Mapping From Pathogenetic Factors to Behavioral Observations

The next step is to define the generative model, which represents how the pathogenetic factors are translated to behavioral observations. We assume that the pathogenetic factors X are translated to behavioral observations Y via some function f with some added noise ϵ. In vector form, this can be written as

In the following simulations and analyses (Cases 1–5), we consider a simple model with linear mapping and Gaussian noise, called the linear Gaussian model. The mathematical formulation of this model is presented in Katahira and Yamashita (2017, Appendix A). In the linear Gaussian model, each pathogenetic factor is assumed to be independently drawn from a Gaussian (normal) distribution. Each behavioral observation y_i is the linear combination of X and the Gaussian noise ϵ_i. From this assumption, each y_i also obeys the Gaussian distribution, which means that behavioral observations are continuous variables. Many inclusion criteria in the current diagnostic systems (i.e., DSM and ICD) take on discrete values (e.g., existence or absence of a symptom). For such cases, y_i may be interpreted as a behavioral phenotype, based on which a psychiatrist or a patient makes decisions regarding each symptom rather than the symptom itself. In Case 6, rather than a linear Gaussian model, a reinforcement learning model is used as a generative model for behavioral observations related to psychosis.

Category-Based Approach

In the proposed framework, the category-based approach first classifies the individuals into the patient group or the control group, depending on the values of their behavioral observation Y. For example, if y_i for all i exceeds the cutoff point h_i (y_i ≥ h_i ∀_i), the individual is classified into the patient group (in Figure 1, the individuals indicated with red dots belong to the patient group). Except for Case 2, where we examine the effect of the margin between the patient group and control group, individuals who have any behavioral observation that does not satisfy the criterion (y_i < h_i ∃_i) are classified into the control group (the individuals indicated with gray dots in Figure 1). Note that a subject is classified into a patient group only when all of the M behavioral observations exceed the threshold. In this article, we do not consider a polythetic criteria approach, in which the diagnosis is assigned when a patient exhibits a designated number from a list of symptoms provided for each disorder category (e.g., five of nine for MDD). Such a polythetic criteria approach can be incorporated in the proposed framework. For simplicity, however, we leave them as a future work. In the following simulations, we set h_i = h = 0.5 ∀_i unless otherwise stated.

The category-based approach seeks the pathogenetic factors that significantly differ between the two groups. The estimated or measured value of x_j, which is denoted by ${\widehat{x}}_j$, is assumed to contain a measurement error. This error is modeled by adding a Gaussian variable δ_j to the true value x_j (see Katahira & Yamashita, 2017, Appendix A). Note that we formally and explicitly model the measurement or estimation error rather than incorporate a specific estimation process.

In the simulation, the samples of subjects (n₁ subjects from the control group and n₂ subjects from the patient group, resulting in a total of n₁ + n₂ = n subjects) are randomly selected from both groups, and their observed pathogenetic factors $\widehat{x}$ are subjected to an unpaired t test with the equal variance assumption. The null hypothesis is that the population means of ${\widehat{x}}_j$ for the patient group and that for the control group are the same. If the significance of the difference is detected at the significance level α (α = 0.01 for Cases 1-5 and α = 0.05 for Case 6), then the factor x_j is considered to be a pathogenetic factor relevant to the mental disorder. When multiple candidate factors are submitted to statistical tests, a correction should be made for multiple comparisons (e.g., Bonferroni correction) to suppress family-wise error rates. However, for simplicity, we do not perform such a correction in this article. Incorporating a correction is straightforward and does not influence the quantitative results reported herein.

When more than one pathogenetic factor can be observed at the same time, one may use logistic regression, in which the objective variable is diagnostic category (0 control, 1 patient) and the regressors (predictors) are the observed values of potential pathogenetic factors $\widehat{x}$. For this case, the hypothesis test can be performed for each pathogenetic factor with the null hypothesis for which the regression coefficient for the factor is zero. In all the cases that we considered, however, we found that logistic regression provided a lower statistical power compared with an independent t test while showing a similar tendency with a t test. Thus we do not present the logistic regression results.

Dimensional (RDoC) Approach

The dimensional approach addresses the behavioral observations, including symptoms and pathogenetic factors, without categorical labels. This approach utilizes the natural variation of the population. RDoC basically encourages the dimensional approach. In the proposed framework, the dimensional approach is simulated by sampling n subjects from the population irrespective of the behavioral phenotype (symptom). A statistical hypothesis test is then conducted. When there is one measured potential pathogenetic factor, one simple approach tests the null hypothesis that the correlation coefficient between y_i and ${\widehat{x}}_j$ is zero. When the correlation is significant (the null hypothesis is rejected), then the jth pathogenetic factor x_j is deemed to be a factor that is relevant to the behavioral observation y_i.

When more than one potential pathogenetic factor can be observed at the same time, one may use multiple linear regression, in which the objective variable is each behavioral measure y_j and the regressors are potential pathogenetic factors $\widehat{x}$. For this case, the hypothesis test can be performed for each pathogenetic factor with the null hypothesis that the regression coefficient for the factor is zero. We will report the multiple linear regression results in Case 1 and Case 5. In reality, all of the true causes of the generative process of mental disorders that may be included in the generative model are rarely observed in a single study: Researchers can observe only part of them. Thus, in general, the statistical model in the analysis of the observed data would be simpler than the generative model: the number of pathogenetic factors that can be included in the analysis is less than the number of those included in the generative model. Case 5 also considers this situation.

RDoC is more than just a dimensional approach to mental disorders. It emphasizes the consideration of constructs of the mental disorders based on neurobiological grounding. In addition, RDoC encourages investigations that target multiple units of analysis. The targeted units of analysis can all be biological ones (e.g., “cells” and “circuits”). However, to relate the biological mechanisms to mental disorders, it at least requires knowledge that relates some biological factors to some behavioral observations as a starting point. Additionally, RDoC is intended to create a novel discrete category of mental disorder after sufficient research progress. Thus the dimensional approach in the present framework models are intended to capture only one aspect of the RDoC approach, particularly at the beginning phase.

Case 1: Multiple Disorder Categories

The first two cases (Cases 1-1 and 1-2) consider the basic problem in psychiatric research. Consider that there are two disorder categories, which we call Disorder A and Disorder B (e.g., depression and psychosis, respectively). For simplicity, we assume that each disorder has two symptoms and that one of these symptoms is shared by both disorders (Figures 2A and 2C). Behavioral observation y₂ represents the common symptom between the two disorders (e.g., anhedonia), and y₁ and y₃ are specific symptoms for each disorder. Assume that the goal of the researcher is to detect the pathogenetic factor of the common symptom y₂. An individual is assumed to be diagnosed with Disorder A if y₁ ≥ h and y₂ ≥ h; here h is the common cutoff point, and we set h = 0.5. He or she is also diagnosed with Disorder B if y₂ ≥ h and y₃ ≥ h. Comorbidity (a single individual can be diagnosed with both Disorder A and Disorder B) is allowed. We calculated the statistical powers of five methods (Methods 1–5) for detecting the target factor. The category-based approaches (Methods 1–3) compare the observed pathogenetic factor (${\widehat{x}}_j$) between the control group and the patient group. Methods 1–3 differed in terms of the inclusion criteria for the two groups. We also consider the category-based analysis using only a single criterion, which compares individuals with y₂ ≥ h and those with y₂ < h (Method 1).

Here we consider two possible etiological mechanisms for this situation. Case 1-1 assumes that there are two distinct pathogenetic factors for each disorder category (Figure 2A). In this case, the common symptom arises from different pathogenetic factors, denoted as x₁ and x₂. Figure 2B shows the statistical powers of several analyses for detecting the target factor x₁. In this case, the category-based analysis using only a single criterion (Method 1) did not yield a good result: Half of the trials failed to obtain the significant difference in ${\widehat{x}}_1$ (at the critical level, α = 0.01; top bar of Figure 2B).¹ In contrast, the category-based approaches using two symptoms as criteria (Methods 2 and 3) provided a better result. In Method 2, the patient group consists of individuals who satisfy the criteria of Disorder A, whereas the control group consists of the other individuals. Method 2 yielded a significant difference with a probability of greater than 60% (Figure 2B).

The reason for the difference between the statistical powers of Method 1 and Method 2 can be understood by checking the distributions of samples for each group in each method (Figure 3A). Method 2 includes only individuals with y₁ ≥ h and y₂ ≥ h, which are indicated with orange-filled circles in Figures 3A and 3B. In contrast, Method 1 also includes the individuals with y₂ ≥ 1 but y₁ < h, who are marked with blue triangles. As shown in Figure 3A, the individuals marked with blue triangles tend to have smaller values of x₁ compared to the individuals marked with orange filled circles. Thus, Method 2, which employs only the individuals indicated with orange filled circles, improves the discriminability compared to Method 1, which includes the individuals marked with blue triangles (dashed lines in Figure 3A). The discriminability is measured using Cohen’s d, which is defined as the difference between two means divided by the pooled standard deviation (see Katahira & Yamashita, 2017, Appendix B). Method 1 yielded d = 1.06 for x₁ (d = 0.71 for ${\widehat{x}}_1$), whereas Method 2 yielded d = 1.61 for x₁ (d = 1.02 for ${\widehat{x}}_1$), which is a remarkable improvement in discriminability. This result is directly related to the statistical power: The larger d is, the greater the power is (note that an actual statistical test is performed for the measured/estimated value ${\widehat{x}}_1$ rather than for the true value x₁).

Method 3 is a diagnostic category-based approach that utilizes the information about both Disorder A and Disorder B: Individuals in the patient group are with Disorder A but without Disorder B, whereas individuals in the control group are without both disorders. Method 3 provided slightly higher power than Method 2 (Figure 2B). This result is because the patients with Disorder A but without Disorder B have more specificity of pathogenetic factor x₁ compared to those with both disorders. If the individuals have Disorder B, then they tend to have a higher value of x₂. Having a larger common symptom value y₂ may be due to this higher value of x₂ and not due to x₁. Excluding such individuals and choosing patients only with Disorder A helps to illuminate the effect of x₁.

Dimensional approaches, which test the correlation between ${\widehat{x}}_1$ and y₂ (Method 4), yielded greater power than Method 1 but less power than the two category-based approaches (Methods 2 and 3). Including both pathogenetic factors in the explanatory variables of multiple regression increased the power (Method 5), but it did not exceed the power of the two category-based approaches.

Case 1-2, which assumes a one-to-one mapping from the pathogenetic factors to the symptoms, produced quantitatively different results. In this case, there is one distinct pathogenetic factor for each symptom. The use of the disorder categories with multiple criteria did not increase the power. In contrast, the analyses using double criteria (Methods 2 and 3) yielded lower power compared to the category-based analysis using only a single criterion (y₂ ≥ h; Method 1). The reason for the deterioration in the power of the double criteria methods can also be understood by examining the distributions of samples (Figure 3C). Method 2 includes the individuals with y₂ ≥ h but y₁ < h, who are marked with blue triangles, in the control group, whereas Method 1 classified these individuals into the patient group. In this case, the individuals indicated with blue triangles also have higher values of x₂, which are comparable to those of individuals indicated with orange dots. Thus including the subjects marked with blue triangles pulls the distribution of x₂ of the control group (black solid line in Figure 3B) toward that of the patient group (red solid line), which reduces the discriminability. Method 1 yielded d = 1.40 for x₂ (d = 0.89 for ${\widehat{x}}_2$), whereas Method 2 yielded d = 0.99 for x₂ (d = 0.66 for ${\widehat{x}}_2$). Moreover, in this case, dimensional approaches, which test the correlation between ${\widehat{x}}_2$ and y₂ (Method 4), yielded greater power than the category-based approaches. Here including other variables in the multiple regression did not increase the power (Method 5).

The implications of the results are as follows. The diagnostic categories based on the syndrome can be useful for detecting the pathogenetic factor if the factor is related to those symptoms (as in Case 1-1). However, if there is no such one-to-many mapping, using multiple criteria is not useful: Using a single observation is more efficient for detecting the underlying factor (as in Case 1-2). Among the methods based on a single behavioral observation, the dimensional (correlation) approach provides greater statistical power (compare Method 1 and Method 4 in Figures 2B and 2D). These properties are systematically investigated in the following analyses (Cases 2 and 3).

Case 2: Category-Based Versus Dimensional Approaches

In Case 2, we compared the statistical powers of the category-based approach and the dimensional (correlation) approach for the simplest case in which there is a single pathogenetic factor (M = 1) and a single behavioral observation (N = 1). This case is intended to examine the result of Case 1, which shows that the dimensional (correlation) approach provides higher statistical power when one behavioral observation is used. The model structure is illustrated in Figure 4A. Here we also examined the effect of the margin (denoted as m) between the patient group and control group. Suppose that the individuals with y less than h − m are classified into the control group and that the individuals with y larger than h are classified into the patient group (Figure 4B). The individuals with y falling into the margin are not included in the study. Actual samples in psychiatry studies may include such a margin: Researchers may exclude individuals who are not classified into the clinical group but present behavioral phenotypes that are close to the cutoff point.

Figure 4C shows the power with which the pathogenetic factor x₁ is detected as a function of the total number of individuals. For this case, the statistical powers of both methods can be analytically obtained (see Katahira & Yamashita, 2017, Appendix B; Figure 4C, solid lines for the category-based approach and chain line for the dimensional approach). The symbols (squares for the category-based approach and triangles for the dimensional approach) represent the numerical results obtained from 100,000 runs of the Monte Carlo simulations. The analytical results (lines) perfectly agree with those obtained from the simulations (symbols), thereby validating the analytical calculations. The results indicate that if there is no margin (m = 0), then the dimensional approach (using correlation coefficients) yields a higher power compared to the category-based approach (using the unpaired t test). This result is because the correlation coefficients can utilize full information on the magnitude of x₁, whereas the category-based approach ignores the information of the distribution within the group. If there is a margin, then the category-based approach can outperform the dimensional approach. With a larger margin, the category-based approach can distinguish clusters in the distribution x₁ while suppressing the impact of the noise added to x₁. However, note that with a larger margin, it becomes more difficult to find samples for the control group.

In the preceding results, the cutoff point was fixed to h = 0.5. Next, we varied the cutoff point h to examine how it affects the power. The results are shown in Figure 4D. As h moved from zero, the power increased. The model yields minimum power when the distribution of the control group and patient group is symmetric (which occurs when h − m/2 = 0). Figure 4E shows an example of the histogram of ${\widehat{x}}_1$. As the cutoff point h became large, the difference between the means of the two groups increased (from 1.12 to 1.27). Consequently, as h moved away from the mean of the population, the effect size (Cohen’s d) and statistical power increased.

Note that the samples to be analyzed are different between the two approaches. The dimensional approaches randomly draw samples from the population without any inclusion criteria. In Case 2, if the same sample (which is sampled by the category-based approach) was used for both of the approaches, then the dimensional (correlation) approach always provided superior power to the category-based approaches (Figure 4D, dashed lines with filled triangles).

Case 3: The Effect of the Number of Diagnostic Criteria in the Category-Based Approach

As shown in Case 1-1, if more than one symptom has a common pathogenetic factor, then including such symptoms in a single disorder category for the category-based approach improves the power for detecting the factor compared to the approach based on a single symptom. In Case 3, we systematically examined the effect of using multiple criteria that share a common pathogenetic factor. Figure 5A shows the structure of the generative model. We assumed that there are two pathogenetic factors (N = 2): x₁ is a factor relevant to the mental disorder and is of interest, and x₂ is irrelevant to the mental disorder (Figure 5A). We included the irrelevant factor to examine the false-positive rate, which is the probability that the analysis mistakenly identifies the irrelevant factor as significant. The weight of x₁ for behavioral observation y_j(j = 1, … , M) is set to 1 and that of x₂ is set to zero.

The standard deviation of the noise σ_ϵ and the number of behavioral observations M were varied in the simulations. Recall that for a subject to be classified into a patient group, all of the M observations need to exceed the threshold. Examples of the histograms of ${\widehat{x}}_1$ are presented in Figure 5B. The larger the number of criteria M is, the greater the difference in the means of the two groups is. Consequently, the larger M is, the greater the discriminability and thus the statistical powers are (Figure 5B and Figure 5, left). The power can exceed that of the dimensional approach in which a single behavioral observation is used. These effects are especially prominent when the noise level is high (σ_ϵ = 2.0).

Here the samples submitted to analysis are again different between the category-based approach and the dimensional approach. If the same category-based samples are submitted in both of the approaches, then the dimensional (correlation) approach provides higher power than the category-based approach, particularly when M is small (Figure 5C, filled triangles). However, as M increases, the power of the category-based approach can even exceed the power of the dimensional approach. The reason for this result is as follows. The power of the correlation approach is influenced by the noise in the chosen behavioral observation y_i. The cat egorical analysis uses ys only for classifying the individuals. The categorical analyses are also affected by the noise in each y_i, but the effect is reduced when the number of ys increases.

For the irrelevant factor x₂, the fraction of the factor deemed significant was kept to the preset significance level of 0.01 (Figure 5C, right). This result confirms that the false-positive rate for the irrelevant factor is maintained, as we intended.

Case 4: The Effect of a Mixture of Pathogenetic Factors

We now discuss the case in which a single behavioral observation y_i is affected by more than one pathogenetic factor x_j. It is conceivable that a larger mixture degree leads to difficulty in detecting each pathogenetic factor. For simplicity, we consider the case with two pathogenetic factors and two behavioral observations (N = 2 and M = 2).

The transformation matrix is parametrized using a parameter c that represents the mixture degree (Figure 6A; also see Eq. (13) in Katahira & Yamashita, 2017, Appendix A). When c = 1, x₁ and x₂ equally contribute to both behavioral observations y₁ and y₂ (complete mixture). When c = 0, x₁ and x₂ independently contribute to y₁ and y₂, respectively (no mixture). When c < 0, x₁ and x₂ have opposite effects on the behavioral measures (one has a positive impact, whereas the other has a negative impact). The effect of c on the transformation from pathogenetic factors to behavioral observations is illustrated in Figure 6B.

We consider two cases in the category-based approach: One uses only a single behavioral observation y₁ as a criterion, and the other uses both behavioral observations. The resulting statistical powers are plotted in Figure 6C. As the mixture degree c departs from zero in either the positive or negative direction, the power for the methods using a single criterion (y₁ ≥ h; dimensional approach and category-based approach) decreases. This result is because the other pathogenetic factor functions as noise in terms of detecting the target x_j when c has a nonzero value. In contrast, the power of the category-based approach using two criteria monotonically increases as c increases, even when c is negative. The reason for this behavior is as follows. This approach equally uses y₁ and y₂; c does not largely change the total information extracted from y₁ and y₂. The increase in the power for positive c is due to the noise reduction effect reported in Case 3. In contrast, when c is negative, individuals whose x₁ is higher can easily be classified into the control group because of the inhibition from other x₂. Distributing subjects with higher values of x₁ into two groups makes the discrimination difficult, thus reducing the statistical power.

The additional pathogenetic factor x₂ is added to y₁ when c is nonzero; thus x₂ is detected as a relevant pathogenetic factor even when the single criterion y₁ is used (Figure 6C, right panel).

Case 5: The Effect of the Number of Pathogenetic Factors

The effect of the mixture reported in Case 4 was not drastic because there were only two pathogenetic factors (N = 2). As the next simulation shows, when N is large, the effect is large: It is more difficult to detect the individual pathogenetic factor x_j. We varied N and the mixture degree c while keeping the number of behavioral criteria fixed to M = 1 (Figure 7A). We consider the statistical power for detecting the first pathogenetic factor x₁, which is assumed to be the target of analysis.

The results are presented in Figure 7B. Overall, the influences of the number of pathogenetic factors N and the mixture degree c are similar for both the category-based and dimensional approaches. When the mixture degree is maximum (c = 1), the statistical power drastically decreases as the number of pathogenetic factors increases. This decrease is modest when the mixture degree is small (e.g., c = 0.3). Of course, when there is no mixture (c = 0), the statistical power does not depend on the number of pathogenetic factors (data not shown).

Thus far, we have considered the situation in which researchers can measure only a single pathogenetic factor (out of many factors) in one study. Thus we have focused on the simple correlation, or equivalently, simple linear regression analysis. However, large-scale psychiatry studies, such as genome-wide analysis, may measure multiple factors (alleles) in a single study (e.g., Cross-Disorder Group of the Psychiatric Genomics Consortium, 2013). For such situations, multiple regression analysis, which includes more than one candidate pathogenetic factor as regressors, may be used. The filled triangles in Figure 7B show the results of an ideal analysis in which all N pathogenetic factors are used as regressors. Here the power for detecting x₁ is computed based on the null hypothesis that the regression coefficient for ${\widehat{x}}_1$ is zero. These results provided greater statistical power than the simple regression (correlation) analysis did, which used only ${\widehat{x}}_1$ as a regressor, particularly when c was large. This result is because multiple regression can estimate the weight of x₁, suppressing the influence of other confounding factors on the behavioral observation. We also examined the intermediate situation between single regression and full multiple regression: The case in which only L (< N) potential pathogenetic factors (including the target factor x₁) are available. The power for the case with N = 10 is shown in the left small panel of Figure 7B. As expected, the power monotonically increased as the number of regressors increased.

Case 6: Incorporating a Computational Model

Thus far, we have considered simple linear Gaussian models as models of generative processes of behavioral observations. In reality, the generative processes must be more complex. Using computational models may provide an explicit and more realistic form of the generative processes (Kurth-Nelson et al., 2016). To illustrate how a computational model can be incorporated into our framework, we consider opponent actor-learning (OpAL), a variant of the reinforcement learning model proposed by Collins and Frank (2014). Using this model, Maia and Frank (2017) attempted to explain how the symptoms in schizophrenia emerge from the aberrant activities of dopamine (DA) neurons.

The details of the model are provided in Katahira and Yamashita (2017, Appendix C). In short, this model assumes that several symptoms, including positive and negative symptoms, arise from two types of aberrant activity of DA neurons: (1) increased spontaneous DA transients (parametrized by p_SDT), which can cause DA activity at inappropriate times, and (2) decreased tonic DA level (parametrized by τ). Increased spontaneous DA transients induce the aberrant valuation of thoughts, which is assumed to be a cause of delusion. A decreased tonic DA level induces diminished engagement with high-cost activities, which is assumed to correspond to avolition. We synthesized a dataset through a simulation using the model. Specifically, we varied the two parameters that characterize the DA activities and measured behavioral observations. One is a positive symptom, namely, the existence of dominant thought (action), which is caused by aberrant valuation, and the second is a negative symp tom, namely, the diminished engagement with high-cost activities. Using these data, we computed the statistical power for detecting two DA parameters as pathogenetic factors for the symptoms.

Figures 8A and 8B present an example of the formation of dominant thought through the aberrant valuation. Because we set the actual reward to always be zero, any thought (action) should not be reinforced in the standard reinforcement learning. However, the spontaneous DA transients, which occur with probability p_SDT(= 0.4), allow the prediction error signal (denoted by δ) to have a nonzero value. Consequently, a randomly chosen thought (action) can be reinforced even without an actual reward. In this simulation, from approximately the 200th time step to approximately the 500th time step, Action 10 was reinforced and frequently selected. After approximately the 400th time step, Action 19 was reinforced and subsequently became dominant. We consider this dominance of a few thoughts without external reinforcement as an occurrence of the aberrant valuation of thoughts (i.e., a positive symptom). An individual is assumed to experience 1,000 discrete time steps. We counted the episode with aberrant valuation of a thought if there at least one thought (action), except for the default action, is selected for 20% of the time steps in the later 500 time steps.

A negative symptom, a diminished engagement with high-cost activities, is examined in the simulation as follows (for details, see Katahira & Yamashita, 2017, Appendix C). An OpAL, as a model of an individual, is given 100 independent opportunities for taking an effortful action. The action values for the effortful action in the model are fixed such that they can represent a high cost of the action by assigning higher values to the NoGo value compared to the Go value. The model can choose not to take that action. Individuals whose choice of taking the effortful action is less than 50% are deemed as having diminished engagement with the high-cost activity (i.e., negative symptom, avolition). The DA level exerts an influence on the probability of taking the effortful action through balancing the weights of the Go value and the NoGo value: A higher DA level imposes more weight on the Go value than on the NoGo value.

Figures 8C and 8D present the relation between the DA parameters and behavioral observations (the fraction of individuals who have each “symptom” out of 1,000 individuals). Overall, the probability of spontaneous DA transients p_SDT has a direct positive influence on the development of aberrant valuation of thoughts (dominance of a thought), whereas the tonic DA level τ has a direct negative relation with how likely the individual is to show diminished engagement with high-cost activities. The tonic DA level τ has an inhibitory influence on how likely the individual is to develop a dominant thought (Figure 8C). Meanwhile, the larger p_SDT is, the less the individuals tend to show diminished engagement with high-cost activities (Figure 8D). These results correspond to the situation in which two pathogenetic factors have opposite effects on each symptom, such as Case 4, where the degree of the mixture c is negative. Thus, as we can predict from the results of Case 4, using both criteria in the category-based approach provided a lower power compared to the category-based approaches using each criterion independently (Figure 8E). The results suggest that researchers should treat positive symptoms and negative symptoms separately to find the specific aspect of DA dysfunctions as a pathogenetic factor of the symptoms. In addition, we can hypothesize that the information about the aberrant valuation of thoughts is more effective for detecting spontaneous DA transients as a pathogenetic factor, whereas the measurement of diminished engagement with high-cost activities can be a better variable to be related to the tonic DA level.

The statistical power of the approaches based on the aberrant valuation of thoughts is relatively weak compared to that based on diminished engagement with high-cost activities. This result occurs because the relation between the probability of DA transients p_SDT and the emergence of dominant thought are highly stochastic: Even when p_SDT is very large, more than 20% of individuals do not show an aberrant valuation of thoughts (Figure 8C). In contrast, when the tonic DA level τ is very low, almost all of the individuals suffer from diminished engagement with high-cost activities (Figure 8D); however, this may be based on an overly simplified assumption, and the results depend on the hypothetical population distribution of DA parameters. Maia and Frank (2017) suggested that the aberrant spontaneous DA transients may cause other observable effects, such as neural or behavioral effects responding to neutral stimuli, which correlate with positive symptoms. Using other such behavioral observations may help find that spontaneous DA transients are a cause of the symptoms. Focusing on such behavioral observations that directly reflect the effect of the cause of mental disorders would be one of the core proposals of RDoC.

Note that this simulation is intended only as a simple illustration. In reality, psychosis (including schizophrenia) must be a more complex disorder that may involve several etiological mechanisms. Nevertheless, the present demonstration illustrates the first step to incorporating computational models into the proposed framework to evaluate a psychiatric research strategy.

Implications

The results of the computer simulations highlight the effectiveness of dissociating a behavioral measure from other behavioral phenotypes that reflect different pathophysiological states. If one uses a diagnostic category whose criteria contain symptoms that can arise from different pathogenetic factors, then the chance of finding the corresponding factor is lowered compared with when one classifies the subjects based on a single symptom separately (as in Cases 1-2 and 3). When two factors have opposite effects on the symptoms (i.e., one factor influences one symptom agonistically, another symptom antagonistically), the statistical power would be weak if both symptoms were used to classify the individuals (Case 4, when the mixture parameter c is negative). This may also be true in more realistic situations, as observed in the reinforcement learning model of psychosis (Case 6). The RDoC approach that decomposes the factors and measures into distinct constructs would be promising in this regard.

Meanwhile, the behavioral observations can be contaminated with noise, including errors in the subjective report and individual differences in the reactivity to pathogenetic factors. By using the behavioral observations that share common pathogenetic factors to define the category, the category-based approach can reduce the effect of the noise. Consequently, increasing the number of independent criteria can reduce the impact of such noise and make the detection of the pathogenetic factors easier, given that the errors are mutually independent (as observed in Cases 1-1 and 3).

Therefore, in some cases, the conventional diagnostic category-based approach could be more efficient in detecting a pathogenetic factor than the dimensional (RDoC) approach (as in Case 3). Which approach is better depends on the case. The proposed model provides a promising approach for designing an efficient research strategy to investigate a specific target. By incorporating detailed generative models of psychiatric diseases, the researcher can determine the better research strategy, as we demonstrated in Case 6, which suggests that separating the positive symptoms and negative symptoms is better than treating them as symptoms of a single disorder category (e.g., psychosis).

Limitations and Possible Extensions

Nevertheless, there are several limitations of the proposed framework. The results and their implications strongly depend on the model assumption. If invalid models are used, then the simulation may recommend a suboptimal or even worse strategy. For example, the selection of the population distribution of model parameters (e.g., DA parameters in Case 6, which we arbitrarily set) might quantitatively change the results. Although the proposed method provides a quantitative prediction, that is, statistical power, keeping the conclusion qualitative would be better. For example, one may draw the conclusion that separating the positive symptom and negative symptom is better for finding the pattern of aberrant DA activity, but one should not trust the specific value of the power to determine the number of subjects to obtain statistically significant results (as an ordinary power analysis does). Seeking an appropriate model of mental disorders itself is a challenging task and within the scope of computational psychiatry.

We have primarily considered the linear Gaussian model as a generative model. This model assumes that the variables take continuous values and obey a Gaussian distribution. Although this assumption makes the theoretical analysis easier, it is an obvious oversimplification. For example, consider a genetic mutation as a pathogenetic factor. The presence or absence of an allele is represented as a categorical variable. The behavioral measure or symptom can also be categorical (e.g., the existence or absence of a specific symptom). The distribution of scores for some symptom ratings can be best explained using an exponential distribution with a cutoff (Melzer, Tom, Brugha, Fryers, & Meltzer, 2002). The use of the link function that maps variables onto the exponential function with a shift parameter may be suitable for such cases. Although the basic properties reported in this study may hold in various other situations, a careful investigation would be needed, depending on the situation.

Another drastic simplification in the present model is the assumption of independence among errors and also among pathogenetic factors. In realistic situations, there may be considerable correlations among them. A second-order correlation can be modeled using a multivariate Gaussian distribution, which is a simple extension of the current model. However, there may be a higher order correlation, for example, in gene expression (Nakahara, Nishimura, Inoue, Hori, & Amari, 2003). Such a correlation structure should be included in the model, depending on the specific situation, particularly for discussing the impact of the relationships between the pathogenetic factors.

Strategies in Sampling and Analysis

As we have emphasized, the category-based approach and dimensional approach differ in how they sample the subjects. The category-based approach uses diagnostic criteria for selecting the subjects (it samples the “patients”), whereas the dimensional approach is assumed to gather subjects without prior criteria. As shown in Case 2, when the same data (those gathered by the category-based approach) are used, then the dimensional (correlation) approach tends to provide greater statistical power compared to the categorical approach (t test). This result suggests that it might be better to use diagnostic criteria when sampling subjects and then perform a dimensional analysis that ignores the diagnostic label. Of course, this also depends on the validity of the model assumption. The critical assumption related to this issue is that the pathogenetic factors and the behavioral observations have a monotonic relation: The greater the measured value of the pathogenetic factor is, the greater the behavioral observation is. Owing to this relation, the severe inclusion criteria for the patient group make their pathogenetic factors easily distinguishable from those of the control group. If there is no such simple monotonic relation, the result can change. Such a violation may occur when the mapping from the pathogenetic factor to behavior has a nonlinear shape, such as the inverted U-shaped function or step function, which has a critical point above which the pathogenetic factor influences the behavior.

On the basis of the proposed framework, one can optimize the inclusion criteria (cutoff point) of specific disorders. As shown in Case 2, the more severe the inclusion criteria of the patient group are, the higher the statistical power is, given our assumption. However, there is a trade-off between the power and difficulty in finding samples. Severe criteria make finding the “patient” individuals difficult. The proposed framework can help determine the criteria considering the trade-off for specific situations. Note that this is the issue of basic research. For practical clinical applications, the optimal criteria would differ. A treatment can be effective even for individuals with modest symptoms. For clinical diagnosis, the optimal boundary should depend on the treatment response rather than be based solely on the statistical power.

Relation to Computational Psychiatry

We demonstrate how to incorporate the computational model in the proposed framework by using a reinforcement learning model with dopamine dysfunction. Candidate mathematical or computational models can span Marr’s three levels: computational, algorithmic, and implementational (Kurth-Nelson et al., 2016). To discuss how the dysfunction at the cellular or molecular level influences the symptom, models at a detailed biophysical level (e.g., biophysical neural circuit models; Wang & Krystal, 2014) would be suitable, whereas to discuss how the circuit-level dysfunction affects disorders, models at the intermediate level (e.g., connectionist models; Yamashita & Tani, 2012) would be useful. For the computational level or algorithm level, more abstract models, such as the Bayesian cognitive models (e.g., Lee & Wagenmaker, 2014) or reinforcement learning models, are possible candidates. In principle, the proposed framework can incorporate mathematical models at any level, as long as they can represent the rule of translating the pathogenetic factor to behavioral phenotypes. However, the models at a low abstraction level tend to have a large number of variables; thus generating samples for Monte Carlo simulations has considerable computational cost. For such cases, some approximation techniques based on the small number of simulated results would be helpful. For example, the relationship between DA parameters and the fraction of symptoms in Figures 8C and 8D can be approximated using a sigmoid function that is parametrized by these DA parameters. Some model reduction techniques developed in computational neuroscience, such as the mean-field method, would also be helpful (Deco, Jirsa, Robinson, Breakspear, & Friston, 2008; Wang & Krystal, 2014).

Currently the most successful applications of computational approaches to psychiatry may be those based on fitting models to behavior and/or neural activities. For example, model parameters that are fit to the subject’s behavior (e.g., Ahn et al., 2014; Culbreth, Westbrook, Daw, Botvinick, & Barch, 2016; Kunisato et al., 2012; Voon et al., 2015; Yechiam, Busemeyer, Stout, & Bechara, 2005) or the model latent variables that are correlated with blood oxygen level–dependent (BOLD) signals (e.g., Gradin et al., 2011; Murray et al., 2008) have been compared between subjects with a mental disorder and healthy controls. The parameters and variables of computational models are often associated with neuromodulators (Dayan & Huys, 2008; Doya, 2008; Stephan, Iglesias, Heinzle, & Diaconescu, 2015; Yu & Dayan, 2005). If there are indeed such associations, then the estimate of a model parameter or a latent variable can be used as an estimate of a pathogenetic factor. To discuss the effectiveness of such model-based approaches, the model fit procedures can be simulated in our framework: The estimation error of various model fit methods (e.g., maximum likelihood method or hierarchical Bayesian method) can be explicitly examined based on the synthesized dataset generated from a hypothetical “true model” (as in Katahira, 2016).

Related Work

Recently, Flagel et al. (2016) proposed a novel framework for psychiatric nosology, termed the Bayesian integrative framework. This framework includes the generative models that explicitly represent how symptoms, signs, and diagnoses arise from putative causes through a physiological state and “latent constructs,” which correspond to the constructs in RDoC. This framework uses Bayesian inference to infer the posterior probability of latent variables and to evaluate the models from an individual’s data. The procedures of the inference and model selection were demonstrated in Friston (2016).

The Bayesian integrative framework shares a common feature with our framework: Both frameworks use mathematical or computational models to model the generative processes of mental disorders. However, the goals of the two frameworks differ. The Bayesian integrative framework is designed to analyze individual data (including the diagnosis): It infers the latent cause of the disorder of the individuals through Bayesian inference. The Bayesian integrative framework is intended also to be used by clinicians to gather data for improving the model and nosology. The ultimate goals are aiding the diagnosis, prognosis, prevention, and treatment of mental disorders. In contrast, the scope of our framework is basic research strategies in psychiatry rather than a clinical use. In addition, the target of modeling in our framework is the population rather than the individual. Our framework is concerned with the sampling method of subjects, whereas the Bayesian integrative framework does not explicitly deal with the sampling procedure, at least currently. Thus our framework cannot provide useful information about the cause of the disorder of an individual patient, whereas the Bayesian integrative framework would provide such information.

The statistical methods considered in the framework also differ. The Bayesian integrative framework uses the Bayesian method, as its name suggests, whereas our framework is formulated with the classical hypothesis testing in mind, although replacing it with Bayesian hypothesis testing is straightforward. Whereas the Bayesian approach is more flexible, the classical statistical framework is more prevalent in psychiatry studies. The relations between the Bayesian integrative framework and our framework are complementary rather than competing. Our framework would be useful in choosing the research strategy in standard psychiatric studies. As sufficient knowledge is accumulated, more detailed models and precise data become available. Submitting these models and data into the Bayesian integrative framework would help further refine the model and predict treatment outcomes for individual patients.