A distinct inferential mechanism for delusions in schizophrenia

Abstract

Delusions, a core symptom of psychosis, are false beliefs that are rigidly held with strong conviction despite contradictory evidence. Alterations in inferential processes have long been proposed to underlie delusional pathology, but previous attempts to show this have failed to yield compelling evidence for a specific relationship between inferential abnormalities and delusional severity in schizophrenia. Using a novel, incentivized information-sampling task (a modified version of the beads task), alongside well-characterized decision-making tasks, we sought a mechanistic understanding of delusions in a sample of medicated and unmedicated patients with schizophrenia who exhibited a wide range of delusion severity. In this novel task, participants chose whether to draw beads from one of two hidden jars or to guess the identity of the hidden jar, in order to minimize financial loss from a monetary endowment, and concurrently reported their probability estimates for the hidden jar. We found that patients with higher delusion severity exhibited increased information seeking (i.e. increased draws-to-decision behaviour). This increase was highly specific to delusion severity as compared to the severity of other psychotic symptoms, working-memory capacity, and other clinical and socio-demographic characteristics. Delusion-related increases in information seeking were present in unmedicated patients, indicating that they were unlikely due to antipsychotic medication. In addition, after adjusting for delusion severity, patients as a whole exhibited decreased information seeking relative to healthy individuals, a decrease that correlated with lower socioeconomic status. Computational analyses of reported probability estimates further showed that more delusional patients exhibited abnormal belief updating characterized by stronger reliance on prior beliefs formed early in the inferential process, a feature that correlated with increased information seeking in patients. Other decision-making parameters that could have theoretically explained the delusion effects, such as those related to subjective valuation, were uncorrelated with both delusional severity and information seeking among the patients. In turn, we found some preliminary evidence that subjective valuation (rather than belief updating) may explain group differences in information seeking unrelated to delusions. Together, these results suggest that abnormalities in belief updating, characterized by stronger reliance on prior beliefs formed by incorporating information presented earlier in the inferential process, may be a core computational mechanism of delusional ideation in psychosis. Our results thus provide direct empirical support for an inferential mechanism that naturally captures the characteristic rigidity associated with delusional beliefs.

Keywords: Bayesian inference; belief updating; computational psychiatry; delusions; schizophrenia.

Figure 1

Modified beads task schematic and behaviour for an example subject. (A) Schematic depicting trial structure in the beads task. During sequential periods within a trial (estimation, choice, and outcome), participants were first asked for probability estimates about the identity of the hidden jar, and were then prompted to choose between drawing (for $0.30) or guessing at the identity of the hidden jar (incurring a penalty of $15 if their guess was incorrect). Their goal was to keep as much money as possible from an initial endowment of $30. A visual aid indicating the sequence of draws up to the current one was presented throughout (bottom left of screen). The bead-ratio condition (60:40, 75:25, 90:10, or 100:0) was also shown as the percentage of the majority bead probability in the hidden jar (bottom right of screen). The remaining winnings for a given trial were also displayed during the choice period (top centre of choice screen). The outcome period either revealed the drawn bead or provided feedback on the accuracy of a given guess and indicated the final winnings for the trial. (B) Behaviour for a representative subject on four different trials, one for each bead-ratio condition (majority bead ratios of 60:40, 75:25, 90:10, and 100:0). Probability estimates given before each draw are presented for each trial’s bead sequence (top). Below, draws-to-decision are shown for each trial (bottom). These two measures represent the two main behaviours of interest in the task.

Figure 2

Specific relationship between draws-to-decision behaviour and delusion severity in patients. (A) Mean draws-to-decision (y-axis) for each bead-ratio condition (x-axis, probability of majority bead colour in the hidden jar) are shown in patients with schizophrenia. Error bars represent SEM. Lines are coloured by delusional severity (PDI score), with greater severity indicated in red and lower severity in blue. Patients with more severe delusions show increased draws-to-decision in the 60:40 condition and increased draws-to-decision slope (significant effects held after excluding subjects with draws-to-decision above 2 in the 100:0 condition; all P < 0.03). (B) Top: Scatterplots depicting the relationship between draws-to-decision slope (indicating the change in draws-to-decision as a function of bead-ratio condition) and severity of delusions before (top left) and after (top right) adjusting for severity of perceptual disturbances (CAPS score) in patients. Bottom: Scatterplot showing the relationship between severity of perceptual disturbances (CAPS score) and draws-to-decision slope, before (bottom left) and after (bottom right) adjusting for delusional severity (PDI score). (A and B) a.u. = arbitrary units. Dots are coloured by delusional severity (PDI score) as in A. (C) For post hoc assessment of specificity and of generalizability across scales, correlation coefficients (Pearson’s r for summed scores and Spearman’s ρ for single-item scores) are presented describing the strength of the relationships between the draws-to-decision slope and various clinical, neurocognitive, and socioeconomic variables in patients. Only delusion-related measures show significant (P < 0.05; gold) or trend-level (0.05 < P < 0.1; darker gold) effects. PDI = PDI total score; CAPS = Cardiff Anomalous Perceptions Scale, global (summed) score; PANSS-P1 refers to the ‘delusions’ item score, PANSS-P3 to the ‘hallucinatory behaviour’ item score, PANSS-P6 to the ‘persecution/suspiciousness’ item score, PANSS-PT to the positive subscale total score, PANSS-NT to the negative subscale total score, and PANSS-GT to the general subscale total score; PSYRATS-A refers to auditory hallucination total scores and PSYRATS-B refers to delusion total scores; Dose = antipsychotic medication dose in chlorpromazine equivalents (mg/day); Illness duration = duration of illness in years as per the SCID-IV; LNS = Letter-Number Span working-memory (WM) task performance score; Numeracy = per cent accuracy on the numeracy module of the 2002 HRS; Income = monthly income ($) measured by the employment section of the ASI support status; SES = personal socioeconomic status measured via the Hollingshead scale.

Figure 3

Task behaviour for patient subgroups, healthy controls, and ideal observer. (A) Mean draws-to-decision by group, with schizophrenia patients median-split into high-delusion (red) and low-delusion (blue) subgroups, for each bead-ratio condition. The socio-demographically matched healthy control group is shown in grey. The behaviour of the (parameter-free POMDP) ideal-observer model is indicated by the dashed black line. (B) Mean draws-to-decision slope for each group. Shown in shades of grey is this slope for controls and for all the schizophrenia patients grouped together (with and without adjustment by PDI score). Dots represent data for individual subjects. Asterisks indicate statistically significant effects at P < 0.05. (C) Accuracy by group for each bead-ratio condition. (D) Mean probability estimate (for the actual hidden jar) before (draw 0) and after the first bead draw (draw 1) by group and condition. (E) Mean probability estimates (for the actual hidden jar) before each bead draw, by group, across correct trials in the 60:40 condition. For ease of visualization, the corresponding probability estimates for the ideal-observer model are shown as black dots. (F) Mean probability estimate (for the actual hidden jar) at guess (i.e. probability estimate immediately preceding a guess choice) by group, in each bead-ratio condition. (A–F) The colour scheme in A applies to all panels. Error bars represent SEM.

Figure 4

Model-based analyses of belief updating and relationship to delusion severity. (A) Mean BIC (left y-axis) and exceedance probability (right y-axis) values for competing belief-updating models, sorted by BIC (worst to best from left to right): the winning model for all patients, controls, and all groups combined is at the rightmost end of the x axis (‘$1{\omega }_1,4{\omega }_2$‘). a.u. = arbitrary units. (B) Mean fitted probability estimates (for the actual hidden jar) before each draw based on individual fits of the winning model across all correct 60:40 trials (note that this represents the mean fits of the data in Fig. 3E). Error bars are SEM. (C and D) Scatterplots showing subject probability estimates (for the actual hidden jar) plotted against the predictions of the unweighted (parameter-free) Bayesian belief-updating model (C) and the weighted, winning belief-updating model (D). Colour scheme is the same as in B. (E) Correlations between model parameters (belief-updating [${\omega }_1$, ${\omega }_2(0.6)$], value [$C_{sub}(0.6)$], and choice parameters [$\gamma$] from the beads task on the left, and value parameters from the control decision-making tasks on the right [loss aversion $\lambda$, risk aversion $\alpha$, ambiguity aversion $\beta$]) and draws-to-decision slope (top) and between model parameters and delusional severity (PDI score; bottom). Note that $\lambda$, which reflects subjective valuation on the loss-aversion task, correlated with the subjective-valuation parameter of the beads task, $C_{sub}(0.6)$, but not with other parameters of this task (Supplementary material). (F and G) Scatterplots indicating correlations between the prior weight ${\omega }_1$ parameter and draws-to-decision slope (F) and between ${\omega }_1$ and delusional severity (PDI score, G). Dots are coloured by delusional severity with greater severity indicated in red and lower severity in blue.

Figure 5

Model-agnostic analysis of belief updating and relationship to delusion severity. (A) Regression coefficients by group are shown from the time-lagged regression analysis predicting draw-wise probability estimates (for the actual hidden jar) from the bead colour (majority colour or not) in the current draw and the previous two draws. Error bars represent SEM. (B) Scatterplot depicting the relationship between the difference in regression coefficients from the current draw and two draws back (${\beta }_d-{\beta }_{d-2}$) and delusional severity (PDI score). Note that we observed a significant correlation between this model-agnostic measure of primacy bias (${\beta }_d-{\beta }_{d-2}$) and the model-derived measure of primacy bias (${\omega }_1$), but not between the model-agnostic measure of primacy bias and the other model-derived parameters from the winning belief-updating model (Supplementary material), indicating convergence between the model-agnostic and model-based analyses. Dots are coloured by delusional severity with greater severity indicated in red and lower severity in blue. a.u. = arbitrary units.

Figure 6

Fitted and simulated draws-to-decision behaviour. (A) Mean fitted draws-to-decision by group for each bead-ratio condition using the parameterized variant of the POMDP model (five free parameters for valuation and choice). The behaviour of the ideal-observer model is indicated by the black dashed line. (B and C) Mean draws-to-decision from a modified ideal-observer model with either varying the ${\mathrm{\omega }}_1$ (B) or varying the ${\omega }_2$(0.6) (C) parameters (other aspects of the model are kept intact to simulate the specific effects of a single change in each of the relevant belief-updating parameters). Note that here, increased ${\omega }_1$ leads to slower belief updating and consequently smaller estimates of the probability for the hidden jar at a given point within the trial (Fig. 3E); this results in smaller expected values for guessing relative to drawing and an increased tendency to draw. (B and C) The parameter values cover the approximate range of the individually fitted parameters in the patient data. Greater numerical values for the model parameters are indicated with darker colours. (A–C) Error bars represent SEM.