Robustness of linear mixed models

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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.

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Improving efficiency in RCTs using propensity scores

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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).

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Is the two sample t-test/ANOVA really biased in RCTs?

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A couple of months ago I came across this paper, “Bias, precision and statistical power of analysis of covariance in the analysis of randomized trials with baseline imbalance: a simulation study”, published in the open access online journal BMC Medical Research Methodology, by Egbewale, Lewis and Sim. Using simulation studies, as the title says, the authors investigate the bias, precision and power of three analysis methods for a randomized trial with a continuous outcome and a baseline measure of the same variable, when there is an imbalance at baseline in the baseline measure. The three methods considered are ANOVA (a two-sample t-test here), an analysis of change (CSA, change from baseline to follow-up) scores, and analysis of covariance (ANCOVA), which corresponds to fitting a linear regression model with outcome measurement as the dependent variable, with randomized treatment and baseline measure as covariates.

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