1. Danni Yu Eli Lilly and Company 2018-07-31 (Tue)
Discovering biomarkers jointly modeled with multiple efficacy variables in early phase clinical trials
Danni Yu
Eli Lilly and Company
(Tue)
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E-Poster Number 28

2. Background
“Biomarker is a characteristic that is objectively measured and evaluated as an indicator of normal biological process, pathogenic processes, or biological responses to a therapeutic intervention.”
Drug-related biomarkers include, but not limited to, baseline predictive biomarkers for patient stratification, efficacy and toxicity; longitudinal pharmacodynamics biomarkers for target engagement evidence, dose decision, or early response detection.
Biomarkers studies need to be involved in all the clinical trial stages.
Preclinical Lab Studies
Phase I Human Safety
Phase I/II Safety Confirm
Phase III
Efficacy & Safety
Sample size of phase I trials for biomarker identification is typically small, e.g. n=20~50.
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3. Problem and proposed solution
Sensitivity can be low due to the potential bias from small group systematic errors.
Traditional approach with one efficacy variable in the model makes decision difficult if it is on-the-boundary significance.
Jointly considering tumor change and survival time may help. Integrative approach is required.
Observe difference in tumor change between two baseline biomarker levels, but marginal significance in KM.
How to confirm in the next step?
Structural Equation Modeling (SEM) fits networks of constructs to data and can impute relationships between unobserved latent variables from observed variables.
It combines exploratory factor analysis and multiple multi-variates regressions (Ullman 2001) through structural equations.
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4. Simulation and analysis method
Simulate the biological and clinical association from predictive markers to efficacy variables.
Setup structural equations
Observed variables
Baseline markers: bmk.t1, bmk.fc1, bmk.fn1…
ChangeFromBaseline markers: pmk.t1, pmk.f1…
Tumor change ‘tc’, survival time ‘tte’ and ‘cnsr’
Latent variables
‘eff =~ tc + tte’, ‘bsl =~ bmk.t1+bmk.fc1+bmk.fn1+…’ and ‘log =~ pmk.t1+pmk.f1+…’
Regressions
‘eff ~ bsl + log’ if only one marker in bsl or log, then the latent variable is removed.
Residual covariance
‘tte ~~ tc’ assume the correlation between tumor change and survival time is nonzero.
Predictive marker: bmk.t1~Ber(prevalence).
Tumor change: tc~Gamma(sp, rt) where {rt, sp}= F[bmk.t1].
Survival time: tte~Weibull(sp, sc) where sp=1 and sc=G[tc, bmk.t1] if death, max(G[tc,bmk.t1]) if censored.
ChangeFromBaseline markers: pmk.t~N(mu,sd) where {mu, sd}=Z[tc].
Markers not related with any efficacy variables: bmk.fc~Ber(p) where p~U(0.2,0.8), bmk.fn and pmk.f~N(m,s) where m~N(0,1) and s~Chisq(1).
sp: shape parameter; rt: rate parameter; sc: scale parameter
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5. Single Y variable pval=0.064
Results:
The proposed method and the BEACH tool providing GUI for users help identify meaningful baseline biomarkers.
Single Y variable pval=0.064
Data Simulation in BEACH
SEM analysis in BEACH: bmk.t1 is identified. tc
tte
eff
Predictive bmk
The predictive biomarker ‘bmk.t1’ was not significant in separate models but meaningful association was identified while structuring ‘tc’ and ‘tte’ in the joint model.
n=30
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6. Conclusion & Future work Reference & Acknowledgement
SEM can be used to jointly analyze biomarkers in multiple multi-variates models. It enables us to increase the sensitivity of identifying biomarkers with joint efficacy approach.
A user-interface GUI tool coded in R/Shiny BEACH platform (Yu 2018) is created to implement the analyses dynamically and interactively.
The proposed simulation method has a potential to estimate the minimum sample size with controlled FDR.
Real clinical data with more efficacy variables can be applied to further improve this method with adjusted structural models.
Yu, D. and Man, M. (2018). BEACH: an open platform for building interactive and automatic analysis powered by R/Shiny. AD05 PharmaSUG.
Ullman, J. B. (2001). Structural equation modeling. In B. G. Tabachnick & L. S. Fidell (Eds.), Using multivariate statistics (4th ed.). Needham Heights, MA: Allyn & Bacon.
Yves, R. (2012). lavaan: An R package for structural equation modeling. Journal of statistical software vol. 048 i02.
Acknowledge Dr. Yanping Wang and Dr. Michael Man for their advice.
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