Compulsiveness drives evidence accumulation during ambiguity

Doubt can modulate our decision-making process. Although conceptually different, conflict (choice similarity: difficult or easy ) and uncertainty (individual reward-likelihoods: uncertain or certain ) are commonly related and often conflated. By posing as an evidence-accumulation problem, we assessed doubt, dissociating contextual conflict, and uncertainty and showed obsessive-compulsive disorder patients have specific impairments while processing difficult-uncertain contexts. It remains unclear whether this deficit is disorder-specific or a reflection of broader mental-health dimension. Multi-dimensional transdiagnostic approaches help to tease out the mechanistic nature (specific or usual) of clinical observations and their validity in sub-clinical populations. Here, we first aimed to validate our conflict-uncertainty analysis approach in a larger non-clinical cohort ( n>1300 ). Second, we assessed the relationship between decisional-parameters of difficult-uncertain contexts and a trans-diagnostic factor capturing individual differences in ‘compulsive-behavior and intrusive-thoughts’. We replicate our previous findings in a large, general population sample and highlight that the amount of evidence accumulated in difficult–uncertain scenarios increases functionally with compulsive-behavior and intrusive-thought emphasizing greater cautiousness. We further show that those with high social-withdrawal tendencies gather less evidence irrespective of context reflecting a ‘jumping to conclusions’ tendency in judgment. We attempt to bridge the gap between behavior and psychological markers by integrating trans-diagnostic and computational methods.


Introduction
Doubt can influence our decisions from the mundane: 'did I turn off the stove?' to the consequential: 'Should I change my job?', or 'Should I go to the pub at the end of lockdown?' Obsessive-compulsive disorder (OCD) [1][2][3] has been postulated to be characterized by impairments in doubt, potentially triggering pathological symptoms such as checking or washing, which, following the execution of repeated actions 4-6 further increases the doubt 1 .
How doubt drives 'how' or 'what' we decide depends on context. Here we focus on contextual uncertainty and conflict. Individual features of choices such as value and the reward-likelihood form the basis for constructs such as conflict (based on similarity between choices: difficult vs easy), and uncertainty (based on individual likelihoods of obtaining a reward: uncertain vs certain). Though commonly related and often conflated, conflict and uncertainty are dissociable experimentally 7,8 and aid to capture the aberrant functioning of the underlying neural structures relevant to the disorder 1,[9][10][11][12][13] .
Uncertainty processing has specific relevance to OCD 1,14-18 , with 'doubt' being one of the central features thought to drive symptoms 1 . OCD patients experience higher subjective uncertainty, despite no differences in objective uncertainty 17 . This increased subjectiveuncertainty might reflect in repetitive behavior 19,20 particularly while processing ambiguous (where the probability of choices are unknown) rather than risky choices (where the probabilities are known) 14,21 . Concerning conflict, behaviourally, no differences in response time and accuracy were observed between OCD and healthy controls in a random motion kinetic dots task. But computational parameters estimated using a hierarchical drift-diffusion model (HDDM) showed an increase in the threshold parameter (which indicates the amount of evidence accumulated before a choice is selected) in OCD patients when the randomness of the dots increased 9 . OCD patients with higher doubt scores had low drift rates and lower certainty in their decisions 2 . Hauser and colleagues show increased thresholds 22,23 and decreased drift rates along with meta-cognitive deficits in individuals with higher compulsive traits 24 . In contrast, OCD patients show mixed findings with conflict monitoring 10,25,26 .
We devised a novel analysis to dissociate conflict and uncertainty using a sequential learning task 11 . Conflict reflects the difference between reward probabilities of the stimuli pairs and depends on the relationship between them whereas uncertainty reflects the variance in the probability of a single stimulus and is independent of the other. In healthy controls, we first showed that difficult-uncertain (where choices are similar and their individual likelihoods being uncertain) scenarios were associated with lower evidence accumulation. In contrast, OCD patients accumulated evidence (drift rate-v) more slowly in difficult-uncertain contexts with a generalized increase in the amount of evidence accumulated (threshold-a) 11 .
Multi-dimensional trans-diagnostic approaches, focused on identifying common mechanistic underpinnings across various psychiatric conditions for better diagnosis and outcomes, are attaining wide attention [27][28][29] . Using an integrated factor-based trans-diagnostic approach, Gillan and colleagues studied goal-directed behavior using the 2-step sequential learning task in a large cohort (n>1300) 30 . They showed that deficits are not specific when we look at disorder-symptoms in isolation, but that specific associations were recoverable, when transdiagnostic methods are used. Specifically, they revealed that deficits in goal-directed control were linked to a trans-diagnostic factor reflecting individual differences in 'compulsive behaviour and intrusive thought' 31 . A recent meta-analytic study also showed that subclinical OCD groups display low confidence levels while performing a range of cognitive tasks 32 . However, these effects might be an artefact of comorbidity: when co-occurring anxiety and depression symptoms are accounted for, compulsive individuals actually exhibit greater confidence in their decisions 29,33 .
Given that contradictory findings can emerge when using case-control studies versus transdiagnostic methods, a major gap remains in our understanding of behavioural and cognitive markers of decision making under conflict and uncertainty in mental illness. Here, we aim to address this issue by first testing if our previous findings of evidence accumulation in the context of conflict and uncertainty 11 would generalise across a larger non-clinical sample 31 .
We then examined the relationship between the computational estimates of decision making and the trans-diagnostic factors, hypothesizing that the amount of evidence accumulation in the difficult-uncertain context is related to individual differences in 'compulsive behaviour and intrusive thought'. Finally, we extracted the computational estimates independent to the context of conflict or uncertainty and explored their relationship with trans-diagnostic factors.

Participants
Data were analysed from a previously collected, open-source dataset 31 , gathered using the online platform Amazon's Mechanical Turk, where participants were paid a base rate ($2.50) in addition to a bonus based on their earnings during the reinforcement-learning task (M = $0.54, SD = 0.04). The participants were based in the USA (US billing address with an associated US credit card, debit card or bank account), with an age range between 18 to 76.
The research team were unknown of participants' identities. Informed consent was obtained from the participants, who provided their consent online by clicking 'I Agree' after reading information on the study and consent language following procedures approved by the New York University Committee on Activates Involving Human Subjects. The study was conducted and approved in accordance with the guidelines and regulations. For further details on recruitment, inclusion, and exclusion criteria please refer to 31 .

The sequential learning task
The task consisted of two stages (Figure 1a) 30 ; subjects chose between a stimulus-pair (fractals) at stage 1 (display for 2.5 seconds) which led to one of two stimuli-pairs (orange or blue) with a fixed probability (P = 0.70 (common) or 0.30(rare)). The choice of a stimulus at stage 2 (another set of fractals) led to a reward (25¢) or no reward) with probability gradually shifting based on a random Gaussian walk (P = 0.25 to 0.75, Figure 1b). Responses were made using the left ('E') and right ('I') keys. Subjects were allowed a decision time of 2.5seconds at each stage1, 1 second at stage2, and the outcome was displayed for 1 second.
The participants completed 200 trials. (See 31 for details).
Insert Figure 1 here

Hierarchical Drift Diffusion model (HDDM)
HDDM falls under the class of sequential sampling methods which utilize Bayesian methods to estimate the DDM parameters such as the threshold (a) and the drift rate (v), starting bias (z), and non-decision time (t). We focus our analysis on the first three parameters as t primarily concerns motor and non-decision-making processes. The Bayesian based HDDM, estimates parameters as posterior probability distributions with the mean of the distribution representing the group's average. The model utilizes the Markov Chain Monte Carlo sampling method to estimate the distributions. The prior distribution for each parameter was based on 23 studies that reported the best fitting DDM parameters for multiple cognitive tasks 34,35 . The pre-analysis code was written in MATLAB version 2018a and the built-in HDDM python package by 35 was used for the parameter estimation.
Trials with response times less than 50 ms were discarded from the analysis to ensure model convergence and to constrain the data to realistic response times. The parameters were estimated by drawing 120000 samples with the first 10000 samples being discarded as burnin and saving only every 10 th sample. The convergence of the model was assessed by visual inspections for the caterpillar type Monte-Carlo chains.

Analysis 1 -Context of Conflict and Uncertainty
We utilized our previous analysis to dissociate the concept of conflict (difficult vs easy) and uncertainty (uncertain vs certain) 11 . The methodology of the analysis is as follows.
We first calculated a measure of conflict per trial, using the reward probabilities of the stimuli at stage 2. The conflict variable (C) indicated the degree of similarity or dissimilarity between the reward probabilities for each stimulus-pair ( Figure- Where is the conflict variable, and is the reward probabilities of the transitioned stimuli 1 and 2 at stage 2 for trial i and subject j.
We then calculated uncertainty, which is dependent on the variance in the probability of a single stimulus and is independent of the other stimulus ( Figure-2a Where is the uncertainty variable, is the reward probability of the transitioned stimulus 'x' at stage 2 for trial i and subject j. The probabilities for each stimulus ranged For the accuracy based estimate, the individual conflict-uncertainty categories were collapsed and a single value of threshold and drift rate was estimated using choice (correct vs incorrect) and response time.
We also labelled the participant's response to be either risky vs non-risky. To mark whether the choice selected was risky or not, we applied the variance expression (eqn. 2 ( Figure 2e)) 36,37 on the stimuli presented at each trial. The riskiest or uncertain choice was the stimulus whose reward probability was at chance level (P = 0.5), i.e., associated with the greatest variance in outcomes, and the least risky or certain choice was associated with either P = 0.25 or P = 0.75 with a greater likelihood of either winning or not winning and hence greater certainty or lower uncertainty. This information about the choice was then compared with the participant's selected choice in a given trial, to classify it to be either a risky or a non-risky one. This was repeated for all the trials and subjects and used as input to the HDDM model ( Figure 2f). For this category alone, we estimated response bias (z) in addition to 'a' & 'v'.

Trans-diagnostic factors
Using factor analysis on 209 question items drawn from a set of 9 psychological questionnaires, Gillan et al (2016) extracted 3 factors that corresponded to dimensions of anxious-depression (factor 1), compulsive behaviour and intrusive thought (factor 2), and social withdrawal (factor 3) (See 31 for details). We tested for associations between individual differences in scores on each of these 3 factors and the computational (conflict-uncertainty and context independent) estimates from the HDDM model.

Statistical Analyses
In line with the HDDM estimation of a and v, we used Bayesian methods as implemented in JASP for statistical analysis. Bayesian repeated measures ANOVA was used to test the significance, across the conditions and, if significant, post-hoc Bayesian paired and independent t-tests were used to assess the mean difference. Evidence for hypothesis testing was inferred from the Bayes Factors(BF10), with a BF10 >3 indicating moderate evidence and >100 strong evidence in support of the alternate hypothesis 38 . The Bayes Factor used to report the evidence for a hypothesis was obtained from JASP which is based on the algorithm described in [39][40][41] .
Repeated measures ANOVA was used to test the significance in the accuracy levels and response time across the different conflict-uncertainty categories, which was greenhousegeisser corrected for sphericity violation. A non-parametric spearman correlation was used as the trans-diagnostic factors did not obey normality. This was performed in SPSS version27.   Table 1. A post-hoc analysis for individual differences shows strong evidence across each of the conditions except difficult-certain and easy-medium conditions (See Supp. Table S1).
The above results confirm our previous findings 11 Table S2.
Insert Figure 4 here For drift rate, there were no significant correlations between the 3 factors and each of the conditions except for LCLU (r = 0.05, p < 0.05) and HCMU (r = 0.05, p < 0.05), which correlated with Anxious-depression scale (factor 1).
Additionally, we also conducted a correlation analysis between the original 9 questionnaires and to the conflict-uncertainty parameters. Particularly noteworthy is the fact that, in contrast to the compulsivity dimension, scores on the OCD questionnaire did not reach significance in their association to thresholds in the difficult-uncertain condition (r = 0.04, p = 0.16). For contexts which correlated significantly with factor 3, a correlation with the Leibowitz Social Anxiety Scale score and AUDIT was also observed (See Supp. Table S3).

Analysis 2: HDDM estimates independent of context
Accuracy based estimates: The threshold (a) and drift rate (v) were estimated whose values were checked for convergence by visually inspecting the Monte Carlo chains. We then calculated the correlation between the 3 factors and these estimates. We found a statistically significant negative correlation only between the threshold and factor 3 (r = -0.08, p = 0.002) but not factor 1 (r = -0.004, p = 0.88) and factor 2 (r = 0.03, p = 0.17) while controlling for age and IQ levels. In terms of drift rate, factor2 (r = -0.03, p = 0.33) and factor 3 didn't correlate (r = 0.04, p = 0.12) but factor1 did (r = 0.056, p = 0.04).

Risk based estimates:
The threshold (a), drift rate (v), and response bias (z) were estimated with choice (risky vs non-risky) and reaction time as the input variables. We then calculated the correlation between the 3 factors and these estimates. We found a statistically significant negative correlation only between the threshold and factor 3 (r = -0.077, p = 0.004) but not factor 1 (r = -0.001, p = 0.98) and factor 2 (r = 0.03, p = 0.17) while controlling for age and

Discussion
We first validated our previous observations 11 in a larger cohort demonstrating that within difficult-uncertain contexts, evidence accumulation is lower and at a slow rate (Figure 3). In This study adopted a trans-diagnostic approach, based on the idea that these dimensions of symptomatology may show a better fit to underlying cognitive or brain changes than disorder-based measures. This proved true in this dataset; the simple association between OCD symptom severity and exit thresholds was not significant for the difficult-uncertain condition, while the compulsivity dimension was. This follows a pattern seen in other datasets studying these same factors, where for example associations between metacognitive changes (excessive confidence and poorer metacognitive accuracy) are more strongly linked to individual differences in this compulsive factor than OCD symptom severity itself 29,33 . The same is true for confidence biases in the opposing direction, where the anxious-depression factor appears to have a stronger association to reductions in confidence than depression or anxiety alone 29,33 .
An exploratory analysis revealed a generalized inverse relationship between the amount of evidence accumulated and social withdrawal. This finding appears to be independent of context. Social anxiety disorder or generalized social phobia is a debilitating condition in which an individual experiences an overwhelming fear of social interactions or performance demanding situations as they feel they are being judged and tends to avoid social situations 44,45 . Here, social anxiety appears to be associated with lower evidence accumulation suggesting more rapid impulsive decision making irrespective of the decision-making scenario. Classically, patients with SAD display behaviours linked to being shy, submissive, behaviourally inhibited, and risk-aversive 46,47 . Our findings suggest social anxiety may be related to inadequate evaluation of evidence. This is consistent with the concept of 'jumping to conclusions' 48,49 in which a subject might rapidly interpret someone glancing at them or yawning in specific personal negative judgmental terms without adequately considering the objective evidence. However, these findings are somewhat at odds with recent work indicating an excess of deliberation, at least in social contexts, is associated with scores on this same dimension 50 . Perhaps it is the nature/outcome of the deliberation that is at issue, consistent with cognitive behavioural therapy approaches for social anxiety to better evaluate and consider the objective evidence prior to making a decision that they are being judged socially. Future studies designed to probe this directly will be needed to follow-up on this interesting result.
The study is not without limitations. We have used a discretized approach to study conflict and uncertainty rather than a continuous regressor based approach. As the rationale of the 2step task design 30 was neither to study conflict nor uncertainty, utilizing it to study the psychological constructs of trial-wise variations in conflict/uncertainty may require more refinement of the task structure.
Thus, we replicate and extend our original findings dimensionally in a larger normative data set demonstrating specific impairments in evidence accumulation in difficult uncertain contexts in those with traits characterized by compulsivity and intrusive thoughts. We further highlight rapid decision making, or a 'jumping to conclusions' style of decision making in those with social anxiety. Our findings suggest potential targets for cognitive behavioural therapy approaches.
Author Contributions: AM designed the method, analysed the data and, drafted the manuscript. CMG collected the data, analysed behavioural data and drafted the manuscript.