching variables (or least the means and standard deviations) appear quite close, as we can see by looking at the males and females separately.

##    rx  N mu.age sd.age mu.bmi sd.bmi
## 1:  0 77   44.8   12.4   28.6   3.65
## 2:  1 77   44.6   12.4   28.6   3.71

##    rx  N mu.age sd.age mu.bmi sd.bmi
## 1:  0 94   47.8   11.1   29.7   4.63
## 2:  1 94   47.8   11.3   29.7   4.55

Incorporating the design into the analysis plan

The study - which is formally named Integrated Community-Clinical Linkage Model to Promote Weight Loss among South Asians with Pre-Diabetes - is still in its early stages, so no outcomes have been collected. But when it comes time to analyzing the results, the models used to estimate the effect of the intervention will have to take into consideration two important design factors: (1) the fact that the individuals in the treatment and control groups are not independent, because they were assigned to their respective groups in pairs, and (2) the fact that the individuals in the treatment groups will not be independent of each other, since the intervention is group-based, so this a partially cluster randomized trial. In a future post, I will explore this model in a bit more detail.

This study is supported by the National Institutes of Health National Institute of Diabetes and Digestive and Kidney Diseases R01DK11048. The views expressed are those of the author and do not necessarily represent the official position of the funding organizations.