Appendix S1: Patterns of second- and third-trimester growth and discordance in twin pregnancy: analysis of the Southwest Thames Obstetric Research Collaborative (STORK) multiple pregnancy cohort

The nested nature of the sets of measurements obtained for each fetus and pairs of twins within each pregnancy means that the analysis of fetal growth in twin pregnancies is particularly suited to the application of multilevel modelling. The term ‘multilevel modelling’ describes a mixed effects approach in which sets of measurements within each individual and/or individuals within groups form a nested structure. Multilevel modelling is therefore an extension of the general linear regression framework that involves the fitting of a combination of ‘fixed effects’ and ‘random effects’ to different hierarchical levels1;2. The fixed effects provide the expected mean value for any given combination of predictive variables, whilst the random effects are used to model the random variation associated with each level of the analysis and the covariance between different measurements obtained from the same individual or between individuals within the same group. Analysis of this nature is required in order to create adequate statistical models that take account of the dependency within data that results from obtaining serial measurements from individuals or the clustering of individuals within distinct groups. The simplest example of a multilevel model is a two-level ‘random intercept’ model. In the context of analysis of longitudinal data, this could result when serial measurements are obtained from individuals and the measurement at each time point is dependent on age, with an overall mean intercept (β0) and slope (β1) for the relationship between the measurement and age and random components associated with both each separate measurement occasion (2i j ) and each individual overall (u0 j ). For the value (yi j ) of the ith measurement occasion within the jth individual at age (ti j ), this