Continuous Interventions in Epidemiology: from Theory to Practice

• Applicant: Dr. Michael Schomaker
• Subject Area: Epidemiology and Medical Biometry/Statistics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 465412441

The overall aim of the proposed research is the development of statistical methods for estimation of causal dose-response curves (CDRCs) when the intervention of interest is continuous and measured at multiple time points. The motivational analyses relate to estimation of the effects of efavirenz and nevirapine concentrations on viral suppression in HIV-positive children, i.e., how the counterfactual probability of suppression would vary as a function of concentration level, follow-up time and metabolic subgroup. Due to time-dependent confounding with treatment-confounder feedback, regression cannot be used to estimate CDRCs in this case.The first suggested approach relates to working with g-formula and sequential g-computation estimators to compute counterfactual outcomes for multiple values of the continuous intervention at each time point, and combine them non-parametrically to construct CDRCs. However, for continuous interventions, positivity violations may be common, i.e., violations of the assumption that individuals have a positive probability to obtain the intervention of interest at a specific time point, given that they have followed the respective intervention strategy so far and conditional on the covariate history. Those possible violations will be addressed by the development of projection functions, which reweight the estimand based on the data support for the respective interventions. The suggested methods will be implemented in a flexible package for the statistical software R and evaluated by means of Monte-Carlo simulations. The second suggested approach relates to the development of a doubly robust estimator. Such an estimator requires fitting of the conditional intervention density and the conditional expected outcome at each time point. This allows the integration of machine learning (ML) algorithms into effect estimation. As existing options to estimate conditional densities flexibly are limited, novel ML wrappers for techniques such as (boosting of) generalized additive models of location, scale and shape will be implemented.Both approaches will be developed in light of the motivating analyses, which require estimates that are as close as possible to the true CDRC. However, under strong positivity violations, this may be challenging and alternative causal estimands, where this assumption can be relaxed, may be considered. This includes longitudinal modified treatment policies (LMTPs), where treatment effects are allowed to depend on the natural value of treatment, i.e., the treatment value in the absence of any intervention. Monte-Carlo simulations will compare how severe positivity violations have to be such that approximately unbiased effect estimation is not possible anymore, and nominal coverage cannot be achieved – for both the developed approaches and LMTPs. Those comparisons will provide guidance for epidemiologists as to how to approach particular analyses.

• DFG Programme: Research Grants
• International Connection: South Africa, USA
• Co-Investigator: Professor Dr. Bernd Bischl
• Cooperation Partners: Professor Dr. Paolo Denti; Professor Dr. Iván Diaz; Professorin Dr. Helen McIlleron