Abstract: The ability of matched sampling and linear regression adjustment to reduce the bias of an estimate of the treatment effect in two sample observational studies is investigated for a simple matching method and five simple estimates. Monte Carlo results are given for moderately linear exponential response surfaces and analytic results are presented for quadratic response surfaces. The conclusions are (1) in general both matched sampling and regression adjustment can be expected to reduce bias, (2) in some cases when the variance of the matching variable differs in the two populations both matching and regression adjustment can increase bias, (3) when the variance of the matching variable is the same in the two populations and the distributions of the matching variable are symmetric the usual covariance adjusted estimate based on random samples is almost unbiased, and (4) the combination of regression adjustment in matched samples generally produces the least biased estimate.

INTRODUCTION

This paper is an extension of Rubin [1973a] to include regression adjusted estimates and parallel nonlinear response surfaces. The reader is referred to Sections 1 and 2 of that paper for the statement of the general problem and an introduction to the notation.

After presenting the estimates of the treatment effect to be considered in the remainder of Section 1, we go on in Section 2 to present Monte Carlo results for the expected bias of the estimates assuming four exponential response surfaces, normally distributed X, and the random order, nearest available matching method.