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

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

Why Drug Combinations? • Making better use of our assets • Some marketed compounds are combinations e.g. Symbicort AstraZeneca Discovery Statistics • 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 3 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

Combination Studies [B] AstraZeneca Discovery Statistics [A] 4 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

Combination Studies [B] AstraZeneca Discovery Statistics Benefit? : Better than monotherapy Synergy? : More effect than expected [A] 5 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

Assessing Synergy Loewe Additivity Based around “sham synergy” or “self synergy” A combination of a compound with itself should give the same AstraZeneca Discovery Statistics effect as a monotherapy at the IC70 sum of the doses. IC50 Effect Contours IC30 IC30 IC50 IC70 6 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

Interaction Index – Berenbaum Combination Index – Chou & Talalay Doses in d d τ = + A B Combination D D A B AstraZeneca Discovery Statistics ICx’s for the IC70 two compounds where x is the IC50 response shown by the IC30 combination IC30 IC50 IC70 7 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

Interaction Index – Berenbaum Combination Index – Chou & Talalay d d τ = + A B D D A B τ = fraction of expected dose, AstraZeneca Discovery Statistics IC70 assuming additivity, required to have same effect IC50 IC30 τ IC30 IC50 IC70 8 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

Interaction Index – Berenbaum Combination Index – Chou & Talalay d d τ = + A B D D A B τ < AstraZeneca Discovery Statistics 1 Synergy IC70 τ = 1 Additivity IC50 τ > 1 Antagonism IC30 IC30 IC50 IC70 9 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

Interaction Indices • Wish to calculate these: • With standard errors / confidence intervals • Statements of confidence – significance tests AstraZeneca Discovery Statistics • 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 10 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

Unified Tau ⎧ d d + = A B d or d 0 ⎪ Monotherapies A B D D ⎪ A B = ⎨ 1 d d A B τ τ ⎪ + > ( i ) ( i ) ⎪ Combinations d and d 0 AstraZeneca Discovery Statistics A B ⎩ D D A B τ • Where is either: ( i ) • 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 11 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

An Example Monotherapies Combinations AstraZeneca Discovery Statistics 12 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

EDA Suggests Synergy At Higher Doses Of Drug A AstraZeneca Discovery Statistics 13 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

Identify Individual Combinations Significantly Demonstrating Synergy AstraZeneca Discovery Statistics 14 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

Estimates Of Synergy With 95% CIs Overall & For Different Dose Levels AstraZeneca Discovery Statistics 15 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

Fitting in R fit <- mynls(formula , start=inits) Selection of Robust starting version AstraZeneca Discovery Statistics parameters of nls() response ~ tau.model(…..) Formula expressed as Flexibly 1 ~ f(Y , parameters) building Not formula Y ~ f(parameters) as.formula(paste(…)) Iterative fitting 16 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

Flexibly Building Formula Varying number of combination parameters to be fit: as.formula(paste(“resp ~ tau.model( parameters , AstraZeneca Discovery Statistics paste("logtau" , 1:ntaus , sep="" , collapse=","), “gp= c(",paste(groupindex,collapse=",") , “))” )) • 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 17 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

Iterative Fitting of Formula Iterative Non-linear curve-fitting performed by nls() : monotherapy and tau parameters tau.model(d 1 ,d 2 ,m 1 ,m 2 ,lower 1 ,lower 2 ,ldm 1 ,ldm 2 ,taus) For each observation : AstraZeneca Discovery Statistics Make initial estimate of Y Calculate D 1 & D 2 – monotherapies required to achieve Y using Hill equation Adjust Y up or down depending on whether d d 1 2 τ τ is >1 or < 1 + ( i ) ( i ) D D 1 2 Iterate until Y is accurately estimated Based on code developed by Lee et al 18 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

mynls() : A less temperamental nls() Parameter Estimates Calculate Deviance AstraZeneca Discovery Statistics Calculate Direction Calculate Test Parameters =Estimates + Factor * Direction Half Calculate New Deviance Factor Reduced N Deviance? Estimates = Test Parameters 19 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

mynls() : A less temperamental nls() This cannot be calculated from Parameter Estimates unrealistic Calculate Deviance parameter estimates. AstraZeneca Discovery Statistics Calculate Direction tau.model() fails to fit Calculate Test Parameters =Estimates + Factor * Direction Half Calculate New Deviance Factor Reduced N Deviance? Estimates = Test Parameters 20 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

mynls() : A less temperamental nls() Extra error check prevents Parameter Estimates crashing when Calculate Deviance iterative algorithm steps AstraZeneca Discovery Statistics Calculate Direction too far Calculate Test Parameters =Estimates + Factor * Direction Half Calculate New Deviance Factor Calculated & Reduced N Deviance? Estimates = Test Parameters 21 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

Starting Parameters • Good starting parameters from fitting marginal distributions (e.g. monotherapies) and direct calculations AstraZeneca Discovery Statistics • 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 of local minima • Identify and fix parameters likely to shoot off to infinity beforehand 22 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009

Summary • Early identification of synergistic drug combinations of strategic importance within the pharmaceutical industry AstraZeneca Discovery Statistics • 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 23 Chris Harbron, Using R For Flexible Modelling Of Pre-Clinical Combination Studies, USE-R 2009