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. ^

A nested case-control study of radiation exposure and brain cancer incidence in the United States Air Force

A nested case-control study design was used to investigate the relationship between radiation exposure and brain cancer risk in the United States Air Force (USAF). The cohort consisted of approximately 880,000 men with at least 1 year of service between 1970 and 1989. Two hundred and thirty cases were identified from hospital discharge records with a diagnosis of primary malignant brain tumor (International Classification of Diseases, 9th revision, code 191). Four controls were exactly matched with each case on year of age and race using incidence density sampling. Potential career summary extremely low frequency (ELF) and microwave-radiofrequency (MWRF) radiation exposures were based upon the duration in each occupation and an intensity score assigned by an expert panel. Ionizing radiation (IR) exposures were obtained from personal dosimetry records.^ Relative to the unexposed, the overall age-race adjusted odds ratio (OR) for ELF exposure was 1.39, 95 percent confidence interval (CI) 1.03-1.88. A dose-response was not evident. The same was true for MWRF, although the OR = 1.59, with 95 percent CI 1.18-2.16. Excess risk was not found for IR exposure (OR = 0.66, 45 percent CI 0.26-1.72).^ Increasing socioeconomic status (SES), as identified by military pay grade, was associated with elevated brain tumor risk (officer vs. enlisted personnel age-race adjusted OR = 2.11, 95 percent CI 1.98-3.01, and senior officers vs. all others age-race adjusted OR = 3.30, 95 percent CI 2.0-5.46). SES proved to be an important confounder of the brain tumor risk associated with ELF and MWRF exposure. For ELF, the age-race-SES adjusted OR = 1.28, 95 percent CI 0.94-1.74, and for MWRF, the age-race-SES adjusted OR = 1.39, 95 percent CI 1.01-1.90.^ These results indicate that employment in Air Force occupations with potential electromagnetic field exposures is weakly, though not significantly, associated with increased risk for brain tumors. SES appeared to be the most consistent brain tumor risk factor in the USAF cohort. Other investigators have suggested that an association between brain tumor risk and SES may arise from differential access to medical care. However, in the USAF cohort health care is universally available. This study suggests that some factor other than access to medical care must underlie the association between SES and brain tumor risk. ^