Estimating Population Parameters

Assume we have data for a population of individuals, where for each individual we are given:

• measured covariates such as age or body weight

• the parameters of the study they were involved in such as the amount of drug administered

• a time series of one or more observed variables such as drug or biomarker concentration

For a given mathematical model of the PK/PD for any individual drawn from the population, we now want to estimate the population averages (fixed effects) and deviations from those averages (random effects) giving rise to model parameters that best predict the observed time series.

Being able to estimate parameters enables us to:

• compare different mathematical models based on their ability to predict observed data

• sample new populations with similar properties and analyse the predicted PK/PD to predict the effect of a drug on a new, random population

In this part, we explore concepts related to estimating parameters of the mathematical model (“fitting the model”) using PoPy examples to generate data and figures to aid our explanations.