Graphical display of population data
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1 Graphical display of population data E. Niclas Jonsson Division of Pharmacokinetics and Drug Therapy Department of Pharmaceutical Biosciences Uppsala University
2 Nature of population data Hierarchical Variable Multi-dimensional Potentially non-continuous Potentially lots of it!
3 Scope of the presentation. Basic graphical techniques for continuous population data 2. Graphical techniques for ordered categorical data
4 Spaghetti plots Hierarchy and variability Concentration Time (h)
5 Data dilution Multitude 66 6 All data 6 Concentration Time (h) Random selection 7% MP selection % Concentration Concentration
6 Multi-panel conditioning Dimensionality Conditioning variable Strip Level of the conditioning variable SEX: SEX : Concentration Panel Time (h) Visual reference grid
7 Continuous conditioning variable Panel 6 2 Shingle plot Range Concentration Time (h)
8 Multiple conditioning variables SEX:2 SEX:2 SEX:2 SEX:2 SEX:2 SEX:2 Concentration SEX: SEX: SEX: SEX: SEX: SEX: Time (h)
9 Main effects ordering ID : 22 ID : ID : 2 ID : :2 ID : 626 ID : 7 2 ID : 8 26 ID : 99 ID :7 :2 ID : 8 2 Concentration ID : 2 ID : 2 ID : 9 ID :8 : ID : 6 ID : 66 ID : 72 ID : 2 8 ID : :9 ID : 22 ID : ID : 2 ID : ID : : ID :
10 Further reading The elements of graphing data William S. Cleveland Visualizing data William S. Cleveland
11 Ordered categorical data Percent of total 2 2 Observation category
12 Taking one predictor into account 2 2 Percent of total 6 2 DOSE : DOSE : 2 DOSE : DOSE : 2 2 Observation category
13 Taking another predictor into account 2 2 OCC : OCC: 6 OCC : 7 OCC : 8 6 Percent of total 6 OCC : OCC: 2 OCC : OCC : Observation category
14 Both Dose and Occasion Percent of total DOSE: OCC : DOSE: OCC : DOSE: 2 OCC : DOSE: OCC : DOSE: OCC : 2 DOSE: OCC : 2 DOSE: 2 OCC : 2 DOSE: OCC : 2 DOSE: OCC : DOSE: OCC : DOSE: 2 OCC : DOSE: OCC : DOSE: OCC : DOSE: OCC : DOSE: 2 OCC : DOSE: OCC : DOSE : OCC : DOSE : OCC : DOSE : 2 OCC : DOSE : OCC : DOSE : OCC : 6 DOSE : OCC : 6 DOSE : 2 OCC : 6 DOSE : OCC : 6 DOSE : OCC : 7 DOSE : OCC : 7 DOSE : 2 OCC : 7 DOSE : OCC : 7 DOSE : OCC : 8 DOSE : OCC : 8 DOSE : 2 OCC : 8 DOSE : OCC : Observation category 2
15 Stacked bar graphs..8 Probability Dose = Percent of total 2 DOSE : DOSE : DOSE : DOSE: 2 2 Observation category
16 The same for Occasion..8 Probability Occasion
17 Visualizing the cumulative probabilities by Dose..8 Probability Dose Probability Dose
18 Visualizing the cumulative probabilities by Occasion..8 Probability Occasion
19 Model diagnostics linear logit model. Observations Predictions Probability Dose 2
20 Using expected probabilities. Observations Predictions Probability Dose 2
21 The uncertainty in the predicted probabilities Prediction interval. Observations Predictions Probability Dose 2
22 Changing the model an Emax logit model Prediction interval. Observations Predictions Probability Dose 2
23 Comparing observations and predictions in a continuous manner. Observations Predictions Probability Dose 2 One Another observation observation The prediction The prediction
24 Observed vs predicted linear logit model Observed probabilities Predicted probabilities
25 Simulations for checking goodness of fit graphs. Fit the model to the observed data. 2. Create the goodness of fit graph.. Simulate a new data set under the model from.. Fit the model from to the simulated data.. Create the goodness of fit graph based on the fit to the simulated data. 6. Compare the graphs 2 and, using as a reference.
26 Using the simulated goodness of fit graph as reference Based on the original data Based on simulated data Observed probabilities...2 Observed probabilities Predicted probabilities Predicted probabilities
27 The Emax logit model Observed probabilities Predicted probabilities
28 Summary There are graphical techniques that handles the hierarchical, variable and multitude of population data. Multi-panel conditioning is a powerful way of visualizing high dimension data. Ordered categorical data can be visualized and diagnosed by viewing the data as probabilities. Simulations can be a useful tool when evaluating goodness of fit graphs.
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