Bioequivalence and Bioavailability Forum

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There are two types of potential outliers in a BE study; only the second one influences the outcome:

1. Concordant outlier
   The PK responses for both test and reference deviate from the majority of the study sample.
   E.g., poor metabolizers may lead to high concentrations in 5-10% of subjects.
   Does not effect the BE-assessment, but should be discussed (polymorphism known?) in the report.
   
2. Discordant outlier
   The PK response of either test or reference deviates from the majority of the study sample.

Inspection of data (EDA - exploratory data analysis) before performing the actual BE assessment is considered good statistical practice.

Some methods:

1. An XY-plot of subject’s PK responses, where X=reference and Y=test.
   Applying a linear regression on the data, concordant outlier(s) will be close to the line but shifted from the cluster of subjects showing ‘normal’ responses. Discordant outlier(s) will show a shift from the line.
   
2. Tukey Sum-Difference plot (X=ℯ^{(ln Test + ln Reference)} and Y=ℯ^{(ln Test - ln Reference)}, both axes in log-scale) will show concordant outlier(s) as a horizontal shift, and discordant outlier(s) as a vertical shift.
   
3. Analysis of residuals from ANOVA/GLM:
   • Concordant outlier(s) will show a horizontal shift in an XY-plot (X=predicted value, Y=studentized intra-subject residual), whereas discordant outlier(s) will show a small horizontal shift and a large vertical shift.
     
   • In a normal probability plot (X=normal score, Y=studentized intra-subject residual) concordant outlier(s) will show no deviation from the best fit (Hazen line), whereas discordant outlier(s) will show a large vertical shift.
     
   • Tukey’s equal variance plot¹ (X=predicted value, Y=sqrt(|raw residual in period 1|), will help in evaluating the equal variance assumption.
     
   • A Cook’s Distance plot helps in identifying most influential subjects.
     
   • Box-plots of intra-subject residuals will show discordant outliers, whereas box-plots of inter-subject residuals will show concordant outliers.
     
   • The Lund-test² was recommended in FDA's guideline in 1993, but dropped in later editions.

For details see Pikounis et al. (2001).³

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1. JW Tukey
   Exploratory Data Analysis
   Addison-Wesley, Reading (1977)
   
2. RE Lund
   Tables for An Approximate Test for Outliers in Linear Models
   Technometrics 17(4), 473-6 (1975)
   
3. Pikounis B, Bradstreet TE, and SP Millard
   Graphical Insight and Data Analysis for the 2,2,2 Crossover Design
   in: SP Millard and A Krause
   Applied Statistics in the Pharmaceutical Industry
   Springer, New York, pp 153-188 (2001)
   download-link for chapter 7