Level of aggregation for optimal epidemiological analysis: the case of time to surgery and unnecessary removal of the normal appendix.
STUDY OBJECTIVE: To illustrate the concept of "individualised fallacy", the result of improper interpretation and inference about aggregate level associations on the basis of associations at the individual level, in epidemiology. DESIGN: Cohort study. SETTING: Canadian province of Ontario. PATIENTS: All patients who underwent primary appendicectomy in 175 Ontario hospitals from 1989 to 1992. The association between rate of normal appendix removal and time to surgery was analysed at two levels: (1) at individual patient level, in which, for each patient, the exact number of days to surgery was derived, and (2) at hospital level, in which hospital specific proportions of time to surgery was calculated. MAIN RESULTS: Measured at individual level, compared with patients who had an operation on the same day of admission, the odds ratio was 2.41 (95% confidence intervals 2.28, 2.56) for patients who had an operation > 1 day after admission. Measured at hospital level, each 10% increase in the proportion of patients who had an operation > 1 day after admission resulted in a 15% reduction in the odds of normal appendix removal (odds ratio 0.85, 95% confidence intervals 0.82, 0.88) CONCLUSIONS: In this case study, hospital level measure correctly predicted a reduction in the rate of normal appendix removal by delaying surgery, whereas individual level measure biased the direction of the relation to the opposite. This example illustrates that bias in across level inference can occur either at individual or ecological level. The preferred level of analysis is the one that minimises confounding; often, it must be selected on the basis of a priori knowledge of the subject area.