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.

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.

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).

The finite bandwidth model for spin fluctuations in Pd

The frequency dependence of the electron-spin fluctuation spectrum, P(Q), is calculated in the finite bandwidth model. We find that for Pd, which has a nearly full d-band, the magnitude, the range, and the peak frequency of P(Q) are greatly reduced from those in the standard spin fluctuation theory. The electron self-energy due to spin fluctuations is calculated within the finite bandwidth model. Vertex corrections are examined, and we find that Migdal's theorem is valid for spin fluctuations in the nearly full band. The conductance of a normal metal-insulator-normal metal tunnel junction is examined when spin fluctuations are present in one electrode. We find that for the nearly full band, the momentum independent self-energy due to spin fluctuations enters the expression for the tunneling conductance with approximately the same weight as the self-energy due to phonons. The effect of spin fluctuations on the tunneling conductance is slight within the finite bandwidth model for Pd. The effect of spin fluctuations on the tunneling conductance of a metal with a less full d-band than Pd may be more pronounced. However, in this case the tunneling conductance is not simply proportional to the self-energy.