The index lift in data mining has a close relationship with the association measure relative risk in epidemiological...

Data mining tools have been increasingly used in health research, with the promise of accelerating discoveries. Lift is a standard association metric in the data mining community. However, health researchers struggle with the interpretation of lift. As a result, dissemination of data mining results can be met with hesitation. The relative risk and odds ratio are standard association measures in the health domain, due to their straightforward interpretation and comparability across populations. We aimed to investigate the lift-relative risk and the lift-odds ratio relationships, and provide tools to convert lift to the relative risk and odds ratio.

We derived equations linking lift-relative risk and lift-odds ratio. We discussed how lift, relative risk, and odds ratio behave numerically with varying association strengths and exposure prevalence levels. The lift-relative risk relationship was further illustrated using a high-dimensional dataset which examines the association of exposure to airborne pollutants and adverse birth outcomes. We conducted spatial association rule mining using the Kingfisher algorithm, which identified association rules using its built-in lift metric. We directly estimated relative risks and odds ratios from 2 by 2 tables for each identified rule. These values were compared to the corresponding lift values, and relative risks and odds ratios were computed using the derived equations.

As the exposure-outcome association strengthens, the odds ratio and relative risk move away from 1 faster numerically than lift, i.e. |log (odds ratio)| ≥ |log (relative risk)| ≥ |log (lift)|. In addition, lift is bounded by the smaller of the inverse probability of outcome or exposure, i.e. lift≤ min (1/P(O), 1/P(E)). Unlike the relative risk and odds ratio, lift depends on the exposure prevalence for fixed outcomes. For example, when an exposure A and a less prevalent exposure B have the same relative risk for an outcome, exposure A has a lower lift than B.

Lift, relative risk, and odds ratio are positively correlated and share the same null value. However, lift depends on the exposure prevalence, and thus is not straightforward to interpret or to use to compare association strength. Tools are provided to obtain the relative risk and odds ratio from lift.