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Estimation of causal effects of an exposure at multiple time points through Multivariable Mendelian randomization.

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Eleanor Sanderson

MRC Integrative Epidemiology Unit,

University of Bristol

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October 2021

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Overview

    • What is Mendelian Randomization?

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    • Multivariable MR

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    • Multivariable MR with time varying exposures
      • Testing instrument strength

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    • Application to estimation of the effect of childhood and adulthood BMI

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Mendelian Randomization

  • Genetic variants are;
      • Associated with phenotypes
      • randomly allocated

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  • Can use this to test for and estimate causal effects

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  • Statistically implemented as instrumental variables estimation

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Mendelian Randomization

  • Standard IV assumptions apply
  1. IV is associated with the exposure
  2. No confounders of the outcome and the IV
  3. No effect of the IV on the outcome that doesn’t act through the exposure

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Mendelian Randomization

  • Implemented using individual level or summary level data

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  • Genetic variants typically SNPs (single nucleotide polymorphisms)
  • Discovered in a GWAS (Genome-wide association study)

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What is Multivariable Mendelian Randomization?

  • MR including multiple exposures in the same estimation
    • Here have two exposures – could have more.

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MR:

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MVMR:

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What is Multivariable Mendelian Randomization?

MR: Estimates the total effect of the exposure on the outcome

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MVMR: Estimates the direct effect of each exposure on the outcome

NOT via the other exposures included in the estimation.

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How these differ will depend on the relationship between the exposures.

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Pleiotropy

Pleiotropy

    • Suspect multiple exposures are associated with an overlapping set of SNPs
      • MR is biased
      • MVMR can give unbiased causal effects

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e.g. estimating causal effects of lipids

    • Multiple SNPs associated with more than one of HDL, LDL and Triglycerides

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MVMR IVW estimation.

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Assumptions of MVMR

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C

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Y

SNPs

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Instrument strength in MVMR

Instruments can appear strong

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But actually be weakly associated with each exposure conditional on the other

A/B – Conditionally weak instruments

But could appear individually strong

C/D - Individually strong instruments

But could be conditionally weak

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Instrument strength in MVMR

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Test instrument strength with a conditional F-statistic

Sanderson, E,Β Spiller, W,Β Bowden, J.Β Testing and correcting for weak and pleiotropic instruments in

two-sample multivariable Mendelian randomization.Β Statistics in Medicine.Β 2021;Β 1– 19.

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Including multiple time points in MVMR

  • Two time periods – could be more!

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  • Multiple genetic variants
    • Together they affect the latent genetically predicted level of X at each period
    • Trajectory effect of each SNP may differ

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  • Observed value of the exposure is also influence by;
    • Environmental exposures
    • Confounders
    • Measurement error etc.

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Including multiple time points in MVMR

  • Need to be able to separate genetic effects on each period
    • These could be overlapping
    • Test with a conditional F-statistic

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Simulations:

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  1. Two latent periods

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  • One latent period

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Including multiple time points in MVMR

Total effect – 0.34

Direct effect – 0.20

Total effect – 0.375

Direct effect – 0.30

𝝆(L1 L2) = 0.25

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Including multiple time points in MVMR

Total effect – 0.53

Direct effect – 0.20

Total effect – 0.48

Direct effect – 0.30

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Including multiple time points in MVMR

  • 3 time periods matter
  • only 2 are included in estimation

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Including multiple time points in MVMR

𝝆(L1 L2) = 0.25

𝝆(L1 L3) = 0.10

𝝆(L2 L3) = 0.25

Total effect – 0.39

Direct effect – 0.21

Total effect – 0.44

Direct effect – 0.37

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Application – Estimating the effects of child and adulthood BMI

  • Outcomes:
    • Coronary Heart disease
    • Type 2 diabetes
    • Breast Cancer

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    • Anorexia Nervosa
    • Smoking

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Bmj 2020

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Data - exposures

  • UK Biobank: 500,000 individuals
        • From range of areas of UK
        • aged between 40 and 69

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  • Initial assessment centre:
    • Blood samples collected for genotyping
    • BMI measured
    • Participants asked β€˜When you were 10 years old, compared to average would you describe yourself as thinner, plumper or about average?’

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Analysis:

Categorised BMI into 3 categories

Distribution matched to early life body size

Ran GWAS for each age point

Caveats;

  • white European individuals
  • With observations for both ages

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Separating out child and adult effects

Childhood

adiposity

Adulthood

adiposity

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Estimation

Childhood

adiposity

Adulthood

adiposity

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Data – CHD, Type 2 diabetes, Breast cancer

Coronary Heart Disease:

CARDIoGRAM plus C4D

Nikpay (2015)

cases: 60,801, controls: 123,504

Mixed population

Used previous GWAS that exclude UK Biobank:

Type 2 Diabetes:

DIAGRAM

Morris (2012)

cases: 12,171, controls: 56,862

European population

Breast cancer:

BCAC

Michailidou (2017)

cases:122,977, controls: 105,974

European population

Female only

Re-estimated exposure GWAS restricted to female only

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Separating out child and adult effects

Test whether instruments are strong with an F-statistic:

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  • Univariable MR: mean F-statistic
  • Multivariable MR: conditional F-statistic

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F > 10 -> reject null hypothesis that the instruments are weak

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Univariable analysis

Multivariable analysis

Outcome

Early life

Adulthood

Early life

Adulthood

Coronary Artery Disease - Nikpay et al (2015)

30.70

42.35

13.63

16.00

Type 2 Diabetes - Morris et al (2012)

34.15

45.15

13.40

15.25

Breast cancer - Michailidou et al (2017)

31.96

35.74

13.28

14.67

Accounts for the association between the SNPs and the other exposure

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Results

Implied relationship

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Data – Anorexia nervosa, Smoking behaviour

Used previous GWAS that exclude UK Biobank:

Anorexia nervosa

Duncan et al (2017)

Cases; 3,495, Controls;10,982

Smoking

Lui et al (2019)

Smoking initiation

N = 248,871 56% ever smokers

Smoking cessation

N = 143,851 45% current smokers

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Results

Anorexia

Smoking

But:

Outcomes occur before adult BMI…

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Effect could be due to any time after age 10

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Thank you!

Collaborators

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George Davey Smith

Kate Tilling

Jack Bowden

Tom Richardson

Tim Morris

Wes Spiller

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References

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Sanderson, Eleanor, et al. "An examination of multivariable

Mendelian randomization in the single-sample and two-sample summary data settings."Β International journal of epidemiologyΒ 48.3 (2019): 713-727.

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Sanderson, Eleanor, Wes Spiller, and Jack Bowden. "Testing and correcting for weak and pleiotropic instruments in two-sample multivariable mendelian randomisation."Β  Statistics in Medicine (2021).

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Richardson, Tom G., et al. "Use of genetic variation to separate the effects of early and later life adiposity on disease risk: mendelian randomisation study."Β bmjΒ 369 (2020).

MRC Integrative Epidemiology Unit