The illness-death model serves as a critical framework for characterizing the progression of diseases over time. This model typically addresses transitions between different health states leading to disease outcomes. In existing literature, much attention has been given to either the statistical estimation aspects without causal interpretations or to approaches that impose a strong Markov assumption. This assumption posits that the terminal event is dependent solely on the current health state, disregarding the timing of any intermediate events.
This research addresses these limitations by introducing a non-parametric mediation analysis specifically aimed at the non-Markov illness-death model. Given the absence of comprehensive causal frameworks, this study seeks to bridge existing research gaps and enhance our understanding of causal pathways in healthcare outcomes.
Causal analysis is vital for exploring the relationships among variables in medical research, particularly in illness-death models. Traditional approaches often hinder the exploration of causal relationships due to the constraints of Markov properties. This study proposes advances in causal interpretation by defining a new concept of counterfactual hazard. This approach attends to both the potential mediating effects of intermediate events and their temporal relationships.
The fundamental shift is that the model encompasses the entirety of the history concerning these intermediate events, thus allowing for a richer understanding of disease progression and the impact of various exposures.
The proposed counterfactual hazard definition allows for a nuanced approach that incorporates the timing and nature of intermediate events. Using this framework, the study formulates an identification formula that integrates an integral concerning the probability density function of the time associated with the intermediate event. This formula is pivotal for deriving insights about the relationships between exposures and the final health outcomes.
This advancement enables researchers to dissect the complexities inherent in the progression of diseases while explicitly accounting for intermediate events, thereby creating a robust tool for causal analysis.
In this framework, the study delineates direct effects—where an exposure influences a terminal event without the mediation of any intermediate events—and indirect effects, which occur when the influence of the exposure is mediated through one or more intermediate variables. This bifurcation enables a comprehensive view of how exposures impact outcomes, especially in chronic disease contexts.
These distinctions are essential for tailoring interventions and understanding the complete action pathways of various health determinants.
To facilitate the practical application of this new model, the authors propose non-parametric kernel estimators for quantifying both direct and indirect effects. These estimators serve as computational tools to analyze the relationships revealed through the counterfactual hazard approach. Notably, the study assesses the asymptotic properties of these estimators, ensuring their reliability in various sample sizes.
Numerical simulations further demonstrate the robustness of the proposed methods, showcasing their efficacy in finite-sample scenarios. Thus, the kernel estimators are positioned as valuable resources for researchers employing non-parametric techniques in their analyses.
The proposed methodologies are applied to a notable case study investigating hepatitis C and its implications for mortality rates. This application underscores the value of employing a non-Markov approach as the results indicate that the effect of hepatitis C on mortality is not mediated through the occurrence of septicemia during the first 15 years of follow-up.
This finding not only provides a clearer understanding of hepatitis C's long-term impacts but also illustrates the utility of non-parametric mediation analysis in uncovering critical insights related to disease outcomes.
In summary, this study provides essential advancements in causal inference strategies within the context of illness-death modeling, contributing important methodologies to the field of infectious disease research.