Bridging the gap between complexity science and clinical practice by formalizing idiographic theories: a computational model of functional analysis

Current movements in psychotherapy strongly align with technical advances in dynamical modeling tools—yet their implementation in clinical practice is rather scarce. To bridge this gap, we call for a stronger focus on tools that make use of frameworks and theories embedded in clinical practice. In this paper, we discussed the formalization of idiographic theories, through the use of differential equations, as an alternative to data-driven network modeling approaches. Our main objective for promoting the use of formalized idiographic theories is that data models cannot always account for considerations relevant to clinical practice. In consequence, even though techniques seem to be promising in analyzing patient data, their implementation might be hampered due to the lack of options to incorporate theoretical and practical considerations. This barrier can be addressed through grounding dynamical systems in the theories of practitioners. Differential equations are commonly used in a variety of other scientific fields to describe systems, and are a promising avenue for formalizing theories of mental health.

To illustrate this approach, we formulated a computational model based on dynamics of the functional analysis for a patient suffering from panic disorder and examined implications for the case conceptualization and the effects of commonly applied CBT interventions. The results of the simulations are largely congruent with phenomena observed in clinical practice and in line with predictions of other theoretical frameworks. In the following, we discuss further benefits for clinical practice, concrete examples for theory adaptation, and future directions.

We identify at least five benefits from formalizing case conceptualizations in respect to challenges faced in clinical practice.

One of the main advances in mental health care over the past decades is its increasing focus on scientific practices. The introduction of the scientist-practitioner model [54] was an attempt to strengthen scientific practices in psychotherapy, for instance through theory-guided hypothesis testing. It became vital for designing patient-tailored psychotherapy to formulate a testable theory regarding intervention effects. The case conceptualization is an example of a framework for such scientific theories in clinical practice. However, if a theory is vague, the resulting hypotheses, predictions, and tests become scientifically questionable [45]. Especially in the current landscape of replicability issues [55, 56], we see value in enhancing theory development through formalizing idiographic systems in clinical practice. As became evident in this report, especially when comparing the initial verbal theory in Fig. 2 to the system of differential equations, the process of formalizing idiographic theories is mostly a process of increasing specificity, in which clinicians need to thoroughly reflect on and justify all relations between system variables.

While the model used in this paper uses concepts that are relevant for a broader range of patients suffering from panic disorder (generic approach), there are many individual differences in how exactly these relations should be specified. For instance, patient A might have more exposure to their discriminant stimulus in their everyday life compared to patient B, or patient C has stronger avoidance tendencies than patient D. These considerations can be reflected in altering the parameters in the system, aligning this approach with the idea of idiographic modeling. Further, specific components in the system can be added/removed, if applicable for a given individual. The framework of functional analysis is transdiagnostic in nature and can be applied to a broad range of disorders that involve dysfunctional coping, for example, substance abuse, post-traumatic stress disorder, obsessive-compulsive disorder, and depression.

Functional analysis provides a framework that allows explaining the function of maladaptive behavior and helps understanding symptom maintenance. The explanatory character of these verbal theories can be advanced through formalization, since case conceptualizations can subsequently be evaluated in respect to how well they can reproduce clinical phenomena [46, 47]. If a case conceptualization fails to explain relevant phenomena, this will more easily be detected if data is simulated from a formalized case conceptualization, compared to a verbal theory.

While computational modeling can foster the development of theoretical relations, it is also a useful tool for predicting theory-implied system behavior under given interventions. Most relevant for clinical practice, this allows the clinician to examine the effects of formalized clinical intervention in silico. Testing interventions in computational models offers efficient insight into intervention effects without having to collect data.

Simulation outcomes of a formalized idiographic theory can be beneficial for didactics in clinical practice. First, visualizing the simulation results allows the clinician to collaboratively examine symptom dynamics with the patient. This can be used in the process of psychoeducation, and communicating a treatment rationale, especially for interventions that might be aversive for the patient (e.g., exposure). Second, in the long term, we see potential in implementing formalized idiographic theories to enhance more concise communication between clinicians through more rigorous documentation and visualization.

A main benefit to formalizing idiographic theories is that simulated data can directly be compared against expected/reported behavior in the patient. One potential interpretation of discrepancies between simulated data and clinical phenomena is that the case conceptualization in its current form cannot account for potentially relevant clinical phenomena, for instance, if important relations or variables are missing. If this is the case, the clinician might want to adapt specific theoretical relations until the simulated data adequately represents clinical phenomena. This is crucial when testing formalized interventions in a patient’s system.

In some aspects, the computational model presented in this paper is congruent with clinical phenomena, while in other aspects theory adaptation might be needed. Note that the set-up of the simulation represents panic-symptomatology experienced by one hypothetical individual. Phenomena observed in simulations might differ if parameters are altered, which allows capturing individual differences in experiencing panic symptoms, and differences in treatment response. First, the simulations showed that for this patient, persistent avoidance behavior is accompanied by increasing tendencies to catastrophize and increasing credibility of the catastrophic interpretation. This finding highlights the role of falsification in fear disorders; avoidant coping is associated with a lack of opportunities to falsify the catastrophic interpretation, subsequently leading to increasing tendencies to experience panic in confrontation with discriminant stimuli. Second, the simulations indicate that all interventions (exposure, cognitive reappraisal, and combination) are effective in decreasing panic tendencies for this patient, which is in line with empirical studies testing the efficacy of CBT interventions for panic disorder [57]. Third, the simulation results showed that panic manifests in the long term, if no intervention is applied. This finding does not seem to adequately represent the experience of panic attacks, since these usually emerge rapidly and decline after a short amount of time. To account for this feature of panic attacks, we propose to model stronger decay of panic. Alternatively, one could conceptualize this variable as a tendency to experience panic in the presence of the discriminant stimulus, rather than the actual experience of panic itself.

The approach of formalizing idiographic theories is still fairly new to clinical psychology, and there is a lot of research that needs to be conducted to help implementing it in clinical practice. In this section, we aim to give some directions for future research.

A crucial barrier for implementation is that the explanations and predictions provided by a theory need to be as accurate as possible, especially if the aim is to test formalized clinical interventions; such interventions will depend heavily on the accuracy of the model. We outlined that through comparisons of theory-implied and empirical data, systems can be evaluated to increase accuracy. Notably, any systematic comparison between theory-implied and empirical data models would require that variables used in data collection either directly map on to components in the theory, or that they can be precisely derived from those components. As outlined above, there are many elements in idiographic systems that are difficult to capture in common forms of data collection (e.g., ESM data), suggesting direct mapping of theory components to variables in empirical data may be difficult. Accordingly, it will be necessary for researchers to not only formalize theories, but also the auxiliary hypotheses about measurement that link the theory components to the variables in empirical data. In this paper, we opted for modeling idiographic systems without restrictions to what can be operationalized and compared how well theory-implied data qualitatively resembles clinical phenomena based on expert discussions, but did not go through the process of formalizing our assumptions about measurement or deriving what should be expected in any given empirical data model.

Second, it needs to be noted that the origin of a potential mismatch between theory-implied and empirical data remains unknown. Such discrepancies can have a multitude of sources and can be ascribed to either shortcomings in the structure of the theory (e.g., missing crucial variables in the theory, mis-specified or missing relations between present elements of the theory), the set-up of the simulation (e.g., exact initial conditions, valid parameter values, input and boundary conditions), or shortcomings in empirical data collection and modeling (e.g., inappropriate modeling assumptions, measurement issues). Further, estimating parameters from non-linear time-series data is often difficult and undergoes strong limitations [58]. We call for future research to investigate systematic ways of identifying the core of such discrepancies.

Another barrier to implementation is that, in the current practice of formalizing idiographic theories, constructing a series of differential equations to formalize a patient’s system can be immensely challenging and requires technical expertise that is not part of psychotherapy trainings. To address this issue, we propose that methodologists elaborate on a set of functions relevant to relations between clinical variables that can readily be used by clinicians to formalize idiographic theories. To enhance accessibility, this set of functions could be implemented in an interactive tool to visualize variable interactions. Clinicians could then pick from this set and construct formalized systems without the need for understanding the mathematical background in depth. Further, implementation would greatly benefit from a procedure that allows clinicians to formalize idiographic theories using graphical tools. Such tools could incorporate a simple three-step procedure: In a first step, clinician and patient collaboratively specify variables and sketch relations between the variables. Second, they select the qualitative nature of these specified relationships from the aforementioned list. This step encompasses the derivation of differential equations adapted to clinical practice. Third, simulations are conducted and patient and therapist can interpret and explore symptom dynamics given the case conceptualization and the differential effects of interventions.

Recent investigations suggest that clinicians are skeptical regarding the utility of idiographic assessment approaches, specifically regarding ESM data collection and modeling techniques [24, 59]. While these surveys suggest that clinicians find idiographic data models to be generally intuitive and aligning well with their clinical reasoning, it was also found that clinicians are not always convinced that they can learn something new from idiographic data models. Further, recent studies suggest that there is little incremental information in time-series measures beyond mean levels and general variability [60] and that time-series effects show largely unacceptable reliability after partialling out redundancies with mean and variability [61]. It is important to note that these findings pertain to the utility of idiographic data models. As discussed above, these data models face several challenges in the clinical context (e.g., insufficient number of observations, time-scaling, measurement artifacts, modeling assumptions), offering a potential explanation for the questionable performance of time-series measures.

Formalized idiographic theories, on the other hand, aim to explain phenomena that can be observed in the patient. They do so by representing the system posited to give rise to the phenomenon. We outlined how formalizing such systems can foster theory development and therefore potentially help clinicians gaining insight into the effects of (formalized) clinical interventions. Valid inferences from such intervention simulations require clinicians to thoroughly evaluate their theories, and formalizing theories can help in doing so. We argue that, if proof-of-principle studies can support the hypothesis that formalizing idiographic theories improve treatment planning, this could greatly benefit clinical practice. However, to facilitate implementation, future research should conduct surveys with practitioners to understand potential barriers of implementing formalized idiographic theories.

We introduced two perspectives in constructing idiographic systems: First, a top-down approach in which generic factors are modeled and subsequently personalized through adapting parameters, and second, a bottom-up approach in which personalized factors are modeled directly—extending the search horizon to incorporate any factor that can be related to the patient’s system. In the present paper, we formalized a case conceptualization within the generic framework of functional analysis, using (primarily) linear equations. It is important to note that, especially when following the bottom-up approach of constructing idiographic systems for and with each patient, system dynamics should encompass not only linear, but also non-linear dynamics. Indeed, prior research examining the quality of system dynamics found that processes in therapy are often non-linear and chaotic [41, 62]. Such dynamics are, by definition, hard to predict and are heavily dependent on the specific set-up of the simulation; slight changes in the set-up of initial conditions and parameters might have dramatic effects on the simulated behavior. In such cases, it may only be possible to make broad predictions about expected behavior, for example, not when a panic attack will occur, but rather whether a system is vulnerable to such attacks. We encourage future research to further investigate how such dynamics should precisely be incorporated in the formalization of theories.

Computational models, as the one presented in this paper, can account for processes that occur within an individual, and explain psychopathology on the basis of reinforcing factors. However, it seems unrealistic that these processes occur in isolation, independent from a social context. Indeed, clinical reasoning often includes the influence of the social environment on certain psychological processes, for instance, the link between avoidant coping tendencies and a certain attachment style, or the influence of peers in substance use. Incorporating interactions between different systems could open doors to model these clinical phenomena. Future research could use methods from agent-based modeling to simulate social interactions between patient-specific computational models and investigate how these interactions can inform parameters or variables in the patient’s system.

In order for new techniques to be considered relevant to clinical practice, they should provide practitioners with a clear incentive, and a main incentive for psychotherapy is to improve treatment outcomes. For many health care systems, case conceptualizations form the starting point for hypothesis-driven intervention planning and execution. We expect that formalizing idiographic theories can improve the precision of intervention predictions, through enhancing explanatory and predictive precision in formulating case conceptualizations; however, this idea needs empirical support. We hope that future research will follow up on this hypothesis and provide us with proof-of-principle studies validating the utility of formal theories in enhancing predictive precision of case conceptualizations.