Computational Modelling Reveals Slower Safety Learning and Threat Extinction are Associated With Higher Anxiety Severity in Remote Fear Conditioning

Anxiety disorders

Approximately one third of individuals are likely to have an anxiety disorder at some time in their lives (Bandelow & Michaelis, 2015). These disorders typically begin in the second or third decade of life (Kessler et al., 2005; Kessler et al., 2012), and given their treatment resistance (Bystritsky, 2006), impart a high societal cost. Central to the diagnosis of any anxiety disorder is pathological anxiety, which generates the pathognomonic symptom clusters which interfere with the activities of normal life (National Institute for Health and Care Excellence [NICE], 2014). Whilst normal anxiety describes the state, comprising subjective and physiological responses combined with behavioural urges, elicited by non-imminent threats (LeDoux & Pine, 2016), pathological anxiety denotes where the subjective, physiological, or behavioural responses are excessive in relation to the level of threat, or persist long after the initial event (Rosen & Schulkin, 1998). Given the role of anxiety in providing an adaptive response to novel threats, whilst facilitating exploration when threats are no longer relevant, experimentally probing the associative learning mechanisms underpinning threat responding may shed light on anxiety disorder development or persistence.

Fear conditioning

Fear conditioning is a commonly used aversive learning paradigm, capable of revealing several facets of threat processing – threat learning, safety learning, and threat extinction (Lonsdorf et al., 2017a). Typically beginning with an acquisition phase, threat learning is invoked when an initially neutral cue is repeatedly paired with an aversive stimulus. At each presentation of the cue, the conditional, anticipatory threat responding can be measured via physiological, behavioural, or self-reported changes. Whilst not a finding replicated by a subsequent meta-analysis, anxiety disorder patients have been shown to exhibit greater physiological responding to conditional threat cues (threat cue, CS+) (Lissek et al., 2005). Interestingly, depressive patients are shown to exhibit impaired fear acquisition, suggesting separate mechanisms may underpin these two often comorbid diagnoses (Luo et al., 2024; Otto et al., 2014; Wurst et al., 2021).

Safety learning is invoked through concurrent control trials included within the acquisition phase, where a different neutral cue is presented with no aversive pairing (safety cue, CS–). The strength of responding to the CS+ and CS– by the end of acquisition training can be compared to establish threat discrimination. Reduced threat discrimination, the ability to distinguish threatening from safe cues, is widely seen in both children and adults with anxiety disorders; predominantly a result of increased threat responding to the safe cue (Craske et al., 2008; Duits et al., 2015; Waters et al., 2009).

During extinction the CS+ is repeatedly delivered without an aversive pairing, lessening the strength of conditional responding. However, impaired threat extinction is often seen in anxiety disorder patients, and is likely a separate learning process from threat acquisition (Duits et al., 2015). There is some evidence to suggest this process is also altered in depression (Dibbets et al., 2015; Wurst et al., 2021).

Fear conditioning paradigms allow the investigation of these distinct learning processes and their role in pathological anxiety (Yamamori & Robinson, 2023). Typically, fear conditioning is performed in the laboratory, however, there is an increasing desire to expand both sample size and diversity beyond the confines of laboratory-based procedures (Gillan & Rutledge, 2021; Ney et al., 2023). Our Fear Learning and Anxiety Response (FLARe) smartphone app enables the remote collection of fear conditioning data (McGregor et al., 2022). Previous research using FLARe demonstrates impaired threat discrimination in anxious subjects, in line with the prior meta-analytic studies of fear conditioning (McGregor et al., 2021).

Computational modelling

Fear conditioning data can be measured in a number of ways, before associations with anxiety severity are subjected to formal hypothesis testing. Descriptive measures of fear conditioning data, such as comparing the difference in average responding to CS+ and CS– across a whole phase (threat discrimination), only highlight the presence of an effect, rather than the mechanism subtending the effect. The arbitrary selection of which data points to average, or which measure to use, also results in analytic flexibility within the literature (Lonsdorf et al., 2022; Ney et al., 2018). Standard linear statistical models go further, identifying patterns across trials, however still fail to account for the highly heterogeneous subject level trial by trial dynamics seen in fear conditioning data. Attempts to capture all variance with increasing orders of polynomial curves or machine learning approaches can lead to overfitting and issues of interpretation (Bennett et al., 2019; Huys et al., 2016). In a hypothesis-driven manner, generative computational modelling tests different proposed learning mechanisms against one another, and establishes which mechanism offers the best explanation of the observed data (Friston et al., 2017). The individually fitted free parameters underpinning the proposed mechanisms, such as the learning rates of threat learning, safety learning, and threat extinction learning, can be used to test associations with anxiety severity (Yamamori & Robinson, 2023). Individual differences in these rates, and their associations with anxiety severity, have been demonstrated in both remotely delivered aversive learning tasks (Pike & Robinson, 2022), and laboratory-based fear conditioning tasks (Abend et al., 2022; Gershman & Hartley, 2015; Tzovara et al., 2018). Interestingly, there is some evidence that patterns in learning rates differ between anxiety and depression (Cavanagh et al., 2019), and that computational approaches may be suited to exploring such differences (Huys et al., 2016). However, this modelling approach has yet to be deployed in a remote study of fear conditioning.

Summary

This study modelled individual differences in fear conditioning learning rates, using data from a smartphone delivered paradigm, and examined their associations with anxiety severity. In line with the existing literature, we pre-registered several hypotheses to test these associations – that threat learning rate would positively correlate with anxiety severity, whereas safety learning, and threat extinction learning rates, would show negative associations with anxiety severity.

Sample

In total, n = 235 participants were tested in this study, pooled from three prior studies. Some were pooled from two of our FLARe app validation studies (n = 47 and n = 68, from studies one and two described in Table 1) (Purves et al., 2019). A later, unpublished validation study recruited n = 120 participants (study three in Table 1).

The additional participants comprising study three were recruited via the King’s College London trial recruitment portal. Participants responded to an advert and were followed up with instructions from the research group if they met the inclusion criteria – adults between the ages of 21 and 26, with no documented neurological, cardiac, or psychiatric history, and owning a smartphone. Participants were paid £15 if they completed the study. The study was approved by the Kings College London Psychiatry, Nursing and Midwifery Research Ethics Subcommittee (reference HR15/16-2349).

Task

A fear conditioning paradigm was delivered remotely, via the Fear Learning and Anxiety Response (FLARe) application, which was downloaded and installed onto participants’ smartphone devices. Participants followed instructions relating to the set-up of the experiment, asking them to connect headphones, set their device volume to maximum, and complete the subsequent experiment alone in a quiet room. Task-specific instructions were then delivered.

First, participants were presented with a sequence of conditional stimuli (CS) on screen. These were two differentially sized coloured circles. One circle was usually reinforced (CS+) with the unconditional stimulus (US), an unpleasantly loud noise of 500 ms duration played through headphones. The other circle was always non-reinforced (CS–). The stimuli serving as CS+ and CS– were counterbalanced between participants. At each presentation of CS, participants were asked to rate the certainty with which they expected to hear the US (Figure 1).

Figure 1

The fear acquisition phase consisted of 24 trials in a pseudo-randomised order, twelve trials each of CS+ and CS–. US occurred on 75% of the CS+ trials, i.e. nine of the twelve CS+ trials. Each trial was eight seconds in duration, participants entered their US expectancy rating after three seconds. Each trial was separated by an inter-trial interval of either one, two, or three seconds duration.

Following a ten minute break, in which participants completed questionnaires, participants completed the fear extinction phase, where 36 unreinforced trials were presented to participants, 18 each of CS+ and CS–. At no point was a US delivered. Participants entered their US expectancy rating during each trial, as per the acquisition phase. The extinction phase was longer than acquisition to increase the chances of full extinction despite remote delivery.

Compliance with the task procedure was assessed through a post-experiment questionnaire, where participants were asked if they removed their headphones, or restarted the application at any point (with the caveat that participants would still receive remuneration if they answered yes to these questions). Participants were also asked how unpleasant they found the US on an integer scale of 1–10, and whether they established contingency awareness (i.e. awareness of the pairing between the US and the CS+). Finally, objective data, such as headphone volume manipulation, and application restarts, was automatically gathered by the software (McGregor et al., 2022).

Safety

The maximal volume deemed safe to be deployed on participants for the 4.5 seconds of unconditioned stimulus was estimated by the formula:

The maximal volume outputted by most commercial headphones is estimated to be 110dB, well within our permitted safety level.

Measures

Exclusions

In line with previous studies using the FLARe app, participants who removed their headphones, reduced their headphone volume to below 80% of the maximum, restarted the application during either phase, or rated the unpleasantness of the US as less than five (out of ten) were excluded from the analysis, leaving a ‘medium’ exclusion sample.

Statistical analysis

Conventional descriptive measures of fear conditioning were initially applied to the data, to allow comparison with the novel computational modelling approaches. These were 1) end phase CS discrimination – the difference between the US expectancy rating for CS+ and CS– at the final trial of either phase, and 2) the mean of the US expectancy ratings for each CS and phase. These offered a subject level measure of threat sensitivity, and a crude account of the trial data preceding end phase scores. Both measures were correlated with GAD-7 scores, to examine associations between fear conditioning measures, and anxiety severity. Non-parametric Wilcoxon Signed Rank tests were used to assess CS discrimination, given the bounded and therefore non-normal distributions of expectancy rating data. Likewise, given the zero-inflated, ordinal nature of the GAD-7 score, the non-parametric Spearman’s rho correlation was used to estimate associations.

Computational modelling

Twenty eight Rescorla Wagner associative learning models were fitted to the data, with estimated individual learning rates weighting the trial-by-trial, error based latent updating which produces participant responding. The individual learning rate parameters within the models were estimated through hierarchical Bayesian modelling, whereby estimated group level hyperparameters influence subject level parameters. Bayesian model selection identified a best fitting model, from which individual median point estimates of learning rates were extracted and correlated to measures.

Parameter estimation

The models were fit within a hierarchical Bayesian framework. Group level hyperparameters were estimated, which constrained the subject level parameters estimated (Figure 2). Prior predictive checks were performed on all models and visually inspected to ensure hyperparameter compatibility with the underlying task structure. Uninformative priors and hyperpriors were used to allow the models to reflect the data without undue influence from the models, except for the lapse parameter which had a more informative prior (Equation 5). For learning rate, start value, and jump parameters, group level gamma hyperpriors were used to constrain the hyperparameters to positive numbers. The subject level parameters were then derived from a beta distribution, which inherently constrained the parameters within the interval [0,1]. The component shape hyperparameters were iterated by one to ensure the beta distribution did not invert. The lapse parameter, requiring a lower bound of zero, but with values near zero not desired, was derived from a gamma distribution hyperprior. The hyperparameters were also derived from gamma distributions, informed by testing, and previous literature which suggested values of around five to balance model flexibility against precision.

5

$\begin{array}{l}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}L{R}_{\mathit{\text{shape}}1}^{\mathit{\text{Group}}}\hspace{0.17em}\sim \hspace{0.17em}\mathit{\text{Gamma}}\left(0.5,1\right) \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}L{R}_{\mathit{\text{shape}}2}^{\mathit{\text{Group}}}\hspace{0.17em}\sim \hspace{0.17em}\mathit{\text{Gamma}}\left(0.5,1\right) \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}L{R}^{\mathit{\text{Subject}}}\hspace{0.17em}\sim \hspace{0.17em}\mathit{\text{Beta}}\left(L{R}_{\mathit{\text{shape}}1}^{\mathit{\text{Group}}}+1,\hspace{0.17em}L{R}_{\mathit{\text{shape}}2}^{\mathit{\text{Group}}}+1\right) \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathit{\text{Laps}}{e}_{\mathit{\text{shape}}}^{\mathit{\text{Group}}}\hspace{0.17em}\sim \hspace{0.17em}\mathit{\text{Gamma}}\left(5,1\right)\\ \mathit{\text{Laps}}{e}_{\mathit{\text{inv}}\_\mathit{\text{scale}}}^{\mathit{\text{Group}}} \sim \hspace{0.17em}\mathit{\text{Gamma}}\left(5,1\right) \\ \hspace{0.17em}\hspace{0.17em}\mathit{\text{Laps}}{e}^{\mathit{\text{Subject}}}\hspace{0.17em}\sim \hspace{0.17em}\mathit{\text{Gamma}}\left(\mathit{\text{Laps}}{e}_{\mathit{\text{shape}}}^{\mathit{\text{Group}}},\hspace{0.17em}\mathit{\text{Laps}}{e}_{\mathit{\text{inv}}\_\mathit{\text{scale}}}^{\mathit{\text{Group}}}\right)\end{array}$

Figure 2

Data were simulated using fixed predefined hyperpriors to generate fixed parameters and therefore data. Each model was fitted to these data, with Markov chain Monte Carlo (MCMC) sampling used to estimate posterior probability distributions for each parameter. The median value with 95% credible intervals (95CI) of these posteriors was used as the parameter estimate, which were compared to the known input parameters. Recovery was deemed successful if the 95CI of the posterior estimate contained the true value of the parameter.

Other diagnostic checks were performed to assess chain convergence, with an R ̂ of less than 1.01 considered acceptable. Each model was then fitted to participant data using 500 warm-up iterations, and 500 sampling iterations. Following model selection, the winning model was re-run using 2000 sampling iterations to ensure maximum accuracy for parameter estimates.

Measures

Task

Computational modelling

MCMC computational checks

All models tested achieved post-warmup chain convergence, with no model displaying a Gelman-Rubin statistic (R̂) above 1.01, nor were any divergences discovered. Visual checks of hyperparameter traceplots and rank plots supported this quantitative assessment of convergence (Baribault & Collins, 2023). Posterior predictive checks were performed to assess model fit, with the model generating data which closely matched the observed data upon visual inspection (Figure 3, panel A). This was corroborated quantitatively, with the whole phase mean of generated data compared to whole phase means of participant data through correlation (Figure 3, panel B). This demonstrated that, on average, individual differences in generated data matched that of real data, and that the model is capturing observed behaviour.

Figure 3

Associations of computational parameters with anxiety severity

Residual analysis

The residual scores for GAD-7 and PHQ-8 failed to display significant associations with the safety learning or threat extinction learning rates. However, the shared variance component remained significant in both (ρ = –0.18, p = 0.03 & ρ = –0.24, p < 0.01 respectively).

Sensitivity analysis

The total sample was reduced to n = 88 following the application of strict exclusion criteria indicating task inattentiveness or non-compliance. No significant differences were noted in outcome measures between the groups before and after the exclusion criteria were applied (Table 1).

In this sample, the associations between the threat extinction and safety learning rates and anxiety severity were stronger and remained significant (ρ = –0.32, p < 0.01 & ρ = –0.33, p < 0.01). However, in addition, the learning rate towards unreinforced trials in acquisition phase CS+ trials became negatively associated with anxiety severity (ρ = –0.30, p < 0.01).

Examining the residual scores in this sample, the association between GAD-7 residual and safety learning rate was significant (ρ = –0.28, p < 0.01). The associations between all other residuals and all other learning rates were non-significant, with the shared variance significant in threat extinction (ρ = –0.31, p < 0.01), safety learning (ρ = –0.22, p = 0.04), and learning rate towards unreinforced trials in acquisition phase CS+ trials (ρ = –0.26, p = 0.01).

Steigers Z comparison of correlations

Although the relationship between computational parameters and anxiety severity was uniformly higher than the corresponding descriptive measure associations, these differences were not significant where direct comparisons were possible (Table 5).

Limitations

Remotely collected data inherently lacks experimenter control, and therefore adherence to the task cannot be guaranteed. As a result, the attrition from the initial sample to the two test groups was large, although consistent with other remote fear conditioning paradigms (Berwian et al., 2024). This is likely compounded by the repetitive and aversive nature of the task. These biases are partially offset through questioning the subjects following the task, including questions about headphone removal or contingency awareness. There is no guarantee these questions are answered honestly, so the biases cannot be completely discounted. Only a third of participants engaged with the task as fully intended, surviving the strictest exclusion criteria. Indeed, model fit, and associations with anxiety, were strengthened when maximally controlling for deviations from the task, indicating that these control measures offset some of the disadvantages posed by the limitations of remote collection. The large sample sizes collected through FLARe further offset the loss of sample size through the application of exclusion criteria.

Aversive auditory unconditional stimuli are increasingly used in lab based fear conditioning (Hyde et al., 2024; Lonsdorf et al., 2017), appearing to generate physiological fear responding alongside contemporaneous responding via self-report measures (Sperl et al., 2016). Our remote study assumes this US-response relationship is maintained, not least through exclusion criteria ensuring volume was high or maximal, and headphones were not removed. However, we cannot exclude the possibility that instead the US offers a cognitive aversive stimulus, more analogous to those seen in bandit tasks (Yamamori & Robinson, 2023). Unfortunately, highly temporally resolved physiological measures are unavailable on current consumer smartphone technology, so the absence of this measurement modality remains a limitation of the remote approach.

The GAD-7 anxiety measure was taken mid-task, where participants are in a conditioned fear state. Although the GAD-7 scale is retrospective, it is likely biased by current state anxiety, ergo by the fear conditioning task. Whilst the state bias is likely to be consistent across all individuals, an impact on the associations between learning rates and GAD-7 anxiety severity cannot be ruled out (Tang & Gibson, 2005). It should also be noted that the GAD-7 scale is predominantly a measure of generalised anxiety disorder, whereas fear conditioning is shown to be more relevant to fear-based disorders, including specific phobias and PTSD (Lonsdorf & Merz, 2017). These disorders tend to have a specific threat at their core (analogous to a specific CS), in contrast to the more abstract or distal threats perceived in generalised anxiety disorder. Therefore, we might expect to see even stronger associations towards a measure of fear-based disorders.

The standard Rescorla Wagner model is sufficiently parameterised for estimating individual differences in learning rates, but is by no means fully accounting for all responding variance, most notably in acquisition CS- trials, where responding is occasionally seen to increase in early trials, against the direction mandated by the model. This is likely due to other cognitive and learning processes co-occurring during the task (Lonsdorf et al., 2017b), most likely a counter-factual or fictive updating process, with a direction change in later trials. The lapse parameter attempts to account for these overlapping cognitive processes, in addition to measurement error. However, more advanced models might better account for this ‘deviance’ from the Rescorla Wagner model, including counter-factual reasoning and reversal learning models (Gershman & Hartley, 2015; Zika et al., 2023).

Unfortunately, exploratory models tested on this current dataset, using counterfactual or fictive updating, failed to adequately recover parameters of interest, and produced divergences when fitted to real data (Supplementary Methods & Supplementary Results) (Baribault & Collins, 2023). These issues likely stem from, and are compounded by, the relative lack of trial-by-trial data available for each phase, compared to analogous modelling tasks in the literature using hundreds of trials (Pike & Robinson, 2022).

Likewise, the fixed severity, and unidirectionally valenced US, precluded any attempts to fit models with additional ‘punishment sensitivity’ parameters, which have previously demonstrated associations with anxiety in avoidance paradigms (Mkrtchian et al., 2017; Yamamori et al., 2023). However, the winning model used separate learning rates, contingent on US delivery, in the acquisition phase CS+ trials. This captured differential responding to reinforced and non-reinforced trials, analogous to the use of punishment and reward sensitivity parameters in other paradigms. Here, in contrast to some findings in the avoidance learning literature, we demonstrated no association between threat learning (cf. punishment sensitivity) and anxiety severity.

Other studies suggest probabilistic models may better account for fear conditioning, albeit using physiological conditioned responses with far greater response noise and measurement error (Tzovara et al., 2018).

Future work

Future work may look to add complexity to the task structure, generating data in which models would have stronger predictive power over descriptive measures. In addition, confirmatory studies using the more stringent exclusion criteria, to counterbalance the lack of experimenter control inherent to remotely delivered paradigms, may further strengthen the associations elicited through computational modelling.

This study cannot ascribe a direction to the mechanism demonstrated. It is reasonable to suggest that those with a pre-existing slow learning rate may be at risk of developing anxiety disorders, but equally it could be the case that those with anxiety disorders then develop a slow learning rate as a symptom, contributing to the persistence of the disorders. Future work might look to repeat this novel approach longitudinally to establish a causal direction.

Summary

Computational modelling offers a credible account of the learning processes contributing to anxiety severity, complimenting the traditional descriptive measures which can only hint at them. This theory driven, reproducible analytic method paves the way for larger scale studies using similar computational modelling in smartphone delivered paradigms, to further instigate these novel mechanistic insights into anxiety.