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Robust causal inference using non-randomized longitudinal data


Philip Clare

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Acknowledgements

Funding:

  • I receive an RTP Scholarship from the Australian Government and a Scholarship from NDARC
  • NDARC receives funding from the Australian Government Department of Health

Thanks to my PhD Supervisors: Tim Dobbins, Richard Mattick and Raimondo Bruno.

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Overview

  1. Background;
  2. Bias in causal inference;
  3. Assumptions in causal inference;
  4. Methods for causal inference;
  5. Targeted maximum likelihood estimation;
  6. TMLE Examples;
  7. Conclusions;
  8. References;
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Background

  • Causal inference at its simplest:
    • "the difference in a given outcome, based on some prior event, compared with what would have happened had that event not occurred"
  • RCTs are, and will remain, the gold standard
  • There are times when RCTs aren't possible
  • Causal inference is possible without randomization
    • It just requires more caution
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Bias in causal inference

  • General to all observational studies
    • Selection bias
    • Confounding
    • Collider bias
    • Measurement error
  • Specific to longitudinal analysis
    • Loss to follow-up
    • Exposure affected time-varying confounding
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Bias in causal inference

Figure 1

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Bias in causal inference

Figure 2

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Bias in causal inference

Figure 3

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Assumptions in causal inference

  • No interference
  • Consistency
  • Positivity
  • No unmeasured confounding
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Methods for causal inference

  • Propensity score matching (PSM)
  • Marginal Structural models (MSM)
  • G-computation
  • Doubly-robust methods (DR)
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Methods for causal inference

  • Doubly-robust methods (DR)
    • At their simplest: DR methods are those that provide consistent estimates even when one of either the propensity or outcome models are estimated consistently 'Simple' DR methods:
    • adjusted IPTW
    • IPTW weighted
    • G-computation
    • A-IPTW
  • Similar to IPTW, but adjusts the IPTW estimate by a function of the outcome model
  • There is some discussion about the best approach for this in terms of estimating the models
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Targeted maximum likelihood estimation

  • TMLE is a targeted substitution estimator that treats everything except the target estimand as 'nuisance' parameters
  • TMLE involves:
    • estimating an initial conditional expectation of an outcome using maximum likelihood,
    • estimating the propensity score,
    • using the propensity score to create a 'clever' covariate h, and
    • updating the outcome model based on a function of the initial estimates and the clever covariate
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Targeted maximum likelihood estimation

  • This can be repeated if necessary, and will iterate to the target parameter

    Figure 4

  • However, it has been shown that most common effect measures can be estimated in one iteration
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Targeted maximum likelihood estimation

  • Because it is a substitution estimator that doesn't use the parameters of the initial models, TMLE is commonly estimated using ensemble machine learning
    • The ensemble machine learning algorithm 'Super Learner' was developed in parallel with TMLE
    • The packages 'tmle' and 'ltmle' in R both call 'SuperLearner' by default
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Targeted maximum likelihood estimation

  • TMLE is relatively new
  • There are a number of areas of ongoing investigation regarding the performance:
  • Balance SuperLearner: an adaptation of the SL algorithm optimized for balance rather than accuracy of prediction
  • Collaborative TMLE, which uses a loss function based on Q to fluctuate the nuisance parameter, instead of a loss function of the nuisance parameter itself. C-TMLE can be a consistent estimator even when both models are misspecified
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TMLE Examples

  • Random data following the DAG from earlier
  • True parameter is:

Joint = 0.5×A_0 + 1.5×A_1 - 1.0×A_0×A_1 = 1.0

Figure 5

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TMLE Examples

Figure 6

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TMLE Examples

Figure 7

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TMLE Examples

Figure 8

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TMLE Examples

Figure 9

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Conclusions

  • Unbiased causal inference is possible in non-randomized studies
  • There are methods to deal with bias
  • Newer methods are more robust
  • Even for analysis of association, bias is an issue that can be addressed by these methods
  • Markdown for a TMLE tutorial currently under review at Statistics in medicine: https://github.philipclare.com/tmletutorial
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References

  1. Clare PJ, Dobbins TA, Mattick RP. Causal models adjusting for time-varying confounding-a systematic review of the literature. Int J Epi. 2019;48(1):254-265.
  2. Robins JM. Marginal Structural Models. 1997 Proceedings of the American Statistical Association, Section on Bayesian Statistical Science. 1998:1-10.
  3. Robins JM. A new approach to causal inference in mortality studies with a sustained exposure period-application to control of the healthy worker survivor effect. Mathematical Modelling. 1986;7(9):1393-512.
  4. Bang H, Robins JM. Doubly robust estimation in missing data and causal inference models. Biometrics. 2005;61(4):962-72.
  5. Van der Laan MJ, Rubin D. Targeted Maximum Likelihood Learning. Int J Biostat. 2006;2(1).
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Acknowledgements

Funding:

  • I receive an RTP Scholarship from the Australian Government and a Scholarship from NDARC
  • NDARC receives funding from the Australian Government Department of Health

Thanks to my PhD Supervisors: Tim Dobbins, Richard Mattick and Raimondo Bruno.

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