Validity and efficiency issues are considered with regard to the use of matching and random sampling as alternative methods of subject selection in follow-up and case-control studies. We discuss the simple situation involving dichotomous disease and exposure variables and a single dichotomous matching factor, and we consider the influence on efficiency of a possible loss of subjects due to matching constraints. The decision to match or not should be motivated by efficiency considerations. An efficiency criterion based on a comparison of confidence intervals under matching and random sampling for the effect measure of interest (the risk ratio and risk difference in follow-up studies, and the odds ratio in case-control studies) leads to the following conclusions when the sampling method does not influence the size of the comparison group. In follow-up studies, matching on a confounder is expected to lead to a gain in efficiency over random sampling, while matching on a nonconfounder is not expected to result in a loss of efficiency. In case-control studies, the same conclusions hold, except that matching is not as advantageous as in follow-up studies and can lead to a loss of efficiency in some situations (usually of little practical importance). When matching reduces the size of the comparison group, there is likely to be a meaningful gain in efficiency due to random sampling only when the matched comparison group is at most 40-50% the size of the randomly-sampled comparison group is a follow-up study, and at most 50-65% the size in a case-control study.