Bayesian dual threshold design with Dirichlet distribution: An alternative way to frequentist multi-stage phase II designs in oncology

Many phase II clinical studies in oncology use two-stage frequentist design such as Simon's optimal design. However, they have a common logistical problem regarding the patient accrual at the interim. Strictly speaking, patient accrual at the end of the first stage may have to be suspended until all patients have events, success or failure. For example, when the study endpoint is six-month progression free survival, patient accrual has to be stopped until all outcomes from stage I is observed. However, study investigators may have concern when accrual is suspended after the first stage due to the loss of accrual momentum during this hiatus. We propose a two-stage phase II design that resolves the patient accrual problem due to an interim analysis, and it can be used as an alternative way to frequentist two-stage phase II studies in oncology. ^

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. ^

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 joint modeling of longitudinal and survival data

The joint modeling of longitudinal and survival data is a new approach to many applications such as HIV, cancer vaccine trials and quality of life studies. There are recent developments of the methodologies with respect to each of the components of the joint model as well as statistical processes that link them together. Among these, second order polynomial random effect models and linear mixed effects models are the most commonly used for the longitudinal trajectory function. In this study, we first relax the parametric constraints for polynomial random effect models by using Dirichlet process priors, then three longitudinal markers rather than only one marker are considered in one joint model. Second, we use a linear mixed effect model for the longitudinal process in a joint model analyzing the three markers. In this research these methods were applied to the Primary Biliary Cirrhosis sequential data, which were collected from a clinical trial of primary biliary cirrhosis (PBC) of the liver. This trial was conducted between 1974 and 1984 at the Mayo Clinic. The effects of three longitudinal markers (1) Total Serum Bilirubin, (2) Serum Albumin and (3) Serum Glutamic-Oxaloacetic transaminase (SGOT) on patients' survival were investigated. Proportion of treatment effect will also be studied using the proposed joint modeling approaches. ^ Based on the results, we conclude that the proposed modeling approaches yield better fit to the data and give less biased parameter estimates for these trajectory functions than previous methods. Model fit is also improved after considering three longitudinal markers instead of one marker only. The results from analysis of proportion of treatment effects from these joint models indicate same conclusion as that from the final model of Fleming and Harrington (1991), which is Bilirubin and Albumin together has stronger impact in predicting patients' survival and as a surrogate endpoints for treatment. ^

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.^

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. ^

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 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.^

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.^