Multilevel modelling for measuring interaction of effects between multiple categorical variables: An illustrative...

Measuring multiple and higher-order interaction effects between multiple categorical variables proves challenging.

To illustrate a multilevel modelling approach to studying complex interactions.

We apply a two-level random-intercept linear regression to a binary outcome for individuals (level-1) nested within strata (level-2) defined by all observed combinations of multiple categorical exposure variables. As a pedagogic application, we analyse 36 strata defined by five risk factors of preeclampsia (parity, previous preeclampsia, chronic hypertension, multiple pregnancies, body mass index category) among 652,603 women in the Swedish Medical Birth Registry between 2002 and 2010.

The absolute risk of preeclampsia was 4% but was predicted to vary from 1% to 44% across strata. The stratum discriminatory accuracy was 30% according to the variance partition coefficient (VPC) and 0.73 according to the area under the receiver operating characteristic curve (AUC). While the risk heterogeneity across strata was primarily due to the main effects of the categories defining the strata, 5% of the variation was attributable to their two- and higher-way interaction effects. One stratum presented a positive interaction, and two strata presented negative interaction.

Multilevel modelling is an innovative tool for identifying and analysing higher-order interaction effects. Further work is needed to explore how this approach can best be applied to making causal inferences.