Reference Sheet

Key Points

You can fit multiple models with a single Population by calling the fit function with different arguments
The inspect function calculates in one go preds, ipreds, wres, ebes, icoefs, and dose control parameters, if applicable for any fitted Pumas model
You can convert any output of an inspect into a NM-TRAN-formatted DataFrame
Everything that inspect computes can be individually computed using specific functions if necessary

Summary of Basic Commands

Action	Command	Observations
Fit a Model using `FOCE()`	`fit(model, population, initial_parameters, FOCE())`	`initial_parameters` is a `NamedTuple` of parameter name and values
Generate a `inspect` result	`inspect(fit_result)`	Calculates pred, ipred, wres, ebe, icoef, and dcp (if applicable), in one go
Generate a `inspect` result with NPDE	`inspect(fit_result; nsim=200)`	Calculates pred, ipred, wres, ebe, icoef, dcp (if applicable), and NPDE with 200 times each subject is simulated in one go
Convert an `inspect` result into a `DataFrame`	`DataFrame(inspect_result)`	The resulting `DataFrame` will be NM-TRAN-formatted and can be parsed as a `Population`
Generate a `DataFrame` of pred and ipred	`DataFrame(predict(fit_result))`	NM-TRAN-formatted `DataFrame`
Generate a `DataFrame` of wres	`DataFrame(wresiduals(fit_result))`	NM-TRAN-formatted `DataFrame`
Generate a `DataFrame` of ebe	`DataFrame(ebe(fit_result))`	NM-TRAN-formatted `DataFrame`
Generate a `DataFrame` of icoef	`DataFrame(icoef(fit_result))`	NM-TRAN-formatted `DataFrame`
Generate a `DataFrame` of dcp	`DataFrame(dosecontrol(fit_result))`	NM-TRAN-formatted `DataFrame`
Generate a `DataFrame` of pred and ipred with custom time profile	`DataFrame(predict(fit_result; obstimes=interval))`	NM-TRAN-formatted `DataFrame` and interval is a Julia interval (e.g. `1:10`)
Generate a `DataFrame` of all metrics from a fitted model	`metrics_table(fit_result)`	Need to load `PumasUtilities` package
Calculate the log-likelihood of a fitted model	`loglikelihood(fit_result)`	This value is with the constant
Calculate the log-likelihood of any model given any population, parameter estimates, and estimation method	`loglikelihood(model, population, parameter_estimates, estimation_method)`	This value is with the constant. `parameter_estimates` is a `NamedTuple` of parameter estimates and `estimation_method` is a Pumas' estimation method (e.g. `FOCE()` or `LaplaceI()`)
Plot goodness of fit	`goodness_of_fit(inspect_result)`	4-panel plot with observations versus pred/ipred and wres versus time/ipred. If the `inspect_result` has NPDEs it will plot these instead of wres. Need to load `PumasUtilities` package
Plot a visual predictive check	`vpc_plot(vpc_result)`	`vpc_result` is the result of `vpc(fit_result)`. Need to load `PumasUtilities` package
Plot a prediction-corrected visual predictive check	`vpc_plot(vpc_result)`	`vpc_result` is the result of `vpc(fit_result; prediction_correction=true)`. Need to load `PumasUtilities` package

Glossary

pred: Population predictions, i.e. predictions using only the fixed effects and without random effects.
ipred: Individual predictions, i.e. predictions using the fixed effects and random effects.
wres: Individual Weighted residuals. They are the difference between observed data and the predicted data. In other words, it's a measure of the error in the prediction. But weighted by the precision of the observations, i.e. they are divided by the standard deviation of the observations.
ebe: Empirical Bayes estimates. They are commonly known as the individual parameters, or, also known as the "etas" (η).
icoef: Individual coefficients. They are calculated using the population coefficients and the individual parameters.
Dose control parameters (DCP): Parameters that govern the dosage regimen of a drug, and the associated pharmacokinetic properties of the drug in the body. In Pumas models they are: lag of the dose, bioavability of the dose, rate of dosing, and duration of the dosing.
Individual normalized prediction distribution errors (NPDE): Similar to the individual weighted residuals, but goes further by transforming the prediction error so that, under the correct model, should be standard normally distributed.
NM-TRAN: Official NONMEM dataset format. Check Pumas documentation on Data Representation for more information.
Log-likelihood: The log of the joint probability of the observed data viewed as a function of the parameters of a statistical model.
Akaike Information Criterion (AIC): An estimator of prediction error and thereby relative quality of statistical models for a given set of data. It uses the model's log-likelihood and penalizes the model's by the number of parameters used. Models with higher log-likelihood values and less parameters are preferred.
Bayesian Information Criterion (BIC): An estimator of prediction error and quality of statistical models for a given set of data. It is similar to the AIC and also uses the log-likelihood.
Goodness of fit: How well a model can accurately predict or reproduce the observed data. In Pumas, there is a standard four-panel plot that plots established goodness of fit plots.
Visual predictive check (VPC): Graphical model diagnostic tool to assess the performance of a pharmacometric model. It involves generating simulations from the model for the observed covariate values (generally time) and comparing these simulations to the observed data graphically.
Prediction-corrected visual predictive check (VPC): Variant of the VPC that adjusts both observed and simulated data by the model predictions. This is done to remove the effects of potentially confounding factors.

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