Improving the observed-to-expected ratio method to identify true patterns of multimorbidity

AbstractBackground In the study of multimorbidity, the observed-to-expected ratio is frequently used to identify triads of conditions associated with each other. However, the method may wrongly identify spurious triads which are only partially associated as being true triads. This paper aims to improve the method to identify mutually associated triads. Methods Data were simulated to emulate the characteristics of our empirical data. Using 25 simulated binary variables, 2,300 triads were created. For each triad, the following statistics were calculated: the observed-to-expected ratio, the logarithm of the observed-to-expected ratio known as the information component, and the lower confidence interval of the information component (\(\:{IC}_{0.025}\)). Furthermore, for each triad, we calculated three lift values (using association rule mining) to assess the dependency of each condition with the other two. Then, within each triad, \(\:{IC}_{0.025}\) for all three constituent pairs were calculated. \(\:{IC}_{0.025}<0\) indicates independent of conditions. Triads with three pairs having \(\:{IC}_{0.025}>0\) were defined as true. Triads with at least one of the pairs having \(\:{IC}_{0.025}<0\) were defined as false. Among the false triads, those with the triad \(\:{IC}_{0.025}>0\) were defined as spurious (i.e., the lower bound of the information component for the whole triad exceeding 0). Methods were then applied to the Australian national mortality data. Results In simulated data, 53.2% of false triads were spurious (i.e., while at least one pair was independent, \(\:{IC}_{0.025}\) of the triad exceeded 0). Through algebra, we illustrated that the closeness of the observed-to-expected ratio and lift is an indication of independence among some conditions within the triad. For all spurious triads, the observed-to-expected ratio and lift were close, suggesting dependency of a pair within the triad. The observed-to-expected ratio was about twice as high as the lift for true triads, indicating mutual associations. In the Australian national mortality data, for 95% of triads with high OE ratios, the observed-to-expected ratios and lifts were close suggesting dependency of a pair within the triad. Conclusion An associated pair may attract an unrelated condition and create a spurious triad. To guard against spurious findings, the observed-to-expected method should be used alongside the association rule mining.