Likelihood Free Bayesian Inference for Stochastic Kinetic Models

Ph.D thesisStochastic kinetic models are used to describe a variety of biological, physical and chemical phenomena. One particularly interesting application is computational systems biology, where models are useful for contributing to the quantitative understanding of cellular processes through in{silico experimentation that would otherwise be difficult to undertake in a laboratory. Interest lies in statistical inference for the parameters which govern the dynamics of the system. Likelihood based inference is typically problematic, as discrete time transition kernels for models of this type are intractable in all but the most trivial systems. However, exact realisations can be drawn using a stochastic simulation algorithm. Techniques that rely only on the ability to forward simulate from the model, so called likelihood free inference methods, such as particle Markov chain Monte Carlo and approximate Bayesian computation (ABC) can be leveraged to infer system rate parameters. What is not clear however is how each technique behaves as the nature of the problem changes. This thesis explores the likelihood free methodology applied to stochastic kinetic models in a range of scenarios in order to draw comparisons between the various developments in each. A variety of models and data observation regimes on synthetic data are used to examine the effect of the choice of summary statistics and metrics on the inferred posterior distributions, prevalent questions within the ABC framework. Likelihood free techniques are considered computationally expensive hence it is necessary to consider the relative efficiency of the various approaches. The relative strengths and weaknesses of particle Markov chain Monte Carlo and approximate Bayesian computation are explored and utilised to develop a hybrid technique exploiting the stronger elements of each approach. The thesis concludes with inference of rate parameters for a logistic growth model applied to observations of a uorescent protein in different strains of the gram- positive bacterium, Bacillus subtilis.Engineering and Physical Sciences Research Council (EPSRC)

An Intraocular Pressure Polygenic Risk Score Stratifies Multiple Primary Open-Angle Glaucoma Parameters Including Treatment Intensity

Purpose: To examine the combined effects of common genetic variants associated with intraocular pressure (IOP) on primary open-angle glaucoma (POAG) phenotype using a polygenic risk score (PRS) stratification. Design: Cross-sectional study. Participants: For the primary analysis, we examined the glaucoma phenotype of 2154 POAG patients enrolled in the Australian and New Zealand Registry of Advanced Glaucoma, including patients recruited from the United Kingdom. For replication, we examined an independent cohort of 624 early POAG patients. Methods Using IOP genome-wide association study summary statistics, we developed a PRS derived solely from IOP-associated variants and stratified POAG patients into 3 risk tiers. The lowest and highest quintiles of the score were set as the low- and high-risk groups, respectively, and the other quintiles were set as the intermediate risk group. Main Outcome Measures: Clinical glaucoma phenotype including maximum recorded IOP, age at diagnosis, number of family members affected by glaucoma, cup-to-disc ratio, visual field mean deviation, and treatment intensity. Results: A dose–response relationship was found between the IOP PRS and the maximum recorded IOP, with the high genetic risk group having a higher maximum IOP by 1.7 mmHg (standard deviation [SD], 0.62 mmHg) than the low genetic risk group (P = 0.006). Compared with the low genetic risk group, the high genetic risk group had a younger age of diagnosis by 3.7 years (SD, 1.0 years; P < 0.001), more family members affected by 0.46 members (SD, 0.11 members; P < 0.001), and higher rates of incisional surgery (odds ratio, 1.5; 95% confidence interval, 1.1–2.0; P = 0.007). No statistically significant difference was found in mean deviation. We further replicated the maximum IOP, number of family members affected by glaucoma, and treatment intensity (number of medications) results in the early POAG cohort (P ≤ 0.01). Conclusions: The IOP PRS was correlated positively with maximum IOP, disease severity, need for surgery, and number of affected family members. Genes acting via IOP-mediated pathways, when considered in aggregate, have clinically important and reproducible implications for glaucoma patients and their close family members

Multitrait analysis of glaucoma identifies new risk loci and enables polygenic prediction of disease susceptibility and progression

Glaucoma, a disease characterized by progressive optic nerve degeneration, can be prevented through timely diagnosis and treatment. We characterize optic nerve photographs of 67,040 UK Biobank participants and use a multitrait genetic model to identify risk loci for glaucoma. A glaucoma polygenic risk score (PRS) enables effective risk stratification in unselected glaucoma cases and modifies penetrance of the MYOC variant encoding p.Gln368Ter, the most common glaucoma-associated myocilin variant. In the unselected glaucoma population, individuals in the top PRS decile reach an absolute risk for glaucoma 10 years earlier than the bottom decile and are at 15-fold increased risk of developing advanced glaucoma (top 10% versus remaining 90%, odds ratio = 4.20). The PRS predicts glaucoma progression in prospectively monitored, early manifest glaucoma cases (P = 0.004) and surgical intervention in advanced disease (P = 3.6 × 10). This glaucoma PRS will facilitate the development of a personalized approach for earlier treatment of high-risk individuals, with less intensive monitoring and treatment being possible for lower-risk groups

Effects of antiplatelet therapy on stroke risk by brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases: subgroup analyses of the RESTART randomised, open-label trial

Background Findings from the RESTART trial suggest that starting antiplatelet therapy might reduce the risk of recurrent symptomatic intracerebral haemorrhage compared with avoiding antiplatelet therapy. Brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases (such as cerebral microbleeds) are associated with greater risks of recurrent intracerebral haemorrhage. We did subgroup analyses of the RESTART trial to explore whether these brain imaging features modify the effects of antiplatelet therapy

Meta-analysis of genome-wide association studies identifies novel loci that influence cupping and the glaucomatous process

Glaucoma is characterized by irreversible optic nerve degeneration and is the most frequent cause of irreversible blindness worldwide. Here, the International Glaucoma Genetics Consortium conducts a meta-analysis of genome-wide association studies of vertical cup-disc ratio (VCDR), an important disease-related optic nerve parameter. In 21,094 individuals of European ancestry and 6,784 individuals of Asian ancestry, we identify 10 new loci associated with variation in VCDR. In a separate risk-score analysis of five case-control studies, Caucasians in the highest quintile have a 2.5-fold increased risk of primary open-angle glaucoma as compared with those in the lowest quintile. This study has more than doubled the known loci associated with optic disc cupping and will allow greater understanding of mechanisms involved in this common blinding condition

Cross-ancestry genome-wide association analysis of corneal thickness strengthens link between complex and Mendelian eye diseases

Central corneal thickness (CCT) is a highly heritable trait associated with complex eye diseases such as keratoconus and glaucoma. We perform a genome-wide association meta-analysis of CCT and identify 19 novel regions. In addition to adding support for known connective tissue-related pathways, pathway analyses uncover previously unreported gene sets. Remarkably, >20% of the CCT-loci are near or within Mendelian disorder genes. These included FBN1, ADAMTS2 and TGFB2 which associate with connective tissue disorders (Marfan, Ehlers-Danlos and Loeys-Dietz syndromes), and the LUM-DCN-KERA gene complex involved in myopia, corneal dystrophies and cornea plana. Using index CCT-increasing variants, we find a significant inverse correlation in effect sizes between CCT and keratoconus (r =-0.62, P = 5.30 × 10-5) but not between CCT and primary open-angle glaucoma (r =-0.17, P = 0.2). Our findings provide evidence for shared genetic influences between CCT and keratoconus, and implicate candidate genes acting in collagen and extracellular matrix regulation

Cross-ancestry genome-wide association analysis of corneal thickness strengthens link between complex and Mendelian eye diseases.

Central corneal thickness (CCT) is a highly heritable trait associated with complex eye diseases such as keratoconus and glaucoma. We perform a genome-wide association meta-analysis of CCT and identify 19 novel regions. In addition to adding support for known connective tissue-related pathways, pathway analyses uncover previously unreported gene sets. Remarkably, >20% of the CCT-loci are near or within Mendelian disorder genes. These included FBN1, ADAMTS2 and TGFB2 which associate with connective tissue disorders (Marfan, Ehlers-Danlos and Loeys-Dietz syndromes), and the LUM-DCN-KERA gene complex involved in myopia, corneal dystrophies and cornea plana. Using index CCT-increasing variants, we find a significant inverse correlation in effect sizes between CCT and keratoconus (r = -0.62, P = 5.30 × 10-5) but not between CCT and primary open-angle glaucoma (r = -0.17, P = 0.2). Our findings provide evidence for shared genetic influences between CCT and keratoconus, and implicate candidate genes acting in collagen and extracellular matrix regulation