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Super Learner Based Conditional Density Estimation with Application to Marginal Structural Models

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  • Díaz Muñoz Iván
  • van der Laan Mark J.

Abstract

In this paper, we present a histogram-like estimator of a conditional density that uses cross-validation to estimate the histogram probabilities, as well as the optimal number and position of the bins. This estimator is an alternative to kernel density estimators when the dimension of the covariate vector is large. We demonstrate its applicability to estimation of Marginal Structural Model (MSM) parameters in which an initial estimator of the exposure mechanism is needed. MSM estimation based on the proposed density estimator results in less biased estimates, when compared to estimates based on a misspecified parametric model.

Suggested Citation

  • Díaz Muñoz Iván & van der Laan Mark J., 2011. "Super Learner Based Conditional Density Estimation with Application to Marginal Structural Models," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-20, October.
    • Handle: RePEc:bpj:ijbist:v:7:y:2011:i:1:n:38
    DOI: 10.2202/1557-4679.1356
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    References listed on IDEAS

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    1. Vaart Aad W. van der & Dudoit Sandrine & Laan Mark J. van der, 2006. "Oracle inequalities for multi-fold cross validation," Statistics & Risk Modeling, De Gruyter, vol. 24(3), pages 351-371, December.
    2. van der Laan Mark J. & Dudoit Sandrine & Keles Sunduz, 2004. "Asymptotic Optimality of Likelihood-Based Cross-Validation," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-25, March.
    3. van der Laan Mark J. & Rubin Daniel, 2006. "Targeted Maximum Likelihood Learning," The International Journal of Biostatistics, De Gruyter, vol. 2(1), pages 1-40, December.
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    Cited by:

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    3. Iván Díaz & Katherine L. Hoffman & Nima S. Hejazi, 2024. "Causal survival analysis under competing risks using longitudinal modified treatment policies," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 30(1), pages 213-236, January.
    4. Rachael V. Phillips & Mark J. van der Laan, 2022. "Rachael V. Phillips and Mark J. van der Laan’s contribution to the Discussion of ‘Assumption‐lean inference for generalised linear model parameters’ by Vansteelandt and Dukes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 717-718, July.
    5. Jacqueline A. Mauro & Edward H. Kennedy & Daniel Nagin, 2020. "Instrumental variable methods using dynamic interventions," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(4), pages 1523-1551, October.
    6. Iván Díaz & Nicholas Williams & Katherine L. Hoffman & Nima S. Hejazi, 2025. "Author correction to: “causal survival analysis under competing risks using longitudinal modified treatment policies”," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 31(2), pages 442-471, April.
    7. Iván Díaz Muñoz & Mark van der Laan, 2012. "Population Intervention Causal Effects Based on Stochastic Interventions," Biometrics, The International Biometric Society, vol. 68(2), pages 541-549, June.

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