Matching to Remove Bias in Observational Studies

Abstract

: Several matching methods that match all of one sample from another larger sample on a continuous matching variable are compared with respect to their ability to remove the bias of the matching variable. One method is a simple mean-matching method and three are nearest available pair-matching methods. The methods' abilities to remove bias are also compared with the theoretical maximum given fixed distributions and fixed sample sizes. A summary of advice to an investigator is included. INTRODUCTION Matched sampling is a method of data collection and organization designed to reduce bias and increase precision in observational studies, i.e., in those studies in which the random assignment of treatments to units (subjects) is absent. Although there are examples of observational studies which could have been conducted as properly randomized experiments, in many other cases the investigator could not randomly assign treatments to subjects. For example, consider the Kihlberg and Robinson [1968] study comparing severity of injury in automobile accidents for motorists using and not using seatbelts. One would not want to randomly assign subjects to “seatbelt” and “no seatbelt” treatments and then have them collide at varying speeds, angles of impact, etc. Neither, however, would one want to simply compare the severity of injury in “random” samples of motorists in accidents using and not using seatbelts; important variables such as “speed of automobile at time of accident” may be differently distributed in the two groups (i.e., seatbelted motorists are generally more cautious and therefore tend to drive more slowly).