demonstrating the impact of statistics in the preclinical area using bayesian analysis with...
TRANSCRIPT
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
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ן Strategy to demonstrate impact • Features of Bayesian designs• Selling points
ן Preclinical setting• Contrast with Clinical• Related issues
ן Case study
ן First steps
ן Types of control groups
ן Bayesian methodology
ן Summary to date
Outline
Co-branding logo
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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
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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 suggests little 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
*
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Preclinical setting
Contrast with clinical
Preclinical Clinical
Data recording Focus on individual study Hard to pool
Standardized, locatable Easy to pool
Software Graphpad PRISM, EXCEL SAS, R
Relevant data for priors
In house, Run to same protocol; any changes noted.Fantastic source.
Usually from publications. Differences between protocols & populations. Summary level data only.
Size of experiment For in vivo studies, typicallyN=3-10 per group
Typically, N=20-100 per group for a PoC.
Protocol finalisation A set of experiments may be further optimised during their running
Reluctance to trigger a protocol amendment
Novel stats methods
Very traditional approaches used. Little stats support.
Bayesian and adaptive methods implemented and published.
Data interpretation Common to compare compounds across experiments
Focus on individual experimental compound
Preclinical setting
Related issues to consider
Bayesian designs for repeated studies
Allied designs: modelled approach, QC charts
Getting hold of the data; in the right
format
Different output:
internally & externally
Supplement a group with prior info analysis
issues
Rely entirely on historic data for
one group
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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
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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:
1. A statistical paper
• case studies with details removed
2. 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
3. Publish data relating to specific compounds
• having de-risked by the preceding 2 publications
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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.
Bayesian analysis can use the historic control information, down-weighting it according to the amount of experiment-to-experiment variation
Low expt-to-expt variation High expt-to-expt variation
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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
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Bayesian methodology
Outline
■ Analyse historic 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 Neuenschwander et al
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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, σa
2)
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*, σa
2/n*) predictive dn for next study
■ Priors and hyperpriors
μ has vague normal prior
Τ has vague half normal prior (sensitivity analysis carried out)
σa2 has vague gamma prior
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Bayesian methodology (2)
“Replacing” control groups with predictive distributions
New study data: 8 per group (for the
other groups)
Traditional analysis of current study
Bayesian analysis of historic control
data
QC-chart like limits for control group
Overlay Bayesian analysis in data presentationsSuitable for control groups not
used in statistical comparisons
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Case study
Predictive distribution
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Bayesian methodology (4)
Full Bayesian analysis
This is a simplification of the exact analysis
Bayesian analysis of current study
Results and conclusions
New study data: 8 per group
Bayesian analysis of historic control
data
Effectively N control animals with mean, m
Suitable for any control groups but requires a Bayesian analysis for each data set.
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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
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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
,
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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)
Questions?
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Thanks!