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

In observational studies that match several controls to each treated subjec t, substantially greater bias reduction is possible if the number of contro ls is not fixed but rather is allowed to vary from one matched set to anoth er. In certain cases, matching with a fixed number of controls may remove o nly 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 ha ve the same number of controls in total. An example of matching in a study of surgical mortality is discussed in detail.