Matching when covariables are normally distributed

The use of matched pairs to reduce effects of concomitant variation in observational studies is considered when covariables have multivariate normal distributions. A case is matched by the nearest control, provided the control lies within a specified distance; otherwise the case is unmatched. Simulation studies indicate that if the number of cases to be matched is less than half the number of controls to choose from, cases rarely compete for the same control, so that matched pairs are effectively independent. The probability, P1 of being able to construct a matched pair, together with moments and other parameters of the distributions of matched cases and controls, are expressed in terms of single or double integrals. These have been evaluated. The relationship of P1 to the number of covariables, the number of controls to choose from and other parameters is outlined. The optimal radius of search depends on the method of analysis. Matching can double the precision of a study.