Targeted Learning with Moderated Statistics for Biomarker Discovery

Authors: Nima Hejazi, Mark van der Laan, and Alan Hubbard

What’s biotmle?

The biotmle R package facilitates biomarker discovery through a generalization of the moderated t-statistic (Smyth 2004) that extends the procedure to locally efficient estimators of asymptotically linear target parameters (Tsiatis 2007). The set of methods implemented modify targeted maximum likelihood (TML) estimators of statistical (or causal) target parameters (e.g., average treatment effect) to apply variance moderation to the standard variance estimator based on the efficient influence function (EIF) of the target parameter (van der Laan and Rose 2011, 2018). By performing a moderated hypothesis test that pools the individual probe-specific EIF-based variance estimates, a robust variance estimator is constructed, which stabilizes the standard error estimates and improves the performance of such estimators both in smaller samples and in settings where the EIF is poorly estimated. The resultant procedure allows for the construction of conservative hypothesis tests that reduce the false discovery rate and/or the family-wise error rate (Hejazi, van der Laan, and Hubbard 2020). Improvements upon prior TML-based approaches to biomarker discovery (e.g., Bembom et al. (2009)) include both the moderated variance estimator as well as the use of conservative reference distributions for the corresponding moderated test statistics (e.g., logistic distribution), inspired by tail bounds based on concentration inequalities (Rosenblum and van der Laan 2009); the latter prove critical for obtaining robust inference when the finite-sample distribution of the estimator deviates from normality.


For standard use, install from Bioconductor using BiocManager:

if (!requireNamespace("BiocManager", quietly=TRUE)) {

To contribute, install the bleeding-edge development version from GitHub via remotes:


Current and prior Bioconductor releases are available under branches with numbers prefixed by “RELEASE_”. For example, to install the version of this package available via Bioconductor 3.6, use

remotes::install_github("nhejazi/biotmle", ref = "RELEASE_3_6")


For details on how to best use the biotmle R package, please consult the most recent package vignette available through the Bioconductor project.


If you encounter any bugs or have any specific feature requests, please file an issue.


Contributions are very welcome. Interested contributors should consult our contribution guidelines prior to submitting a pull request.


After using the biotmle R package, please cite both of the following:

      author = {Hejazi, Nima S and Cai, Weixin and Hubbard, Alan E},
      title = {biotmle: Targeted Learning for Biomarker Discovery},
      journal = {The Journal of Open Source Software},
      volume = {2},
      number = {15},
      month = {July},
      year  = {2017},
      publisher = {The Open Journal},
      doi = {10.21105/joss.00295},
      url = {}

      author = {Hejazi, Nima S and {van der Laan}, Mark J and Hubbard, Alan
      title = {A generalization of moderated statistics to data adaptive
        semiparametric estimation in high-dimensional biology},
      journal={under review},
      year = {2020},
      doi = {},
      url = {}

      author = {Hejazi, Nima S and {van der Laan}, Mark J and Hubbard, Alan
      title = {{biotmle}: {Targeted Learning} with moderated statistics for
        biomarker discovery},
      doi = {10.18129/B9.bioc.biotmle},
      url = {},
      note = {R package version 1.10.0}


The development of this software was supported in part through grants from the National Institutes of Health: P42 ES004705-29 and R01 ES021369-05.


© 2016-2020 Nima S. Hejazi

The contents of this repository are distributed under the MIT license. See file LICENSE for details.


Bembom, Oliver, Maya L Petersen, Soo-Yon Rhee, W Jeffrey Fessel, Sandra E Sinisi, Robert W Shafer, and Mark J van der Laan. 2009. “Biomarker Discovery Using Targeted Maximum-Likelihood Estimation: Application to the Treatment of Antiretroviral-Resistant Hiv Infection.” *Statistics in Medicine* 28 (1). Wiley Online Library: 152–72.
Hejazi, Nima S, Mark J van der Laan, and Alan E Hubbard. 2020. “A Generalization of Moderated Statistics to Data Adaptive Semiparametric Estimation in High-Dimensional Biology.” *Under Review*. .
Rosenblum, Michael A, and Mark J van der Laan. 2009. “Confidence Intervals for the Population Mean Tailored to Small Sample Sizes, with Applications to Survey Sampling.” *The International Journal of Biostatistics* 5 (1). De Gruyter.
Smyth, Gordon K. 2004. “Linear Models and Empirical Bayes Methods for Assessing Differential Expression in Microarray Experiments.” *Statistical Applications in Genetics and Molecular Biology* 3 (1). Walter de Gruyter: 1–25. .
Tsiatis, Anastasios. 2007. *Semiparametric Theory and Missing Data*. Springer Science & Business Media.
van der Laan, Mark J., and Sherri Rose. 2011. *Targeted Learning: Causal Inference for Observational and Experimental Data*. Springer Science & Business Media.
van der Laan, Mark J, and Sherri Rose. 2018. *Targeted Learning in Data Science: Causal Inference for Complex Longitudinal Studies*. Springer Science & Business Media.