Figure 1.

Fundamental principles of the population approach. A population model to describe the typical time course of tumor size and quantify the interpatient variability is built based on infrequent and sparse observations from patients. In this example, the covariate, the tumor type (A or B), was found to explain some of the interpatient variability and therefore was included in population model, leading to one typical population tumor size profile for each type of tumor (θ_COV). The population approach also allows one to describe the individual profiles (η_i represents the deviation from the typical tumor profile and it is assumed to follow a normal distribution with a mean of 0 and variance of ω²) and to quantify the remaining residual error at each j observation for i patient (difference between individual prediction and real observation explained by ε_i, which is a random variable from a normal distribution with a mean of 0 and variance of σ²).

Abbreviations: IPV, interpatient variability; λ_POP, typical value representing disease (tumor) progression; TS_0POP, typical value of tumor size at baseline; TS(t)_i, tumor size at t measurement time for the ith individual.