Presented at 2013 Computer-Aided Drug Design Gordon conference and subtitled, 'Eu prefiro a minha comida cozida e meus dados brutos' and the chicken in the title slide photo had been walking around the day before the photo was taken.

1. Tales of correlation inflation
(Eu prefiro a minha comida cozida e meus dados brutos)
Peter W Kenny, Universidade de São Paulo

2. Correlation
• Strong correlation implies good predictivity
– I have observed a correlation so you must use my rule
• Multivariate data analysis (e.g. PCA) usually involves
transformation to orthogonal basis
• Applying cutoffs (e.g. MW restriction) to data can
distort correlations

3. Quantifying strengths of relationships between
continuous variables
• Correlation measures
– Pearson product-moment correlation coefficient (R)
– Spearman's rank correlation coefficient ()
– Kendall rank correlation coefficient (τ)
• Quality of fit measures
– Coefficient of determination (R2) is the fraction of the
variance in Y that is explained by model
– Root mean square error (RMSE)

4. Difference in mean values of Y for X = A and X = B
Scale by standard
deviation
Scale by standard
error
Cohen’s d
(independent of
sample size)
Student’s t
(depends on
sample size)
Size of effect for categorical X
R2 can be seen as analogous to Cohen’s d

5. r
N 1202
R 0.247 ( 95% CI: 0.193 | 0.299)
 0.215 ( P < 0.0001)
 0.148 ( P < 0.0001)
N 8
R 0.972 ( 95% CI: 0.846 | 0.995)
 0.970 ( P < 0.0001)
 0.909 ( P = 0.0018)
Correlation Inflation in Flatland
See Lovering, Bikker & Humblet (2009) JMC 52:6752-6756 DOI

6. Preparation of synthetic data sets
Kenny & Montanari (2013) JCAMD 27:1-13 DOI
Add Gaussian noise
(SD=10) to Y

7. Correlation inflation by hiding variation
See Hopkins, Mason & Overington (2006) Curr Opin Struct Biol 16:127-136 DOI
Leeson & Springthorpe (2007) NRDD 6:881-890 DOI
Data is naturally binned (X is an integer) and mean value of Y is calculated for each
value of X. In some studies, averaged data is only presented graphically and it is left to
the reader to judge the strength of the correlation.
R = 0.34 R = 0.30 R = 0.31
R = 0.67 R = 0.93 R = 0.996

8. Masking variation with standard error
See Gleeson (2008) JMC 51:817-834 DOI
Partition by value of X into 4 bins with equal numbers of data points and display 95%
confidence interval for mean (green) and mean ± SD (blue) for each bin.
R = 0.12 R = 0.29 R = 0.28

9. N Bins Degrees of Freedom F P
40 4 3 0.2596 0.8540
400 4 3 12.855 < 0.0001
4000 4 3 115.35 < 0.0001
4000 2 1 270.91 < 0.0001
4000 8 7 50.075 < 0.0001
“In each plot provided, the width of the errors bars and the difference in the mean
values of the different categories are indicative of the strength of the relationship
between the parameters.” Gleeson (2008) JMC 51:817-834 DOI
The error of standard error
ANOVA for binned data sets

10. Know your data
• Assays are typically run in replicate making it possible
to estimate assay variance
• Every assay has a finite dynamic range and it may not
always be obvious what this is for a particular assay
• Dynamic range may have been sacrificed for
thoughput but this, by itself, does not make the
assay bad
• We need to be able analyse in-range and out-of-
range data within single unified framework
– See Lind (2010) QSAR analysis involving assay results which are only known to
be greater than, or less than some cut-off limit. Mol Inf 29:845-852 DOI

11. Depicting variation with
percentile plots
This graphical representation of data makes it easy
to visualize variation and can be used with mixed
in-range and out-of-range data. See Colclough et
al (2008) BMCL 16:6611-6616 DOI

12. Binning continuous data restricts your options for analysis and
places burden of proof on you to show that your conclusions are
independent of the binning scheme. Think before you bin!
Averaging the
binned data was
your idea so don’t
try blaming me this
time!

13. Some stuff to think about
• Model continuous data as continuous data
– RMSE is most relevant to prediction but you still need R2
– Fitted parameters may provide insight (e.g. solubility is more sensitive than
potency to lipophilicity)
• When selecting training data think in terms of Design of Experiments
(e.g. evenly spaced values of X)
• Try to achieve normally distributed Y (e.g. use pIC50 rather than IC50)
• Never make statements about the strength of a relationship when
you’ve hidden variation in the data (unless you want a starring role in
Correlation Inflation 2)
• To be meaningful a measure of the spread of a distribution must be
independent of sample size
• Reviewers/editors, mercilessly purge manuscripts of statements like,
“A negative correlation was observed between X and Y” or “A and B are
correlated/linked”