Simulating A Population Of Individuals

Because people vary in many, many ways, we should rarely draw conclusions of any analysis based on a single individual.

This part therefore introduces concepts related to variability within a population of individuals (and Population PK/PD from which PoPy gets its name), using PoPy example scripts to generate data and figures for ease of learning.

Variability between individuals comes in two flavours:

  1. Observable variability that can be measured directly before a trial even takes place, such as age, body weight and exposure to other drugs that may have an impact on an individual’s PK/PD. These variables are known as covariates and are usually recorded in the data before analysis takes place.

  2. Unobservable Variability that must be estimated as part of the data analysis.

Early attempts at estimating the unobservable variability 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 model unobservable variability between individuals as random deviations (known as random effects) from population averages (known as fixed effects). Furthermore, 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.

The population on average is therefore characterized by the fixed effects, while each individual in the population has PK/PD parameters that are also dependent on both covariates and random effects.