8 th -10 th October 2014

1. Demonstrating the impact of statistics in the preclinical area using Bayesian analysis with informative priors • 8th-10th October 2014 • Non Clinical Statistics Conference Ros Walley, John Sherington, Joe Rastrick, Gill Watt

2. Outline • Strategy to demonstrate impact • Features of Bayesian designs • Selling points • Preclinical setting • Contrast with Clinical • Related issues • Case study • First steps • Types of control groups • Bayesian methodology • Summary to date

3. Strategy to demonstrate impact Features of Bayesian designs • Explicit way of combining information sources • Forces early agreement as to relevance of all information sources • Reduce costs and resources (animal numbers) through informative priors/predictive distributions • Reduce costs and resources through interim analysis • Allows more relevant statements to be made at the end of the study e.g. the probability the response rate for drug A is more than 10% better than drug B • Ranking compounds • Comparing a combination with its components • Flexibility in estimation. E.g. one can analyse on the log scale and estimate differences on the linear scale • Allows for a wide variety of models to be fitted and can address issues such as lack of convergence or outlier-prone data • Model averaging, model selection

4. Strategy to demonstrate impact “Selling points of Bayesian methods” • High impact • Focus on in vivo studies that are run again and again • Saving even a few animals per study results in large savings, easily demonstrated • Ground-breaking • Quick search in the literature suggestslittle use in vivo except some focused applications: • PK & PK/PD models • SNPS/genes – pathway analysis. Including a Nature reviews article called “The Bayesian revolution in genetics” • Lookup proteins • Complements clinical strategy • *

5. Preclinical setting Contrast with clinical

6. Preclinical setting Related issues to consider Different output: internally & externally Getting hold of the data; in the right format Bayesian designs for repeated studies Rely entirely on historic data for one group Allied designs: modelled approach, QC charts Supplement a group with prior info  analysis issues

7. Case study Background • Mouse model to study inflammatory response after a challenge. • Measures a number of cytokines at 2.5 or 3hrs. • Includes test compounds + three control treatments: • Negative group (no challenge). • ‘Positive’ group (challenge, no treatment). • Comparator with known efficacy • Main comparisons of interest: • Test compound vs. +ve group (untreated) – Does test compound reduce the response? • Data on 19 studies available (reasonably consistent protocol). • Most frequent in-vivo assay in this therapeutic area. • Data typically presented an experiment at a time, in PRISM

8. First steps Strategy to smooth the introduction of Bayesian methods • QC charts to demonstrate reproducibility over time • Promoting interval estimates rather than a focus on p-values • Before committing to reducing animals, show “what would have happened if we had done this in the last study” by removing observations from the data set • Advertising and speaking to stakeholders • Publication strategy: • A statistical paper • case studies with details removed • For each assay, publish the meta-analysis of the historic data and the planned future data analysis • preferably in the selected journal to be used for data for new compounds • Publish data relating to specific compounds • having de-risked by the preceding 2 publications

9. First steps QC charts for control groups Well received. Introduces the idea of expt-to-expt variation. Intuitively, the relevance of the historic controls depends on the size of the study to study variation. High expt-to-expt variation Low expt-to-expt variation Bayesian analysis can use the historic control information, down-weighting it according to the amount of experiment-to-experiment variation

10. Types of control groups • Not used for formal statistical comparisons. Example uses: • To ensure challenge is working; to establish a “window”; to check consistency with previous studies; to convert values to %. • Replace group with a range from a predictive distribution • Used for formal comparison vs. test compounds/doses • Used as the comparison in t-tests ..etc • Combine down-weighted historic data with the current experiment

11. Bayesian methodology Outline • Analysehistoric control treatment group data, excluding the last study. • Bayesian meta-analysis • Analyse the last study • Show what would have happened if we had “bought into” the Bayesian approach; omit animals if necessary • Possible options for future studies: • Omit all/some animals from all/some control groups. • Use historic data as prior information combined with observed data in a Bayesian analysis. • Use historic data to give a predictive distribution for control group. i.e. don’t include that treatment group in current study. • Statistical model based on meta-analytic predictive methodology in Neuenschwanderet al

12. Bayesian meta-analytic predictive approach Statistical model based on Neuenschwander et al (2010) • Historic data:, h=1…H: Observed study data: h | θh, σa2~ N(θh, σa2) Study means: θ1…θH ~ N(μ, τ2) • Predictions for next study, denoted by *: True study mean θ* ~ N(μ, τ2)  prior for next study Observed study mean *| θ*, σa2~ N(θ*, σa2/n*)  predictive dn for next study • Priors and hyperpriors • μ has vague normal prior • Τhas vague half normal prior (sensitivity analysis carried out) • σa2 has vague gamma prior

13. Bayesian methodology (2) “Replacing” control groups with predictive distributions Bayesian analysis of historic control data New study data: 8 per group (for the other groups) Traditional analysis of current study QC-chart like limits for control group Overlay Bayesian analysis in data presentations Suitable for control groups not used in statistical comparisons

14. Case study Predictive distribution

15. Bayesian methodology (4) Full Bayesian analysis This is a simplification of the exact analysis Bayesian analysis of historic control data New study data: 8 per group Bayesian analysis of current study Effectively N control animals with mean, m Suitable for any control groups but requires a Bayesian analysis for each data set. Results and conclusions

16. Case Study Full Bayesian analysis The Bayesian analysis gives narrower confidence intervals. It is comparable to using 3 extra animals (11 instead of 8) __________ A@3mg/kg ___________ A@30mg/kg __________ B@3mg/kg ___________ B@30mg/kg

17. Summary to date • Predictive approach developed for two models • Biologists very positive; implementation being considered • Potential saving: one control group per study • Full Bayesian approach developed for one model • Modest savings in numbers of animals • Software issue; potentially lengthening turnaround times for rapid screens • Biologists suggested starting with something slightly more low-key • QC charts provided an excellent introduction to between and within study variation • Bayesian methods can reduce required resource (animal numbers) • To have the greatest impact, focus on studies repeated very frequently • Even for well controlled in vivo experiments study-to-study variation is not negligible • ,

18. References • Neuenschwander, B., Capkun-Niggli, G., Branson, M. and Spiegelhalter, DJ. Summarizing historical information on controls in clinical trials., Clin Trials 2010 7: 5 • Di Scala L, Kerman J, Neuenschwander B. Collection, synthesis, an interpretation of evidence: a proof-of-concept study in COPD. Statistics in Medicine 2013; 32: 1621–1634. • Evans, M, Hastings, N and Peacock, B (2000). Statistical Distributions. 3rd Edition. New York: Wiley • Beaumont and Rannala, The Bayesian revolution in genetics. Nature Reviews Genetics 5, 251-261 (April 2004)

20. Thanks!