Maximum Likelihood model plot output

Plot output

Phoenix model plot output depends on the run mode selected and whether the model is population or individual. Most plots for non-population models are prefixed with “Ind” while population plots are prefixed with “Pop”. Users can always disable and enable plots manually in the Plots tab. The table below describes the content of each potential plot that the Maximum Likelihood Models object creates.

Users can double-click a plot in the Results tab to display it in a separate window for editing. (See the menu options discussion in the Plots chapter of the Data Tools and Plots Guide for plot editing options.)

Double-clicking a point in one of these plots will open the worksheet used to create the plot in a separate window and highlight the corresponding row of data.

Boot Omega Histogram (Population; Bootstrap): Histogram plot of omega elements for all bootstrap replicates.

Boot Theta Histogram (Population; Bootstrap): Histogram plot of fixed effects, residual error, and secondary parameters (if defined) for all bootstrap replicates.

Convergence (Population; Simple, Scenarios): Plots the values for each model parameter at each iteration.

Covariate Box Plots (Population; Simple, Scenarios): Box plots of specified categorical covariates vs Etas. Covariates of interest need to be specified but covariate effects do not need to be part of the model to obtain these plots. Note: The labels in these plots will contain the values of the categorical covariate, even if a categorical name was specified in the Covar. Type tab.

Covariate Plots (Population; Simple, Scenarios): Scatter plots of specified continuous covariates vs Etas. Covariates of interest need to be specified but covariate effects do not need to be part of the model to obtain these plots. These plots are created for all covariates but, if a covariate changes over time, the first value is selected for plotting purposes, which might make that specific plot meaningless. This will often occur with plots where dose is a covariate.

CWRES Histogram (Population; Simple, Scenarios): Histogram plot of the conditional weighted residual values. If scenarios are present, each histogram is presented by scenario.

CWRES vs IVAR (Population; Simple, Scenarios): Plot of CWRES (conditional weighted residuals; a proposed replacement for the classical WRES (weighted residuals) goodness of fit statistic) against IVAR (the independent variable; typically time in a PK fit, concentration or dose in a PD fit). Values of CWRES should be approximately N(0,1) and hence concentrated between y= –2 and y=+2. Values significantly above 3 or below –3 are suspect and may indicate a lack of fit and/or model misspecification.

CWRES vs PRED (Population; Simple, Scenarios): Same as CWRES vs IVAR, but with the population predictions (i.e., the predictions obtained by setting the random effect values to zero) used for the X-axis.

CWRES vs TAD (Population; Simple, Scenarios): Same as CWRES vs IVAR, but independent variable is Time After Dose.

DV vs IPRED (Individual/Population; Simple, Scenarios): Plot of the dependent variable (DV, e.g., concentrations for PK models) versus individual predicted values (IPRED, e.g., predicted concentrations). Individual prediction obtained by setting random effects to the 'post hoc' or empirical Bayesian estimate of the random effects for the individual from which the DV observation was made. Thus, the plot shows observed vs fitted values of the model function. Ideally, points should fall close to the line of unity y=x.

DV vs IPRED Lattice (Individual; Simple): Same as DV vs IPRED plots for individual models, but latticed by sort.

DV vs IPRED Log (Population; Simple, Scenarios): DV vs IPRED plot for population models, with log transformed DV and IPRED axes.

DV vs PRED (Population; Simple, Scenarios): Analog of DV vs IPRED with population predictions used instead of individual predictions. Since population predictions are typically less accurate, this plot will show larger deviations around the y=x line of unity than DV vs IPRED.

DV vs PRED Log (Population; Simple, Scenarios): DV versus PRED plot with log transformed DV and PRED axes.

DV vs TAD (Population; Simple, Scenarios): Plot of observations vs Time After Dose.

DV, IPRED vs IVAR (Individual/Population; Simple, Scenarios): Plot of the dependent variable (DV), and individual predicted estimates (IPRED) versus the independent variable (IVAR, e.g., time). Ideally, points should fall close to the line of unity y=x.

DV, IPRED vs IVAR Lattice (Individual/Population; Simple, Scenarios): Same plot as DV, IPRED vs IVAR, but latticed by sort.

DV, IPRED vs DV2, IPRED2 Lattice (Individual/Population; Simple, Scenarios): Plots (latticed by individual) of DV (dependent variable), IPRED (individual prediction) vs a second dependent variable (DV2), and a second individual prediction (IPRED2). Generated when there are two residual errors requested.

DV2, IPRED2 vs DV, IPRED Lattice (Individual/Population; Simple, Scenarios): Inverse of DV, IPRED vs DV2, IPRED2 Lattice. Generated when there are two residual errors requested.

DV, IPRED vs TAD (Individual/Population; Simple, Scenarios): Plot of dependent variable and individual prediction vs Time After Dose.

DV, IPRED vs TAD Lattice (Individual/Population; Simple, Scenarios): Same plot as DV, IPRED vs TAD, but latticed by sort.

DV, IPRED, PRED vs IVAR Lattice (Population; Simple, Scenarios): Plots (latticed by individual) containing all population observations, population prediction, and individual predictions vs the independent variable.

DV, IPRED, PRED vs TAD Lattice (Population; Simple, Scenarios): Plots (latticed by individual) containing observations, population prediction, and individual predictions vs Time After Dose.

DV, PRED vs IVAR (Population; Simple, Scenarios): Plots containing observations and population prediction vs the independent variable.

DV, PRED vs IVAR Lattice (Population; Simple, Scenarios): Same plot as DV, PRED vs IVAR, but latticed by individual.

DV, PRED vs TAD (Population; Simple, Scenarios): Plots containing observations and population prediction vs Time After Dose.

DV, PRED vs TAD Lattice (Population; Simple, Scenarios): Same as DV, PRED vs TAD, but latticed.

Eta Histogram (Population): Histogram plot of the eta values. If scenarios are present, each histogram is presented by scenario.

Eta QQ (Population; Simple, Scenarios): Quantile-quantile plot for each eta in the model. If the components of eta are well described by a normal distribution, plotted values will fall roughly along a straight line of unity y=x. Significant deviations from normality, particularly in the tails of the distribution, can be seen by deviations from this line.

Eta Scatter (Population; Simple, Scenarios): Scatter plot of all combinations of etas also known as scatter plot matrix of etas. This allows visual confirmation of correlations between random effects.

IWRES vs IPRED (Individual/Population; Simple, Scenarios): Plot of individual weighted residuals (IWRES) versus individual predicted values (IPRED, e.g., predicted concentrations). Ideally, the blue line should be at 0 and the red line (with its negative reflection) should not show any fanning. Fanning indicates room for improving the distribution of residuals.

IWRES vs IPRED Lattice (Individual; Simple): Plots (latticed by sort) of individual weighted residuals (IWRES) versus individual predicted values (IPRED, e.g., predicted concentrations).

IWRES vs IVAR (Individual; Simple): Plot of individual weighted residuals (IWRES) versus the independent variable (IVAR, e.g., time). Ideally, the blue line should be at 0 and the red line (with its negative reflection) should not show any fanning. Fanning indicates room for improving the distribution of residuals.

IWRES vs IVAR Lattice (Individual; Simple): Plots (latticed by sort) individual weighted residuals (IWRES) versus the independent variable (IVAR, e.g., time).

IWRES vs TAD (Individual; Simple): Plot of individual weighted residuals (IWRES) versus time after dose.

IWRES vs TAD Lattice (Individual; Simple): Plots (latticed by sort) of individual weighted residuals (IWRES) versus time after dose.

NP Covariate Box Plots (Population; Simple, Scenarios): Box plots of specified covariates vs nonparametric Eta.

NP Covariate Plots (Population; Simple, Scenarios): Scatter plots of specified covariates vs nonparametric Eta.

NP Eta Scatter (Population; Simple, Scenarios): Scatter plot of all combinations of nonparametric Etas.

Partial Derivatives (Individual; Predictive Check): Plot of the partial derivative of each prediction with respect to each fixed effect (which is 1-to-1 with structural parameters).

PCWRES vs IVAR (Population; Simple, Scenarios): Plot of PCWRES (predictive check weighted residuals; a proposed replacement for the classical WRES (weighted residuals) goodness of fit statistic) against IVAR (the independent variable; typically time in a PK fit, concentration or dose in a PD fit). Values of CWRES should be approximately N(0,1) and hence concentrated between y= –2 and y=+2. Values significantly above 3 or below –3 are suspect and may indicate a lack of fit and/or model misspecification.

PCWRES vs PRED (Population; Simple, Scenarios): Same as PCWRES vs IVAR, but with the population predictions (i.e., the predictions obtained by setting the random effect values to zero) used for the X-axis.

PCWRES vs TAD (Population; Simple, Scenarios): Same as PCWRES vs IVAR, but independent variable is Time After Dose.

Posthoc Histogram (Population; Simple): Histogram plot of the posthoc values. If scenarios are present, each histogram is presented by scenario.

PredCheck BQLFraction (Population; Predictive Check): Plot created when BQL Fraction mode is specified.

PredCheck ObsQ_SimQ (Population; Predictive Check): Plot created when the model involves continuous observed variables. For each stratification, the observed quantiles are superimposed with the predictive check quantiles over the observed data.

The default color scheme is as follows:
- Red lines: observed quantiles
- Black lines: predicted quantiles
- Blue symbols: observed data

PredCheck ObsQ_SimQCI (Population; Predictive Check): Plot created when the model involves continuous observed variables.
For each stratification, the observed quantiles and the confidence intervals of the simulated quantiles are plotted (with observed data overlaid).

The default color scheme is as follows:
- Black lines: observed quantiles
- Gray lines: confidence intervals of the predicted quantiles
- Blue symbols: observed data

The meaning of the default legend is:
- 05%.05%=5% confidence interval of the 5% quantile of simulated data
- 05%, 95%=95% CI on the 5% quantile of simulated data
- 05%=5% quantile of observed (raw observations)
and so on.

PredCheck Cat ObsQ_SimQ (Population; Predictive Check): A series of plots created when the models involve categorical and/or count observations. The plots show the observed fraction and quantiles of simulated fraction for each category level or grouped level versus the chosen X-axis.

PredCheck_TTE (Population; Predictive Check): Created when the Time-to-event option is specified on the observation tab. This is a Kaplan-Meier plot that describes the fraction of patients that reached some state to a specific point of time with confidence interval of observations.

QQ CWRES (Population; Simple, Scenarios): A qq (quantile-quantile) plot of the components of CWRES.
If the components of CWRES are well described by a normal distribution, plotted values will fall roughly along a straight line of unity y=x. Significant deviations from normality, particularly in the tails of the distribution, can be seen by deviations from this line. Can be considered as a diagnostic of model mis-specification.

QQ IWRES (Individual/Population; Simple, Scenarios): Quantile-quantile plot of the individual weighted residuals.
If the components of IWRES are well described by a normal distribution, plotted values will fall roughly along a straight line of unity y=x. Significant deviations from normality, particularly in the tails of the distribution, can be seen by deviations from this line. Can be considered as a diagnostic of model misspecification.

QQ IWRES Lattice (Individual; Simple): Quantile-quantile plot (latticed by sort) of the individual weighted residuals (IWRES). If the components of IWRES are well described by a normal distribution, plotted values will fall roughly along a straight line of unity y=x. Significant deviations from normality, particularly in the tails of the distribution, can be seen by deviations from this line. Can be considered as a diagnostic of model misspecification.

QQ PCWRES (Population; Simple, Scenarios): Same as QQ CWRES but with PCWRES replacing CWRES.

QQ WRES (Population): Same as QQ CWRES but with WRES replacing CWRES.

Simulation (Individual; Simulation): In Simulation run mode, plots (latticed by subject) the simulated and observed dependent variable versus independent variable (IVAR).

Str Covariate Box Plots (Population; Simple, Scenarios): Box plots of the specified categorical covariates vs fixed effects (i.e., model structural parameters). Covariates of interest need to be specified but covariate effects do not need to be part of the model to obtain these plots.

Str Covariate Plots (Population; Simple, Scenarios): Plots of the specified continuous covariates vs fixed effects (i.e., model structural parameters). Covariates of interest need to be specified but covariate effects do not need to be part of the model to obtain these plots.

WRES Histogram (Population; Simple, Scenarios): Histogram plot of the weighted residuals.

WRES vs IVAR (Population; Simple, Scenarios): WRES (weighted residuals) vs IVAR (independent variable) plot.

WRES vs PRED (Population; Simple, Scenarios): WRES (weighted residuals) vs PRED plot.

WRES vs TAD (Population; Simple, Scenarios): Plot of the weighted residuals vs time after dose.

Note:Default plots from library Phoenix models will always generate plots with Time After Dose (TAD) in the X-axis. These plots are generated by default, even if time is not the x-variable in the model (for example pharmacodynamic Emax models) or if dose is an inappropriate concept in the model. In these cases, these plots just duplicate the plots with IVAR in the X-axis.

IWRES is the Individual Weighted RESidual.

IWRES = (DV – IPRED)/STD, where IPRED is the individual prediction and STD is the estimate of the standard deviation of the observation.

For example, for an additive residual error model: DV = IPRED+eps, the corresponding STD is given by: STD = stdev(eps), where stdev(eps) is the estimated standard deviation for the normal residual error eps. For a multiplicative (proportional) residual error model: DV = IPRED + IPRED*eps, the corresponding STD is given by: STD = abs(IPRED)*stdev(eps).

Assuming the residual error model is correct, IWRES should be N(0,1) random variable.

WRES vs CWRES: WRES (weighted residuals) is a standardized estimate of the components of the population residual vector (observations-population predictions). If a Gaussian observation and random effect model is correct, the components of the population residual vector for a given individual are approximately multivariate normally distributed with a covariance matrix reflecting correlation induced by the fact that all observations from a given individual share a common set of random effect values specific to that individual. The computation of WRES decorrelates these values and standardizes them to unit variance, so the components of WRES are approximately independent N(0,1) random variables. Plots of WRES against population predictions (or QQ plots of WRES) are often used as a diagnostic of model misspecification, excessive deviations from the nominal N(0,1) distribution being regarded as indicative of model misspecification.

Recently, Hooker, Staatz, and Karlsson (2007) noted that WRES is not always a reliable indicator of model misspecification when an FOCE method is used and gave an example where the WRES plot from a highly mis-specified model was better, or closer to what would be expected from the nominal N(0,1) case, than the WRES plot from a correctly specified model. They proposed a modification to WRES as CWRES (“conditional WRES”) which, in the case of correctly specified models, often results in a statistic for which the N(0,1) approximation is better than in the WRES case. In the example, CWRES correctly differentiates between the correctly specified and mis-specified model whereas WRES is completely misleading. CWRES has been gaining acceptance and is one of the diagnostic outputs for POP PK modeling suggested by European Medicines Agency guidelines.