Statistical Analysis of IC50s Nick Andrews, Statistics Unit CFI, HPA

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Statistical Analysisof IC50sNick Andrews,
Statistics Unit CFI, HPA
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Outline

• Curve fitting to estimate IC50
• Determining cut-offs for outliers (high IC50)
• Monitoring trends in IC50

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Curve fitting

• The data in each run consists of measuring the
  RFU of a sample against the antiviral at
  different concentrations (ten 4-fold dilutions)
  as well as with no-antiviral (virus-control)
• Estimate IC50 the concentration at which the rfu
  is 50 of that from the virus control.

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Sources of variation in IC50

• Curve fitting
• Within a run (2 replicates)
• Between runs (Reference samples)

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Point to Point (Excel)
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Smooth Curves (S-shaped Graph-pad)
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Comparison-curve fitting

• Sample P-P S-shape Ratio (Hi/Low)
• 292R 0.69 0.69 1.00
• 292K gt4000 8551 -
• 119V 40.3 40.7 1.01
• A/Lisbon22/2207 0.59 0.56 1.05
• A/Latvia/685/2007 0.68 0.69 1.01
• A/Denmark/1/2007 0.43 0.41 1.05
• A/Denmark/2/2007 0.54 0.51 1.06
• A/Denmark/3/2007 0.54 0.48 1.12

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Comments (Curve fitting)

• For most samples curve will make no more than
  about 5 difference to results.
• Must be clear exactly how the curve fitting and
  calculation of IC50 works e.g. is IC50 based on
  50 of OD of virus control or 50 of fitted upper
  asymptote.
• Need to ensure problems in curve fitting are
  flagged.

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Between replicate variation (Point to point)

• Sample Rep1 Rep2 Ratio(High/Low)
• 292R 0.75 0.63 1.19
• 292K 3769 gt4000 -
• 119V 42.0 38.6 1.09
• A/Lisbon22/2207 0.57 0.61 1.07
• A/Latvia/685/2007 0.70 0.66 1.06
• A/Denmark/1/2007 0.40 0.46 1.15
• A/Denmark/2/2007 0.58 0.49 1.18
• A/Denmark/3/2007 0.54 0.53 1.02

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Comments on replicates

• Between replicates in a run variation is greater
  than curve fitting with most results within about
  15-20.
• Using replicates and taking the average reduces
  this effect.
• Large differences between replicates should be
  flagged (e.g. gt30).

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Between run variation
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Comparison runs (Reference Virus)

• Sample Run1 Run2 Ratio(High/Low)
• 274H Osel 0.42 0.36 1.17
• 274H Zan 0.17 0.22 1.29
• 274Y Osel 300 303 1.01
• 274Y Zan 0.31 0.37 1.19
• 119V Osel 43.7 34.0 1.29
• 199V Zan 1.41 1.32 1.07
• DB Osel 920 1316 1.43
• DB Zan 239 351 1.47

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Comments

• Between runs variation is higher still at about
  40. Hence retest those with high values and use
  controls in runs to identify problems in a run.

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Determining Cut-offs

• The aim is to pick up outliers with high IC50
  results as they may indicate resistant strains.
• Need a method to determine the normal range in
  the absence of outliers.
• Various statistical methods may be used the
  important thing is to ensure the outliers do not
  unduly affect the cut-off.

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Methods used

• Need sufficient data points for initial estimate
  (about 30-50). These can be refined later with
  more data.
• Advisable to transform data to approximate
  normality (log-transform).
• Obtain a robust estimation of the Standard
  deviation (1.48Median absolute deviation or
  using 0.75Inter-quartile range).
• Use median say 1.65, 3 SD.

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Example Initial 30 results
Median0.47 Robust SD (log-scale) 0.17 Cut1
1.07 Cut21.81
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Example Final results 2006/07
Median0.48 Robust SD (log-scale) 0.12 Cut1
0.93 Cut21.35
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Do we need to log-transform?

• Most results from dilution assays produce
  geometric results so likely to be sensible
• Sometimes doesnt seem to matter but sometimes
  data are skewed. (e.g. lower quartile much closer
  to median than upper quartile) important to
  transform as robust methods assume data are
  normal once outliers are removed.

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Non-log scale
1.6
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Log-scale (y-axis)
2.7
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Alternative presentation Box and Whisker
PlotUses median 1.5 IQR (2SD)Could be
adjusted to match the scatter plots
3.0
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Monitoring ICD50 (outliers) over time

• First look at the data (scatter
  plots/box-whisker)
• Calculate statistics for different time periods
• Median
• Outliers
• Geometric means with 95 CI with outliers removed
• Kruskal Wallis test for medians
• Calculate Geometeric Means with 95 CI and
  t-test/ anova (outliers removed)
• regression for time trend (outliers removed).

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Monitoring ICD50 (outliers) over time

• Perform statistical tests
• Kruskal Wallis test for medians
• Chi-squared or Fishers exact test for outliers
• Anova or t-tests for comparing means (oultiers
  removed). Alternatively look for non-overlapping
  95 CI which is a conservative method (approx
  plt0.007)

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Graphical Presentation Box and Whisker
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Scatter Plot
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Scatter plot
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Statistics H3N2 Zanamivir NIMR

• Year Samples gt3SD () median Geomean (95 CI)
• 2005/06 88 1 (1.1) 0.67 0.69 (0.62-0.76)
• 2006/07 173 4 (2.3) 0.59 0.58 (0.56-0.61)
• P-value comparing gt3SD 0.67
• P-value comparing medians 0.0002 significant
  although actual difference small.
• 95 CI for Geometric means do not overlap
• Note of caution Changes may occur within a year
  so this comparison maybe too simplistic. For
  example there appears to be some evidence of a
  change within 2006/07

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Summary

• Good use of statistical methods can help
  interpret the IC50 results and ensure assay
  results are reliable.
• Many appropriate methods already in place but
  more could be incorporated