Triangulation for causal loop diagrams: constructing biopsychosocial models using group model building, literature review, and causal discovery

The paper addresses how to construct more valid and reproducible causal loop diagrams (CLDs) for complex health problems by triangulating different sources of evidence. Traditional participatory methods such as group model building (GMB) aggregate expert knowledge but can suffer from subjectivity, reproducibility concerns, and structural biases. Literature reviews add theory-driven evidence but may still reflect researcher assumptions and may not systematically cover all possible links. Causal discovery offers a quantitative, data-driven approach to infer causal diagrams from observational data, including longitudinal settings where feedback can be identified, but its performance can be affected by unmet assumptions (e.g., latent confounding, measurement error, selection bias, sample size, missing data). The authors propose a triangulation approach integrating GMB, literature review, and causal discovery to leverage complementary strengths and mitigate individual weaknesses. As a case example, they map biopsychosocial feedback mechanisms underlying the course of depressive symptoms in response to a stressor among healthy adults using data from the Healthy Brain Study, aiming to evaluate how triangulation affects CLD development in terms of comprehensiveness, feedback structure, and uncertainty transparency.

Literature reviews were conducted iteratively after each GMB session for every newly proposed causal link. Evidence was sought for longitudinal associations, robustness across studies, temporal precedence, experimental support, and plausible mechanisms. The review informed revisions to the expert CLD: the updated diagram contained 31 links. For four links, no literature was found; two of these were removed (Daily hassles → Sleep disturbance; Proinflammatory cytokines → Perceived stress) after further expert discussion deemed them less plausible. Two links without supporting literature (Depressive symptoms → Perceived stress; Perceived stress → Sleep disturbance) were retained as plausible but labeled hypothetical (dotted arrows). The review also prompted reorientation of one link: Proinflammatory processes → Loneliness was revised to Loneliness → Proinflammatory processes. During final triangulation, literature was also used to arbitrate discrepancies between GMB and causal discovery; links suggested by causal discovery but absent from GMB were added when literature support existed, and some were retained as plausible despite absent literature when experts judged them reasonable.

Design: Mixed-methods triangulation to build a biopsychosocial CLD by integrating (1) expert-driven GMB, (2) targeted literature review for each proposed link, and (3) data-driven causal discovery on longitudinal cohort data.

Setting and data: Healthy Brain Study (HBS), a population-based cohort of healthy adults (30–39 years) with three assessments over one year (approximately 4-month intervals). A cohort subset was defined once 300 participants completed the third assessment; baseline measures were available for 403 participants, with varying completeness across time points. Variables operationalized CLD constructs across biological (e.g., pro/anti-inflammatory cytokines), psychological (e.g., perceived stress, depressive symptoms, rumination, mindfulness), behavioral (e.g., sleep disturbance, smoking, physical inactivity, prosocial behavior), and social (e.g., loneliness, perceived social support) domains. Context variables (sex, education) were included in causal discovery as exogenous covariates.

GMB process: Experts from social, behavioral, psychological, and biological domains (four domain experts total) identified and mapped causal links among 14 core variables selected via nominal group technique. Seven one-hour online GMB sessions (Sep 2022–Jan 2023) plus supplemental meetings were held, facilitated by the corresponding author. Consensus was required for inclusion. After each session, the proposing expert performed a literature review for new links.

Causal discovery: Applied J-PCMCI+ (implemented in Tigramite v5.2), a constraint-based time-series causal discovery algorithm suitable for multiple datasets (participants) and mixed data types. It infers an undirected graph via conditional independence testing, then orients links using graphical rules. Assumptions include causal Markov and faithfulness, acyclicity of contemporaneous links, stability of causal structure over time and across individuals, and no unobserved confounders except those constant across time/contexts when modeled. Independence testing used RegressionCI (linear/logistic regression-based), with significance level p_c = 0.05. Both contemporaneous and lag-1 (six months) links were considered; with three assessments, at most one lag was estimable. Sex and education were included as context variables. Missingness was handled via sliding-window sampling using only complete windows per participant. Link strengths were quantified by standardized regression coefficients regressing each destination on its parents from the discovered graph. Polarities were inferred from coefficient signs.

Triangulation: A final two-hour GMB session (Sep 2023) integrated evidence from GMB, literature, and causal discovery. Rules for link adjudication: (1) retain links supported by both GMB and causal discovery; (2) for links supported by causal discovery but not GMB, include when plausible and preferably supported by literature; (3) for links supported by GMB but not by causal discovery, reevaluate primarily if literature support was absent; consider indirect pathways suggested by causal discovery conditional independencies. Undirected links (o–o) from causal discovery were treated as potential evidence for either direction when consistent in polarity and not contradicting directed evidence. Sensitivity analyses examined different significance thresholds, alternative independence tests, and a complete-case subset (N=51) to assess robustness to attrition.

• Group model building (GMB): Experts mapped 33 links among 14 variables across biological, psychological, behavioral, and social domains; full consensus was achieved.
• Literature review: Updated the CLD to 31 links. Four links had no literature; two were removed (Daily hassles → Sleep disturbance; Proinflammatory cytokines → Perceived stress), two retained as hypothetical (Depressive symptoms → Perceived stress; Perceived stress → Sleep disturbance). Direction of Proinflammatory processes ↔ Loneliness reversed to Loneliness → Proinflammatory processes.
• Causal discovery (J-PCMCI+): Identified 12 links (contemporaneous and lagged). Examples with standardized coefficients include: Daily hassles o–o Perceived stress (+0.58, p=1e-5); Perceived stress o–o Depressive symptoms (+0.50, p=0.001); Sleep disturbance o–o Depressive symptoms (+0.26, p=0.01); Depressive symptoms o–o Loneliness (+0.12, p=0.004). Links not initially in GMB included, e.g., Body mass index → Perceived social support (−0.46, p=0.008), Mindfulness → Loneliness (−0.13, p=0.003), Sleep disturbance → Prosocial behavior (−0.04, p=0.02), Perceived stress → Mindfulness (−0.18, p=2e-5). A contemporaneous link Anti-inflammatory processes ↔ Proinflammatory processes showed positive polarity; experts deemed the discovered direction likely reversed, supporting a balancing loop Proinflammatory → Anti-inflammatory. Sensitivity analyses showed: changing significance level or independence test yielded similar graphs with some links missing; restricting to complete cases (N=51) reduced overlap (6/11 links), indicating attrition sensitivity.
• Triangulation outcome: Final CLD contained 36 links.
  • Five links were supported by both GMB and causal discovery and were retained; undirected links prompted considering both directions, leading to addition of Depressive symptoms → Sleep disturbance (subsequently supported by literature).
  • Of seven links suggested by causal discovery but absent from GMB, five were added (based on plausibility and/or literature), one was reinterpreted in the opposite direction (Proinflammatory → Anti-inflammatory), and one (Loneliness → Perceived social support) was not added due to implausibility and lack of literature.
  • For GMB-only hypothetical links without literature, experts re-evaluated. The direct link Sleep disturbance → Perceived stress was removed in favor of an indirect pathway Sleep disturbance → Depressive symptoms → Perceived stress; Perceived stress → Sleep disturbance was retained due to supporting literature.
• Overall effects of triangulation: Increased comprehensiveness (additional links across domains), modified feedback structure (e.g., removal of reinforcing Perceived stress ↔ Proinflammatory loop; introduction of Body mass index ↔ Perceived social support feedback), and enhanced transparency about uncertainty (visual encoding of agreement and evidence).

Triangulating domain expertise, literature evidence, and data-driven causal discovery improved the quality of the CLD in three ways. First, comprehensiveness increased by adding plausible links missed by experts and by revising or removing weakly supported connections. Second, the feedback structure was refined: some reinforcing loops were removed or reoriented, and new loops spanning multiple domains emerged, which are crucial for understanding nonlinear system behavior. Third, uncertainty became explicit by distinguishing links with convergent evidence from those with limited or conflicting support, guiding priorities for further research and enabling uncertainty-aware simulation. The case example highlights potential self-reinforcing pathways in depressive symptom trajectories, such as short reinforcing loops involving Depressive symptoms with Perceived stress, Loneliness, Sleep disturbance, and Proinflammatory processes, as well as cross-domain pathways linking biological states (e.g., inflammatory processes, BMI) to social/behavioral outcomes (e.g., perceived social support, prosocial behavior). Causal discovery complemented expert knowledge by proposing links outside individual disciplinary perspectives, while the participatory GMB process fostered consensus and coherence. The findings suggest triangulation can yield more reproducible and valid causal diagrams and can inform subsequent system dynamics modeling, model comparison under uncertainty, and targeted intervention design. Determining optimal workflows for integrating methods warrants further empirical evaluation across contexts and datasets.

The study demonstrates a practical mixed-methods triangulation framework for constructing biopsychosocial causal loop diagrams by integrating group model building, literature review, and causal discovery. Applied to depressive symptom trajectories in response to stressors among healthy adults, triangulation produced a more comprehensive CLD, refined feedback loops, and increased transparency about evidential uncertainty. This approach encourages critical examination of expert assumptions, highlights data-driven insights, and identifies research gaps. Future work should: (1) scale triangulation with more systematic or AI-assisted literature assessment; (2) extend causal discovery to larger, multi-study panels and alternative algorithms; (3) explore initiating with data-driven discovery followed by expert interpretation and constraint-based refinement; and (4) broaden variables and time frames (e.g., additional neurobiological measures, longer follow-up). The evolution of causal discovery methods and interdisciplinary collaboration platforms may streamline triangulation and enhance the development of valid computational models and effective interventions for complex health problems.

• Data limitations: Only three assessments over one year constrained temporal resolution and detection of feedback operating at shorter timescales; substantial missingness and selective attrition affected robustness (complete-case sensitivity showed reduced link overlap).
• Confounding: Limited ability to account for unobserved confounders beyond context variables (sex, education); J-PCMCI+ assumptions (causal Markov/faithfulness, contemporaneous acyclicity, stability) may be violated in practice.
• Measurement issues: Mixed-type measures and potential measurement error could bias conditional independence tests and link estimation; some variables may change at different rates, limiting detectability.
• Literature review scope: Reviews were targeted rather than fully systematic across all possible pairs due to feasibility constraints, potentially missing evidence.
• Process complexity and resources: Triangulation is time-consuming and involves managing conflicting findings; balancing thoroughness with efficiency is necessary.
• Generalizability: Case example focused on healthy adults aged 30–39 and a selected set of variables; findings and the resulting CLD structure may not generalize to other populations or broader time frames.