Improved methodology for understanding the genetics of complex traits, with particular application to epilepsy.

The heritability of a trait determines an upper bound on how well we can understand its underlying genetics. For the case of a human disease, this determines how successfully we can predict an individual's disease risk, and how well we can develop effective drugs and treatments. Many human diseases are known to be highly heritable, based on measurements made in twin, sibling-risk, or other family-based studies. However, at present we are have not been able to fully make use of this heritability. Evidence suggests that this is because disease are more complicated than once thought. It is rarely the case that a single gene determines whether an individual develops a condition. Instead, it has been realised that more often an individual's risk is affected by a large number of genetic factors. This realisation means it is necessary to develop new methods for analysing genetic data. These methods must appreciate that many factors are likely to be important for any given trait. My project outlines new methodologies designed with this in mind.

One of these methods explains how to better predict whether an individual will develop a disease based on their DNA. For example, suppose that an individual experiences an epileptic seizure. There is a 50% chance that this individual will have further seizures and will therefore be diagnosed with epilepsy. In this case, it would be necessary to administer anti-epileptic drugs to treat the condition. However, there is also a 50% chance that the individual will never experience another seizure. However, to be sufficiently certain that this is the case, the individually will have to be observed for a year, and would not be allowed to drive a motor vehicle during that time. I propose a prediction method which will improve our ability to determine whether an individual who experiences a seizure will subsequently develop epilepsy. This will either speed-up the time taken to administer drugs, or speed-up the time taken to receive the all-clear.

For the case that an individual is diagnosed with epilepsy, it is necessary to decide what is the most appropriate type of drugs to provide. This decision depends on what subtype of epilepsy the individual has, as different medications are more suitable for different subtypes. However, it is often difficult to determine what type of epilepsy an individual has. Therefore, I will develop a method for better classifying individuals, again based on their genetic data.

So that my methods as useful as possible, I will make them freely-available, and design them to be used by all types of scientists.

Heritability analysis supposes a random effects model where the correlation structure of the random effect is specified by a kinship matrix K. When K corresponds to allelic correlations, it is convenient to view the underlying model in terms of an equivalent linear regression model, where each individual's phenotype is determined by a linear combination of its SNP genotypes (plus an environmental noise term), and each SNP's effect size is assumed normally distributed with constant variance. To realise the full potential of heritability analysis, it is necessary to appreciate that there are many varieties of this underlying model, meaning many different K can be computed. For example, I intend to improve BLUP by incorporating more than one kinship matrix, such that each corresponds to a separate variance term. For example, if allowing K1 and K2, the revised BLUP would benefit when K1 tends to correspond to stronger effect SNPs and K2 to weaker ones.

The standard kinship matrix corresponds to assigning each SNP an independent effect size. When rare variants are included, the (effective) degrees of freedom becomes prohibitively large to allow useful estimation of h^2. However, the degrees of freedom can be reduced by placing restrictions on variant effect sizes, such as hierarchical priors.

Two of my proposed methods concern enhancements of the REML algorithm. Although a classical technique, this can be viewed from a Bayesian angle. For example, estimation of h^2 equates to computing the posterior mode of h^2. This task is optimised through use of an eigen decomposition. When using this trick, including a prior on h^2 requires only a slight amendment (the need to differentiate this prior), so computation time will be barely affected. To estimate the distribution of h^2 for use in heritability meta analysis, requires sampling from its posterior distribution. But again, as the bottle-neck of REML is the decomposition, this will result in only a modest delay.

It is simply the case that everyone can potentially benefit from this type of research. The obvious example is the application of these methods to human diseases (or equally to health-related quantitative traits such as BMI or cholesterol). There is tremendous value in detecting variants, genes or pathways which are causal for a disease; each finding will improve our understanding of the condition, and bring us a step closer to developing adequate treatment. Similarly, there is clear advantage to developing effective prediction models, or better classification of phenotypic subtypes, as these move us nearer to the possibility of personalised medicine.

To give a clear example for epilepsy, through earlier work I have determined that approximately 30% of the trait's variance (on the liability scale) can be explained by common variants. This 30% corresponds to an upper bound on how effectively common variants could explain risk susceptibility. Although to get close to this bound, we would require studies across many millions of individuals, experience with traits such as human height suggest that for reasonable numbers of individuals, using BLUP it should be possible to develop a prediction model explaining between 3 and 6% of underlying variation. Simulations suggest that a model explaining 10% of variation would be clinically useful for selecting which single-seizure individuals are most likely to develop epilepsy. This target is not too far away; potentially the information obtained by performing heritability meta analysis across the 50,000 individuals of the ILAE consortium, integrated into my improved BLUP methodology, would bring this figure within reach.

Moreover, the benefits of improved prediction and detection of causal variants are not just limited to human traits. There is also great benefit in better understanding complex traits for animals and plants. For example, genomic selection uses BLUP-based methods to determine which animals or plants to breed in order to efficiently produce the most desirable breeding stock (here, the phenotype might be, say, weight of bull or yield of wheat). Because of the way heritability analysis and BLUP are inextricably linked, any methodological improvement in one, will invariably benefit the other. A nice example of the power of genomic selection, presented at a recent conference, was the case where maize was bred to increase its vitamin levels, so as to benefit people living in under-nourished areas. Additionally, with organisms such as maize having short breeding cycles, and fewer safety concerns compared to dealing with human traits, this type of benefit can be brought to bear relatively quickly.