fit.variability¶

The variability between the subjects of a fit problem and its predictive check.

A fit predicts the data of a mapping with one subject per simulation, the typical subject of its study group. The subjects of a study differ from it: Variability declares how, as relative distributions of targets of the model, e.g. LogNormal(cv=0.3) of a clearance, whose factor has the median 1 and a coefficient of variation of 30 %. A subject has every target at its factor times the value its simulation gives the target (the value the experiment sets for the study group, the value of a fitted parameter or the value of the model), so the inputs of the study groups stay what they are and the subjects vary around them (OptimizationProblem.evaluations(..., factors=), see sbmlsim.simulator.plan.Plan.scaled). The factors are correlated by Covariances of the targets: a correlation of their normal scores, or the covariance of the logarithms of log-normal factors (scale="log", the omega matrix of a population analysis), see sbmlsim.uncertainty.draws. The studies differ as well, in their populations, assays and protocols: Variability(between=Variability(...)) is the variability between the studies, the factors of a study, which all its subjects share and multiply with their own.

subject_predictions evaluates the mappings of a problem for n subjects of a variability at one parameter vector. predictive_check nests the subjects in the parameter vectors it is given, e.g. draws of the uncertainty of the fitted parameters (uncertainty outside, variability inside), and compares every observation with the distribution its prediction has over the subjects: with a variability between the studies the subjects of a vector are studies studies of n_subjects subjects each. A data point of a group of N subjects (the count of the data point) is a mean of N subjects, so it is compared with the distribution of the mean of virtual groups of N subjects drawn from the subjects of a study (the geometric mean for a mapping of geometric standard deviations); a data point without a count is one subject. The distributions of all parameter vectors are pooled, the predictive distribution of the observation, and its quantiles are the band of a visual predictive check (Holford 2005; Bergstrand et al. 2011). The share of the observations inside the outer quantiles is the coverage, about the probability between them for a model whose variability is that of the data.

Holford N (2005). The visual predictive check: superiority to standard diagnostic (Rorschach) plots. PAGE 14, Abstr 738. Bergstrand M, Hooker AC, Wallin JE, Karlsson MO (2011). Prediction-corrected visual predictive checks for diagnosing nonlinear mixed-effects models. AAPS J 13:143-151.

Variability(factors, covariance=tuple(), between=None)

targets

all_targets

draw(n, *, seed, design='sobol', start=0)

SubjectPredictions(
    targets, factors, predictions, failed, study=dict()
)

PredictiveCheck(
    quantiles,
    n_subjects,
    n_vectors,
    n_studies,
    groups,
    seed,
    targets,
    failed,
    points,
    subjects,
)

coverage

coverage_by_mapping()

subject_predictions(
    problem,
    x,
    variability,
    n,
    *,
    indices=None,
    seed,
    design="sobol",
    start=0,
    study=None,
)

quantile_column(q)

predictive_check(
    problem,
    parameters,
    variability,
    n_subjects,
    *,
    indices=None,
    quantiles=(0.05, 0.5, 0.95),
    groups=1000,
    seed=None,
    design="sobol",
    studies=16,
)