Addressing issues in sparseness, ecological bias and formulation of the adjacency matrix in Bayesian spatio-temporal analysis of disease counts

The main objective of this PhD was to further develop Bayesian spatio-temporal models (specifically the Conditional Autoregressive (CAR) class of models), for the analysis of sparse disease outcomes such as birth defects. The motivation for the thesis arose from problems encountered when analyzing a large birth defect registry in New South Wales. The specific components and related research objectives of the thesis were developed from gaps in the literature on current formulations of the CAR model, and health service planning requirements. Data from a large probabilistically-linked database from 1990 to 2004, consisting of fields from two separate registries: the Birth Defect Registry (BDR) and Midwives Data Collection (MDC) were used in the analyses in this thesis. The main objective was split into smaller goals. The first goal was to determine how the specification of the neighbourhood weight matrix will affect the smoothing properties of the CAR model, and this is the focus of chapter 6. Secondly, I hoped to evaluate the usefulness of incorporating a zero-inflated Poisson (ZIP) component as well as a shared-component model in terms of modeling a sparse outcome, and this is carried out in chapter 7. The third goal was to identify optimal sampling and sample size schemes designed to select individual level data for a hybrid ecological spatial model, and this is done in chapter 8. Finally, I wanted to put together the earlier improvements to the CAR model, and along with demographic projections, provide forecasts for birth defects at the SLA level. Chapter 9 describes how this is done. For the first objective, I examined a series of neighbourhood weight matrices, and showed how smoothing the relative risk estimates according to similarity by an important covariate (i.e. maternal age) helped improve the model’s ability to recover the underlying risk, as compared to the traditional adjacency (specifically the Queen) method of applying weights. Next, to address the sparseness and excess zeros commonly encountered in the analysis of rare outcomes such as birth defects, I compared a few models, including an extension of the usual Poisson model to encompass excess zeros in the data. This was achieved via a mixture model, which also encompassed the shared component model to improve on the estimation of sparse counts through borrowing strength across a shared component (e.g. latent risk factor/s) with the referent outcome (caesarean section was used in this example). Using the Deviance Information Criteria (DIC), I showed how the proposed model performed better than the usual models, but only when both outcomes shared a strong spatial correlation. The next objective involved identifying the optimal sampling and sample size strategy for incorporating individual-level data with areal covariates in a hybrid study design. I performed extensive simulation studies, evaluating thirteen different sampling schemes along with variations in sample size. This was done in the context of an ecological regression model that incorporated spatial correlation in the outcomes, as well as accommodating both individual and areal measures of covariates. Using the Average Mean Squared Error (AMSE), I showed how a simple random sample of 20% of the SLAs, followed by selecting all cases in the SLAs chosen, along with an equal number of controls, provided the lowest AMSE. The final objective involved combining the improved spatio-temporal CAR model with population (i.e. women) forecasts, to provide 30-year annual estimates of birth defects at the Statistical Local Area (SLA) level in New South Wales, Australia. The projections were illustrated using sixteen different SLAs, representing the various areal measures of socio-economic status and remoteness. A sensitivity analysis of the assumptions used in the projection was also undertaken. By the end of the thesis, I will show how challenges in the spatial analysis of rare diseases such as birth defects can be addressed, by specifically formulating the neighbourhood weight matrix to smooth according to a key covariate (i.e. maternal age), incorporating a ZIP component to model excess zeros in outcomes and borrowing strength from a referent outcome (i.e. caesarean counts). An efficient strategy to sample individual-level data and sample size considerations for rare disease will also be presented. Finally, projections in birth defect categories at the SLA level will be made.

A recurrent mutation in the BMP type I receptor ACVR1 causes inherited and sporadic fibrodysplasia ossificans progressiva

Fibrodysplasia ossificans progressiva (FOP) is a rare autosomal dominant disorder of skeletal malformations and progressive extraskeletal ossification. We mapped FOP to chromosome 2q23-24 by linkage analysis and identified an identical heterozygous mutation (617G→A; R206H) in the glycine-serine (GS) activation domain of ACVR1, a BMP type I receptor, in all affected individuals examined. Protein modeling predicts destabilization of the GS domain, consistent with constitutive activation of ACVR1 as the underlying cause of the ectopic chondrogenesis, osteogenesis and joint fusions seen in FOP.

Next-generation sequencing: A frameshift in skeletal dysplasia gene discovery

In the last decade, huge breakthroughs in genetics - driven by new technology and different statistical approaches - have resulted in a plethora of new disease genes identified for both common and rare diseases. Massive parallel sequencing, commonly known as next-generation sequencing, is the latest advance in genetics, and has already facilitated the discovery of the molecular cause of many monogenic disorders. This article describes this new technology and reviews how this approach has been used successfully in patients with skeletal dysplasias. Moreover, this article illustrates how the study of rare diseases can inform understanding and therapeutic developments for common diseases such as osteoporosis. © International Osteoporosis Foundation and National Osteoporosis Foundation 2013.

Interaction of myxomatosis and Rabbit Haemorrhagic Disease in wild rabbit

Increasing resistance of rabbits to myxomatosis in Australia has led to the exploration of Rabbit Haemorrhagic Disease, also called Rabbit Calicivirus Disease (RCD) as a possible control agent. While the initial spread of RCD in Australia resulted in widespread rabbit mortality in affected areas, the possible population dynamic effects of RCD and myxomatosis operating within the same system have not been properly explored. Here we present early mathematical modelling examining the interaction between the two diseases. In this study we use a deterministic compartment model, based on the classical SIR model in infectious disease modelling. We consider, here, only a single strain of myxomatosis and RCD and neglect latent periods. We also include logistic population growth, with the inclusion of seasonal birth rates. We assume there is no cross-immunity due to either disease. The mathematical model allows for the possibility of both diseases to be simultaneously present in an individual, although results are also presented for the case where co infection is not possible, since co-infection is thought to be rare and questions exist as to whether it can occur. The simulation results of this investigation show that it is a crucial issue and should be part of future field studies. A single simultaneous outbreak of RCD and myxomatosis was simulated, while ignoring natural births and deaths, appropriate for a short timescale of 20 days. Simultaneous outbreaks may be more common in Queensland. For the case where co-infection is not possible we find that the simultaneous presence of myxomatosis in the population suppresses the prevalence of RCD, compared to an outbreak of RCD with no outbreak of myxomatosis, and thus leads to a less effective control of the population. The reason for this is that infection with myxomatosis removes potentially susceptible rabbits from the possibility of infection with RCD (like a vaccination effect). We found that the reduction in the maximum prevalence of RCD was approximately 30% for an initial prevalence of 20% of myxomatosis, for the case where there was no simultaneous outbreak of myxomatosis, but the peak prevalence was only 15% when there was a simultaneous outbreak of myxomatosis. However, this maximum reduction will depend on other parameter values chosen. When co-infection is allowed then this suppression effect does occur but to a lesser degree. This is because the rabbits infected with both diseases reduces the prevalence of myxomatosis. We also simulated multiple outbreaks over a longer timescale of 10 years, including natural population growth rates, with seasonal birth rates and density dependent(logistic) death rates. This shows how both diseases interact with each other and with population growth. Here we obtain sustained outbreaks occurring approximately every two years for the case of a simultaneous outbreak of both diseases but without simultaneous co-infection, with the prevalence varying from 0.1 to 0.5. Without myxomatosis present then the simulation predicts RCD dies out quickly without further introduction from elsewhere. With the possibility of simultaneous co-infection of rabbits, sustained outbreaks are possible but then the outbreaks are less severe and more frequent (approximately yearly). While further model development is needed, our work to date suggests that: 1) the diseases are likely to interact via their impacts on rabbit abundance levels, and 2) introduction of RCD can suppress myxomatosis prevalence. We recommend that further modelling in conjunction with field studies be carried out to further investigate how these two diseases interact in the population.

The revolution in human monogenic disease mapping

The successful completion of the Human Genome Project (HGP) was an unprecedented scientific advance that has become an invaluable resource in the search for genes that cause monogenic and common (polygenic) diseases. Prior to the HGP, linkage analysis had successfully mapped many disease genes for monogenic disorders; however, the limitations of this approach were particularly evident for identifying causative genes in rare genetic disorders affecting lifespan and/or reproductive fitness, such as skeletal dysplasias. In this review, we illustrate the challenges of mapping disease genes in such conditions through the ultra-rare disorder fibrodysplasia ossificans progressiva (FOP) and we discuss the advances that are being made through current massively parallel (“next generation”) sequencing (MPS) technologies.

A rare P2X7 variant Arg307Gln with absent pore formation function protects against neuroinflammation in multiple sclerosis

Multiple sclerosis (MS) is a chronic relapsing-remitting inflammatory disease of the central nervous system characterized by oligodendrocyte damage, demyelination and neuronal death. Genetic association studies have shown a 2-fold or greater prevalence of the HLA-DRB1*1501 allele in the MS population compared with normal Caucasians. In discovery cohorts of Australasian patients with MS (total 2941 patients and 3008 controls), we examined the associations of 12 functional polymorphisms of P2X7, a microglial/macrophage receptor with proinflammatory effects when activated by extracellular adenosine triphosphate (ATP). In discovery cohorts, rs28360457, coding for Arg307Gln was associated with MS and combined analysis showed a 2-fold lower minor allele frequency compared with controls (1.11% for MS and 2.15% for controls, P = 0.0000071). Replication analysis of four independent European MS case–control cohorts (total 2140 cases and 2634 controls) confirmed this association [odds ratio (OR) = 0.69, P = 0.026]. A meta-analysis of all Australasian and European cohorts indicated that Arg307Gln confers a 1.8-fold protective effect on MS risk (OR = 0.57, P = 0.0000024). Fresh human monocytes heterozygous for Arg307Gln have >85% loss of ‘pore’ function of the P2X7 receptor measured by ATP-induced ethidium uptake. Analysis shows Arg307Gln always occurred with 270His suggesting a single 307Gln–270His haplotype that confers dominant negative effects on P2X7 function and protection against MS. Modeling based on the homologous zP2X4 receptor showed Arg307 is located in a region rich in basic residues located only 12 Å from the ligand binding site. Our data show the protective effect against MS of a rare genetic variant of P2RX7 with heterozygotes showing near absent proinflammatory ‘pore’ function.

Weather variability, tides, and Barmah Forest Virus Disease in the Gladstone region, Australia

In this study we examined the impact of weather variability and tides on the transmission of Barmah Forest virus (BFV) disease and developed a weather-based forecasting model for BFV disease in the Gladstone region, Australia. We used seasonal autoregressive integrated moving-average (SARIMA) models to determine the contribution of weather variables to BFV transmission after the time-series data of response and explanatory variables were made stationary through seasonal differencing. We obtained data on the monthly counts of BFV cases, weather variables (e.g., mean minimum and maximum temperature, total rainfall, and mean relative humidity), high and low tides, and the population size in the Gladstone region between January 1992 and December 2001 from the Queensland Department of Health, Australian Bureau of Meteorology, Queensland Department of Transport, and Australian Bureau of Statistics, respectively. The SARIMA model shows that the 5-month moving average of minimum temperature (β = 0.15, p-value < 0.001) was statistically significantly and positively associated with BFV disease, whereas high tide in the current month (β = −1.03, p-value = 0.04) was statistically significantly and inversely associated with it. However, no significant association was found for other variables. These results may be applied to forecast the occurrence of BFV disease and to use public health resources in BFV control and prevention.

Electrochemistry of Heteroleptic Tris(phthalocyaninato) Rare Earth(III) Complexes

The electrochemical characteristics of a series of heteroleptic tris(phthalocyaninato) complexes with identical rare earths or mixed rare earths (Pc)M(OOPc)M(OOPc) [M = Eu...Lu, Y; H2Pc = unsubstituted phthalocyanine, H2(OOPc) = 3,4,12,13,21,22,30,31-octakis(octyloxy)phthalocyanine] and (Pc)Eu(OOPc)Er(OOPc) have been recorded and studied comparatively by cyclic voltammetry (CV) and differential pulse voltammetry (DPV) in CH2Cl2 containing 0.1 M tetrabutylammonium perchlorate (TBAP). Up to five quasi-reversible one-electron oxidations and four one-electron reductions have been revealed. The half-wave potentials of the first, second and fifth oxidations depend on the size of the metal center, but the fifth changes in the opposite direction to that of the first two. Moreover, the difference in redox potentials of the first oxidation and first reduction for (Pc)M(OOPc)M(OOPc), 0.85−0.98 V, also decreases linearly along with decreasing rare earth ion radius, clearly showing the rare earth ion size effect and indicating enhanced π−π interactions in the triple-deckers connected by smaller lanthanides. This order follows the red-shift seen in the lowest energy band of triple-decker compounds. The electronic differences between the lanthanides and yttrium are more apparent for triple-decker sandwich complexes than for the analogous double-deckers. By comparing triple-decker, double-decker and mononuclear [ZnII] complexes containing the OOPc ligand, the HOMO−LUMO gap has been shown to contract approximately linearly with the number of stacked phthalocyanine ligands.

Sandwich complexes of naphthalocyanine with the rare earth metals

Over the past two decades and in particular the past five years, numerous sandwich-type rare earth complexes containing naphthalocyanine ligands have been synthesized. The more extended delocalized π-electron system of naphthalocyanine in comparison with phthalocyanine generates unique physical, spectroscopic, electrochemical and photoelectrochemical properties which have aroused significant research interest in these compounds. This review summarizes recent progress in research on this important class of molecular materials and overviews the current status of the field.

Synthesis and characterization of K2Ca5(SO4)6· H2O, the equivalent of görgeyite, a rare evaporite mineral

Görgeyite, K2Ca5(SO4)6··H2O, is a very rare monoclinic double salt found in evaporites related to the slightly more common mineral syngenite. At 1 atmosphere with increasing external temperature from 25 to 150 °C, the following succession of minerals was formed: first gypsum and K2O, followed at 100 °C by görgeyite. Changes in concentration at 150 °C due to evaporation resulted in the formation of syngenite and finally arcanite. Under hydrothermal conditions, the succession is syngenite at 50 °C, followed by görgyeite at 100 and 150 °C. Increasing the synthesis time at 100 °C and 1 atmosphere showed that initially gypsum was formed, later being replaced by görgeyite. Finally görgeyite was replaced by syngenite, indicating that görgeyite is a metastable phase under these conditions. Under hydrothermal conditions, syngenite plus a small amount of gypsum was formed, after two days being replaced by görgeyite. No further changes were observed with increasing time. Pure görgeyite showed elongated crystals approximately 500 to 1000 µ m in length. The infrared and Raman spectra are mainly showing the vibrational modes of the sulfate groups and the crystal water (structural water). Water is characterized by OH-stretching modes at 3526 and 3577 cm–1 , OH-bending modes at 1615 and 1647 cm–1 , and an OH-libration mode at 876 cm–1 . The sulfate 1 mode is weak in the infrared but showed strong bands at 1005 and 1013 cm–1 in the Raman spectrum. The 2 mode also showed strong bands in the Raman spectrum at 433, 440, 457, and 480 cm–1 . The 3 mode is characterized by a complex set of bands in both infrared and Raman spectra around 1150 cm–1 , whereas 4 is found at 650 cm–1.

Comparative Electrochemical Study of Unsubstituted and Substituted Bis(phthalocyaninato) Rare Earth(III) Complexes

The electrochemistry of homoleptic substituted phthalocyaninato rare earth double-decker complexes M(TBPc)2 and M(OOPc)2 [M = Y, La...Lu except Pm; H2TBPc = 3(4),12(13),21(22),30(31)-tetra-tert-butylphthalocyanine, H2OOPc = 3,4,12,13,21,22,30,31-octakis(octyloxy)phthalocyanine] has been comparatively studied by cyclic voltammetry (CV) and differential pulse voltammetry (DPV) in CH2Cl2 containing 0.1 M tetra-n-butylammonium perchlorate (TBAP). Two quasi-reversible one-electron oxidations and three or four quasi-reversible one-electron reductions have been revealed for these neutral double-deckers of two series of substituted complexes, respectively. For comparison, unsubstituted bis(phthalocyaninato) rare earth analogues M(Pc)2 (M = Y, La...Lu except Pm; H2Pc = phthalocyanine) have also been electrochemically investigated. Two quasi-reversible one-electron oxidations and up to five quasi-reversible one-electron reductions have been revealed for these neutral double-decker compounds. The three bis(phthalocyaninato)cerium compounds display one cerium-centered redox wave between the first ligand-based oxidation and reduction. The half-wave potentials of the first and second oxidations and first reduction for double-deckers of the tervalent rare earths depend on the size of the metal center. The difference between the redox potentials of the second and third reductions for MIII(Pc)2, which represents the potential difference between the first oxidation and first reduction of [MIII(Pc)2]−, lies in the range 1.08−1.37 V and also gradually diminishes along with the lanthanide contraction, indicating enhanced π−π interactions in the double-deckers connected by the smaller, lanthanides. This corresponds well with the red-shift of the lowest energy band observed in the electronic absorption spectra of reduced double-decker [MIII(Pc′)2]− (Pc′ = Pc, TBPc, OOPc).