Structural Functional Response Models for Complex Intervention Trials

Estimating causal effect under different treatment exposures in empirical research is sometimes difficult because of lack of control for the distribution of such exposure in either randomly assigned or self-selected treatment groups. In clinical studies,

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Structural Functional Response Models for Complex Intervention Trials Pan Wu and Xin M. Tu

Abstract Estimating causal effect under different treatment exposures in empirical research is sometimes difficult because of lack of control for the distribution of such exposure in either randomly assigned or self-selected treatment groups. In clinical studies, when the treatment doesn’t follow standard design under a consistent and single-layer intervention for each subject, the estimation and inference on causal treatment effect would become more complicated than the standard intervention for the most of the statistical models. In this book chapter, we are interested in introducing a new class of structural models in estimation of causal treatment effect, the structural functional response models (SFRM), which is an extended version of existing structural mean models (SMM), but more effectively used in addressing imperfect of treatment compliance in clinical trials. In contrast with SMM, the SFRM has a flexible model structure and is naturally adaptive to complex intervention design for both experimental and non-experimental studies. The computation of the SFRM is more straightforward than the G-estimation algorithm that is widely used by SMM. Moreover, the SFRM is ready to be generalized to binary and count outcomes through logit and log-linear functions. Simulation studies are conducted to illustrate its strength and superiority of model performance. Then, the SFRM is applied to a randomized clinical trial in comparison of a new intervention with standard therapy in improvement of teenage’s mental health to estimate the causal treatment effect under the multi-layered intervention design.

P. Wu () Value Institute, Christiana Care Health System, 4755 Ogletown-Stanton Road, Newark, DE 19718, USA e-mail: [email protected] X.M. Tu Department of Biostatistics and Computational Biology, University of Rochester, 265 Crittenden Boulevard, Rochester, NY 14642, USA e-mail: [email protected] © Springer International Publishing Switzerland 2016 H. He et al. (eds.), Statistical Causal Inferences and Their Applications in Public Health Research, ICSA Book Series in Statistics, DOI 10.1007/978-3-319-41259-7_12

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P. Wu and X.M. Tu

1 Introduction The randomized controlled trials (RCTs) has been treated as the gold standard in causal inference since the effect of randomization ensures that no pre-treatment variables could potentially confound both treatment assignment and outcomes of interest. This effort is rewarded by a simple design with robust results that is easily understood and implementable in the general public. The RCTs, however, may not always guarantee the causality of treatment on the outcome of interest when the after-randomization treatment suffers imperfect or non-compliance issue in practices, such as the inconsistent exposure of intervention for each individual subject in active treatment arms or less control on other variables (mediators) related to both treatment and outcomes. The traditional