Graphical display of population data
E. Niclas Jonsson
Department of Pharmaceutical Biosciences Uppsala University
Graphical displays are important tools for exploration, goodness of fit assessment and presentation in any type of data analysis and become even more important as the complexity of the models and data structures increase.
The data encountered in non-linear mixed effects modeling are complex. First, the structure is hierarchical (individuals within populations) and it may be necessary or useful to consider visualization of all the levels in the hierarchy. Second, the amount of data (number of observations and/or individuals) may be very large. This requires efficient ways of producing or, sometimes, displaying, graphs. Third, the data are multivariate, i.e. there is potentially more than one independent variable that needs to be considered in the graphical displays.
Categorical data of the "proportional Cox model" type effectively disqualifies our standard graphical techniques. When the dependent variable is continuous, there is a direct relationship between the observations and the predictions from the model. With categorical observations, on the other hand, the model describes the probabilities of the different outcomes. This means that our graphical methods need to be adjusted such that they also relate to these probabilities.
The first part of this tutorial will review common strategies to address the general issues mentioned above, for cases when the dependent variable is continuous, for example drug concentrations. The second part of the tutorial will concern graphical exploration, goodness of fit assessment and presentation when the dependent variable is categorical. The tutorial will cover a variety of graphical displays and techniques suitable for this purpose, many of which up till now have had no or very little use in the population PK/PD community.