# Population Models in PoPy

Estimating model parameters for a single subject requires many observations to differentiate between one model and another. However, because the observation process is usually intrusive (e.g. taking a blood sample to measure drug concentration) it is often practical to take only a few samples from one individual.

To overcome this limitation we can take a few samples from many individuals and pool the data, known as Population PK. Early attempts at doing this relied on the residual error model “taking up the slack” but it quickly became clear that the estimates of population parameters were biased - when dealing with a population of subjects, a single set of model parameters cannot capture the variation in concentration time courses in a sensible way.

A significant advance in the field came with the development of mixed effect models that predict a time course that is personalized to every individual so that the residual error model described earlier remains sensible. This personalization is done by introducing new parameters to capture variability:

1. A stochastic statistical model that uses random effects to capture unpredictable, random variability between subjects from the same population, and possibly between occasions for the same subject
2. A deterministic covariate model that uses additional fixed effects to capture predictable variability as a result of relationships between subject characteristics and structural model parameters (e.g. between weight and the volume of distribution)

The distributional assumptions we choose for the newly introduced random effects constrain the problem mathematically, making it practical to find a “best” local fit even with sparse observations.

- Inter-Subject Variation (ISV)
- Inter-Occasion Variation (IOV)
- Modelling Correlation in Random Effects
- Covariates