RESUMEN
Causal inference is inherently complex, often dependent on key assumptions that are sometimes overlooked. One such assumption is the potential for unidirectional or bidirectional causality, while another is population homogeneity, which suggests that the causal direction between two variables remains consistent across the study sample. Discerning these processes requires meticulous data collection through an appropriate research design and the use of suitable software to define and fit alternative models. In psychiatry, the co-occurrence of different disorders is common and can stem from various origins. A patient diagnosed with two disorders might have one recognized as primary and the other as secondary, suggesting the existence of two types of comorbidity within the population. For example, in some individuals, depression might lead to substance use, while in others, substance use could lead to depression. Identifying the primary disorder is crucial for developing effective treatment plans. This article explores the use of finite mixture models to depict within-sample heterogeneity. We begin with the Direction of Causation (DoC) model for twin data and extend it to a mixture distribution model. This extension allows for the calculation of the likelihood of each individual's data for the two alternate causal directions. Given twin data, there are four possible pairwise combinations of causal direction. Through simulations, we investigate the Direction of Causation Twin Mixture (mixCLPM) model's potential to detect and model heterogeneity due to varying causal directions.
RESUMEN
Mendelian Randomization (MR) has become an important tool for causal inference in the health sciences. It takes advantage of the random segregation of alleles to control for background confounding factors. In brief, the method works by using genetic variants as instrumental variables, but it depends on the assumption of exclusion restriction, i.e., that the variants affect the outcome exclusively via the exposure variable. Equivalently, the assumption states that there is no horizontal pleiotropy from the variant to the outcome. This assumption is unlikely to hold in nature, so several extensions to MR have been developed to increase its robustness against horizontal pleiotropy, though not eliminating the problem entirely (Sanderson et al. 2022). The Direction of Causation (DoC) model, which affords information from the cross-twin cross-trait correlations to estimate causal paths, was extended with polygenic scores to explicitly model horizontal pleiotropy and a causal path (MR-DoC, Minica et al 2018). MR-DoC was further extended to accommodate bidirectional causation (MR-DoC2 ; Castro-de-Araujo et al. 2023). In the present paper, we compared the power of the DoC model, MR-DoC, and MR-DoC2. We investigated the effect of phenotypic measurement error and the effect of misspecification of unshared (individual-specific) environmental factors on the parameter estimates.