Using R For Flexible Modelling Of Pre-Clinical Combination Studies - - PowerPoint PPT Presentation

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Using R For Flexible Modelling Of Pre-Clinical Combination Studies - - PowerPoint PPT Presentation

Jun 24, 2023 207 likes •457 views

Using R For Flexible Modelling Of Pre-Clinical Combination Studies Chris Harbron Discovery Statistics AstraZeneca Modelling Drug Combinations Why? The theory An example AstraZeneca Discovery Statistics The

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Using R For Flexible Modelling Of Pre-Clinical Combination Studies

Chris Harbron Discovery Statistics AstraZeneca

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2 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

AstraZeneca Discovery Statistics

Modelling Drug Combinations

  • Why?
  • The theory
  • An example
  • The practicalities in R
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3 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

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Why Drug Combinations?

  • Making better use of our assets
  • Some marketed compounds are combinations e.g.

Symbicort

  • In some disease areas, e.g oncology, HIV,

polypharmacy is the norm

  • Compounds licensed only for use in combination

with a specific other agent

  • Lapatinib (GSK – Breast cancer) is approved for use in

combination with capecitabine

  • Increased molecular & pathway level understanding
  • Hypothesise and understanding synergistic actions
  • Link with systems biology
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4 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

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Combination Studies

[A] [B]

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5 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

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Combination Studies

[A] [B] Benefit? : Better than monotherapy Synergy? : More effect than expected

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6 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

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Assessing Synergy Loewe Additivity

IC30 IC50 IC70 IC30 IC50 IC70 Effect Contours Based around “sham synergy”

  • r “self synergy”

A combination of a compound with itself should give the same effect as a monotherapy at the sum of the doses.

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7 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

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Interaction Index – Berenbaum Combination Index – Chou & Talalay

IC30 IC50 IC70 IC30 IC50 IC70

B B A A

D d D d + = τ

Doses in Combination ICx’s for the two compounds where x is the response shown by the combination

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8 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

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Interaction Index – Berenbaum Combination Index – Chou & Talalay

IC30 IC50 IC70 IC30 IC50 IC70

B B A A

D d D d + = τ

= fraction of expected dose, assuming additivity, required to have same effect

τ τ

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9 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

AstraZeneca Discovery Statistics

Interaction Index – Berenbaum Combination Index – Chou & Talalay

IC30 IC50 IC70 IC30 IC50 IC70

B B A A

D d D d + = τ

1 < τ

Synergy

1 = τ

1 > τ

Additivity Antagonism

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10 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

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Interaction Indices

  • Wish to calculate these:
  • With standard errors / confidence intervals
  • Statements of confidence – significance tests
  • Use more flexibly and powerfully
  • Combining combination doses together
  • Overall assessments of synergy
  • Covering a wide variety of situations
  • Inactive agent
  • Partial Response Agent
  • Multiple Plates / Experiments
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11 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

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Unified Tau

  • Where is either:
  • a constant – response surface
  • (with discontinuities at the axes)
  • a separate value for each point
  • Berenbaum’s interaction index
  • a separate value for each ray (segment)
  • a separate value for each dose level of a compound
  • could fit tau as a continuous function of dose or ray

⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ > + = + = 1

) ( ) ( B A B i B A i A B A B B A A

d and d D d D d d

  • r

d D d D d τ τ

Monotherapies Combinations

) (i

τ

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12 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

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An Example

Monotherapies Combinations

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13 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

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EDA Suggests Synergy At Higher Doses Of Drug A

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14 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

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Identify Individual Combinations Significantly Demonstrating Synergy

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15 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

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Estimates Of Synergy With 95% CIs Overall & For Different Dose Levels

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16 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

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Fitting in R

fit <- mynls(formula , start=inits) response ~ tau.model(…..)

Iterative fitting as.formula(paste(…))

Robust version

  • f nls()

Selection of starting parameters

Flexibly building formula Formula expressed as 1 ~ f(Y , parameters) Not Y ~ f(parameters)

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17 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

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Flexibly Building Formula

  • Build as a text string, then convert to a formula
  • Varying numbers of tau parameters
  • Convert group index vector into a text string in the

right format as.formula(paste(“resp ~ tau.model(parameters, paste("logtau" , 1:ntaus , sep="" , collapse=","), “gp= c(",paste(groupindex,collapse=",") , “))” )) Varying number of combination parameters to be fit:

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18 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

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Iterative Fitting of Formula

tau.model(d1 ,d2 ,m1 ,m2 ,lower1 ,lower2 ,ldm1 ,ldm2 ,taus) For each observation : Make initial estimate of Y Calculate D1 & D2 – monotherapies required to achieve Y using Hill equation Adjust Y up or down depending on whether

2 ) ( 2 1 ) ( 1

D d D d

i i

τ τ +

is >1 or < 1 Iterate until Y is accurately estimated

Iterative Non-linear curve-fitting performed by nls() :

monotherapy and tau parameters

Based on code developed by Lee et al

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19 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

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mynls() : A less temperamental nls()

Parameter Estimates Calculate Direction Calculate Deviance Calculate Test Parameters =Estimates + Factor * Direction Calculate New Deviance Reduced Deviance? Estimates = Test Parameters Half Factor N

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20 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

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mynls() : A less temperamental nls()

Parameter Estimates Calculate Direction Calculate Deviance Calculate Test Parameters =Estimates + Factor * Direction Calculate New Deviance Reduced Deviance? Estimates = Test Parameters Half Factor This cannot be calculated from unrealistic parameter estimates. tau.model() fails to fit N

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21 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

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mynls() : A less temperamental nls()

Parameter Estimates Calculate Direction Calculate Deviance Calculate Test Parameters =Estimates + Factor * Direction Calculate New Deviance Calculated & Reduced Deviance? Estimates = Test Parameters Half Factor Extra error check prevents crashing when iterative algorithm steps too far N

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22 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

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Starting Parameters

  • Good starting parameters from fitting marginal

distributions (e.g. monotherapies) and direct calculations

  • In some situations, this can be done exactly, so nls()

converges immediately to the starting parameters, but with standard errors added

  • Starting from multiple starting points decrease risks
  • f local minima
  • Identify and fix parameters likely to shoot off to

infinity beforehand

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23 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

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Summary

  • Early identification of synergistic drug combinations
  • f strategic importance within the pharmaceutical

industry

  • Powerful and flexible methodology for identifying and

characterising synergy

  • R provides a powerful environment for fitting and

visualising these models

  • Careful programming increases the of robustness

and success rate of R in fitting these models