Trial design

A popular inferential method is maximum likelihood estimation (MLE) for full-parametric specification of the response distribution, often including highly parsimonious covariance functional forms (few covariance parameters). Inference on parameter estimates are valid [UNDER THESE CONDITIONS].

These models often invoke a subject-level model conditional on un-observable subject random effects combined with non-random (fixed) global regression parameters common across all subjects, and which induce the desired within-subject covariance marginally (averaging over the random effects). These models are often called linear mixed models (LMMs) for normal data and generalised linear mixed models (GLMMs) for binary and count data.

A major advantage of GLMMs is that observed covariances can be well approximated when the true data distribution broadly has the specified form, but poorly if mis-specified. Furthermore parameter inference is valid under missing at random assumptions (MAR), meaning baseline adjustment for variables correlated with, or causing, subject drop-out is sufficient to ensure parameter estimates are un-biased.

Another popular inferential method is quasi-likelihood estimation (qMLE) for specifying only the mean and variance of the response distribution rather than it’s full functional form. These models can be applied to normal, binary and count data, and are often called marginal models since they work at the global rather than subject-level (almost always there is no subject-level random effects model that is equivalent - i.e that gives the same marginal covariance structure).

These methods only require a “working” covariance structure which [UNDER CERTAIN CONDITIONS] yields un-biased regression (non-covariance) parameter estimates even when the true covariance structure is not well approximated - an apparent magic trick that crops up often in statistical theory (often when incorrectly assuming independence of dependent data). However regression estimate standard errors are in-valid, but “corrected for” through a sandwich-type empirical estimator of the covariance as a post-regression parameter estimation step.

The main advantage of these models is not requiring a-priori knowledge of the true covariance structure. The main disadvantage is that un-biased regression parameter estimates is only guaranteed under missing completely at random (MCAR) mechanisms for subject drop-out, which can be a poor assumption for many clinical settings.