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Population model

Key Features

Central tendency

  1. Mean - the arithmetic average of all the available values of the descriptor
  2. Median - the descriptor value such that 50% of the remaining values are larger and 50% are smaller
  3. Mode - the descriptor value at which the probability density attains its maximum value

Variability in the group

  1. Variance: The average of the squared deviations of the random effects from the mean
  2. Standard deviation: The square root of the variance
  3. Coefficient of variation: The ratio between standard deviation and mean
  4. Quantiles: Percentile distributions of individuals

General approaches to population

  1. Naive Pooling:

    • All data points are assumed to arise from a singel individual
    • A single function is to
    • IGNORES inter-individual variability as well as correlation in time within individuals

  2. Fitting average profile

    • Data points are averaged at each point in the measurement sequences
    • Measurement must be made at the same time across individuals
    • The averaged points across time are then used to fit or produce estimates for the PK model

  3. Standard two-stage

    • Given complete PK profiles, estimate seperately.
    • The sample mean and covariance of all the parameters is computed
    • Cons: Requires richly sampled data, ignores the precision of the individual estimates, and overestimates the population variance

  4. Iterative two-stage

    • New population mean and variance are used as empirical bayes prior in individual estimateon
    • Pros: Works in some sparse data situations, gives more reliable individual estimates

  5. Nonlinear mixed effect model

    • Adding a stochastic model answers
      • What is the extent of variability of PK parameters between subjects (between-subject variability)
      • What is the extent of variability of model parameters in the same subject studied on multiple occasions? (between-ocasion variabiltiy)
      • What is the extent of model misspecification and of unexplained variability in the concentration or effect measurement (residual unknown variability)