Assessing time-by-covariate interactions in Cox proportional hazards regression models using cubic spline functions

This dissertation develops and explores the methodology for the use of cubic spline functions in assessing time-by-covariate interactions in Cox proportional hazards regression models. These interactions indicate violations of the proportional hazards assumption of the Cox model. Use of cubic spline functions allows for the investigation of the shape of a possible covariate time-dependence without having to specify a particular functional form. Cubic spline functions yield both a graphical method and a formal test for the proportional hazards assumption as well as a test of the nonlinearity of the time-by-covariate interaction. Five existing methods for assessing violations of the proportional hazards assumption are reviewed and applied along with cubic splines to three well known two-sample datasets. An additional dataset with three covariates is used to explore the use of cubic spline functions in a more general setting. ^

Effects of air pollution on asthma hospitalization rates in different age groups in metropolitan cities of Korea

Many studies have shown relationships between air pollution and the rate of hospital admissions for asthma. A few studies have controlled for age-specific effects by adding separate smoothing functions for each age group. However, it has not yet been reported whether air pollution effects are significantly different for different age groups. This lack of information is the motivation for this study, which tests the hypothesis that air pollution effects on asthmatic hospital admissions are significantly different by age groups. Each air pollutant's effect on asthmatic hospital admissions by age groups was estimated separately. In this study, daily time-series data for hospital admission rates from seven cities in Korea from June 1999 through 2003 were analyzed. The outcome variable, daily hospital admission rates for asthma, was related to five air pollutants which were used as the independent variables, namely particulate matter <10 micrometers (μm) in aerodynamic diameter (PM10), carbon monoxide (CO), ozone (O3), nitrogen dioxide (NO2), and sulfur dioxide (SO2). Meteorological variables were considered as confounders. Admission data were divided into three age groups: children (<15 years of age), adults (ages 15-64), and elderly (≥ 65 years of age). The adult age group was considered to be the reference group for each city. In order to estimate age-specific air pollution effects, the analysis was separated into two stages. In the first stage, Generalized Additive Models (GAMs) with cubic spline for smoothing were applied to estimate the age-city-specific air pollution effects on asthmatic hospital admission rates by city and age group. In the second stage, the Bayesian Hierarchical Model with non-informative prior which has large variance was used to combine city-specific effects by age groups. The hypothesis test showed that the effects of PM10, CO and NO2 were significantly different by age groups. Assuming that the air pollution effect for adults is zero as a reference, age-specific air pollution effects were: -0.00154 (95% confidence interval(CI)= (-0.0030,-0.0001)) for children and 0.00126 (95% CI = (0.0006, 0.0019)) for the elderly for PM 10; -0.0195 (95% CI = (-0.0386,-0.0004)) for children for CO; and 0.00494 (95% CI = (0.0028, 0.0071)) for the elderly for NO2. Relative rates (RRs) were 1.008 (95% CI = (1.000-1.017)) in adults and 1.021 (95% CI = (1.012-1.030)) in the elderly for every 10 μg/m3 increase of PM10 , 1.019 (95% CI = (1.005-1.033)) in adults and 1.022 (95% CI = (1.012-1.033)) in the elderly for every 0.1 part per million (ppm) increase of CO; 1.006 (95%CI = (1.002-1.009)) and 1.019 (95%CI = (1.007-1.032)) in the elderly for every 1 part per billion (ppb) increase of NO2 and SO2, respectively. Asthma hospital admissions were significantly increased for PM10 and CO in adults, and for PM10, CO, NO2 and SO2 in the elderly.^

Role of obesity, weight gain, physical activity, and polymorphisms in the mTOR pathway and the risk of renal cell carcinoma

The interplay between obesity, physical activity, weight gain and genetic variants in mTOR pathway have not been studied in renal cell carcinoma (RCC). We examined the associations between obesity, weight gain, physical activity and RCC risk. We also analyzed whether genetic variants in the mTOR pathway could modify the association. Incident renal cell carcinoma cases and healthy controls were recruited from the University of Texas MD Anderson Cancer Center in Houston, Texas. Cases and controls were frequency-matched by age (±5 years), ethnicity, sex, and county of residence. Epidemiologic data were collected via in-person interview. A total of 577 cases and 593 healthy controls (all white) were included. One hundred ninety-two (192) SNPs from 22 genes were available and their genotyping data were extracted from previous genome-wide association studies. Logistic regression and regression spline were performed to obtain odds ratios. Obesity at age 20, 40, and 3 years prior to diagnosis/recruitment, and moderate and large weight gain from age 20 to 40 were each significantly associated with increased RCC risk. Low physical activity was associated with a 4.08-fold (95% CI: 2.92-5.70) increased risk. Five single nucleotide polymorphisms (SNPs) were significantly associated with RCC risk and their cumulative effect increased the risk by up to 72% (95% CI: 1.20-2.46). Strata specific effects for weight change and genotyping cumulative groups were observed. However, no interaction was suggested by our study. In conclusion, energy balance related risk factors and genetic variants in the mTOR pathway may jointly influence susceptibility to RCC. ^