Causal mediation analysis methods for polytomous, functional and high-dimensional data

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The long-term goal of the proposed research program is to develop data-adaptive methods for the purpose of producing evidence of causal pathways and mechanisms, and extend these to complex types of data. Synthesizing statistical inference and machine learning in the estimation of specific target parameters has become one of the key research areas in statistics, aimed at reducing parametric assumptions about parts of the model that are not of direct interest. The target parameter is often a causal effect of an intervention/exposure, and estimation of this usually involves modeling of the exposure and/or outcome variables, needed for controlling for confounding with non-experimental data. Flexible data-adaptive methods can be used for this task; for example, the recent resurgence in the use of deep neural networks for applied problems has motivated attempts to incorporate these in constructing statistical estimators. However, finding the right compromise between variance inflation due to overfitting and bias introduced by regularization in attempts to control the variation has not been easy. Recent progress in establishing the theoretical properties of the resulting procedures has been made in the context of doubly robust estimators, where employing two models simultaneously reduces bias in the estimation. Causal mediation analysis aims at producing evidence of causal pathways by decomposing total causal effects into indirect effects through specific mediator variables, and direct effects operating through other pathways. While methods exist for dichotomous and continuous exposure, mediator and outcome variables, extensions are needed for more complex types of data. Furthermore, advances in semi-parametric causal inference need to be extended to causal mediation analysis, incorporating data-adaptive methods to control for high-dimensional confounders. The proposed research program will contribute towards the theoretical and methodological knowledge base of causal mediation analysis through developing novel effect decompositions and estimators for multi-category polytomous exposures and functional exposures, developing semi-parametric estimators for causal mediation analysis incorporating deep neural networks, and developing methods for high-dimensional mediation analysis based on imaging data. The methods will have applications in multiple fields of research; the interest in polytomous exposures is motivated by institutional comparisons for example in education and healthcare. An example of a functional exposure is radiation exposure represented in terms of a dose-volume histogram. Many of the other mediation questions are motivated by data produced by high throughput technology where the high-dimensional biomarkers are not causal variables as such, but manifestations of latent factors on the causal pathway, and mediation analysis will necessarily require dimension reduction techniques.