Causal diagrams for understanding when correlations doesn’t imply causation

Andy Stein

October 13, 2021

Translational Clinical Oncology

Pharmacometrics

Who am I? Andy Stein

• Group: Pharmacometrics
• What I do:
• Support quantitative analysis of early clinical trials, with a focus on identifying the right dose.
• My background:
• Mechanical Engineering and Applied Mathematics
• My passion:
• Learning and bringing insights from other fields into drug development and vice versa (environmental modeling, managing uncertainty, parenting)

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Motivation – the importance of finding the right dose of a drug

• Tylenol helps to reduce pain and fever and is safe at daily doses ≤3,000 mg/day
• >5,000 mg/day can cause liver damage
• >10,000 mg/day can be lethal.
• You can learn about safety and efficacy from clinical trials
• Making best use of this data requires models to integrate the data

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(paracetamol)

Understanding which factors to control for (age) is critical

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Overview

• Situation:
• We use models relating drug concentration to response to guide drug development.
• Models are useful when they describe a causal relationship
• If relationships are only correlative relationship, they can lead to poor decisions
• Question: How to assess whether a relationship is causal or just correlative?
• Answer: Causal diagrams can help identify confounders
• Outline
• Introduce PKPD concepts and exposure-response modeling
• Present two examples of exposure-response confounding
• Introduce causal diagrams and their key structures
• Conclude with COVID-19 example

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The “PKPD” pathway of drug effect

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Oral Dose

Elimination

from body

Pharmacokinetics (PK):

How body affects drug

Pharmacodynamics (PD):

How drug affects body

Should children and adults receive the same dose?

What dose is needed to shrink a tumor without causing severe neutropenia

Drug Concentration

Measurement

Measuring PKPD

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PK (Pharmacokinetics) example

Measurement of drug concentration from circulation

PD (Pharmacodynamics) example

Change in tumor size, as measured by X-Ray

Dose Regimen

• amount given
• frequency
• method (oral, patch, etc.)

Understanding PKPD can help in picking the optimal dose regimen

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From Rowland and Tozer

Drug doesn’t work

Drug is too toxic

Novartis was developing a PD-L1 Inhibitor. Other PD-L1 drugs on the market

• Atezolizumab dosed at 1200 mg q3w
• Our drug had similar properties to atezolizumab
• Is 1200 mg q3w the right dose for us?

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Higher exposure of atezolizumab correlates with better response

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2 4 6 8 10 12

Atezolizumab, 1200 mg q3w

Only one dose tested

2^nd Line Non Small Cell Lung Cancer (NSCLC)

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From Feb 2016 FDA Clin. Pharm. Review

Clearance decreases (and exposure increases) with improved response^1-2

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1. Liu, Chao, et al. "Association of Time‐Varying Clearance of Nivolumab With Disease Dynamics and Its Implications on Exposure Response Analysis." Clinical Pharmacology & Therapeutics 101.5 (2017): 657-666.
2. FDA Clin Pharm Review for atezolizumab in NSCLC (2016)
3. Bajaj, G., et al. "Model‐based population pharmacokinetic analysis of nivolumab in patients with solid tumors." CPT: pharmacometrics & systems pharmacology 6.1 (2017): 58-66.

Atezolizumab in NSCLC

(observed for most PD-1, PD-L1 inhibitors)

Cachexia in non-responders might lead to faster clearance of drug³

Exposure drives response AND response drives exposure

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Exposure

Response

Assumption

Dose

Reality

(sometimes)

Exposure

Response

Dose

Prognostic factors may also confound the analysis

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Exposure

Response

Prognostic

Factors

- Patient health

- metastases

- cachexia

Assumption

Dose

Reality

(sometimes)

Exposure

Response

Dose

For trastuzumab in metastatic Gastric Cancer, exposure-OS relationship observed

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1. Yang, Jun, et al. "The combination of exposure‐response and case‐control analyses in regulatory decision making." The Journal of Clinical Pharmacology 53.2 (2013): 160-166.

Q1

Q2, Q3, Q4

Trough conc. at end of day 21 (model predicted)

Poor response at Q1 exposure was due to prognostic factors affecting both exposure and response¹

Key prognostic factors

• ECOG
• Prior gastrectomy
• # metastatic sites
• Asian ethnicity
• HER2 IHC score

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1. Yang, Jun, et al. "The combination of exposure‐response and case‐control analyses in regulatory decision making." The Journal of Clinical Pharmacology 53.2 (2013): 160-166.

Draw a causal graph of the �dose-exposure-biomarker-resp. relationship

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Fork: �you must stratify by covariate, otherwise estimated E-R relationship will not be causal

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Dose

Exposure

Response

Covariate

Simpson’s Paradox:

https://en.wikipedia.org/wiki/Simpson%27s_paradox

Mediators and Colliders: �you must not stratify by covariate, otherwise E-R will be confounded [these are post-baseline covariates]

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Dose

Exposure

Response

Covariate

Dose

Exposure

Response

Covariate

Mediator

Collider

Feedback Loop:�You must think about the consequences of the feedback loop(s) and choose the appropriate analysis.

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Dose

Exposure

Response

1. https://arxiv.org/abs/1907.07271

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Using dose or exposure only at day 1 help avoid confounding.�

COVID-19 example�

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* Andy’s guess for upper level of quantification

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Get

Vaccine

Hospitalization

Due to COVID-19

Age

1. https://www.covid-datascience.com/post/israeli-data-how-can-efficacy-vs-severe-disease-be-strong-when-60-of-hospitalized-are-vaccinated�Israel data with Pfizer Vaccine, August 2021

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Reason for confounding: Older people are both more likely to be vaccinated and more likely to be hospitalized, irrespective of vaccination.

Drug development is challenging because biology is so complex

• Causal diagrams can help by identifying potentially confounding factors

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Forks

Feedback Loops

Acknowledgements

• Exposure-Response Guidance Team
• Thomas Dumortier
• Guenter Heimann
• Yu-Yun Ho
• Alison Margolskee
• Oliver Sander
• Marina Savelieva-Praz
• Xinrui Zhang
• Analytics colleagues
• Mark Baille
• Bjorn Bornkamp
• Christian Bartels
• External Colleague
• Mike Perry

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