A multivariate frailty model for disease recurrences and survival

A multivariate frailty hazard model is developed for joint-modeling of three correlated time-to-event outcomes: (1) local recurrence, (2) distant recurrence, and (3) overall survival. The term frailty is introduced to model population heterogeneity. The dependence is modeled by conditioning on a shared frailty that is included in the three hazard functions. Independent variables can be included in the model as covariates. The Markov chain Monte Carlo methods are used to estimate the posterior distributions of model parameters. The algorithm used in present application is the hybrid Metropolis-Hastings algorithm, which simultaneously updates all parameters with evaluations of gradient of log posterior density. The performance of this approach is examined based on simulation studies using Exponential and Weibull distributions. We apply the proposed methods to a study of patients with soft tissue sarcoma, which motivated this research. Our results indicate that patients with chemotherapy had better overall survival with hazard ratio of 0.242 (95% CI: 0.094 - 0.564) and lower risk of distant recurrence with hazard ratio of 0.636 (95% CI: 0.487 - 0.860), but not significantly better in local recurrence with hazard ratio of 0.799 (95% CI: 0.575 - 1.054). The advantages and limitations of the proposed models, and future research directions are discussed. ^

Stages of change and carotene intake in the Paso del Norte region: Que Sabrosa Vida

Understanding a population's dietary behavior is important to promote behaviors which have the most beneficial impact on health. The most recent Dietary Guidelines for Americans (2005) identifies carotenoids as a key nutrient to be consumed through increased intake of fruits and vegetables (FV). While some studies have included or focused on the Hispanic population, few have focused only on Mexican-American populations and staged its intake of FV. Stage of change behavior theory has been used to understand the adoption and promotion of healthy behaviors such as increased intake of FV. It has been shown to effectively aid interventionists' understanding of dietary behavior. Intake patterns of FV of older women, rural residents, and adolescents of Mexican American descent have been conducted but not by stages of change. This study aimed to determine the relationship between stages of change for fruits and vegetables (SOC-FV) and total carotene intake to assess the quality of SOC-FV as a surrogate measure of total carotene. ^ Data from the 2000 Qué Sabrosa Vida Community Nutrition Survey (QSV-CNS) were analyzed to identify the SOC-FV and sources of carotenes in a Mexican American population 18-60 yrs. of the Paso del Norte region. A 107 item interviewer administered food frequency questionnaire (FFQ) specifically calibrated for a Mexican American population was used to collect usual intake of total carotene. The QSV survey study population included 963 participants, 590 (61.3%) women and 373 (38.7%) men. A statistically significant mean difference in caloric intake between men and women was found (p-value = <0.01). When total carotene intake was adjusted for energy, there were significant differences between men and women (p-value = <0.0001) with women consuming a higher amount of total carotene (406 RE/kcal 1,000) than men (332 RE/kcal 1000). The food sources of total carotene for both genders included many items found in a traditional Mexican American diet. Chile, after carrots, was the highest contributor of dietary carotene. Total carotene intake was not associated with stages of change among women or men and their distributions were not linear. Mean differences of total carotene by stages of change were significant for women for pre-contemplation/contemplation (p-value = 0.04) and preparation (p-value = 0.0004) but not for men. ^ SOC-FV may serve as a surrogate measure for dietary carotene intake. This study's Mexican American population had a high carotene quality diet derived from traditional food items irrespective of their stage of change for fruits and vegetables. To better understand this population's dietary intake a measure for acculturation should be included. Interventions aimed at Mexican American populations should aim to promote traditional diets consistent with cultural practices.^ ^

When Policy Opportunity is not Enough: College Access and Enrollment Patterns among Texas Percent Plan Eligible Students

In 1998, Texas initiated a bold new statewide university admission policy aimed at increasing college access for traditionally underserved students in the state. House Bill 588 (known as the Texas Top 10 Percent Plan (TTPP)) guaranteed automatic admission to the college or university of their choice for all top performing students in Texas public high schools. Fourteen years after the plan’s implementation, we see great strides and complexities in understanding student outcomes as a result of the percent plan. However, the legal controversy over the percent plan both in Texas and other states incorporating similar yet distinctly motivated alternative admissions plans continues to play out from institutional decision boards to the highest court in the nation. This study seeks to add to that discussion by exploring two questions. Descriptively, what are the admission and enrollment patterns within racial/ethnic groups of percent plan eligible students, over time, for Texas elite, emergent elite, and remaining public institutions? Given that all eligible percent plan students may enter the institution of choice in Texas, does which type of institution a TTPP student chooses relate to their race/ethnicity? The descriptive story told by the admission and enrollment distributions of equally eligible TTPP students is a complex but compelling one. Fundamentally, it identifies that statistically different application and enrollment patterns exist for Hispanic and especially African American TTPP beneficiaries relative to their White and Asian American counterparts.

Bayesian generalized linear models for meta-analysis of diagnostic tests

With the recognition of the importance of evidence-based medicine, there is an emerging need for methods to systematically synthesize available data. Specifically, methods to provide accurate estimates of test characteristics for diagnostic tests are needed to help physicians make better clinical decisions. To provide more flexible approaches for meta-analysis of diagnostic tests, we developed three Bayesian generalized linear models. Two of these models, a bivariate normal and a binomial model, analyzed pairs of sensitivity and specificity values while incorporating the correlation between these two outcome variables. Noninformative independent uniform priors were used for the variance of sensitivity, specificity and correlation. We also applied an inverse Wishart prior to check the sensitivity of the results. The third model was a multinomial model where the test results were modeled as multinomial random variables. All three models can include specific imaging techniques as covariates in order to compare performance. Vague normal priors were assigned to the coefficients of the covariates. The computations were carried out using the 'Bayesian inference using Gibbs sampling' implementation of Markov chain Monte Carlo techniques. We investigated the properties of the three proposed models through extensive simulation studies. We also applied these models to a previously published meta-analysis dataset on cervical cancer as well as to an unpublished melanoma dataset. In general, our findings show that the point estimates of sensitivity and specificity were consistent among Bayesian and frequentist bivariate normal and binomial models. However, in the simulation studies, the estimates of the correlation coefficient from Bayesian bivariate models are not as good as those obtained from frequentist estimation regardless of which prior distribution was used for the covariance matrix. The Bayesian multinomial model consistently underestimated the sensitivity and specificity regardless of the sample size and correlation coefficient. In conclusion, the Bayesian bivariate binomial model provides the most flexible framework for future applications because of its following strengths: (1) it facilitates direct comparison between different tests; (2) it captures the variability in both sensitivity and specificity simultaneously as well as the intercorrelation between the two; and (3) it can be directly applied to sparse data without ad hoc correction. ^

Estimating the mean and standard deviation of concentration distributions using censored samples

Environmental data sets of pollutant concentrations in air, water, and soil frequently include unquantified sample values reported only as being below the analytical method detection limit. These values, referred to as censored values, should be considered in the estimation of distribution parameters as each represents some value of pollutant concentration between zero and the detection limit. Most of the currently accepted methods for estimating the population parameters of environmental data sets containing censored values rely upon the assumption of an underlying normal (or transformed normal) distribution. This assumption can result in unacceptable levels of error in parameter estimation due to the unbounded left tail of the normal distribution. With the beta distribution, which is bounded by the same range of a distribution of concentrations, $\rm\lbrack0\le x\le1\rbrack,$ parameter estimation errors resulting from improper distribution bounds are avoided. This work developed a method that uses the beta distribution to estimate population parameters from censored environmental data sets and evaluated its performance in comparison to currently accepted methods that rely upon an underlying normal (or transformed normal) distribution. Data sets were generated assuming typical values encountered in environmental pollutant evaluation for mean, standard deviation, and number of variates. For each set of model values, data sets were generated assuming that the data was distributed either normally, lognormally, or according to a beta distribution. For varying levels of censoring, two established methods of parameter estimation, regression on normal ordered statistics, and regression on lognormal ordered statistics, were used to estimate the known mean and standard deviation of each data set. The method developed for this study, employing a beta distribution assumption, was also used to estimate parameters and the relative accuracy of all three methods were compared. For data sets of all three distribution types, and for censoring levels up to 50%, the performance of the new method equaled, if not exceeded, the performance of the two established methods. Because of its robustness in parameter estimation regardless of distribution type or censoring level, the method employing the beta distribution should be considered for full development in estimating parameters for censored environmental data sets. ^

Statistical characterization and development of summary measures of non-normal distributions of nuclear morphometry data from prostate cancer cells for use as prognostic indicators

Nuclear morphometry (NM) uses image analysis to measure features of the cell nucleus which are classified as: bulk properties, shape or form, and DNA distribution. Studies have used these measurements as diagnostic and prognostic indicators of disease with inconclusive results. The distributional properties of these variables have not been systematically investigated although much of the medical data exhibit nonnormal distributions. Measurements are done on several hundred cells per patient so summary measurements reflecting the underlying distribution are needed.^ Distributional characteristics of 34 NM variables from prostate cancer cells were investigated using graphical and analytical techniques. Cells per sample ranged from 52 to 458. A small sample of patients with benign prostatic hyperplasia (BPH), representing non-cancer cells, was used for general comparison with the cancer cells.^ Data transformations such as log, square root and 1/x did not yield normality as measured by the Shapiro-Wilks test for normality. A modulus transformation, used for distributions having abnormal kurtosis values, also did not produce normality.^ Kernel density histograms of the 34 variables exhibited non-normality and 18 variables also exhibited bimodality. A bimodality coefficient was calculated and 3 variables: DNA concentration, shape and elongation, showed the strongest evidence of bimodality and were studied further.^ Two analytical approaches were used to obtain a summary measure for each variable for each patient: cluster analysis to determine significant clusters and a mixture model analysis using a two component model having a Gaussian distribution with equal variances. The mixture component parameters were used to bootstrap the log likelihood ratio to determine the significant number of components, 1 or 2. These summary measures were used as predictors of disease severity in several proportional odds logistic regression models. The disease severity scale had 5 levels and was constructed of 3 components: extracapsulary penetration (ECP), lymph node involvement (LN+) and seminal vesicle involvement (SV+) which represent surrogate measures of prognosis. The summary measures were not strong predictors of disease severity. There was some indication from the mixture model results that there were changes in mean levels and proportions of the components in the lower severity levels. ^

Total cholesterol and anthropometric measurements distributions in a cross-sectional study of school children

Cross-sectional age and sex specific distributions of serum total cholesterol were described for 1091 children age 6-18 years, in The Woodlands, Texas. Associations of serum total cholesterol with five anthropometric measurements (weight, height, body mass index, arm circumference, and triceps skinfold thickness) were examined by correlation and regression analyses. Examination of serum total cholesterol distributions showed lower levels in boys than in girls for most of the age groups studied. Mean levels of total cholesterol peaked at age 9 for boys and 8 for girls. Serum total cholesterol leveled off until age 14 for boys and 11 for girls, and then dropped through age 18 for both boys and girls. These results support the hypothesis that serum total cholesterol concentration drops at pre-adolescence.^ Age adjusted correlations were observed between serum total cholesterol and triceps skinfold thickness for both boys and girls. This association was stronger in boys. Triceps skinfold thickness and arm circumference were consistently the strongest correlates for serum total cholesterol in boys. Weight and arm circumference were consistently the strongest correlates for serum total cholesterol in girls. ^