Objectives The aim of this study was to quantify bias from a partially ecologic analysis due to (i) model misspecification and (ii) an unmeasured confounder, considering various scenarios that may occur in occupational and environmental epidemiology. A study with an aggregate exposure variable, P_E, but with outcome, group membership, and covariates assessed individually is partially ecologic. In this paper, P_E is the proportion exposed; P_E can vary across geographic areas or occupational groups.

Methods Several hypothetical scenarios were considered, varying the baseline risk, the exposure effect, the exposure distribution across groups, the impact of the (unmeasured) confounder, and the confounder distribution across groups. First, confounding within groups was introduced. Thereafter, confounding between groups was introduced by co-varying P_E and the confounder prevalence across the groups. The expected odds ratio (exposed versus unexposed) was calculated in two alternative models, the logistic regression and linear odds models, both with P_E as the independent variable. Moreover, empirical data on noise exposure and sleeping disturbances were analyzed.

Results Compared with the logistic regression model, the linear odds model yielded a markedly less biased odds ratio (OR) when the outcome was rare (≤5% baseline risk). Confounding within groups resulted in marginal bias, whereas confounding between groups resulted in more pronounced bias.

Conclusions A logistic regression analysis, with P_E as an independent variable, can yield substantial model misspecification bias. By contrast, the linear odds model is valid when the outcome is rare. Confounding between groups should be of more concern than confounding within groups in partially ecologic analyses.

Key terms ecologic analysis; epidemiologic method; epidemiology bias; group proportion; model specification; noise exposure; sleeping disturbance; statistical model; unmeasured confounder