Covariate measurement error is a common issue in epidemiology. Many statistical methods have been developed for allowing for covariate measurement error over the last three decades or so. I’ve been playing around with Stata’s structural equation modelling builder, which enables one to allow for covariate measurement error using maximum likelihood for estimation. I’m still very much a beginner with structural equation models and Stata’s implementation of them, but hopefully this YouTube video is a useful illustration of just one of the things that’s possible with them.
Robustness of linear mixed models
Linear mixed models form an extremely flexible class of models for modelling continuous outcomes where data are collected longitudinally, are clustered, or more generally have some sort of dependency structure between observations. They involve modelling outcomes using a combination of so called fixed effects and random effects. Random effects allow for the possibility that one or more covariates have effects that vary from unit (cluster, subject) to unit. In the context of modelling longitudinal repeated measures data, popular linear mixed models include the random-intercepts and random-slopes models, which respectively allow each unit to have their own intercept or (intercept and) slope.
As implemented in statistical packages, linear mixed models assume that we have modelled the dependency structure correctly, and that both the random effects and within-unit residual errors follow normal distributions, and that these have constant variance. While it is possible to some extent to check these assumptions through various diagnostics, a natural concern is that if one or more assumptions do not hold, our inferences may be invalid. Fortunately it turns out that linear mixed models are robust to violations of some of their assumptions.
Improving efficiency in RCTs using propensity scores
Propensity scores have become a popular approach for confounder adjustment in observational studies. The basic idea is to model how the probability of receiving a treatment or exposure depends on the confounders, i.e. the ‘propensity’ to be treated. To estimate the effect of exposure, outcomes are then compared between exposed and unexposed who share the same value of the propensity score. Alternatively the outcome can be regressed on exposure, weighting the observations using the propensity score. For further reading on using propensity scores in observational studies, see for example this nice paper by Peter Austin.
But the topic of this post is on the use of propensity scores in randomized controlled trials. The post was prompted by an excellent seminar recently given by my colleague Elizabeth Williamson, covering the content of her recent paper ‘Variance reduction in randomised trials by inverse probability weighting using the propensity score” (open access paper here).