Figure 1.
Schematic of a generative model for psychiatric morbidity. The model is shown in terms of a (probabilistic) graphical model on the left. In this format, the quantities in white circles correspond to random variables that include (unknown) parameters on the left and hidden or latent states on the right. The arrows denote conditional dependencies and describe the influences among latent variables that generate the observations or outcomes in the cyan circle at the top. Here, the outcomes are clinical symptom scores and a differential diagnosis, measured as a probability distribution over diagnostic classifications. The only difference between these outcomes is that the diagnostic probabilities are constrained to be nonnegative and to sum to 1 (so that they can be treated like a proper probability distribution over a differential diagnosis). The outcomes are generated as functions of psychopathological states that, themselves, are mixtures of pathophysiological states. Finally, the pathophysiological states are perturbed by inputs (such as therapeutic interventions). An example of the form of the conditional dependencies is provided on the right, in terms of functions and random (Gaussian) fluctuations. In this example, a single therapeutic intervention enters the dynamics (or equations of motion) governing the evolution of the pathophysiological states. Here, the therapeutic intervention changes the influence of the second physiological state on the first, where this coupling itself is state-dependent (and changes with the third state). These dynamics are based on a Lorenz attractor (illustrated by the insert in the lower corner). The psychopathological states are generated as a linear mixture of the last two physiological states. In turn, the psychopathological variables are mapped to clinical outcomes through sigmoid functions (to generate symptom scores) and a softmax function of diagnostic potential (to generate a differential diagnosis). The diagnostic potential is based on the proximity of the psychopathological state to locations representing diagnostic categories. The panels in the middle column illustrate a particular realization of this generative model over 64 time bins (i.e., weekly assessments). The lower panels in this sequence show the therapeutic input (starting at 32 weeks) and the dynamic responses of the three pathophysiological states. The ensuing psychopathology is shown both as a function of time and as a trajectory in state-space in the left and right middle panels, respectively. The state-space of psychopathology contains the locations associated with diagnostic categories (colored dots), which determine the diagnostic classification that tiles the state-space (four regions of gray, weighted by the entropy of the probability distribution over diagnoses). This example includes four diagnostic categories (schizophrenia, schizoaffective and affective disorders, and a state of remission). The symptoms and differential diagnosis generated by this trajectory are shown in the upper panels on the left and right, respectively. In this and subsequent simulations, the initial (physiological) states are [8, 10, 32]; the parameters for the symptom scores are sampled from a unit Gaussian distribution, and the remaining parameters are shown in Figure 4.
Figure 2.
Bayesian filtering or model inversion of simulated clinical time-series data. This figure reports the results of model inversion using the data generated by the model described in the previous figure. In this instance, the clinical data were simulated without any therapeutic intervention (shown by the broken line in the lower left panel) over 64 weeks and are shown in a format similar to the middle panels of Figure 1. Here, the solid lines represent predictions, whereas the dotted lines represent prediction errors in terms of the clinical outcomes (upper left panel) and the latent psychopathology (middle left panel). The gray areas around the estimates of pathophysiology (lower right panel) correspond to 90% confidence intervals for the hidden states. The symptom scores and differential diagnoses are shown as a function of time (upper left) and in image format (upper right). The upper image at top right shows the changes in differential diagnosis, with the diagnosis of remission in the first (i.e., top) row, and the lower image shows the fluctuations in the first four symptom scores. Notice here that, in the absence of treatment, the chaotic fluctuations between schizophrenia and schizoaffective regimes of latent psychopathology slowly increase in amplitude.
Figure 3.
Inferred psychopathology and pathophysiology in response to treatment. This figure uses the same format as Figure 2. The only difference here is that we have introduced a therapeutic intervention that has destroyed the chaotic attractor, replacing it with a point attractor in the remitted regime of latent psychopathology. As a consequence, the pathophysiological variables approach zero, and the symptom scores normalize. At the same time, the most probable diagnosis becomes one of remission (solid blue line in the upper left panel—see also the cyan circle in the corresponding predictions in image format).
Figure 4.
Bayesian model identification and comparison. This figure summarizes the results of model identification (parameter estimation) and model selection using Bayesian model reduction. The upper panels show the posterior estimates of the subject-specific (left) and nosological (right) parameters based on single-subject time series and (eight-subject) group data, respectively. The gray bars correspond to the posterior means, and the pink bars report 90% Bayesian confidence intervals. These are superimposed on black bars that correspond to the true values used to simulate the clinical data. The lower left panel shows the combinations of nosological parameters that define 16 competing models that were compared using Bayesian model reduction. This comparison entails evaluating the evidence for each model—namely, the probability of the data under each model—after having marginalized over unknown parameters and states. The model evidence is also known as the marginal or integrated likelihood. Under uninformative or flat priors over models, this also corresponds to the model posterior. The posterior probabilities over 16 models for the group data are shown at the lower right, suggesting that a model that precludes coupling between the second physiological state and the first psychopathological state (mediated by the third nosological parameter at upper right) has greater evidence than all other models.
Figure 5.
Predicted responses to treatment. This figure uses the same format as Figure 3; however, here the results are purely predictive in nature. In other words, the predictions are driven entirely by the pathophysiological dynamics based on subject-specific estimates of the model parameters—and starting from the state last estimated on the basis of an assessment prior to therapy.
