Substantial gains in bias reduction from matching with a variable number of controls

In observational studies that match several controls to each treated subject, substantially greater bias reduction is possible if the number of controls is not fixed but rather is allowed to vary from one matched set to another. In certain cases, matching with a fixed number of controls may remove only 50% of the bias in a covariate, whereas matching with a variable number of controls may remove 90% of the bias, even though both control groups have the same number of controls in total. An example of matching in a study of surgical mortality is discussed in detail.