Mixed models for neonatal outcomes with twins

Question

I am trying to fit a linear mixed model for a randomised controlled trial where women are randomised to one of two treatments, but the outcomes are at the baby level. Most women will give birth to singletons, but there will be some twins (or higher), which will need to be accounted for. I am thinking of using a random effect for the mother, but most of the births will be singletons and only have one observation per group. This can effectively be treated as a cluster trial with most clusters of size 1. The model will be:

$$ y_{ij} = \beta_0 + \beta_1 x_{1ij} + \beta_2 x_{2ij} + u_j + e_{ij} $$ Where $i$ is the baby, $j$ is the mother, $x_1$ is the treatment group, $x_2$ is a dummy variable for singleton or multiple. $u_j$ will be the residuals for the mothers and $e_{ij}$ will be the residual of the baby. If we are estimating birthweight, this will allow correlation between the birthweight of twins, and for twins generally to have a different birthweight to singletons. However, I'm unsure if this model is actually correct, as most of the values for $e_{ij}$ will be 0 due to the fact that there is only one value per group.

Has anybody tried to model this sort of trial before, or can tell me if this model will face problems and any solutions of so. Added complexity is some outcomes will be binary and count, so I will also look to fit a GLMM using the same linear predictor.

Answer 1

It's probably easier to use marginal models in this context when most of the clusters are of size one. That is, you fit a generalised linear model with $$g(E[y_{ij}])=\beta_0 +\beta_1 x_{1ij}+\beta_2 x_{2ij}$$ and use a sandwich variance estimator to handle the correlation within cluster.

I've seen this used in perinatal trials (usually without $x_2$, I think).