Multi-level modelling, the ecologic fallacy, and hybrid study designs.

In this issue, Robinson’s highly influential paper is reprinted, along with a paper advocating the use of multi-level thinking by Subramanian et al., and commentaries by Oakes and Firebaugh. On re-reading Robinson’s paper, I was again struck by the clarity of the basic take-home message: ecological data can estimate individual associations in only very rare situations. Robinson illustrated the ecologic fallacy using correlation coefficients applied at different levels of aggregation, whereas more recent work has focused on loglinear models. For common (in a statistical sense) outcomes, such as the illiteracy-race example considered in Robinson’s paper, a logistic form is more appropriate (and is used by Subramanian et al.) but this form is less amenable to analytic study. There has been an abundance of work on the myriad causes of ecologic bias on estimates of individual-level associations, which include within-area variability in exposure, and within-area confounding. One might think that the estimation of contextual associations can be carried out with ecologic data alone, but Greenland shows this is not the case. A key point is that contrary to what is claimed by some authors, ecologic data alone do not allow one to determine whether ecological bias is likely to be present in a particular dataset. The only solution to the ecologic fallacy is to supplement the ecologic data with individual-level data, a subject that we now briefly review.