Optimal and Robust Designs of Step-stress Accelerated Life Testing Experiments for Proportional Hazards Models

Accelerated life testing (ALT) is widely used to obtain reliability information about a product within a limited time frame. The Cox s proportional hazards (PH) model is often utilized for reliability prediction. My master thesis research focuses on designing accelerated life testing experiments for reliability estimation. We consider multiple step-stress ALT plans with censoring. The optimal stress levels and times of changing the stress levels are investigated. We discuss the optimal designs under three optimality criteria. They are D-, A- and Q-optimal designs. We note that the classical designs are optimal only if the model assumed is correct. Due to the nature of prediction made from ALT experimental data, attained under the stress levels higher than the normal condition, extrapolation is encountered. In such case, the assumed model cannot be tested. Therefore, for possible imprecision in the assumed PH model, the method of construction for robust designs is also explored.

The role of molecular, clinical and socioeconomic factors in the long-term survival of axillary node negative breast cancer patients

The overall objective of this study was to investigate factors associated with long-term survival in axillary node negative (ANN) breast cancer patients. Clinical and biological factors included stage, histopathologic grade, p53 mutation, Her-2/neu amplification, estrogen receptor status (ER), progesterone receptor status (PR) and vascular invasion. Census derived socioeconomic (SES) indicators included median individual and household income, proportions of university educated individuals, housing type, "incidence" of low income and an indicator of living in an affluent neighbourhood. The effects of these measures on breast cancer-specific survival and competing cause survival were investigated. A cohort study examining survival among axillary node negative (ANN) breast cancer patients in the greater Toronto area commenced in 1 989. Patients were followed up until death, lost-to-follow up or study termination in 2004. Data were collected from several sources measuring patient demographics, clinical factors, treatment, recurrence of disease and survival. Census level SES data were collected using census geo-coding of patient addresses' at the time of diagnosis. Additional survival data were acquired from the Ontario Cancer Registry to enhance and extend the observation period of the study. Survival patterns were examined using KaplanMeier and life table procedures. Associations were examined using log-rank and Wilcoxon tests of univariate significance. Multivariate survival analyses were perfonned using Cox proportional hazards models. Analyses were stratified into less than and greater than 5 year survival periods to observe whether known markers of short-tenn survival were also associated with reductions in long-tenn survival among breast cancer patients. The 15 year survival probabilities in this cohort were: for breast cancerspecific survival 0.88, competing causes survival 0.89 and for overall survival 0.78. Estrogen receptor (ER) and progesterone receptor (PR) status (Hazard Ratio (HR) ERIPR- versus ER+/PR+, 8.15,95% CI, 4.74, 14.00), p53 mutation (HR, 3.88, 95% CI, 2.00, 7.53) and Her-2 amplification (HR, 2.66, 95% CI, 1.36, 5.19) were associated with significant reductions in short-tenn breast cancer-specific survival «5 years following diagnosis), however, not with long-term survival in univariate analyses. Stage, histopathologic grade and ERiPR status were the clinicallbiologieal factors that were associated with short-term breast cancer specific survival in multivariate results. Living in an affluent neighbourhood (top quintile of median household income compared to the rest of the population) was associated with the largest significant increase in long-tenn breast cancer-specific survival after adjustment for stage, histopathologic grade and treatment (HR, 0.36, 95% CI, 0.12, 0.89).

Comparison of non-HDL cholesterol and waist circumference vs. triglyceride levels and waist circumference in predicting coronary heart disease risk

BACKGROUND: Dyslipidemia is recognized as a major cause of coronary heart disease (CHD). Emerged evidence suggests that the combination of triglycerides (TG) and waist circumference can be used to predict the risk of CHD. However, considering the known limitations of TG, non-high-density lipoprotein (non-HDL = Total cholesterol - HDL cholesterol) cholesterol and waist circumference model may be a better predictor of CHD. PURPOSE: The Framingham Offspring Study data were used to determine if combined non-HDL cholesterol and waist circumference is equivalent to or better than TG and waist circumference (hypertriglyceridemic waist phenotype) in predicting risk of CHD. METHODS: A total of3,196 individuals from Framingham Offspring Study, aged ~ 40 years old, who fasted overnight for ~ 9 hours, and had no missing information on nonHDL cholesterol, TG levels, and waist circumference measurements, were included in the analysis. Receiver Operator Characteristic Curve (ROC) Area Under the Curve (AUC) was used to compare the predictive ability of non-HDL cholesterol and waist circumference and TG and waist circumference. Cox proportional-hazards models were used to examine the association between the joint distributions of non-HDL cholesterol, waist circumference, and non-fatal CHD; TG, waist circumference, and non-fatal CHD; and the joint distribution of non-HDL cholesterol and TG by waist circumference strata, after adjusting for age, gender, smoking, alcohol consumption, diabetes, and hypertension status. RESULTS: The ROC AUC associated with non-HDL cholesterol and waist circumference and TG and waist circumference are 0.6428 (CI: 0.6183, 0.6673) and 0.6299 (CI: 0.6049, 0.6548) respectively. The difference in the ROC AVC is 1.29%. The p-value testing if the difference in the ROC AVCs between the two models is zero is 0.10. There was a strong positive association between non-HDL cholesterol and the risk for non-fatal CHD within each TO levels than that for TO levels within each level of nonHDL cholesterol, especially in individuals with high waist circumference status. CONCLUSION: The results suggest that the model including non-HDL cholesterol and waist circumference may be superior at predicting CHD compared to the model including TO and waist circumference.

Aspects of spatial and habitat ecology of multiple Anopheles species (Diptera: Culicidae): malaria vectors in the highlands and foothills of Ecuador

The resurgence of malaria in highland regions of Africa, Oceania and recently in South America underlines the importance of the study of the ecology of highland mosquito vectors of malaria. Since the incidence of malaria is limited by the distribution of its vectors, the purpose of this PhD thesis was to examine aspects of the ecology of Anopheles mosquitoes in the Andes of Ecuador, South America. A historical literature and archival data review (Chapter 2) indicated that Anopheles pseudopunctipennis transmitted malaria in highland valleys of Ecuador prior to 1950, although it was eliminated through habitat removal and the use of chemical insecticides. Other anopheline species were previously limited to low-altitude regions, except in a few unconfirmed cases. A thorough larval collection effort (n=438 attempted collection sites) in all road-accessible parts of Ecuador except for the lowland Amazon basin was undertaken between 2008 - 2010 (Chapter 3). Larvae were identified morphologically and using molecular techniques (mitochondrial COl gene), and distribution maps indicated that all five species collected (Anopheles albimanus, An. pseudopunctipennis, Anopheles punctimacula, Anopheles oswaldoi s.l. and Anopheles eiseni) were more widespread throughout highland regions than previously recorded during the 1940s, with higher maximum altitudes for all except An. pseudopunctipennis (1541 m, 1930 m, 1906 m, 1233 m and 1873 m, respectively). During larval collections, to characterize species-specific larval habitat, a variety of abiotic and biotic habitat parameters were measured and compared between species-present and species-absent sites using chi-square tests and stepwise binary logistic regression analyses (Chapter 4). An. albimanus was significantly associated with permanent pools with sand substrates and An. pseudopunctipennis with gravel and boulder substrates. Both species were significantly associated with floating cyanobacterial mats and warmer temperatures, which may limit their presence in cooler highland regions. Anopheles punctimacula was collected more often than expected from algae-free, shaded pools with higher-than-average calculated dissolved oxygen. Anopheles oswaldoi s.l., the species occurring on the Amazonian side of the Andes, was associated with permanent, anthropogenic habitats such as roadside ditches and ponds. To address the hypothesis that human land use change is responsible for the emergence of multiple highland Anopheles species by creating larval habitat, common land uses in the western Andes were surveyed for standing water and potential larval habitat suitability (Chapter 5). Rivers and road edges provided large amounts of potentially suitable anopheline habitat in the western Andes, while cattle pasture also created potentially suitable habitat in irrigation canals and watering ponds. Other common land uses surveyed (banana farms, sugarcane plantations, mixed tree plantations, and empty lots) were usually established on steep slopes and had very little standing water present. Using distribution and larval habitat data, a GIS-based larval habitat distribution model for the common western species was constructed in ArcGIS v.l 0 (ESRI 2010) using derived data layers from field measurements and other sources (Chapter 6). The additive model predicted 76.4 - 97.9% of the field-observed collection localities of An. albimanus, An. pseudopunctipennis and An. punctimacula, although it could not accurately distinguish between species-absent and speciespresent sites due to its coarse scale. The model predicted distributional expansion and/or shift of one or more anopheline species into the following highland valleys with climate warming: Mira/Chota, Imbabura province, Tumbaco, Pichincha province, Pallatanga and Sibambe, Chimborazo province, and Yungilla, Azuay province. These valleys may serve as targeted sites of future monitoring to prevent highland epidemics of malaria. The human perceptions of malaria and mosquitoes in relation to land management practices were assessed through an interview-based survey (n=262) in both highlands and lowlands, of male and female land owners and managers of five property types (Chapter 7). Although respondents had a strong understanding of where the disease occurs in their own country and of the basic relationship among standing water, mosquitoes and malaria, about half of respondents in potential risk areas denied the current possibility of malaria infection on their own property. As well, about half of respondents with potential anopheline larval habitat did not report its presence, likely due to a highly specific definition of suitable mosquito habitat. Most respondents who are considered at risk of malaria currently use at least one type of mosquito bite prevention, most commonly bed nets. In conclusion, this interdisciplinary thesis examines the occurrence of Anopheles species in the lowland transition area and highlands in Ecuador, from a historic, geographic, ecological and sociological perspective.