Coherent modeling of longitudinal causal effects on binary outcomes.

Area of Science:

• Biostatistics
• Longitudinal Data Analysis
• Causal Inference

Background:

• Biomedical studies increasingly require modeling longitudinal causal effects, especially with personalized medicine and effect heterogeneity.
• Structural nested mean models (SNMMs) are key for heterogeneous treatment effects in longitudinal studies.
• Binary outcomes in SNMMs present estimation challenges due to parameter variation dependence.

Purpose of the Study:

• To resolve the variation dependence problem in binary multiplicative SNMMs.
• To enable coherent modeling of heterogeneous treatment effects for longitudinal binary outcomes.
• To develop a foundation for flexible doubly robust estimation.

Main Methods:

• Reparameterization of noncausal nuisance parameters in multiplicative SNMMs.
• Demonstration of variation independence between novel nuisance and causal parameters.
• Proof of non-existence of variation independent parameterization for additive SNMMs with binary outcomes.

Main Results:

• A novel parameterization for binary multiplicative SNMMs is introduced, achieving variation independence.
• The new approach facilitates coherent modeling of heterogeneous treatment effects.
• Additive SNMMs with binary outcomes were shown to lack variation independent parameterization.

Conclusions:

• The proposed reparameterization effectively solves variation dependence issues in binary multiplicative SNMMs.
• This advancement supports more reliable analysis of heterogeneous treatment effects in longitudinal biomedical data.
• The findings justify the focus on multiplicative SNMMs for binary longitudinal outcomes.