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EBEs

Purpose

Although the population parameter estimation algorithm can give a rough estimation of the individual parameters, we can compute the conditional mode, i.e. the most probable value of the individual parameters.

Conditional mode

If the option ”EBEs” is selected, the individual parameters are estimated by maximizing the conditional probabilities p(\psi_i|y_i;\hat{\theta}), i.e.

$$ \hat{\psi}_i^{mode} = \underset{\psi_i}{\textrm{arg max }}p(\psi_i|y_i;\hat{\theta})$$

It corresponds to the “optimal” value for the fit. By default, Monolix uses the conditional mode for computing predictions, taking the philosophy that the “most likely” values of the individual parameters are the most suited for computing the “most likely” predictions.

Display and outputs

In the interface, a summary of the individual parameters is proposed (min, max and some quartiles) as shown in the figure below.

In terms of output, a folder called IndividualParameters is created in the result folder where the following files are created

  • individualParameters.txt. All the individual parameters for each subject-occasion from SAEM, the conditional mean and/or the conditional mode (with extensions _SAEM, _mean and _mode respectively) are written in that file.
  • individualRandomEffects.txt. All the random effects for each subject-occasion from SAEM, the conditional mean and/or the conditional mode (with extensions _SAEM, _mean and _mode respectively) are written in that file.

Best practices: When do we look at the conditional mode and when do we look at the conditional mean?

The choice of using the conditional mean \psi^{mean} or conditional mode \psi^{mode} is arbitrary. By default, Monolix uses the conditional mode for computing predictions, taking the philosophy that the “most likely” values of the individual parameters are the most suited for computing the “most likely” predictions.