In the study in here, it is said that mixed effects models are better in estimating parameters of a ODE system when there is only very small number of data to estimate the parameters. So, in a situation where viral load data are measured over time across several subjects how does mixed effects improve parameter estimation than simply using a nonlinear optimisation technique to minimise an objective function that considers minimising the sum of squared errors?

Is it because the mixed effects models estimate a population mean for the parameters and the individual variability is explained through the random effects?
So, does mixed effects consider the data points of all subjects together when estimating the population parameters?How does it overcome the issue of limited data?

Also, is this mixed effects method effective when the data across subjects show various patterns? For example, the viral load data in the above article all show a similar pattern, although there is individual variation. But in a situation where the patterns are totally different, is this method still effective?


A couple of points:

  1. Standard mixed models also minimize an objective function, namely the negative of the log-likelihood function. Hence, you’re making a parametric assumption for the distribution of your outcome. If this assumption is close to the reality, you gain in efficiency.

  2. Mixed models are typically used to account for correlations in grouped/clustered data. Like in your example, the clusters are the subjects for whom you have repeated measurements over time. It is typically, expected that measurements in the same cluster/subject are (positively) correlated. If you use an approach that does not account for the correlations, then

    • standard errors / p-values are wrongly too small for between subjects effects (e.g., differences between males and females, old and young people), and

    • standard errors / p-values are wrongly too large for within subjects effects (e.g., changes over time).

An additional issue is with missing data / dropout. If you have missing data that are of the missing at random type, then not appropriately modeling the correlations not only influences the standard errors but also can result in biased effect estimates.


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