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.^

Associations between vaccination and childhood cancers in Texas counties

Background. In Dr. Mel Greaves "delayed-infection hypothesis," postponed exposure to common infections increases the likelihood of childhood cancer. Hygienic advancements in developed countries have reduced children's exposure to pathogens and children encounter common infectious agents at an older age with an immune system unable to deal with the foreign antigens. Vaccinations may be considered to be simulated infections as they prompt an antigenic response by the immune system. Vaccinations may regulate the risk of childhood cancer by modulating the immune system. The aim of the study was to determine if children born in Texas counties with higher levels of vaccination coverage were at a reduced risk for childhood cancer.^ Methods. We conducted a case-control study to examine the risk of childhood cancers, specifically leukemia, brain tumors, and non-Hodgkin lymphoma, in relation to vaccination rates in Texas counties. We utilized a multilevel mixed-effects regression model of the individual data from the Texas Cancer Registry (TCR) with group-level exposure data (i.e., the county- and public health region-level vaccination rates).^ Results. Utilizing county-level vaccination rates and controlling for child's sex, birth year, ethnicity, birth weight, and mother's age at child's birth the hepatitis B vaccine revealed negative associations with developing all cancer types (OR = 0.81, 95% CI: 0.67–0.98) and acute lymphoblastic leukemia (ALL) (OR = 0.63, 95% CI: 0.46–0.88). The decreased risk for ALL was also evident for the inactivated polio vaccine (IPV) (OR = 0.67, 95% CI: 0.49–0.92) and 4-3-1-3-3 vaccination series (OR = 0.62, 95% CI: 0.44-0.87). Using public health region vaccine coverage levels, an inverse association between the Haemophilus influenzae type b (Hib) vaccine and ALL (OR: 0.58; 95% CI: 0.42–0.82) was present. Conversely, the measles, mumps, and rubella (MMR) vaccine resulted in a positive association with developing non-Hodgkin lymphoma (OR = 2.81, 95% CI: 1.27–6.22). ^

Whence a healthy mind: Correlation of physical fitness and academic performance among schoolchildren

Background. Public schools are a key forum in the fight for child health because of the opportunities they present for physical activity and fitness surveillance. However, because schools are evaluated and funded on the basis of standardized academic performance rather than physical activity, empirical research evaluating the connections between fitness and academic performance is needed to justify curriculum allocations to physical activity. ^ Methods. Analyses were based on a convenience sample of 315,092 individually-matched standardized academic (TAKS™) and fitness (FITNESSGRAM®) test records collected by 13 Texas school districts under state mandates. We categorized each fitness result in quintiles by age and gender and used a mixed effects regression model to compare the academic performance of the top and bottom fitness groups for each fitness test and grade level combination. ^ Results. All fitness variables except BMI showed significant, positive associations with academic performance after sociodemographic covariate adjustments, with effect sizes ranging from 0.07 (95% CI: 0.05,0.08) in girls trunklift-TAKS reading to 0.34 (0.32,0.35) in boys cardiovascular-TAKS math. Cardiovascular fitness showed the largest inter-quintile difference in TAKS score (32-75 points), followed by curl-ups. After an additional adjustment for BMI and curl-ups, cardiovascular associations peaked in 8th-9 th grades (maximum inter-quintile difference 142 TAKS points; effect size 0.75 (0.69,0.82) for 8th grade girls math) and showed dose-response characteristics across quintiles (p<0.001 for both genders and outcomes). BMI analysis demonstrated limited, non-linear association with academic performance after adjustment for sociodemographic, cardiovascular fitness and curl-up variables. Low-BMI Hispanic high school boys showed significantly lower TAKS scores than the moderate (but not high) BMI group. High-BMI non-Hispanic white high school girls showed significantly lower scores than the moderate (but not low) BMI group. ^ Conclusions. In this study, fitness was strongly and significantly related to academic performance. Cardiovascular fitness showed a distinct dose-response association with academic performance independent of other sociodemographic and fitness variables. The association peaked in late middle to early high school. The independent association of BMI to academic performance was only found in two sub-groups and was non-linear, with both low and high BMI posing risk relative to moderate BMI but not to each other. In light of our findings, we recommend that policymakers consider PE mandates in middle-high school and require linkage of academic and fitness records to facilitate longitudinal surveillance. School administrators should consider increasing PE time in pursuit of higher academic test scores, and PE practitioners should emphasize cardiovascular fitness over BMI reduction.^

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.^

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.

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. ^

Characterization of the ebp(fm) pilus-encoding operon of Enterococcus faecium and its role in biofilm formation and virulence in a murine model of urinary tract infection.

We recently identified 15 genes encoding putative surface proteins with features of MSCRAMMs and/or pili in the Enterococcus faecium TX0016 (DO) genome, including four predicted pilus-encoding gene clusters; we also demonstrated that one of these, ebpABC(fm), is transcribed as an operon, that its putative major pilus subunit, EbpC(fm) (also called pilB), is polymerized into high molecular weight complexes, and that it is enriched among clinical E. faecium isolates. Here, we created a deletion of the ebpABC(fm) operon in an endocarditis-derived E. faecium strain (TX82) and showed, by a combination of whole-cell ELISA, flow cytometry, immunoblot and immunogold electron microscopy, that this deletion abolished EbpC(fm) expression and eliminated EbpC(fm)-containing pili from the cell surface. However, transcription of the downstream sortase, bps(fm), was not affected. Importantly, the ebpABC(fm) deletion resulted in significantly reduced biofilm formation (p < 0.0001) and initial adherence (p < 0.0001) versus the wild-type; both were restored by complementing ebpABC(fm) in trans, which also restored cell surface expression of EbpC(fm) and pilus production. Furthermore, the deletion mutant was significantly attenuated in two independent mixed infection mouse urinary tract experiments, i.e., outnumbered by the wild-type in kidneys (p = 0.0003 and < 0.0001, respectively) and urinary bladders (p = 0.0003 and = 0.002). In conclusion, we have shown that the ebpABC(fm) locus encodes pili on the E. faecium TX82 cell surface and provide the first evidence that pili of this emerging pathogen are important for its ability to form biofilm and to cause infection in an ascending UTI model.

Design of mixed-longitudinal studies

Cross-sectional designs, longitudinal designs in which a single cohort is followed over time, and mixed-longitudinal designs in which several cohorts are followed for a shorter period are compared by their precision, potential for bias due to age, time and cohort effects, and feasibility. Mixed longitudinal studies have two advantages over longitudinal studies: isolation of time and age effects and shorter completion time. Though the advantages of mixed-longitudinal studies are clear, choosing an optimal design is difficult, especially given the number of possible combinations of the number of cohorts and number of overlapping intervals between cohorts. The purpose of this paper is to determine the optimal design for detecting differences in group growth rates.^ The type of mixed-longitudinal study appropriate for modeling both individual and group growth rates is called a "multiple-longitudinal" design. A multiple-longitudinal study typically requires uniform or simultaneous entry of subjects, who are each observed till the end of the study.^ While recommendations for designing pure-longitudinal studies have been made by Schlesselman (1973b), Lefant (1990) and Helms (1991), design recommendations for multiple-longitudinal studies have never been published. It is shown that by using power analyses to determine the minimum number of occasions per cohort and minimum number of overlapping occasions between cohorts, in conjunction with a cost model, an optimal multiple-longitudinal design can be determined. An example of systolic blood pressure values for cohorts of males and cohorts of females, ages 8 to 18 years, is given. ^

Statistical issues on studies of mixed longitudinal design

Mixed longitudinal designs are important study designs for many areas of medical research. Mixed longitudinal studies have several advantages over cross-sectional or pure longitudinal studies, including shorter study completion time and ability to separate time and age effects, thus are an attractive choice. Statistical methodology used in general longitudinal studies has been rapidly developing within the last few decades. Common approaches for statistical modeling in studies with mixed longitudinal designs have been the linear mixed-effects model incorporating an age or time effect. The general linear mixed-effects model is considered an appropriate choice to analyze repeated measurements data in longitudinal studies. However, common use of linear mixed-effects model on mixed longitudinal studies often incorporates age as the only random-effect but fails to take into consideration the cohort effect in conducting statistical inferences on age-related trajectories of outcome measurements. We believe special attention should be paid to cohort effects when analyzing data in mixed longitudinal designs with multiple overlapping cohorts. Thus, this has become an important statistical issue to address. ^ This research aims to address statistical issues related to mixed longitudinal studies. The proposed study examined the existing statistical analysis methods for the mixed longitudinal designs and developed an alternative analytic method to incorporate effects from multiple overlapping cohorts as well as from different aged subjects. The proposed study used simulation to evaluate the performance of the proposed analytic method by comparing it with the commonly-used model. Finally, the study applied the proposed analytic method to the data collected by an existing study Project HeartBeat!, which had been evaluated using traditional analytic techniques. Project HeartBeat! is a longitudinal study of cardiovascular disease (CVD) risk factors in childhood and adolescence using a mixed longitudinal design. The proposed model was used to evaluate four blood lipids adjusting for age, gender, race/ethnicity, and endocrine hormones. The result of this dissertation suggest the proposed analytic model could be a more flexible and reliable choice than the traditional model in terms of fitting data to provide more accurate estimates in mixed longitudinal studies. Conceptually, the proposed model described in this study has useful features, including consideration of effects from multiple overlapping cohorts, and is an attractive approach for analyzing data in mixed longitudinal design studies.^

Evaluation of the Hosmer -Lemeshow global goodness -of-fit statistic for mixed variable logistic regression models

The performance of the Hosmer-Lemeshow global goodness-of-fit statistic for logistic regression models was explored in a wide variety of conditions not previously fully investigated. Computer simulations, each consisting of 500 regression models, were run to assess the statistic in 23 different situations. The items which varied among the situations included the number of observations used in each regression, the number of covariates, the degree of dependence among the covariates, the combinations of continuous and discrete variables, and the generation of the values of the dependent variable for model fit or lack of fit.^ The study found that the $\rm\ C$g* statistic was adequate in tests of significance for most situations. However, when testing data which deviate from a logistic model, the statistic has low power to detect such deviation. Although grouping of the estimated probabilities into quantiles from 8 to 30 was studied, the deciles of risk approach was generally sufficient. Subdividing the estimated probabilities into more than 10 quantiles when there are many covariates in the model is not necessary, despite theoretical reasons which suggest otherwise. Because it does not follow a X$\sp2$ distribution, the statistic is not recommended for use in models containing only categorical variables with a limited number of covariate patterns.^ The statistic performed adequately when there were at least 10 observations per quantile. Large numbers of observations per quantile did not lead to incorrect conclusions that the model did not fit the data when it actually did. However, the statistic failed to detect lack of fit when it existed and should be supplemented with further tests for the influence of individual observations. Careful examination of the parameter estimates is also essential since the statistic did not perform as desired when there was moderate to severe collinearity among covariates.^ Two methods studied for handling tied values of the estimated probabilities made only a slight difference in conclusions about model fit. Neither method split observations with identical probabilities into different quantiles. Approaches which create equal size groups by separating ties should be avoided. ^