A Bayesian approach to estimating the regression coefficients of a multinomial logit model

A Bayesian approach to estimation of the regression coefficients of a multinominal logit model with ordinal scale response categories is presented. A Monte Carlo method is used to construct the posterior distribution of the link function. The link function is treated as an arbitrary scalar function. Then the Gauss-Markov theorem is used to determine a function of the link which produces a random vector of coefficients. The posterior distribution of the random vector of coefficients is used to estimate the regression coefficients. The method described is referred to as a Bayesian generalized least square (BGLS) analysis. Two cases involving multinominal logit models are described. Case I involves a cumulative logit model and Case II involves a proportional-odds model. All inferences about the coefficients for both cases are described in terms of the posterior distribution of the regression coefficients. The results from the BGLS method are compared to maximum likelihood estimates of the regression coefficients. The BGLS method avoids the nonlinear problems encountered when estimating the regression coefficients of a generalized linear model. The method is not complex or computationally intensive. The BGLS method offers several advantages over Bayesian approaches. ^

Logistic regression models for ordinal response: A study of self-efficacy in colorectal cancer screening

The ordinal logistic regression models are used to analyze the dependant variable with multiple outcomes that can be ranked, but have been underutilized. In this study, we describe four logistic regression models for analyzing the ordinal response variable. ^ In this methodological study, the four regression models are proposed. The first model uses the multinomial logistic model. The second is adjacent-category logit model. The third is the proportional odds model and the fourth model is the continuation-ratio model. We illustrate and compare the fit of these models using data from the survey designed by the University of Texas, School of Public Health research project PCCaSO (Promoting Colon Cancer Screening in people 50 and Over), to study the patient’s confidence in the completion colorectal cancer screening (CRCS). ^ The purpose of this study is two fold: first, to provide a synthesized review of models for analyzing data with ordinal response, and second, to evaluate their usefulness in epidemiological research, with particular emphasis on model formulation, interpretation of model coefficients, and their implications. Four ordinal logistic models that are used in this study include (1) Multinomial logistic model, (2) Adjacent-category logistic model [9], (3) Continuation-ratio logistic model [10], (4) Proportional logistic model [11]. We recommend that the analyst performs (1) goodness-of-fit tests, (2) sensitivity analysis by fitting and comparing different models.^

Prospective run theory for multinomial outcomes

The focus of this study was to generalize the theory of runs to multinomial outcomes using the generating function approach. Detailed discussion is provided for determining the probability distributions for all runs of length i in a sequence of n trials for the binomial and trinomial cases. The generalization to multinomial case is also presented. Application to data for patients from a long term disability care facility is presented to illustrate the use of Run Theory in determining the probability of a dominant state of treatment associated with a patient during his/her hospitalization. ^

Multiple imputation for missing continuous and dichotomous data: The effects of patterns of missingness and variable correlations on type I error with small samples

The purpose of this study is to investigate the effects of predictor variable correlations and patterns of missingness with dichotomous and/or continuous data in small samples when missing data is multiply imputed. Missing data of predictor variables is multiply imputed under three different multivariate models: the multivariate normal model for continuous data, the multinomial model for dichotomous data and the general location model for mixed dichotomous and continuous data. Subsequent to the multiple imputation process, Type I error rates of the regression coefficients obtained with logistic regression analysis are estimated under various conditions of correlation structure, sample size, type of data and patterns of missing data. The distributional properties of average mean, variance and correlations among the predictor variables are assessed after the multiple imputation process. ^ For continuous predictor data under the multivariate normal model, Type I error rates are generally within the nominal values with samples of size n = 100. Smaller samples of size n = 50 resulted in more conservative estimates (i.e., lower than the nominal value). Correlation and variance estimates of the original data are retained after multiple imputation with less than 50% missing continuous predictor data. For dichotomous predictor data under the multinomial model, Type I error rates are generally conservative, which in part is due to the sparseness of the data. The correlation structure for the predictor variables is not well retained on multiply-imputed data from small samples with more than 50% missing data with this model. For mixed continuous and dichotomous predictor data, the results are similar to those found under the multivariate normal model for continuous data and under the multinomial model for dichotomous data. With all data types, a fully-observed variable included with variables subject to missingness in the multiple imputation process and subsequent statistical analysis provided liberal (larger than nominal values) Type I error rates under a specific pattern of missing data. It is suggested that future studies focus on the effects of multiple imputation in multivariate settings with more realistic data characteristics and a variety of multivariate analyses, assessing both Type I error and power. ^

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. ^

Does parental monitoring influence the use of alcohol and drugs among inner city 7th grade students?

Objective. To examine associations between parental monitoring and adolescent alcohol/drug use. ^ Methods. 981 7th grade students from 10 inner-city middle schools were surveyed at the 3 month follow-up of an HIV, STD, and pregnancy prevention program. Data from 549 control subjects were used for analyses. Multinomial logistic regression was used to examine associations between five parental monitoring variables and substance use, coded as: low risk [never drank alcohol or used drugs (0)], moderate risk [drank alcohol, no drug use (1)], and high risk [both drank alcohol and used drugs or just used drugs (2)]. ^ Results. Participants were 58.3% female, 39.6% African American, 43.8% Hispanic, mean age 13.3 years. Lifetime alcohol use was 47.9%. Lifetime drug use was 14.9%. Adjusted for gender, age, race, and family structure, each individual parental monitoring variable (perceived parental monitoring, less permissive parental monitoring, greater supervision (public places), greater supervision (teen clubs), and less time spent with older teens) was significant and protective for the moderate and high risk groups. When all 5 variables were entered into a single model, only perceived parental monitoring was significantly associated (OR=0.40, 95% CI 0.29-0.55) for the moderate risk group. For the high risk group, 3 variables were significantly protective (perceived parental monitoring OR=0.28, CI 0.18-0.42, less time spent with older teens OR=0.75, CI 0.60-0.93, and greater supervision (public places) OR=0.79, CI 0.64-0.99). ^ Conclusion. The association between parental monitoring and substance abuse is complex and varied for different risk levels. Implications for intervention development are addressed. ^

Changing epidemiology of trauma deaths leads to a bimodal distribution

Introduction. Injury mortality was classically described with a tri-modal distribution, with immediate deaths at the scene, early deaths due to hemorrhage, and late deaths from organ failure. We hypothesized that trauma systems development have improved pre-hospital care, early resuscitation, and critical care, and altered this pattern. ^ Methods. This is a population-based study of all trauma deaths in an urban county with a mature trauma system (n=678, median age 33 years, 81% male, 43% gunshot, 20% motor vehicle crashes). Deaths were classified as immediate (scene), early (in hospital, ≤ 4 hours from injury), or late (>4 hours post injury). Multinomial regression was used to identify independent predictors of immediate and early vs. late deaths, adjusted for age, gender, race, intention, mechanism, toxicology and cause of death. ^ Results. There were 416 (61%) immediate, 199 (29%) early, and 63 (10%) late deaths. Immediate deaths remained unchanged and early deaths occurred much earlier (median 52 minutes vs. 120). However, unlike the classic trimodal distribution, there was no late peak. Intentional injuries, alcohol intoxication, asphyxia, and injuries to the head and chest were independent predictors of immediate deaths. Alcohol intoxication and injuries to the chest were predictors of early deaths, while pelvic fractures and blunt assaults were associated with late deaths. ^ Conclusion. Trauma deaths now have a bimodal distribution. Elimination of the late peak likely represents advancements in resuscitation and critical care that have reduced organ failure. Further reductions in mortality will likely come from prevention of intentional injuries, and injuries associated with alcohol intoxication. ^

HPV vaccine coverage in Texas counties: An application of multilevel, small area estimation

Health departments, research institutions, policy-makers, and healthcare providers are often interested in knowing the health status of their clients/constituents. Without the resources, financially or administratively, to go out into the community and conduct health assessments directly, these entities frequently rely on data from population-based surveys to supply the information they need. Unfortunately, these surveys are ill-equipped for the job due to sample size and privacy concerns. Small area estimation (SAE) techniques have excellent potential in such circumstances, but have been underutilized in public health due to lack of awareness and confidence in applying its methods. The goal of this research is to make model-based SAE accessible to a broad readership using clear, example-based learning. Specifically, we applied the principles of multilevel, unit-level SAE to describe the geographic distribution of HPV vaccine coverage among females aged 11-26 in Texas.^ Multilevel (3 level: individual, county, public health region) random-intercept logit models of HPV vaccination (receipt of ≥ 1 dose Gardasil® ) were fit to data from the 2008 Behavioral Risk Factor Surveillance System (outcome and level 1 covariates) and a number of secondary sources (group-level covariates). Sampling weights were scaled (level 1) or constructed (levels 2 & 3), and incorporated at every level. Using the regression coefficients (and standard errors) from the final models, I simulated 10,000 datasets for each regression coefficient from the normal distribution and applied them to the logit model to estimate HPV vaccine coverage in each county and respective demographic subgroup. For simplicity, I only provide coverage estimates (and 95% confidence intervals) for counties.^ County-level coverage among females aged 11-17 varied from 6.8-29.0%. For females aged 18-26, coverage varied from 1.9%-23.8%. Aggregated to the state level, these values translate to indirect state estimates of 15.5% and 11.4%, respectively; both of which fall within the confidence intervals for the direct estimates of HPV vaccine coverage in Texas (Females 11-17: 17.7%, 95% CI: 13.6, 21.9; Females 18-26: 12.0%, 95% CI: 6.2, 17.7).^ Small area estimation has great potential for informing policy, program development and evaluation, and the provision of health services. Harnessing the flexibility of multilevel, unit-level SAE to estimate HPV vaccine coverage among females aged 11-26 in Texas counties, I have provided (1) practical guidance on how to conceptualize and conduct modelbased SAE, (2) a robust framework that can be applied to other health outcomes or geographic levels of aggregation, and (3) HPV vaccine coverage data that may inform the development of health education programs, the provision of health services, the planning of additional research studies, and the creation of local health policies.^

Posttraumatic stress disorder among veterans of the Operation Iraqi Freedom (OIF) and Operation Enduring Freedom (OEF) wars: Psychological comorbidities, postdeployment social support and unit support

Much attention has been given to treating Operation Iraqi Freedom/Operation Enduring (OIF/OEF) Veterans with posttraumatic stress disorder (PTSD). However, little attention is given to those Veterans who do not meet diagnostic criteria for PTSD but who may still benefit from intervention. Research is needed to investigate the impact of how different racial/ethnic backgrounds, different levels of social support and comorbid mental health disorders impact OIF/OEF Veterans with varying levels of PTSD. The purpose of this dissertation is to examine the association of comorbid Axis I disorders, race/ethnicity, different levels of postdeployment social support and unit support on OIF/OEF Veterans with varying levels of PTSD. Data for this dissertation were from postdeployment screenings of OIF/OEF Veterans from a large Veterans Affairs hospital in southeast Texas. To examine the study hypotheses, we conducted multinomial logistic regressions of the clinician reported data. ^ The first article examined the prevalence of subthreshold and full levels of PTSD and compared Axis I and alcohol use comorbidity rates among 1,362 OIF/OEF Veterans with varying levels of PTSD. Results suggest that OIF/OEF Veterans with subthreshold PTSD experience similar levels of psychological distress as those with full PTSD and highlight the need to provide timely and appropriate mental health services to individuals who may not meet the diagnostic criteria for full PTSD. ^ These results suggest that OIF/OEF Veterans of all race/ethnicities can benefit from strong social support systems. Postdeployment social support was found to be a protective factor against the development of PTSD among White, Black and Hispanic veterans while deployment unit support was a protective factor only among Black Veterans. The second article investigated the association between postdeployment social support and unit support with varying levels of PTSD by race/ethnicity among 1,115 OIF/OEF Veterans. ^ The results of this study can help to formulate treatment and interventions for OIF/OEF Veterans with varying levels of PTSD and social support systems.^

The prevalence of periodontal disease in Mexican American vs European American elderly in three distinct socio-economic communities in San Antonio, Texas

Purpose of the Study: This study evaluated the prevalence of periodontal disease between Mexican American elderly and European American elderly residing in three socio-economically distinct neighborhoods in San Antonio, Texas. ^ Study Group: Subjects for the original protocol were participants of the Oral Health: San Antonio Longitudinal Study of Aging (OH: SALSA), which began with National Institutes of Health (NIH) funding in 1993 (M.J. Saunders, PI). The cohort in the study was the individuals who had been enrolled in Phases I and III of the San Antonio Heart Study (SAHS). This SAHS/SALSA sample is a community-based probability sample of Mexican American and European American residents from three socio-economically distinct San Antonio neighborhoods: low-income barrio, middle-income transitional, and upper-income suburban. The OH: SALSA cohort was established between July 1993 and May 1998 by sampling two subsets of the San Antonio Heart Study (SAHS) cohort. These subsets included the San Antonio Longitudinal Study of Aging (SALSA) cohort, comprised of the oldest members of the SAHS (age 65+ yrs. old), and a younger set of controls (age 35-64 yrs. old) sampled from the remainder of the SAHS cohort. ^ Methods: The study used simple descriptive statistics to describe the sociodemographic characteristics and periodontal disease indicators of the OH: SALSA participants. Means and standard deviations were used to summarize continuous measures. Proportions were used to summarize categorical measures. Simple m x n chi square statistics was used to compare ethnic differences. A multivariable ordered logit regression was used to estimate the prevalence of periodontal disease and test ethnic group and neighborhood differences in the prevalence of periodontal disease. A multivariable model adjustment for socio-economic status (income and education), gender, and age (treated as confounders) was applied. ^ Summary: In the unadjusted and adjusted model, Mexican American elderly demonstrated the greatest prevalence for periodontitis, p < 0.05. Mexican American elderly in barrio neighborhoods demonstrated the greatest prevalence for severe periodontitis, with unadjusted prevalence rates of 31.7%, 22.3%, and 22.4% for Mexican American elderly barrio, transitional, and suburban neighborhoods, respectively. Also, Mexican American elderly had adjusted prevalence rates of 29.4%, 23.7%, and 20.4% for barrio, transitional, and suburban neighborhoods, respectively. ^ Conclusion: This study indicates that the prevalence of periodontal disease is an important oral health issue among the Mexican American elderly. The results suggest that the socioeconomic status of the residential neighborhood increased the risk for severe periodontal disease among the Mexican American elderly when compared to European American elderly. A viable approach to recognizing oral health disparities in our growing population of Mexican American elderly is imperative for the provision of special care programs that will help increase the quality of care in this minority population.^

The impact of communication and cultural diversity in utilizing dental services among Saudi Arabian students in U.S.A.

Objectives: The purpose of this study is to understand the perceived effects of patient-dental staff communication and cultural diversity on the utilization of dental services in the U.S. by Saudi Arabian students who live in the U.S. and enrolled into the King Abdullah Scholarship program. Methods: The study design was an analytical cross-sectional study. Data for this study was obtained from the Saudi Dental Servicers Utilization Survey, a voluntary internet survey available online for one month through Facebook. Ordered logistic regression analyses and multinomial logistic regression analyses were used to measure the relationships between patient-dental staff communication and cultural diversity on the utilization of dental services. Results: Eight hundred and forty-seven responses were analyzed for this study. Overall, the majority of Saudi students reported having excellent communication experience with dental providers in the U.S. More than 58% of respondents reported at least one regular dental visit last year. Factors that influenced the use of regular dental care were: dentist's explanation of treatment plan, response of dental staff to patient's needs, respectful and polite dental staff, dental staff kindness, availability of up-to-date equipment, and overall communication with dentist. However, the utilization of emergency dental care was not associated with any measurement of patient-dental provider communication. Overall future utilization of dental care is associated with all aspects of patient-dental staff communication measured in this survey. Furthermore, more utilization of regular dental care was related to respondent's perception of the importance of trustworthiness dental staff and the importance of a dentist's reputation was only marginally associated. Respondent's perception of dentist's reputation was associated with more use of emergency dental services. Respondents are more likely to anticipate using dental care in the future if they perceived trustworthiness dental staff, and the dentist's reputation as influencing factors to their usage of dental services. Conclusions: Patient-dental staff communication was partially associated with utilization of regular dental care, not associated with utilization of emergency dental care, and broadly associated with anticipated future utilization of dental care. In addition, trustworthy dental staff, and a dentist's reputation were considered to be strong influencing factors towards utilization of dental services.^

Renal Cryoablation: Investigation of Periprocedural Visualization Tools and Treatment Response Quantification

Cryoablation for small renal tumors has demonstrated sufficient clinical efficacy over the past decade as a non-surgical nephron-sparing approach for treating renal masses for patients who are not surgical candidates. Minimally invasive percutaneous cryoablations have been performed with image guidance from CT, ultrasound, and MRI. During the MRI-guided cryoablation procedure, the interventional radiologist visually compares the iceball size on monitoring images with respect to the original tumor on separate planning images. The comparisons made during the monitoring step are time consuming, inefficient and sometimes lack the precision needed for decision making, requiring the radiologist to make further changes later in the procedure. This study sought to mitigate uncertainty in these visual comparisons by quantifying tissue response to cryoablation and providing visualization of the response during the procedure. Based on retrospective analysis of MR-guided cryoablation patient data, registration and segmentation algorithms were investigated and implemented for periprocedural visualization to deliver iceball position/size with respect to planning images registered within 3.3mm with at least 70% overlap and a quantitative logit model was developed to relate perfusion deficit in renal parenchyma visualized in verification images as a result of iceball size visualized in monitoring images. Through retrospective study of 20 patient cases, the relationship between likelihood of perfusion loss in renal parenchyma and distance within iceball was quantified and iteratively fit to a logit curve. Using the parameters from the logit fit, the margin for 95% perfusion loss likelihood was found to be 4.28 mm within the iceball. The observed margin corresponds well with the clinically accepted margin of 3-5mm within the iceball. In order to display the iceball position and perfusion loss likelihood to the radiologist, algorithms were implemented to create a fast segmentation and registration module which executed in under 2 minutes, within the clinically-relevant 3 minute monitoring period. Using 16 patient cases, the average Hausdorff distance was reduced from 10.1mm to 3.21 mm with average DSC increased from 46.6% to 82.6% before and after registration.

Breast cancer risk factors among Mexican-American women

Introduction: The average age of onset of breast cancer among Hispanic women is 50 years, more than a decade earlier than non-Hispanic white women. Age at diagnosis is an important prognostic factor for breast cancer; younger age at onset is more likely to be associated with advanced disease, poorer prognosis, hormone receptor negative breast tumors, and a greater likelihood of hereditary breast cancer. Studies of breast cancer risk factors including reproductive risk factors, family history of breast cancer, and breast cancer subtype have been conducted predominately in non-Hispanic whites. Breast cancer is a heterogeneous disease with the presence of clinically, biologically, and epidemiologically distinct subtypes that also differ with respect to their risk factors. The associations between reproductive risk factors and family history of breast cancer have been well documented in the literature. However, only a few studies have assessed these associations with breast cancer subtype in Hispanic populations. Methods: To assess the associations between reproductive risk factors and family history of breast cancer we conducted three separate studies. First, we conducted a case-control study of 172 Mexican-American breast cancer cases and 344 age matched controls residing in Harris County, TX to assess reproductive and other risk factors. We conducted logistic regression analysis to assess differences in cases and controls adjusted for age at diagnosis and birthplace and then we conducted a multinomial logistic regression analysis to compare reproductive risk factors among the breast tumor subtypes. In a second study, we identified 139 breast cancer patients with a first- or second-degree family history of breast cancer and 298 without a family history from the ELLA Bi-National Breast Cancer Study. In this analysis, we also computed a multinomial logistic regression to evaluate associations between family history of breast cancer and breast cancer subtypes, and logistic regression to estimate associations between breast cancer screening practices with family history of breast cancer. In the final study, we employed a cross-sectional study design in 7279 Mexican-American women in the Mano a Mano Cohort Study. We evaluated associations with family history of breast cancer and breast cancer risk factors including body mass index (BMI), lifestyle factors, migration history, and adherence to American Cancer Society (ACS) guidelines. Results: In the results of our first analyses, reproductive risk factors differed in the magnitude and direction of associations when stratified by age and birthplace among cases and controls. In our second study, family history of breast cancer, and having at least one relative diagnosed at an early age (<50 years) was associated with triple negative breast cancer (TNBC). Mammography prior to receiving a breast cancer diagnosis was associated with family history of breast cancer. In our third study that assessed lifestyle factors, migration history and family history of breast cancer; we found that women with a first-degree family history of breast cancer were more overweight or obese compared with their counterparts without a family history. There was no indication that having a family history contributed to women practicing healthier lifestyle behaviors and/or adhering to the ACS guidelines for cancer prevention. Conclusions: We observed that among Mexican-American women, reproductive risk factors were associated with breast cancer where the woman was born (US or Mexico). Having a family history of breast cancer, especially having either a first- or second-degree relative diagnosed at a younger age, was strongly associated with TNBC subtype. These results are consistent with other published studies in this area. Further, our results indicate that women with strong family histories of breast cancer are more likely to undertake mammography but not to engage in healthier lifestyle behaviors.^