Meta-Analysis and Response Surface Extrapolation: A Least Squares Approach

Abstract

In meta-analysis, independently executed historical studies are viewed as imperfect replications of one overall but unplanned experiment. Using empirical parameter estimates of those studies as a unit of analysis, a linear model is specified to uncover systematic variation as a function of study design, data characteristics, model specification, etc. Because of the fallible nature of the historical studies, however, the vector of parameter estimates reflects cross-sectional estimation biases as well as inefficiencies. The outcome of many meta-analyses, therefore, is largely a description of those systematic biases and inefficiencies, a result with little intrinsic scientific value given the fundamental meta-analysis objective of improving understanding of the studied phenomenon. Unfortunately, estimating more scientifically interesting effects on the basis of systematic variation in historical parameter estimates is conditional on the fallible character of the historical studies. This paper provides clarity on what is being estimated in meta-analyses and on how scientifically interesting effects can be estimated unbiasedly using response surface extrapolation in a least squares framework.

Key Words:

• Extrapolation
• Least squares
• Meta-analysis.