Figure 1b is equivalent to a standard mediational model as commonly articulated in the psychological literature.⁶ Both these models generate the pattern of findings required by most of the criteria listed in Table 1. For example, both the liability-index and the mediational model would generate data that satisfy both criteria 4 (cosegregate with illness in families) and 5 (found at increased rates in unaffected family members) of Gottesman and Gould.² Furthermore, both the liability-index and the mediational models would be useful in a developmental context. In both models, unaffected individuals with high scores on EP would be predicted to be at elevated risk for the development of PD.

The mediational model predicts that the causal processes captured by the ‘genes’ to ‘EP’ path are shared between EP and PD. The liability-index model does not make this assumption. Most importantly, the mediational model predicts that if it were possible to change EP with an exogenous variable (for example, a cognitive or pharmacological treatment), doing so would result in a decline in risk for PD. The risk-indicator model makes no such prediction.

This critical difference between these two models can perhaps be best illustrated by the different predictions they would make about the target of treatment of unaffected individuals at high risk of PD because of elevated EP scores. The mediational model would suggest that treatments could be targeted toward reducing levels of EP with the conviction that a lowering of disease risk would necessarily follow. The risk-indicator model, by contrast, would indicate that treatments should be directed toward correcting the underlying genetic liability, as there would be no guarantee that interventions that reduced EP would prevent illness onset.

Although the distinction between the liability-index and mediational models for EP is conceptually important, it is devilishly difficult in humans to design experiments to discriminate powerfully between them. Rarely can we directly intervene on EP and determine whether risk for PD is altered. Longitudinal and twin models can potentially discriminate between causal and noncausal relationships between an EP and a PD,^7,8 but sample sizes sufficient to allow for powerful discrimination may be hard to achieve, especially with relatively rare PDs and/or expensive EPs.⁹ Developmental studies in which interventions directly on EP in unaffected individuals can be tested to see whether they reduce disease risk would be another way to test the mediational model.

We can best illustrate this point using path models. Assume, for example, the mediational model for EP as depicted in Figure 1b. As pictured, as long as EP is not perfectly correlated with PD (that is, the standardized path from EP to PD is < |1.00|), it is logically necessary that the genetic effect will be stronger on EP than on PD. However, this model ignores measurement error.

Figure 2a represents a more realistic model incorporating errors of measurement. This figure depicts a mediational model for EP that includes a path from the latent EP to the latent PD (β) and paths from these two latent constructs to the observed constructs, which reflect the accuracy with which they are assessed (λ_EP and λ_PD, respectively). (Latent here refers to an unmeasured ‘true’ construct and is traditionally depicted in path diagrams by circles or ovals, whereas measured variables are depicted in squares or rectangles.) Simple algebra allows us to conclude that the genetic effect will be stronger for EP than PD whenever λ_EP < βλ_PD. Figure 2b depicts the risk-indicator model for EP, which has a direct path from genes to the latent EP (β_EP) and from genes to PD (β_PD). For this model, the genetic effects on EP will exceed those on PD whenever a_EPλ_EP > a_PDλ_PD.

As EPs are often measured using sophisticated imaging, neurophysiological or neuropsychological measures, there is a tendency to assume that such ‘harder’ measures are, of necessity, more reliable than the ‘softer’ psychiatric diagnoses. That is, we commonly assume that λ_EP exceeds λ_PD. However, this assumption may be incorrect. Many putative EPs are measured over short time intervals and can be influenced by transient state effects such as ambient noise, temperature, time of day, or variations in machine functioning—as well as temporary changes in mental state of the participant due to stressors, or consumption of or withdrawal from nicotine, caffeine or alcohol. By contrast, some PDs are assessed using years of medical records and the recording of symptoms occurring over similar periods, or with carefully constructed psychological instruments. For example, Gur et al.¹² report that the 1-year stability for a commonly used measure of the Continuous Performance Test was ‘found to be 0.65 for schizophrenia patients and 0.72 for healthy subjects,’ whereas another such measure had stability over 2 years, which ranged from 0.56 to 0.73. The reliability of brain functional magnetic resonance imaging (fMRI) is quite variable and for some paradigms is under +0.30.^13–15 However, other EPs, such as structural MRI, might be highly reliable as indicated by a recent report showing test–retest correlations > +0.95 for measures of cortical thickness.¹⁶ By contrast, in the Irish Study of High-Density Schizophrenia Families, which used both in-depth personal interviews and extensive reviews of hospital records, the diagnostic reliability, assessed using a weighted κ, was +0.94.¹⁷ Conversely, in the Virginia Adult Twin Study of Psychiatric and Substance Use Disorders, the long-term stability of an interview-based assessment of lifetime major depression was κ = +0.43,¹⁸ considerably lower than the reliability of the short form of the Eysenck’s neuroticism scale (r = +0.69) which has been proposed as an EP for MD—measured over a comparable time period. The major point here is that the relative ‘performance’ of EPs versus PD in assessing a ‘genetic signal’ cannot be divorced from the problems of measurement. It is perfectly possible for us to study an EP that is ‘truly’ closer to gene action than our PD. But if our measures of EP are less reliable than those of our PD, unless we account for this unreliability in our models, we would get the wrong answer—that EP cannot be sitting in the causal path to our PD.

For readers of a more biological bent, it might help to illustrate one possible scenario that would be described by Figure 4a. As seen in Figure 4b, imagine we had a shared pathophysiological pathway from A to D, with each step having its own genetic influences. Then one etiological pathway goes in one direction through steps E and F and influences EP. The other direction, which includes sets G and H, leads to PD. In this case, EP and PD would share genetic influences on A, B, C and D, but have unique genetic influences that affect stages E, F, G and H.

As r_g approaches 1.0, Figure 4a becomes equivalent to Figure 1a (and this becomes equivalent to the paths for EP and PD coming both from step D in Figure 4b). Obviously, the interest and utility of an EP for a given PD would relate to the value of r_g. If r_g were quite low, measuring EP would tell you relatively little about the genetic risk for PD.

Assuming EPs as risk indicators, we illustrate in Figure 5 one such possible model. This model includes three sets of genetic risk factors (which we assume for simplicity are uncorrelated), two EPs (EP1 and EP2) and one PD. We further assume that the third genetic risk factor affects only PD. The paths from these sets of genes to EPs and PD are identified by path names so that a₁₁ reflects the path from the first risk factor to the first EP, and path a_PD2 reflects the path from the second genetic risk factor to PD. Finally, imagine a situation in which paths a₁₂ and a₂₁ are very low. In such a situation, you would expect (at least from a genetic perspective) that the correlation between the scores on EP1 and EP2 would be quite low. However, both could be valuable and complementary from a research perspective. That is, if paths a₁₁ and a_PD1 are high, then EP1 will function as a good risk indicator for the first genetic risk factor. If paths a₂₂ and a_PD2 are high, then EP2 will function as a good risk indicator for the second genetic risk factor. Thus, in this situation, each EP indexes a different set of risk genes for PD.

To make matters more complex, it is perfectly possible that certain EPs reflect both the genetic and the environmental risk factors for a disorder. For example, the cognitive abnormalities considered to be an EP for schizophrenia are likely influenced both by genetic risk factors for schizophrenia, as well as environmental risk factors such as famine,²⁰ in utero viral infections²¹ or birth complications.²²

First, the field has paid insufficient attention to the potential causal claims surrounding EPs. A mediational model for EPs is a stronger scientific claim than a liability-index model. It is more falsifiable and hence, from a Popperian perspective, a ‘stronger’ hypothesis. However, because it contains causal claims, it is more difficult to test, especially in a nonexperimental setting. It is not an accident that models in this paper have largely used the simpler but less informative liability-index model. Walters and Owen⁴ would save the term EP solely for variables fitting our mediational model and would use a new term like ‘biomarker’ for risk-indicator variables. Yet it is difficult in humans to actually discriminate between liability-index and mediational models, especially when joint models (genetic factors operate directly on both EP and PD but there is also a causal path from EP to PD) are plausible alternatives. Whether an alternative term such as biomarker is warranted for genetic correlates of a PD remains a matter of debate.

Second, measurement error is generally conceived of as a ‘nuisance’ variable, which is rarely visible on the radar screen of researchers. However, the models presented above illustrate that researchers using an EP strategy ignore measurement error at their peril. The wrong answer can be obtained about the nature of EP–PD relationship if such error is not properly modeled.

Third, EP models have, to date, been relatively restricted and have incorporated what are likely to be unrealistic assumptions such as all the genetic influences on EP will affect risk for PD, and vice versa, or that environmental risk factors for PD will have no impact on EP. As this article suggests, EPs are probably best considered as part of a family of bi- and multivariate models that can be well captured by a range of developments in statistical genetics.

Fourth, our models illustrate some of the complexity inherent in comparing the predictive power of an EP and PD. EP have one important starting advantage in which they are typically quantitative, thereby providing more information than the dichotomous diagnostic assessment used for PD. This is especially true for relatively rare PDs like schizophrenia, bipolar illness or anorexia nervosa in which being unaffected is rather uninformative, only indicating that the individual is somewhere in the lower 99% of risk in the population. But the predictive power of EP will be attenuated when it is measured with low reliability, if the genetic risk factors of EP are only partially correlated with those of PD, or if EP is reflecting only a subset of the risk genes.