Using Bayesian methods for the estimation of uncertainty in complex statistical models

The research objectives of this thesis were to contribute to Bayesian statistical methodology by contributing to risk assessment statistical methodology, and to spatial and spatio-temporal methodology, by modelling error structures using complex hierarchical models. Specifically, I hoped to consider two applied areas, and use these applications as a springboard for developing new statistical methods as well as undertaking analyses which might give answers to particular applied questions. Thus, this thesis considers a series of models, firstly in the context of risk assessments for recycled water, and secondly in the context of water usage by crops. The research objective was to model error structures using hierarchical models in two problems, namely risk assessment analyses for wastewater, and secondly, in a four dimensional dataset, assessing differences between cropping systems over time and over three spatial dimensions. The aim was to use the simplicity and insight afforded by Bayesian networks to develop appropriate models for risk scenarios, and again to use Bayesian hierarchical models to explore the necessarily complex modelling of four dimensional agricultural data. The specific objectives of the research were to develop a method for the calculation of credible intervals for the point estimates of Bayesian networks; to develop a model structure to incorporate all the experimental uncertainty associated with various constants thereby allowing the calculation of more credible credible intervals for a risk assessment; to model a single day’s data from the agricultural dataset which satisfactorily captured the complexities of the data; to build a model for several days’ data, in order to consider how the full data might be modelled; and finally to build a model for the full four dimensional dataset and to consider the timevarying nature of the contrast of interest, having satisfactorily accounted for possible spatial and temporal autocorrelations. This work forms five papers, two of which have been published, with two submitted, and the final paper still in draft. The first two objectives were met by recasting the risk assessments as directed, acyclic graphs (DAGs). In the first case, we elicited uncertainty for the conditional probabilities needed by the Bayesian net, incorporated these into a corresponding DAG, and used Markov chain Monte Carlo (MCMC) to find credible intervals, for all the scenarios and outcomes of interest. In the second case, we incorporated the experimental data underlying the risk assessment constants into the DAG, and also treated some of that data as needing to be modelled as an ‘errors-invariables’ problem [Fuller, 1987]. This illustrated a simple method for the incorporation of experimental error into risk assessments. In considering one day of the three-dimensional agricultural data, it became clear that geostatistical models or conditional autoregressive (CAR) models over the three dimensions were not the best way to approach the data. Instead CAR models are used with neighbours only in the same depth layer. This gave flexibility to the model, allowing both the spatially structured and non-structured variances to differ at all depths. We call this model the CAR layered model. Given the experimental design, the fixed part of the model could have been modelled as a set of means by treatment and by depth, but doing so allows little insight into how the treatment effects vary with depth. Hence, a number of essentially non-parametric approaches were taken to see the effects of depth on treatment, with the model of choice incorporating an errors-in-variables approach for depth in addition to a non-parametric smooth. The statistical contribution here was the introduction of the CAR layered model, the applied contribution the analysis of moisture over depth and estimation of the contrast of interest together with its credible intervals. These models were fitted using WinBUGS [Lunn et al., 2000]. The work in the fifth paper deals with the fact that with large datasets, the use of WinBUGS becomes more problematic because of its highly correlated term by term updating. In this work, we introduce a Gibbs sampler with block updating for the CAR layered model. The Gibbs sampler was implemented by Chris Strickland using pyMCMC [Strickland, 2010]. This framework is then used to consider five days data, and we show that moisture in the soil for all the various treatments reaches levels particular to each treatment at a depth of 200 cm and thereafter stays constant, albeit with increasing variances with depth. In an analysis across three spatial dimensions and across time, there are many interactions of time and the spatial dimensions to be considered. Hence, we chose to use a daily model and to repeat the analysis at all time points, effectively creating an interaction model of time by the daily model. Such an approach allows great flexibility. However, this approach does not allow insight into the way in which the parameter of interest varies over time. Hence, a two-stage approach was also used, with estimates from the first-stage being analysed as a set of time series. We see this spatio-temporal interaction model as being a useful approach to data measured across three spatial dimensions and time, since it does not assume additivity of the random spatial or temporal effects.

Purine Nucleoside Phosphorylase mediated molecular chemotherapy and conventional chemotherapy: A tangible union against chemoresistant cancer

Background Late stage Ovarian Cancer is essentially incurable primarily due to late diagnosis and its inherent heterogeneity. Single agent treatments are inadequate and generally lead to severe side effects at therapeutic doses. It is crucial to develop clinically relevant novel combination regimens involving synergistic modalities that target a wider repertoire of cells and lead to lowered individual doses. Stemming from this premise, this is the first report of two- and three-way synergies between Adenovirus-mediated Purine Nucleoside Phosphorylase based gene directed enzyme prodrug therapy (PNP-GDEPT), docetaxel and/or carboplatin in multidrug-resistant ovarian cancer cells. Methods The effects of PNP-GDEPT on different cellular processes were determined using Shotgun Proteomics analyses. The in vitro cell growth inhibition in differentially treated drug resistant human ovarian cancer cell lines was established using a cell-viability assay. The extent of synergy, additivity, or antagonism between treatments was evaluated using CalcuSyn statistical analyses. The involvement of apoptosis and implicated proteins in effects of different treatments was established using flow cytometry based detection of M30 (an early marker of apoptosis), cell cycle analyses and finally western blot based analyses. Results Efficacy of the trimodal treatment was significantly greater than that achieved with bimodal- or individual treatments with potential for 10-50 fold dose reduction compared to that required for individual treatments. Of note was the marked enhancement in apoptosis that specifically accompanied the combinations that included PNP-GDEPT and accordingly correlated with a shift in the expression of anti- and pro-apoptotic proteins. PNP-GDEPT mediated enhancement of apoptosis was reinforced by cell cycle analyses. Proteomic analyses of PNP-GDEPT treated cells indicated a dowregulation of proteins involved in oncogenesis or cancer drug resistance in treated cells with accompanying upregulation of apoptotic- and tumour- suppressor proteins. Conclusion Inclusion of PNP-GDEPT in regular chemotherapy regimens can lead to significant enhancement of the cancer cell susceptibility to the combined treatment. Overall, these data will underpin the development of regimens that can benefit patients with late stage ovarian cancer leading to significantly improved efficacy and increased quality of life.

Fibroblast growth factor receptor inhibition synergizes with paclitaxel and doxorubicin in endometrial cancer cells

OBJECTIVE: The fibroblast growth factor (FGF) family of signaling molecules has been associated with chemoresistance and poor prognosis in a number of cancer types, including lung, breast, ovarian, prostate, and head and neck carcinomas. Given the identification of activating mutations in the FGF receptor 2 (FGFR2) receptor tyrosine kinase in a subset of endometrial tumors, agents with activity against FGFRs are currently being tested in clinical trials for recurrent and progressive endometrial cancer. Here, we evaluated the effect of FGFR inhibition on the in vitro efficacy of chemotherapy in endometrial cancer cell lines. METHODS: Human endometrial cancer cell lines with wild-type or activating FGFR2 mutations were used to determine any synergism with concurrent use of the pan-FGFR inhibitor, PD173074, and the chemotherapeutics, doxorubicin and paclitaxel, on cell proliferation and apoptosis. RESULTS: FGFR2 mutation status did not alter sensitivity to either chemotherapeutic agent alone. The combination of PD173074 with paclitaxel or doxorubicin showed synergistic activity in the 3 FGFR2 mutant cell lines evaluated. In addition, although nonmutant cell lines were resistant to FGFR inhibition alone, the addition of PD173074 potentiated the cytostatic effect of paclitaxel and doxorubicin in a subset of FGFR2 wild-type endometrial cancer cell lines. CONCLUSIONS: Together these data suggest a potential therapeutic benefit to combining an FGFR inhibitor with standard chemotherapeutic agents in endometrial cancer therapy particularly in patients with FGFR2 mutation positive tumors.

Variability in odour reception in the peripheral sensory system of Helicoverpa armigera (Hubner) (Lepidoptera : Noctuidae)

Mixtures of single odours were used to explore the receptor response profile across individual antennae of Helicoverpa armigera (Hübner) (Lepidoptera: Noctuidae). Seven odours were tested including floral and green-leaf volatiles: phenyl acetaldehyde, benzaldehyde, β-caryophyllene, limonene, α-pinene, 1-hexanol, 3Z-hexenyl acetate. Electroantennograms of responses to paired mixtures of odours showed that there was considerable variation in receptor tuning across the receptor field between individuals. Data from some moth antennae showed no additivity, which indicated a restricted receptor profile. Results from other moth antennae to the same odour mixtures showed a range of partial additivity. This indicated that a wider array of receptor types was present in these moths, with a greater percentage of the receptors tuned exclusively to each odour. Peripheral receptor fields show variation in the spectrum of response within a population (of moths) when exposed to high doses of plant volatiles. This may be related to recorded variation in host choice within moth populations as reported by other authors.

Document ranking with quantum probabilities

In this thesis we investigate the use of quantum probability theory for ranking documents. Quantum probability theory is used to estimate the probability of relevance of a document given a user's query. We posit that quantum probability theory can lead to a better estimation of the probability of a document being relevant to a user's query than the common approach, i. e. the Probability Ranking Principle (PRP), which is based upon Kolmogorovian probability theory. Following our hypothesis, we formulate an analogy between the document retrieval scenario and a physical scenario, that of the double slit experiment. Through the analogy, we propose a novel ranking approach, the quantum probability ranking principle (qPRP). Key to our proposal is the presence of quantum interference. Mathematically, this is the statistical deviation between empirical observations and expected values predicted by the Kolmogorovian rule of additivity of probabilities of disjoint events in configurations such that of the double slit experiment. We propose an interpretation of quantum interference in the document ranking scenario, and examine how quantum interference can be effectively estimated for document retrieval. To validate our proposal and to gain more insights about approaches for document ranking, we (1) analyse PRP, qPRP and other ranking approaches, exposing the assumptions underlying their ranking criteria and formulating the conditions for the optimality of the two ranking principles, (2) empirically compare three ranking principles (i. e. PRP, interactive PRP, and qPRP) and two state-of-the-art ranking strategies in two retrieval scenarios, those of ad-hoc retrieval and diversity retrieval, (3) analytically contrast the ranking criteria of the examined approaches, exposing similarities and differences, (4) study the ranking behaviours of approaches alternative to PRP in terms of the kinematics they impose on relevant documents, i. e. by considering the extent and direction of the movements of relevant documents across the ranking recorded when comparing PRP against its alternatives. Our findings show that the effectiveness of the examined ranking approaches strongly depends upon the evaluation context. In the traditional evaluation context of ad-hoc retrieval, PRP is empirically shown to be better or comparable to alternative ranking approaches. However, when we turn to examine evaluation contexts that account for interdependent document relevance (i. e. when the relevance of a document is assessed also with respect to other retrieved documents, as it is the case in the diversity retrieval scenario) then the use of quantum probability theory and thus of qPRP is shown to improve retrieval and ranking effectiveness over the traditional PRP and alternative ranking strategies, such as Maximal Marginal Relevance, Portfolio theory, and Interactive PRP. This work represents a significant step forward regarding the use of quantum theory in information retrieval. It demonstrates in fact that the application of quantum theory to problems within information retrieval can lead to improvements both in modelling power and retrieval effectiveness, allowing the constructions of models that capture the complexity of information retrieval situations. Furthermore, the thesis opens up a number of lines for future research. These include: (1) investigating estimations and approximations of quantum interference in qPRP; (2) exploiting complex numbers for the representation of documents and queries, and; (3) applying the concepts underlying qPRP to tasks other than document ranking.