Financial modelling with 2-EPT probability density functions

The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b; c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling.

An exploration through interview and drawings of the experiences of patients diagnosed with oral cancer across their cancer trajectory

Background: The treatment of oral cancer is complex and lengthy. Curative treatment implies a combination of surgery, radiotherapy and chemotherapy. The main goal of treatment is to guarantee long-term tumour free survival with as little functional and cosmetic damage. Despite progress in developing these strategies, cancers of the oral cavity continue to have high mortality rates that have not improved dramatically over the past ten years. Aim: The aim of this study was to uniquely explore the dynamic changes in the physical, psychological, social and existential experiences of newly diagnosed patients with oral cancer at two points across their cancer illness trajectory i.e. at the time of diagnosis and at the end of treatment. Methodology: A qualitative prospective longitudinal design was employed. Non-probability purposive sampling allowed the recruitment of 10 participants. The principal data collection method used was a digital audio taped semi-structured interview along with drawings produced by the participants. Analysis: Data was analysed using latent content analyses. Summary: Three ‘dynamic’ themes, physical, psychosocial and existential experiences were revealed that interact and influence each other in a complex and compound whole. These experiences are present at different degrees and throughout the entire trajectory of care. Patients have a number of specific concerns and challenges that cannot be compartmentalised into unitary or discrete aspects of their daily lives. Conclusion & Implications: An understanding of the patient’s experience of their illness at all stages of the disease trajectory, is essential to inform service providers’ decision making if the delivery of care is to be client centred. Dynamic and fluctuating changes in the patient’s personal experience of the cancer journey require dynamic, energetic and timely input from health care professionals.

Survival analysis of adult tuberculosis disease

Background: We conducted a survival analysis of all the confirmed cases of Adult Tuberculosis (TB) patients treated in Cork-City, Ireland. The aim of this study was to estimate Survival time (ST), including median time of survival and to assess the association and impact of covariates (TB risk factors) to event status and ST. The outcome of the survival analysis is reported in this paper. Methods: We used a retrospective cohort study research design to review data of 647 bacteriologically confirmed TB patients from the medical record of two teaching hospitals. Mean age 49 years (Range 18–112). We collected information on potential risk factors of all confirmed cases of TB treated between 2008–2012. For the survival analysis, the outcome of interest was ‘treatment failure’ or ‘death’ (whichever came first). A univariate descriptive statistics analysis was conducted using a non- parametric procedure, Kaplan -Meier (KM) method to estimate overall survival (OS), while the Cox proportional hazard model was used for the multivariate analysis to determine possible association of predictor variables and to obtain adjusted hazard ratio. P value was set at <0.05, log likelihood ratio test at >0.10. Data were analysed using SPSS version 15.0. Results: There was no significant difference in the survival curves of male and female patients. (Log rank statistic = 0.194, df = 1, p = 0.66) and among different age group (Log rank statistic = 1.337, df = 3, p = 0.72). The mean overall survival (OS) was 209 days (95%CI: 92–346) while the median was 51 days (95% CI: 35.7–66). The mean ST for women was 385 days (95%CI: 76.6–694) and for men was 69 days (95%CI: 48.8–88.5). Multivariate Cox regression showed that patient who had history of drug misuse had 2.2 times hazard than those who do not have drug misuse. Smokers and alcohol drinkers had hazard of 1.8 while patients born in country of high endemicity (BICHE) had hazard of 6.3 and HIV co-infection hazard was 1.2. Conclusion: There was no significant difference in survival curves of male and female and among age group. Women had a higher ST compared to men. But men had a higher hazard rate compared to women. Anti-TNF, immunosuppressive medication and diabetes were found to be associated with longer ST, while alcohol, smoking, RICHE, BICHE was associated with shorter ST.

Cancer associated malnutrition: prevalence of cachexia, sarcopenia and impact on treatment outcomes, survival and health related quality of life

Malnutrition, sarcopenia and cancer cachexia (CC) are prevalent among cancer patients and can have detrimental effects on clinical outcomes such as quality of life (QoL) and overall survival. Cachexia is associated with lower tolerance for chemotherapy, which limits the total dose that can be delivered, the number of symptomatic responses and any survival advantage that might be accrued. Moreover, for the majority who do not respond, cachexia may be exacerbated by systemic chemotherapy, thus increasing the net symptom burden experienced by patients. The multitude of interactions between cancer location, treatments, nutritional status and QoL has never been thoroughly explored in an Irish cancer cohort. The objectives of this thesis were to further understand nutritional status, especially body composition in ambulatory cancer patients and determine the relationship between nutritional status using different assessment criteria and QoL, chemotherapy toxicity and survival among cancer patients undergoing chemotherapy. Results aimed to identify baseline factors that may be predictive of poor outcome, toxicities to chemotherapy and disease-free and overall survival. This thesis broadly divides into two sections. The first section (Chapters 3 & 4) focuses on improving our knowledge of the nutritional status of Irish cancer outpatients using a cross sectional study design. A study of 517 patients referred for chemotherapy was conducted using computed tomography (CT) imaging (body composition) and a survey that documented oncologic data, weight loss (WL) data and QoL data. We revealed that a significant proportion of Irish cancer patients undergoing chemotherapy experience unintentional WL over the previous 6 months (62%), sarcopenia (45%) and CC (43%), and the distribution of WL and nutritional risk were associated with site of primary tumour and treatment intent. Patients that had sarcopenia, nutritional risk, or CC had significantly reduced functional abilities, more symptoms and adverse global QoL. In the second section of this thesis (Chapters 5 & 6) the potential link between developing toxicity to antineoplastic regimens in patients with sarcopenia was conducted by way of retrospective studies. A retrospective serial CT analysis defined the prevalence of sarcopenia in patients with metastatic renal cell carcinoma (mRCC) and metastatic castrate resistant prostate cancer (mCRPC), which was then correlated with dose limiting toxicities of sunitinib and docetaxel respectively. Sarcopenia was prevalent in patients with mRCC and mCRPC, was an occult condition in patients with normal/high BMI, was associated with less treatment days, was a significant predictor of DLT in patients receiving sunitinib and a significant predictor of neutropenia and neurosensory toxicities in patients receiving docetaxel. This thesis attempted to address the underlying research deficiencies in Irish oncology nutritional data at national level. The findings from this thesis have implications for the planning of cancer care interventions and indicate that further research is required to improve nutritional screening, in particular for CC and sarcopenia, in the hope that timely intervention can improve both patient-centered and oncologic outcomes.