Prediction and Prediction Variance Corrections

Including a prediction correction and prediction variance correction as part of predictive checking allows observations that would otherwise be incomparable to be pooled together to narrow the quantiles of predicted data, making a more stringent test for model misspecification. For example, by using time-after-dose (TAD) as the X axis, data following multiple dose events can be combined. If doses are given at widely varying dose amounts, predictions of plasma concentrations will be proportionally scaled together (assuming a linear model). Similarly, variability correction may apply if, for example, the model is linear but the error model is additive.

Prediction and prediction variance corrections deal with these quantities:

Y_ij: j^th observation for i^th subject
PRED_ij: Population (zero-eta) prediction of j^th observation for i^th subject
PRED_bin: Median of PRED_ij over all observations in a particular bin
pcY_ij: Prediction-corrected version of j^th observation for i^th subject

The prediction-corrected observation is calculated either by the proportional rule (default):

or by the additive rule:

Then either the quantity

or

is outputted to Cor_Factor column in the PredCheckAll worksheet, depending on the rule used.

Further, if Pred. Variance is selected, these variables come into play:

sd(pcY_ij): Standard deviation of pcY_ij 
sd(pcY_bin): Median of sd(pcY_ij) over the bin
pvcY_ij: Prediction-variability corrected version of Y_ij 

pvcY_ij is calculated as follows:

Then either the quantity pvcY_ij or pcY_ij is outputted to the DV_Cor column in the PredCheckAll worksheet (for simulated values) and is used in the predictive-check plots (for both observed and simulated values), depending on whether Pred. Variance is selected.

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