A novel method for evaluating an interaction effect of correlated continuous covariates in a linear model

Interaction effect is an important scientific interest for many areas of research. Common approach for investigating the interaction effect of two continuous covariates on a response variable is through a cross-product term in multiple linear regression. In epidemiological studies, the two-way analysis of variance (ANOVA) type of method has also been utilized to examine the interaction effect by replacing the continuous covariates with their discretized levels. However, the implications of model assumptions of either approach have not been examined and the statistical validation has only focused on the general method, not specifically for the interaction effect.^ In this dissertation, we investigated the validity of both approaches based on the mathematical assumptions for non-skewed data. We showed that linear regression may not be an appropriate model when the interaction effect exists because it implies a highly skewed distribution for the response variable. We also showed that the normality and constant variance assumptions required by ANOVA are not satisfied in the model where the continuous covariates are replaced with their discretized levels. Therefore, naïve application of ANOVA method may lead to an incorrect conclusion. ^ Given the problems identified above, we proposed a novel method modifying from the traditional ANOVA approach to rigorously evaluate the interaction effect. The analytical expression of the interaction effect was derived based on the conditional distribution of the response variable given the discretized continuous covariates. A testing procedure that combines the p-values from each level of the discretized covariates was developed to test the overall significance of the interaction effect. According to the simulation study, the proposed method is more powerful then the least squares regression and the ANOVA method in detecting the interaction effect when data comes from a trivariate normal distribution. The proposed method was applied to a dataset from the National Institute of Neurological Disorders and Stroke (NINDS) tissue plasminogen activator (t-PA) stroke trial, and baseline age-by-weight interaction effect was found significant in predicting the change from baseline in NIHSS at Month-3 among patients received t-PA therapy.^

AN ILLNESS-DEATH PROCESS WITH TIME-DEPENDENT COVARIATES

A general model for the illness-death stochastic process with covariates has been developed for the analysis of survival data. This model incorporates important baseline and time-dependent covariates to make proper adjustment for the transition probabilities and survival probabilities. The follow-up period is subdivided into small intervals and a constant hazard is assumed for each interval. An approximation formula is derived to estimate the transition parameters when the exact transition time is unknown.^ The method developed is illustrated by using data from a study on the prevention of the recurrence of a myocardial infarction and subsequent mortality, the Beta-Blocker Heart Attack Trial (BHAT). This method provides an analytical approach which simultaneously includes provision for both fatal and nonfatal events in the model. According to this analysis, the effectiveness of the treatment can be compared between the Placebo and Propranolol treatment groups with respect to fatal and nonfatal events. ^

Logistic regression with Markov chains as covariates

The tobacco-specific nitrosamine 4-(methylnitrosamino)-1-(3-pyridyl)-1-butanone (NNK) is an obvious carcinogen for lung cancer. Since CBMN (Cytokinesis-blocked micronucleus) has been found to be extremely sensitive to NNK-induced genetic damage, it is a potential important factor to predict the lung cancer risk. However, the association between lung cancer and NNK-induced genetic damage measured by CBMN assay has not been rigorously examined. ^ This research develops a methodology to model the chromosomal changes under NNK-induced genetic damage in a logistic regression framework in order to predict the occurrence of lung cancer. Since these chromosomal changes were usually not observed very long due to laboratory cost and time, a resampling technique was applied to generate the Markov chain of the normal and the damaged cell for each individual. A joint likelihood between the resampled Markov chains and the logistic regression model including transition probabilities of this chain as covariates was established. The Maximum likelihood estimation was applied to carry on the statistical test for comparison. The ability of this approach to increase discriminating power to predict lung cancer was compared to a baseline "non-genetic" model. ^ Our method offered an option to understand the association between the dynamic cell information and lung cancer. Our study indicated the extent of DNA damage/non-damage using the CBMN assay provides critical information that impacts public health studies of lung cancer risk. This novel statistical method could simultaneously estimate the process of DNA damage/non-damage and its relationship with lung cancer for each individual.^

Age -period -cohort analysis: An extension of Cox's lifetable regression with time -dependent covariates

It is well known that an identification problem exists in the analysis of age-period-cohort data because of the relationship among the three factors (date of birth + age at death = date of death). There are numerous suggestions about how to analyze the data. No one solution has been satisfactory. The purpose of this study is to provide another analytic method by extending the Cox's lifetable regression model with time-dependent covariates. The new approach contains the following features: (1) It is based on the conditional maximum likelihood procedure using a proportional hazard function described by Cox (1972), treating the age factor as the underlying hazard to estimate the parameters for the cohort and period factors. (2) The model is flexible so that both the cohort and period factors can be treated as dummy or continuous variables, and the parameter estimations can be obtained for numerous combinations of variables as in a regression analysis. (3) The model is applicable even when the time period is unequally spaced.^ Two specific models are considered to illustrate the new approach and applied to the U.S. prostate cancer data. We find that there are significant differences between all cohorts and there is a significant period effect for both whites and nonwhites. The underlying hazard increases exponentially with age indicating that old people have much higher risk than young people. A log transformation of relative risk shows that the prostate cancer risk declined in recent cohorts for both models. However, prostate cancer risk declined 5 cohorts (25 years) earlier for whites than for nonwhites under the period factor model (0 0 0 1 1 1 1). These latter results are similar to the previous study by Holford (1983).^ The new approach offers a general method to analyze the age-period-cohort data without using any arbitrary constraint in the model. ^

Imaging of pulmonary embolism and t-PA therapy effects using MDCT and liposomal iohexol blood pool agent – preliminary results in a rabbit model

Hypothesis and Objectives PEGylated liposomal blood pool contrast agents maintain contrast enhancement over several hours. This study aimed to evaluate (long-term) imaging of pulmonary arteries, comparing conventional iodinated contrast with a liposomal blood pool contrast agent. Secondly, visualization of the (real-time) therapeutic effects of tissue-Plasminogen Activator (t-PA) on pulmonary embolism (PE) was attempted. Materials and Methods Six rabbits (approximate 4 kg weight) had autologous blood clots injected through the superior vena cava. Imaging was performed using conventional contrast (iohexol, 350 mg I/ml, GE HealthCare, Princeton, NJ) at a dose of 1400 mgI per animal and after wash-out, animals were imaged using an iodinated liposomal blood pool agent (88 mg I/mL, dose 900 mgI/animal). Subsequently, five animals were injected with 2mg t-PA and imaging continued for up to 4 ½ hours. Results Both contrast agents identified PE in the pulmonary trunk and main pulmonary arteries in all rabbits. Liposomal blood pool agent yielded uniform enhancement, which remained relatively constant throughout the experiments. Conventional agents exhibited non uniform opacification and rapid clearance post injection. Three out of six rabbits had mistimed bolus injections, requiring repeat injections. Following t-PA, Pulmonary embolus volume (central to segmental) decreased in four of five treated rabbits (range 10–57%, mean 42%). One animal showed no response to t-PA. Conclusions Liposomal blood pool agents effectively identified acute PE without need for re-injection. PE resolution following t-PA was quantifiable over several hours. Blood pool agents offer the potential for repeated imaging procedures without need for repeated (nephrotoxic) contrast injections

Imaging of pulmonary embolism and t-PA therapy effects using MDCT and liposomal iohexol blood pool agent: preliminary results in a rabbit model.

RATIONALE AND OBJECTIVES: Polyethylene glycol-coated liposomal blood pool contrast agents maintain contrast enhancement over several hours. This study aimed to evaluate (long-term) imaging of pulmonary arteries, comparing conventional iodinated contrast with a liposomal blood pool contrast agent. Also, visualization of the (real-time) therapeutic effects of tissue plasminogen activator (t-PA) on pulmonary embolism (PE) was attempted. MATERIALS AND METHODS: Six rabbits (weight approximately 4 kg) had autologous blood clots injected through the superior vena cava. Imaging was performed using conventional contrast (iohexol, 350 mg I/ml; GE HealthCare, Princeton, NJ) at a dose of 1400 mg I per animal, and after wash-out, animals were imaged using an iodinated liposomal blood pool agent (88 mg I/mL, dose 900 mg I/animal). Subsequently, five animals were injected with 2 mg of t-PA and imaging continued for up to 4(1/2) hours. RESULTS: Both contrast agents identified PE in the pulmonary trunk and main pulmonary arteries in all rabbits. Liposomal blood pool agent yielded uniform enhancement, which remained relatively constant throughout the experiments. Conventional agents exhibited nonuniform opacification and rapid clearance postinjection. Three of six rabbits had mistimed bolus injections, requiring repeat injections. Following t-PA, pulmonary embolus volume (central to segmental) decreased in four of five treated rabbits (range 10-57%, mean 42%). One animal showed no response to t-PA. CONCLUSIONS: Liposomal blood pool agents effectively identified acute PE without need for reinjection. PE resolution following t-PA was quantifiable over several hours. Blood pool agents offer the potential for repeated imaging procedures without need for repeated (nephrotoxic) contrast injections.

Ethnic Minority Children’s Active Commuting to School and Association with Physical Activity and Pedestrian Safety Behaviors

Background: Children's active commuting to school, i.e. walking or cycling to school, was associated with greater moderate-to-vigorous physical activity, although studies among ethnic minorities are sparse. Objectives: Among a low-income, ethnic minority sample of fourth grade students from eight public schools, we examined (1) correlates of active commuting to school and (2) the relationship between active commuting to school and moderate-to-vigorous physical activity. Methods: We conducted a cross-sectional analysis of baseline measurements from a sample of participants (n=149) aged 9-12 years from a walk to school intervention study in Houston, Texas. The primary outcome was the weekly rate of active commuting to school. Daily moderate-to-vigorous physical activity, measured by accelerometers, was a secondary outcome. Child self-efficacy (alpha=0.75), parent self-efficacy (alpha=0.88), and parent outcome expectations (alpha=0.78) were independent variables. Participant characteristics (age, gender, race/ethnicity, distance from home to school, acculturation, and BMI percentile) were independent sociodemographic variables. We used mixed-model regression analyses to account for clustering by school and a stepwise procedure with backward elimination of non-significant interactions and covariates to identify significant moderators and predictors. School-level observations of student pedestrians were assessed and compared using chi-square tests of independence. Results: Among our sample, which was 61.7% Latino, the overall rate of active commuting to school was 43%. In the mixed model for active commuting to school, parent self-efficacy (std. beta = 0.18, p=0.018) and age (std. beta = 0.18, p=0.018) were positively related. Latino students had lower rates of active commuting to school than non-Latinos ( 16.5%, p=0.040). Distance from home to school was inversely related to active commuting to school (std. beta = 0.29, p<0.001). In the mixed model for moderate-to-vigorous physical activity, active commuting to school was positively associated (std. beta = 0.31, p <0.001). Among the Latino subsample, child acculturation was negatively associated with active commuting to school (std. beta = -0.23, p=0.01). With regard to school-level pedestrian safety observations, 37% of students stopped at the curb and 2.6% looked left-right-left before crossing the street. Conclusion: Although still below national goals, the rate of active commuting was relatively high, while the rate of some pedestrian safety behaviors was low among this low-income, ethnic minority population. Programs and policies to encourage safe active commuting to school are warranted and should consider the influence of parents, acculturation, and ethnicity.

Impact of medications prescribed for treatment of attention-deficit hyperactivity disorder on physical growth in children and adolescents with HIV.

OBJECTIVE: To examine the relationships between physical growth and medications prescribed for symptoms of attention-deficit hyperactivity disorder in children with HIV. METHODS: Analysis of data from children with perinatally acquired HIV (N = 2251; age 3-19 years), with and without prescriptions for stimulant and nonstimulant medications used to treat attention-deficit hyperactivity disorder, in a long-term observational study. Height and weight measurements were transformed to z scores and compared across medication groups. Changes in z scores during a 2-year interval were compared using multiple linear regression models adjusting for selected covariates. RESULTS: Participants with (n = 215) and without (n = 2036) prescriptions were shorter than expected based on US age and gender norms (p < .001). Children without prescriptions weighed less at baseline than children in the general population (p < .001) but gained height and weight at a faster rate (p < .001). Children prescribed stimulants were similar to population norms in baseline weight; their height and weight growth velocities were comparable with the general population and children without prescriptions (for weight, p = .511 and .100, respectively). Children prescribed nonstimulants had the lowest baseline height but were similar to population norms in baseline weight. Their height and weight growth velocities were comparable with the general population but significantly slower than children without prescriptions (p = .01 and .02, respectively). CONCLUSION: The use of stimulants to treat symptoms of attention-deficit hyperactivity disorder does not significantly exacerbate the potential for growth delay in children with HIV and may afford opportunities for interventions that promote physical growth. Prospective studies are needed to confirm these findings.

Patient Characteristics and Outcomes of Gastrointestinal Stromal Tumor Patients Undergoing Imatinib Plasma Level Testing

Although gastrointestinal stromal tumor (GIST) is effectively treated with imatinib, there are a number of clinical challenges in the optimal treatment of these patients. The plasma steady-state trough level of imatinib has been proposed to correlate with clinical outcome. Plasma imatinib level may be affected by a number of patient characteristics. Additionally, the ideal plasma trough concentration of imatinib is likely to vary based on the KIT genotype (genotype determines imatinib binding affinity) of the individual patient. Patients’ genotype or plasma imatinib level may influence the type and duration of response that is appreciable by clinical evaluation. The objectives of this study were to determine effects of genotype on the type of response appreciable by current imaging criteria, to determine the distribution of plasma imatinib levels in patients with GIST, to determine factors that correlate with plasma imatinib level, to determine the incremental effects of imatinib dose escalation; and to explore the median plasma levels and outcomes of patients with various KIT mutations. We therefore obtained KIT mutation information and analyzed CT response for size and density measurement of GISTs at baseline and within the first four moths of imatinib treatment. In 126 patients with metastatic/unresectable disease, the KIT genotype of patients’ tumor was significantly associated with unique response characteristics measurable by CT. Furthermore, hepatic and peritoneal metastases differed in their response characteristics. A subgroup of patients with KIT exon 9 mutation, who received higher doses of imatinib and experienced higher trough imatinib levels, experienced improved progression-free survival similar to that of KIT exon 11 patients. Therefore, we have found that imatinib plasma levels were higher in patients with elevated Aspartate amino transferase, were women, were older, or were being treated concomitantly with CYP450 substrate drugs. As expected, CYP450 inducers correlated with a lower plasma imatinib levels in GIST patients. Renal metabolism of imatinib accounts for <10%, so it was not included in the analysis but may affect covariates. Interestingly, there was a trend for low imatinib levels and inferior progression-free survival in patients who had undergone complete gastrectomy. Patients with KIT exon 9 mutation in our cohort received higher imatinib doses, experienced higher trough imatinib levels, and experienced a PFS similar to that of KIT exon 11 patients. In conclusion, imatinib plasma levels are influenced by a number of patient characteristics. The optimal imatinib plasma level for individual patients is not known but is an area of intense investigation. Our study confirms patients with KIT exon 9 mutations benefit from high-dose imatinib and higher trough imatinib levels.

Development of a Bayesian Joint Logistic Model to Better Study the Association between Haplotypes and Disease

In 2011, there will be an estimated 1,596,670 new cancer cases and 571,950 cancer-related deaths in the US. With the ever-increasing applications of cancer genetics in epidemiology, there is great potential to identify genetic risk factors that would help identify individuals with increased genetic susceptibility to cancer, which could be used to develop interventions or targeted therapies that could hopefully reduce cancer risk and mortality. In this dissertation, I propose to develop a new statistical method to evaluate the role of haplotypes in cancer susceptibility and development. This model will be flexible enough to handle not only haplotypes of any size, but also a variety of covariates. I will then apply this method to three cancer-related data sets (Hodgkin Disease, Glioma, and Lung Cancer). I hypothesize that there is substantial improvement in the estimation of association between haplotypes and disease, with the use of a Bayesian mathematical method to infer haplotypes that uses prior information from known genetics sources. Analysis based on haplotypes using information from publically available genetic sources generally show increased odds ratios and smaller p-values in both the Hodgkin, Glioma, and Lung data sets. For instance, the Bayesian Joint Logistic Model (BJLM) inferred haplotype TC had a substantially higher estimated effect size (OR=12.16, 95% CI = 2.47-90.1 vs. 9.24, 95% CI = 1.81-47.2) and more significant p-value (0.00044 vs. 0.008) for Hodgkin Disease compared to a traditional logistic regression approach. Also, the effect sizes of haplotypes modeled with recessive genetic effects were higher (and had more significant p-values) when analyzed with the BJLM. Full genetic models with haplotype information developed with the BJLM resulted in significantly higher discriminatory power and a significantly higher Net Reclassification Index compared to those developed with haplo.stats for lung cancer. Future analysis for this work could be to incorporate the 1000 Genomes project, which offers a larger selection of SNPs can be incorporated into the information from known genetic sources as well. Other future analysis include testing non-binary outcomes, like the levels of biomarkers that are present in lung cancer (NNK), and extending this analysis to full GWAS studies.

Contribution of the genes of the renin-angiotensin system to interindividual differences in blood pressure levels in Caucasians from Rochester, Minnesota

The Renin-Angiotensin system (RAS) regulates blood pressure through its effects on vascular tone, renal hemodynamics, and renal sodium and fluid balance. The genes encoding the four major components of the RAS, angiotensinogen, renin, angiotensin I-converting enzyme (ACE), and angiotensin II receptor type 1 (AT1), have been investigated as candidate genes in the pathogenesis of essential hypertension. However, studies have primarily focused on small samples of diseased individuals, and, therefore, have provided little information about the determinants of interindividual variation in blood pressure (BP) in the general population.^ Using data from a large population-based sample from Rochester, MN, I have evaluated the contribution of variation in the region of the RAS genes to interindividual variation in systolic, diastolic, and mean arterial pressure in the population-at-large. Marker genotype data from four polymorphisms located within or very near these genes were first collected on 3,974 individuals from 583 randomly ascertained three-generation pedigrees. Haseman-Elston regression and variance component methods of linkage analysis were then carried out to estimate the proportion of interindividual variance in BP attributable to the effects of variation at these four measured loci.^ A significant effect of the ACE locus on interindividual variation in mean arterial pressure (MAP) was detected in a sample of siblings belonging to the youngest generation. After allowing for measured covariates, this effect accounted for 15-25% of the interindividual variance in MAP, and was even greater in a subset with a positive family history of hypertension. When gender-specific analyses were carried out, this effect was significant in males but not in females. Extended pedigree analyses also provided evidence for an effect of the ACE locus on interindividual variation in MAP, but no difference between males and females was observed. Circumstantial evidence suggests that the ACE gene itself may be responsible for the observed effects on BP, although the possibility that other genes in the region may be at play cannot be excluded.^ No definitive evidence for an effect of the renin, angiotensinogen, or AT1 loci on interindividual variation in BP was obtained in this study, suggesting that the impact of these genes on BP may not be great in the Caucasian population-at-large. However, this does not preclude a larger effect of these genes in some subsets of individuals, especially among those with clinically manifest hypertension or coronary heart disease, or in other populations. ^

Neural tube defects in Mexican-Americans living on the US-Mexico border: The effects of folic acid and dietary folate

Neural tube defects (NTDs) are malformations of the developing brain and spinal cord; the most common are anencephaly and spina bifida. Evidence from many populations suggests that 50% of NTDs can be prevented through daily consumption of folic acid. A recent study has reported that folic acid may not protect populations of Mexican descent. This finding has serious implications for women living along the US-Mexico border. Not only is risk high in these Mexican American women compared with other US women; they also differ markedly in supplemental folic acid and dietary folate consumption, and in NTD-related risks (e.g., obesity, diabetes). This case-control study investigated whether folic acid supplements and dietary folate reduces NTDs in Mexican Americans. Cases included liveborn, stillborn, electively and spontaneously aborted NTD-affected fetuses and infants occurring in the 14-county Texas-Mexico border. Controls were randomly selected from unaffected live births, frequency matched to cases by hospital and year. An in-person interview of 110 case and 113 control mothers solicited data on folic acid supplements, dietary folate, and other covariates. Consumption of folic acid-containing vitamins before conception was only 5% for both case and control women. Taking vitamins the trimester before conception had no apparent effect, after adjusting for covariates [odds ratio (OR) = 1.0, 95% confidence interval (CI) = 0.3–3.4]. Combining folate from vitamins and diet showed a 20% risk reduction for women consuming at least 400 μg of folate daily [OR = 0.8, 95% CI = 0.5–1.5]; however, this estimate is statistically indistinguishable from the null. Although consistent with an inherent ineffectiveness of supplemental folic acid, that so few women consumed multivitamins during the critical time severely limited the assessment of folic acid in this population. A reduced folate response in Mexican descent women may be due to a genetic heterogeneity for metabolizing folate. Alternatively, folate intakes may be insufficient to overcome other underlying risk factors. In conclusion, determining whether folic acid reduces NTD risk in Mexican American women requires further study in populations with higher folic acid exposures. Meanwhile, we should pursue all recommended prevention strategies to reduce risk, including motivating Mexican American women of childbearing age to take folic acid routinely. ^

Analysis of recurrent failure times: A time-dependent Yule process approach

Analysis of recurrent events has been widely discussed in medical, health services, insurance, and engineering areas in recent years. This research proposes to use a nonhomogeneous Yule process with the proportional intensity assumption to model the hazard function on recurrent events data and the associated risk factors. This method assumes that repeated events occur for each individual, with given covariates, according to a nonhomogeneous Yule process with intensity function λx(t) = λ 0(t) · exp( x′β). One of the advantages of using a non-homogeneous Yule process for recurrent events is that it assumes that the recurrent rate is proportional to the number of events that occur up to time t. Maximum likelihood estimation is used to provide estimates of the parameters in the model, and a generalized scoring iterative procedure is applied in numerical computation. ^ Model comparisons between the proposed method and other existing recurrent models are addressed by simulation. One example concerning recurrent myocardial infarction events compared between two distinct populations, Mexican-American and Non-Hispanic Whites in the Corpus Christi Heart Project is examined. ^

Mixed effects model in negative exponential curve

Despite many researches on development in education and psychology, not often is the methodology tested with real data. A major barrier to test the growth model is that the design of study includes repeated observations and the nature of the growth is nonlinear. The repeat measurements on a nonlinear model require sophisticated statistical methods. In this study, we present mixed effects model in a negative exponential curve to describe the development of children's reading skills. This model can describe the nature of the growth on children's reading skills and account for intra-individual and inter-individual variation. We also apply simple techniques including cross-validation, regression, and graphical methods to determine the most appropriate curve for data, to find efficient initial values of parameters, and to select potential covariates. We illustrate with an example that motivated this research: a longitudinal study of academic skills from grade 1 to grade 12 in Connecticut public schools. ^